diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..f729774 --- /dev/null +++ b/.gitignore @@ -0,0 +1,136 @@ +# Byte-compiled / optimized / DLL files +__pycache__/ +*.py[cod] +*$py.class + +# C extensions +*.so + +# Distribution / packaging +.Python +build/ +develop-eggs/ +dist/ +downloads/ +eggs/ +.eggs/ +lib/ +lib64/ +parts/ +sdist/ +var/ +wheels/ +pip-wheel-metadata/ +share/python-wheels/ +*.egg-info/ +.installed.cfg +*.egg +MANIFEST +.vscode/ + +# PyInstaller +# Usually these files are written by a python script from a template +# before PyInstaller builds the exe, so as to inject date/other infos into it. +*.manifest +*.spec + +# Installer logs +pip-log.txt +pip-delete-this-directory.txt + +# Unit test / coverage reports +htmlcov/ +.tox/ +.nox/ +.coverage +.coverage.* +.cache +nosetests.xml +coverage.xml +*.cover +*.py,cover +.hypothesis/ +.pytest_cache/ + +# Translations +*.mo +*.pot + +# Django stuff: +*.log +local_settings.py +db.sqlite3 +db.sqlite3-journal + +# Flask stuff: +instance/ +.webassets-cache + +# Scrapy stuff: +.scrapy + +# Sphinx documentation +docs/_build/ + +# PyBuilder +target/ + +# Jupyter Notebook +.ipynb_checkpoints + +# IPython +profile_default/ +ipython_config.py + +# pyenv +.python-version + +# pipenv +# According to pypa/pipenv#598, it is recommended to include Pipfile.lock in version control. +# However, in case of collaboration, if having platform-specific dependencies or dependencies +# having no cross-platform support, pipenv may install dependencies that don't work, or not +# install all needed dependencies. +#Pipfile.lock + +# PEP 582; used by e.g. github.com/David-OConnor/pyflow +__pypackages__/ + +# Celery stuff +celerybeat-schedule +celerybeat.pid + +# SageMath parsed files +*.sage.py + +# Environments +.env +.venv +env/ +venv/ +ENV/ +env.bak/ +venv.bak/ + +# Spyder project settings +.spyderproject +.spyproject + +# Rope project settings +.ropeproject + +# mkdocs documentation +/site + +# mypy +.mypy_cache/ +.dmypy.json +dmypy.json + +# Pyre type checker +.pyre/ + +# Jupyter Book +_build/ + +# poetry files +pyproject.toml diff --git a/.gitlab-ci.yml b/.gitlab-ci.yml new file mode 100644 index 0000000..ae3fc84 --- /dev/null +++ b/.gitlab-ci.yml @@ -0,0 +1,75 @@ +stages: + - test + - build + - deploy + +variables: + PIP_CACHE_DIR: "$CI_PROJECT_DIR/.cache/pip" + REGISTRY_HOST: localhost:5000 + TAG_LATEST: $REGISTRY_HOST/$CI_PROJECT_NAME/$CI_COMMIT_REF_NAME:latest + TAG_DRAFT: $REGISTRY_HOST/$CI_PROJECT_NAME-draft/$CI_COMMIT_REF_NAME:latest + +cache: + paths: + - .cache/pip + +# This job tests if the book compiles gracefully after a new addition +test-build: + stage: test + image: python:3.11-bullseye + rules: + - if: $CI_PIPELINE_SOURCE == "merge_request_event" + script: + - pip install -r requirements.txt + - jupyter-book clean book/ + - jupyter-book build book/ + +# This job builds the Docker container +build-book: + stage: build + image: docker + rules: + - if: $CI_COMMIT_BRANCH == "publish" && $CI_PIPELINE_SOURCE == "push" + variables: + TAG: $TAG_LATEST + - if: $CI_COMMIT_BRANCH == "main" && $CI_PIPELINE_SOURCE == "push" + variables: + TAG: $TAG_DRAFT + before_script: + - docker info + script: + - if [ "$TAG" = "$TAG_LATEST" ]; then sed --in-place=".bak" '/# START DRAFT/,/# END DRAFT/{//!d}' book/_config.yml; fi + - docker build -t $TAG . + - docker push $TAG + +# This job takes down the existing container and starts the new one +deploy-book: + stage: deploy + image: docker + rules: + - if: $CI_COMMIT_BRANCH == "publish" && $CI_PIPELINE_SOURCE == "push" + before_script: + - docker info + - docker stop $CI_PROJECT_NAME || exit_code=$? + - if [ $exit_code -ne 0 ]; then echo "Container not found, cannot stop"; else docker rm $CI_PROJECT_NAME; fi + script: + - docker run -d --restart always -p 8014:8000 --name $CI_PROJECT_NAME $TAG_LATEST # Make sure to use a different port for each book! + environment: + name: production + url: https://interactivetextbooks.citg.tudelft.nl/$CI_PROJECT_NAME + +# Deploy the draft version of the book +deploy-draft: + stage: deploy + image: docker + rules: + - if: $CI_COMMIT_BRANCH == "main" && $CI_PIPELINE_SOURCE == "push" + before_script: + - docker info + - docker stop $CI_PROJECT_NAME-draft || exit_code=$? + - if [ $exit_code -ne 0 ]; then echo "Container not found, cannot stop"; else docker rm $CI_PROJECT_NAME-draft; fi + script: + - docker run -d --restart always -p 8015:8000 --name $CI_PROJECT_NAME-draft $TAG_DRAFT + environment: + name: draft + url: https://interactivetextbooks.citg.tudelft.nl/$CI_PROJECT_NAME-draft \ No newline at end of file diff --git a/Dockerfile b/Dockerfile new file mode 100644 index 0000000..831eb74 --- /dev/null +++ b/Dockerfile @@ -0,0 +1,9 @@ +FROM continuumio/miniconda3 +WORKDIR /book +COPY book/ . +RUN apt-get update && apt-get -y install git gcc +COPY requirements.txt requirements.txt +RUN pip install -r requirements.txt +RUN jupyter book clean . +RUN jupyter book build . +ENTRYPOINT [ "python", "-m", "http.server", "8000", "--directory", "/book/_build/html"] \ No newline at end of file diff --git a/LICENSE.md b/LICENSE.md new file mode 100644 index 0000000..ba74ac9 --- /dev/null +++ b/LICENSE.md @@ -0,0 +1,3 @@ +This book is licensed under a Creative Commons Attribution 4.0 International License. + +Creative Commons License \ No newline at end of file diff --git a/book/_bibliography/references.bib b/book/_bibliography/references.bib new file mode 100644 index 0000000..09caf27 --- /dev/null +++ b/book/_bibliography/references.bib @@ -0,0 +1,396 @@ +@book{adk2022, + title={Structural and System Reliability}, + author={Der Kiureghian, Armen}, + year={2022}, + publisher={Cambridge University Press} +} + +@article{baecher1982, + author = {Baecher, Gregory B}, + journal = {Engineering Foundations: Updating Subsurface Samplings of Soils and Rocks and their In-Situ Testing, Santa Barbara}, + title = {Statistical methods in site characterization}, + year = {1982}, + pages = {463--492} +} + +@book{baecher2003, + title={Reliability and statistics in geotechnical engineering}, + author={Baecher, Gregory B and Christian, John T}, + year={2003}, + publisher={John Wiley \& Sons} +} + +@misc{baecher2021, + title={IFCEE 2021: Karl Terzaghi Lecture: Greg Baecher: Geotechnical Systems, Uncertainty, and Risk}, + author={Baecher, Gregory B}, + howpublished={Presentation, YouTube: \url{https://www.youtube.com/watch?v=Y5w1p3uAe0I&ab_channel=Geo-InstituteofASCE}}, + year={2021} +} + +@incollection{cardona2012, + title={Determinants of risk: exposure and vulnerability}, + author={Cardona, Omar Dario and Van Aalst, Maarten K and Birkmann, J{\"o}rn and Fordham, Maureen and Mc Gregor, Glenn and Rosa, Perez and Pulwarty, Roger S and Schipper, E Lisa F and Sinh, Bach Tan and D{\'e}camps, Henri and others}, + booktitle={Managing the risks of extreme events and disasters to advance climate change adaptation: special report of the intergovernmental panel on climate change}, + pages={65--108}, + year={2012}, + publisher={Cambridge University Press} +} + +@book{ditlevsen1996, + title={Structural reliability methods}, + author={Ditlevsen, Ove and Madsen, Henrik O}, + volume={178}, + year={1996}, + publisher={Wiley New York} +} + +@article{Eijgenraam2006, + author = {C.J.J. Eijgenraam}, + journal = {CPB discussion paper}, + title = {Optimal safety standards for dike ring areas}, + volume = {62}, + year = {2006}, +} + +@book{moss2020, + title={Applied civil engineering risk analysis}, + author={Moss, Robb Eric S}, + year={2020}, + publisher={Springer} +} + +@article{vandantzig1956, + author = {D. van Dantzig}, + journal = {Econometrica}, + title = {Economic decision problems for flood prevention}, + volume = {24}, + year = {1956} +} + +@article{vnk2014, + author = {{Veiligheid Nederland in Kaart}}, + title = {De veiligheid van Nederland in kaart}, + year = {2014}, + journal = {Rijkswaterstaat}, + url = {https://www.helpdeskwater.nl/publish/pages/131663/eindrapport_vnk.pdf}, +} + +@article{vrijling1990, + author = {Vrijling, J.K. and van Beurden, J.A.}, + journal = {Proceedings of the International Conference on Coastal Engineering}, + title = {Sealevel rise: a probabilistic design problem}, + year = {1990} +} + +@article{vangelder1997, + author = {P.H.A.J.M. Van Gelder and J.K. Vrijling and K.A.H. Slijkhuis}, + journal = {Water for a Changing Global Community}, + pages = {554-559}, + title = {Coping with uncertainty in the economical optimization of a dike design}, + year = {1997}, +} + +@phdthesis{voorendt2017, + title={Design principles of multifunctional flood defences}, + author={Voorendt, Mark}, + school={Delft University of Technology, the Netherlands}, + year={2017} +} + +@misc{sympy_why, + title={Sympy documentation}, + author={{SymPy Development Team}}, + howpublished={\url{https://docs.sympy.org/latest/tutorials/intro-tutorial/intro.html}}, + year={2023} +} + +@misc{jason_moore, + title={Learn Multibody Dynamics, SymPy}, + author={Moore, Jason}, + howpublished={\url{https://moorepants.github.io/learn-multibody-dynamics/sympy.html}}, + year={2023} +} + +@misc{BFG, + title={Animation of the unit circle with angles}, + author={BFG}, + howpublished={\url{https://commons.wikimedia.org/wiki/File:Unitycircle-complex.gif}}, + year={2020} +} + +@article{kaplan1981, + author = {Kaplan, S. and Garrick, B.J.}, + journal = {Risk Analysis}, + pages = {11-27}, + title = {On The Quantitative Definition of Risk}, + year = {1981}, +} + +@inproceedings{farmer1967, + title = {Siting Criteria - A New Approach}, + author = {Farmer, F.R.}, + year = 1967, + month = {April}, + booktitle = {Proceedings of IAEA Symposium on the Containment and Siting of Nuclear Power Plants}, + publisher = {International Atomic Energy Agency (IAEA)}, + address = {Vienna}, + pages = {303-324}, +} + +@book{kendall1977, + title={The Risks of Nuclear Power Reactors, A Review of the NRC Reactor Safety Study WASH-1400 (NUREG-75/014)}, + author={Kendall, H.W. and Hubbard, R.B. and Minor, G.C. and Bryan, W.M. (Union of Concerned Scientists)}, + year={1977}, + publisher={Cambridge} +} + +@article{vlek1996, + author = {Vlek, C.A.J.}, + journal = {Risk Decision and Policy}, + pages = {9-31}, + title = {A multi-level, multi-stage and multi-attribute perspective on risk assessment, decision-making and risk control}, + year = {1996}, +} + +@article{slovic1987, + author = {Slovic, P.}, + journal = {Science}, + pages = {280-285}, + title = {Perception of Risk}, + year = {1987}, +} + +@article{voortman2004, + author = {Voortman, H.G. and Vrijling, J.K.}, + journal = {Heron}, + pages = {75-94}, + title = {Optimal design of flood defence systems in a changing climate}, + year = {2004}, +} + +@article{apostolakis2004, + author = {Apostolakis, G.E.}, + journal = {Risk Analysis}, + pages = {515-520}, + title = {How Useful Is Quantitative Risk Assessment?}, + year = {2004}, +} + +@article{faber2003, +title = {Risk Assessment for Civil Engineering Facilities: Critical Overview and Discussion}, +journal = {Reliability Engineering & System Safety}, +volume = {80}, +number = {2}, +pages = {173-184}, +year = {2003}, +issn = {0951-8320}, +doi = {https://doi.org/10.1016/S0951-8320(03)00027-9}, +url = {https://www.sciencedirect.com/science/article/pii/S0951832003000279}, +author = {Faber, M.H. and Stewart, M.G.}, +} + +@phdthesis{jongejan2008, + title={How safe is safe enough? The government's response to industrial and flood risks}, + author={Jongejan, R.B.}, + school={Delft University of Technology, the Netherlands}, + year={2008} +} + +@misc{CUR1997, + title={Kansen in de Civiele Techniek, Deel 1: Probabilistisch ontwerpen in theorie}, + author={CUR{\ }(Civieltechnisch{\ }Centrum{\ }Uitvoering{\ }Research{\ }en{\ }Regelgeving)}, + howpublished={CUR rapport 190}, + year={1997} +} + +@misc{CIB2001, + title={A framework for risk management and risk communications, Work{\ }Group{\ }32,{\ }CIB}, + author={Vrouwenvelder, T. and Lovegrove, R. and Holicky, M.}, + howpublished={CIB report 259}, + year={2001} +} + +@article{bea1998, + author = {Bea, R.G.}, + journal = {Reliability Engineering & System Safety}, + pages = {109-126}, + title = {Human and Organization Factors: Engineering Operating Safety Into Offshore Structures}, + year = {1998}, +} + +@misc{eurocode2001, + title={Eurocode - Basis of Structural Design}, + author={EN 1990:2002 E, Eurocode}, + howpublished={CEN}, + year={2001} +} + +@book{vrouwenvelder1996, + author = {Vrouwenvelder, A.C.W.M. and Vrijling, J.K}, + title = {Collegedictaat Probabilistisch ontwerpen b3}, + year = {1996}, + publisher={TU Delft} +} + +@article{starr1967, + author = {Starr, C.}, + journal = {Science}, + pages = {1232-1238}, + title = {Social benefit versus technological risk}, + year = {1967}, +} + +@inproceedings{taerwe1986, + title = {Mastering Global Quality by an Interactive Concept}, + author = {Taerwe, L.}, + year = 1986, + booktitle = {Proceedings IABSE Symposium Tokyo 1986: Safety and Quality Assurance of Civil Engineering Structures}, + pages = {317-325}, +} + +@book{raiffa1961, + author = {Raiffa, H. and Schlaifer, R.}, + title = {Applied Statistical Decision Theory}, + year = {1961}, + publisher={Harvard University press}, + address = {Cambridge, Massachusetts, United States}, +} + +@book{benjamin1970, + author = {Benjamin, J.R. and Cornell, C.A.}, + title = {Probability, Statistics and Decision for Civil Engineers}, + year = {1970}, + publisher={McGraw Hill}, +} + +@inproceedings{don2003, + author = {Don, F.H. and Stolwijk, H.J.J.}, + booktitle = {CUR (2003) 50 jaar na stormvloed 1953, terugblik en toekomst}, + title = {Investeren in veiligheid: de watersnoodramp van 1953 en de kosten en baten van het deltaplan}, + pages={79-98}, + year = {2003}, + howpublished={CUR rapport 212}, +} + +@inproceedings{vrijling2000, + title={An Analysis of the Valuation of a Human Life}, + author={Vrijling, J.K. and Gelder, P.H.A.J.M. van}, + booktitle={Foresight and Precaution: Proceedings of ESREL 2000, SARS and SRA-Europe Annual Conference. Edited by M.P. Cottam, D.W. Harvey, R.P. Pape and J. Tait}, + pages={197-200}, + volume={1}, + year={2000}, + address={Edinburgh, Scotland} +} + +@article{jongejan2005, + author = {Jongejan, R.B. and Jonkman, S.N. and Vrijling, J.K.}, + journal = {ESREL}, + title = {Methods for the Valuation of Human Life}, + year = {2005}, +} + +@misc{SWOV2012, + title={Waardering van immateriële kosten van verkeersdoden}, + author={SWOV{\ }(Stichting{\ }Wetenschappelijk{\ }Onderzoek{\ }Verkeersveiligheid)}, + howpublished={Factsheet, \url{http://www.swov.nl/rapport/Factsheets/NL/Factsheet_Immateriele_kosten.pdf}}, + year={2012}, +} + +@inproceedings{jeuken2013, +author = {Jeuken, A. and Kind, J. and Slootjes, N. and Gauderis, J. and Vos, R.}, +year = {2013}, +month = {01}, +pages = {}, +title = {Cost-benefit Analysis of Flood Risk Management Strategies for the Rhine-Meuse Delta}, +booktitle = {Comprehensive Flood Risk Management, Taylor & Francis Group}, +} + +@article{tengs1995, + author = {Tengs, T.O. and Adams, M.E. and Pliskin, J.S. and Gelb Safran, D. and Siegel, J.E. and Weinstein, M.C. and Graham, J.D.}, + journal = {Risk Analysis}, + volume={15}, + number={3}, + pages={369-390}, + title = {Five-hundred Live Saving Interventions and Their Cost Effectiveness}, + year = {1995}, +} + +@misc{TAW1985, + title={Some Considerations of an Acceptable Level of Risk in the Netherlands}, + author={TAW{\ }(Technical{\ }Advisory{\ }Committee{\ }on{\ }Water{\ }Defences)}, + howpublished={Report by TAW workgroup 10 'Probabilistic methods'}, + year={1985}, +} + +@article{vrijling1995, + author = {Vrijling, J.K. and Hengel, W. van and Houben, R.J.}, + journal = {Journal of Hazardous Materials}, + volume={43}, + pages = {245-261}, + title = {A Framework for Risk Evaluation}, + year = {1995}, +} + +@article{vrijling1998, + author = {Vrijling, J.K. and Hengel, W. van and Houben, R.J.}, + journal = {Reliability Engineering and System Safety}, + volume={59}, + pages = {141-150}, + title = {Acceptable Risk as a Basis for Design}, + year = {1998}, +} + +@article{jonkman2003, + author = {Jonkman, S.N. and van Gelder, P.H.A.J.M. and Vrijling, J.K.}, + journal = {Journal of Hazardous Materials}, + volume={A99}, + pages = {1-30}, + title = {An Overview of Quantitative Risk Measures for Loss of Life and Economic Damage}, + year = {2003}, +} + +@article{bottelberghs2000, + author = {Bottelberghs, P.H.}, + journal = {Journal of Hazardous Materials}, + volume={71}, + pages = {117-123}, + title = {Risk Analysis and Safety Policy Developments in the Netherlands}, + year = {2000}, +} + +@article{vrijling2001, +title = {Probabilistic Design of Water Defense Systems in The Netherlands}, +journal = {Reliability Engineering & System Safety}, +volume = {74}, +number = {3}, +pages = {337-344}, +year = {2001}, +issn = {0951-8320}, +doi = {https://doi.org/10.1016/S0951-8320(01)00082-5}, +url = {https://www.sciencedirect.com/science/article/pii/S0951832001000825}, +author = {Vrijling, J.K.}, +} + +@misc{delta2014, + title={Deltaprogramma Veiligheid. Synthesedocument Veiligheid}, + author={Deltaprogramma}, + howpublished={Achtergronddocument B1}, + year={2014} +} + +@article{sitar1987, +title = {First-order Reliability Approach to Stochastic Analysis of Subsurface Flow and Contaminant Transport}, +journal = {Water Resources Research}, +volume = {23}, +number = {5}, +pages = {794-804}, +year = {1987}, +author = {Sitar, N. and Cawlfield, J. D. and Der Kiureghian, A.}, +} + +@misc{usace14, + title={Safety and Health Requirements Manual}, + author={U.S.{\ }Army{\ }Corps{\ }of{\ }Engineers}, + howpublished={EM 385-1-1}, + year={2014} +} \ No newline at end of file diff --git a/book/_config.yml b/book/_config.yml new file mode 100644 index 0000000..52459aa --- /dev/null +++ b/book/_config.yml @@ -0,0 +1,61 @@ +title: Template +author: Robert Lanzafame +logo: figures/cover_small.png +copyright: Delft University of Technology, CC BY 4.0 # overriden by extra footer/sphinx config + +execute: + execute_notebooks: "off" + +launch_buttons: + thebe: true + +only_build_toc_files: true + +repository: + url: https://gitlab.tudelft.nl/interactivetextbooks-citg/risk-and-reliability/ + branch: main/book # for edit button; need to check branch permissions non-TUD user access + +html: +# X START DRAFT # temporarily enable Hypothesis for published book until Library finishes + comments: + hypothesis: true +# X END DRAFT + use_edit_page_button: false + use_repository_button: true + extra_footer: | +

+ © Delft University of Technology, CC BY 4.0 + + + Creative Commons License + +

+ +sphinx: + config: + html_show_copyright: false + html_js_files: + - https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.4/require.min.js + thebe_config: + use_thebe_lite: true + exclude_patterns: ["**/_*.yml", "**/*.md", "**/*.ipynb"] + # Reference issues + # See: https://github.com/executablebooks/jupyter-book/issues/1090 + # and Milestone 10: + # https://gitlab.tudelft.nl/groups/interactivetextbooks-citg/-/milestones/10#tab-issues + # This next line was from Caspar/citg-jb-stack and doesn't work (see Issue 24) + # https://gitlab.tudelft.nl/interactivetextbooks-citg/risk-and-reliability/-/issues/24 + # bibtex_reference_style: author_year + bibtex_reference_style: author_year_round + bibtex_default_style: myapastyle + extra_extensions: + - sphinx.ext.imgconverter + - download_link_replacer + - jupyterbook_patches + # Local extensions are for bibtex (Thirza's hydrology hack); see above + local_extensions: + apastyle: _ext/ + bracket_citation_style: _ext/ + +bibtex_bibfiles: + - _bibliography/references.bib diff --git a/book/_ext/apastyle.py b/book/_ext/apastyle.py new file mode 100644 index 0000000..16828fe --- /dev/null +++ b/book/_ext/apastyle.py @@ -0,0 +1,17 @@ + +# from pybtex.style.formatting.unsrt import Style +from pybtexapastyle.formatting.apa import APAStyle +from pybtexapastyle.labels.apa import LabelStyle as APALabelStyle +from pybtex.plugin import register_plugin +# from pybtex.style.template import names, sentence + +class MyAPALabelStyle(APALabelStyle): + def format_label(self, entry): + return APALabelStyle.format_label(self, entry) + +class MyAPAStyle(APAStyle): + default_label_style = 'myapa' + +def setup(app): + register_plugin('pybtex.style.labels', 'myapa', MyAPALabelStyle) + register_plugin('pybtex.style.formatting', 'myapastyle', MyAPAStyle) \ No newline at end of file diff --git a/book/_ext/bracket_citation_style.py b/book/_ext/bracket_citation_style.py new file mode 100644 index 0000000..cab10f3 --- /dev/null +++ b/book/_ext/bracket_citation_style.py @@ -0,0 +1,27 @@ +from dataclasses import dataclass, field +import sphinxcontrib.bibtex.plugin + +from sphinxcontrib.bibtex.style.referencing import BracketStyle +from sphinxcontrib.bibtex.style.referencing.author_year import AuthorYearReferenceStyle + + +def bracket_style() -> BracketStyle: + return BracketStyle( + left='(', + right=')', + ) + + +@dataclass +class MyReferenceStyle(AuthorYearReferenceStyle): + bracket_parenthetical: BracketStyle = field(default_factory=bracket_style) + bracket_textual: BracketStyle = field(default_factory=bracket_style) + bracket_author: BracketStyle = field(default_factory=bracket_style) + bracket_label: BracketStyle = field(default_factory=bracket_style) + bracket_year: BracketStyle = field(default_factory=bracket_style) + + +def setup(app): + sphinxcontrib.bibtex.plugin.register_plugin( + 'sphinxcontrib.bibtex.style.referencing', + 'author_year_round', MyReferenceStyle) \ No newline at end of file diff --git a/book/_ext/pybtexapastyle/.gitignore b/book/_ext/pybtexapastyle/.gitignore new file mode 100644 index 0000000..49d0093 --- /dev/null +++ b/book/_ext/pybtexapastyle/.gitignore @@ -0,0 +1,114 @@ + +# Created by https://www.gitignore.io/api/python + +### Python ### +# Byte-compiled / optimized / DLL files +__pycache__/ +*.py[cod] +*$py.class + +# C extensions +*.so + +# Distribution / packaging +.Python +build/ +develop-eggs/ +dist/ +downloads/ +eggs/ +.eggs/ +lib/ +lib64/ +parts/ +sdist/ +var/ +wheels/ +*.egg-info/ +.installed.cfg +*.egg +MANIFEST + +# PyInstaller +# Usually these files are written by a python script from a template +# before PyInstaller builds the exe, so as to inject date/other infos into it. +*.manifest +*.spec + +# Installer logs +pip-log.txt +pip-delete-this-directory.txt + +# Unit test / coverage reports +htmlcov/ +.tox/ +.coverage +.coverage.* +.cache +nosetests.xml +coverage.xml +*.cover +.hypothesis/ +.pytest_cache/ + +# Translations +*.mo +*.pot + +# Django stuff: +*.log +local_settings.py +db.sqlite3 + +# Flask stuff: +instance/ +.webassets-cache + +# Scrapy stuff: +.scrapy + +# Sphinx documentation +docs/_build/ + +# PyBuilder +target/ + +# Jupyter Notebook +.ipynb_checkpoints + +# pyenv +.python-version + +# celery beat schedule file +celerybeat-schedule + +# SageMath parsed files +*.sage.py + +# Environments +.env +.venv +env/ +venv/ +ENV/ +env.bak/ +venv.bak/ + +# Spyder project settings +.spyderproject +.spyproject + +# Rope project settings +.ropeproject + +# mkdocs documentation +/site + +# mypy +.mypy_cache/ + +### Python Patch ### +.venv/ + + +# End of https://www.gitignore.io/api/python \ No newline at end of file diff --git a/book/_ext/pybtexapastyle/LICENSE b/book/_ext/pybtexapastyle/LICENSE new file mode 100644 index 0000000..579d367 --- /dev/null +++ b/book/_ext/pybtexapastyle/LICENSE @@ -0,0 +1,21 @@ +MIT License + +Copyright (c) 2018 Naeka + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. \ No newline at end of file diff --git a/book/_ext/pybtexapastyle/formatting/__init__.py b/book/_ext/pybtexapastyle/formatting/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/book/_ext/pybtexapastyle/formatting/apa.py b/book/_ext/pybtexapastyle/formatting/apa.py new file mode 100644 index 0000000..dfa5a58 --- /dev/null +++ b/book/_ext/pybtexapastyle/formatting/apa.py @@ -0,0 +1,486 @@ +# -*- coding:Utf-8 -*- +from __future__ import unicode_literals + +import re +import six + +from pybtex.plugin import find_plugin +from pybtex.style.formatting import BaseStyle, toplevel +from pybtex.style.template import ( + field, first_of, href, join, optional, optional_field, sentence, tag, + together, words, node, FieldIsMissing +) + +from pybtex.richtext import Text, Symbol + + +firstlast = find_plugin('pybtex.style.names', 'lastfirst')() + +if six.PY2: + def format_pages(text): + dash_re = re.compile(r'-+') + pages = Text(Symbol('ndash')).join( + re.split(dash_re, six.text_type(text))) + if re.search('[-‒–—―]', six.text_type(text)): + return Text("pp.", Symbol('nbsp'), pages) + return Text("p.", Symbol('nbsp'), pages) +else: + def format_pages(text): + dash_re = re.compile(r'-+') + pages = Text(Symbol('ndash')).join(text.split(dash_re)) + if re.search('[-‒–—―]', str(text)): + return Text("pp.", Symbol('nbsp'), pages) + return Text("p.", Symbol('nbsp'), pages) + + +pages = field('pages', apply_func=format_pages) +date = words[field('year'), optional[", ", field('month')]] + + +@node +def apa_names(children, context, role, **kwargs): + """ + Returns formatted names as an APA compliant reference list citation. + """ + assert not children + + try: + persons = context['entry'].persons[role] + except KeyError: + raise FieldIsMissing(role, context['entry']) + + style = context['style'] + + if len(persons) > 7: + persons = persons[:6] + persons[-1:] + formatted_names = [style.format_name( + person, style.abbreviate_names) for person in persons] + return join(sep=', ', last_sep=', … ')[ + formatted_names].format_data(context) + else: + formatted_names = [style.format_name( + person, style.abbreviate_names) for person in persons] + return join(sep=', ', sep2=', & ', last_sep=', & ')[ + formatted_names].format_data(context) + + +@node +def editor_names(children, context, with_suffix=True, **kwargs): + """ + Returns formatted editor names for inbook. + """ + assert not children + + try: + editors = context['entry'].persons['editor'] + except KeyError: + raise FieldIsMissing('editor', context['entry']) + + formatted_names = [ + firstlast.format(editor, True) for editor in editors] + + if with_suffix: + return words[ + join(sep=', ', sep2=', & ', last_sep=', & ')[formatted_names], + "(Eds.)" if len(editors) > 1 else "(Ed.)" + ].format_data(context) + + return join(sep=', ', sep2=', & ', last_sep=', & ')[ + formatted_names + ].format_data(context) + + +class APAStyle(BaseStyle): + name = 'apa' + default_name_style = 'lastfirst' + default_sorting_style = 'author_year_title' + default_label_style = 'apa' + + def __init__(self, *args, **kwargs): + super(APAStyle, self).__init__(*args, **kwargs) + self.abbreviate_names = True + + def format_names(self, role, as_sentence=True): + formatted_names = apa_names(role) + if as_sentence: + return sentence(capfirst=False)[formatted_names] + else: + return formatted_names + + def format_author_or_editor_and_date(self, e): + if 'author' in e.persons and 'editor' in e.persons: + return sentence(sep=' ')[ + self.format_names('author'), join["(", date, ")."], + self.format_editor(e, as_sentence=False)] + elif 'author' in e.persons: + return sentence(sep=' ')[ + self.format_names('author'), join["(", date, ")"]] + else: + return sentence(sep=' ')[ + self.format_editor(e, as_sentence=False), + join["(", date, ")"]] + + def format_editor(self, e, as_sentence=True): + editors = self.format_names('editor', as_sentence=False) + if 'editor' not in e.persons: + # when parsing the template, a FieldIsMissing exception + # will be thrown anyway; no need to do anything now, + # just return the template that will throw the exception + return editors + if len(e.persons['editor']) > 1: + word = '(Eds.)' + else: + word = '(Ed.)' + result = join(sep=' ')[editors, word] + if as_sentence: + return sentence[result] + else: + return result + + def format_volume(self, e, for_article=False): + prefix = "Vol." + if for_article: + return join[ + tag('em')[field('volume')], + optional['(', field('number'), ')'], + ] + else: + return optional[together[prefix, field('volume')]] + + def format_title(self, e, which_field, as_sentence=True): + formatted_title = field( + which_field, apply_func=lambda text: text.capitalize() + ) + if as_sentence: + return sentence[formatted_title] + else: + return formatted_title + + def format_btitle(self, e, which_field, as_sentence=True): + formatted_title = tag('em')[field(which_field)] + if as_sentence: + return sentence[formatted_title] + else: + return formatted_title + + def format_web_refs(self, e): + # Based on urlbst output.web.refs + return sentence(add_period=False)[ + optional[self.format_url(e)], + optional[self.format_eprint(e)], + optional[self.format_pubmed(e)], + optional[self.format_doi(e)], + ] + + def format_url(self, e): + # Based on urlbst format.url + return words[ + 'URL:', + href[ + field('url', raw=True), + field('url', raw=True) + ] + ] + + def format_pubmed(self, e): + # Based on urlbst format.pubmed + return href[ + join[ + 'https://www.ncbi.nlm.nih.gov/pubmed/', + field('pubmed', raw=True) + ], + join[ + 'PMID:', + field('pubmed', raw=True) + ] + ] + + def format_doi(self, e): + # Based on urlbst format.doi + return href[ + join[ + 'https://doi.org/', + field('doi', raw=True) + ], + join[ + 'doi:', + field('doi', raw=True) + ] + ] + + def format_eprint(self, e): + # Based on urlbst format.eprint + return href[ + join[ + 'https://arxiv.org/abs/', + field('eprint', raw=True) + ], + join[ + 'arXiv:', + field('eprint', raw=True) + ] + ] + + def get_article_template(self, e): + # Required fields: author, title, journal, year + # Optional fields: volume, number, pages, month, note, key + volume_and_pages = first_of[ + # Volume and pages, with optional issue number + optional[ + join[ + self.format_volume(e, for_article=True), + optional[', ', field('pages')] + ], + ], + # Pages only + pages, + ] + template = toplevel[ + self.format_names('author'), + sentence[ + join["(", date, ")"] + ], + self.format_title(e, 'title'), + sentence[ + tag('em')[field('journal')], + optional[volume_and_pages], + ], + sentence[optional_field('note')], + self.format_web_refs(e), + ] + return template + + def get_book_template(self, e): + # Required fields: author/editor, title, publisher, year + # Optional fields: volume, series, address, edition, month, note, key, + # isbn + return toplevel[ + self.format_author_or_editor_and_date(e), + sentence(sep=' ')[ + self.format_btitle(e, 'title'), + optional[ + sentence[ + optional[field('edition'), ' ed.'], + self.format_volume(e), + ] + ] + ], + sentence(sep=': ')[ + optional_field('address'), + field('publisher'), + ], + sentence[optional_field('note')], + ] + + def get_booklet_template(self, e): + # Required fields: title + # Optional fields: author, howpublished, address, month, year, note, + # key + return toplevel[ + sentence(sep=' ')[ + first_of[ + optional[self.format_names( + 'author', as_sentence=False)], + "None to claim their bones" + ], + join["(", first_of[optional[date], "n.d."], ")"] + ], + self.format_title(e, 'title'), + sentence[optional_field('address')], + sentence[optional_field('note')], + ] + + def get_inbook_template(self, e): + # Required fields: author/editor, title, chapter/pages, publisher, year + # Optional fields: volume, series, address, edition, month, note, key + return toplevel[ + sentence(sep=' ')[ + self.format_names('author'), + join["(", date, ")"] + ], + self.format_title(e, 'title'), + sentence(sep=' ')[ + optional[ + "In ", + editor_names(), + "," + ], + self.format_btitle(e, 'booktitle', as_sentence=False), + optional[ + join[ + "(", + sentence(add_period=False)[ + optional[field('edition'), ' ed.'], + self.format_volume(e), + pages, + ], + ")" + ] + ] + ], + sentence(sep=': ')[ + optional_field('address'), + field('publisher'), + ], + sentence[optional_field('note')], + ] + + def get_incollection_template(self, e): + # Required fields: author, title, booktitle, year + # Optional fields: editor, pages, organization, publisher, address, + # month, note, key + return toplevel[ + self.format_author_or_editor_and_date(e), + self.format_title(e, 'title'), + sentence(sep=' ')[ + self.format_btitle(e, 'booktitle', as_sentence=False), + optional["(", pages, ")"] + ], + sentence(sep=': ')[ + optional_field('address'), + optional_field('publisher'), + ], + sentence[optional_field('note')], + ] + + def get_inproceedings_template(self, e): + # Required fields: author, title, booktitle, year + # Optional fields: editor, pages, organization, publisher, address, + # month, note, key + return toplevel[ + self.format_author_or_editor_and_date(e), + self.format_title(e, 'title'), + sentence(sep=' ')[ + self.format_btitle(e, 'booktitle', as_sentence=False), + optional["(", pages, ")"] + ], + sentence(sep=': ')[ + optional_field('address'), + optional_field('publisher'), + ], + sentence[optional_field('note')], + self.format_web_refs(e) + ] + + def get_manual_template(self, e): + # Required fields: title + # Optional fields: author, organization, address, edition, month, year, + # note, key + return toplevel[ + sentence(sep=' ')[ + first_of[ + optional[self.format_names('author', as_sentence=False)], + optional_field('organization'), + "None to claim their bones" + ], + join["(", first_of[optional[date], "n.d."], ")"] + ], + self.format_btitle(e, 'title'), + sentence[optional_field('address')], + sentence[optional_field('note')], + self.format_web_refs(e) + ] + + def get_mastersthesis_template(self, e): + # Required fields: author, title, school, year + # Optional fields: address, month, note, key + return toplevel[ + sentence(sep=' ')[ + self.format_names('author'), + join["(", date, ")"] + ], + sentence(sep=' ')[ + self.format_btitle(e, 'title', as_sentence=False), + "(Master's thesis)" + ], + sentence[ + field('school'), + optional_field('address'), + ], + sentence[optional_field('note')], + ] + + def get_misc_template(self, e): + # Required fields: aucun + # Optional fields: author, title, howpublished, month, year, note, key, + # type + template = toplevel[ + sentence(sep=' ')[ + first_of[ + optional[self.format_names('author', as_sentence=False)], + optional_field('publisher'), + "None to claim their bones" + ], + join["(", first_of[optional[date], "n.d."], ")"] + ], + optional[self.format_title(e, 'title')], + sentence[optional_field('note')], + self.format_web_refs(e) + ] + return template + + def get_phdthesis_template(self, e): + # Required fields: author, title, school, year + # Optional fields: address, month, note, key + return toplevel[ + sentence(sep=' ')[ + self.format_names('author'), + join["(", date, ")"] + ], + sentence(sep=' ')[ + self.format_btitle(e, 'title', as_sentence=False), + "(Doctoral dissertation)" + ], + sentence[ + field('school'), + optional_field('address'), + ], + sentence[optional_field('note')], + ] + + def get_proceedings_template(self, e): + # Required fields: title, year + # Optional fields: editor, publisher, organization, address, month, + # note, key + return toplevel[ + sentence(sep=' ')[ + first_of[ + optional[self.format_editor(e, as_sentence=False)], + optional_field('organization'), + "None to claim their bones" + ], + join["(", first_of[optional[date], "n.d."], ")"] + ], + self.format_btitle(e, 'title'), + sentence(sep=': ')[ + optional_field('address'), + optional_field('publisher'), + ], + sentence[optional_field('note')], + ] + + def get_techreport_template(self, e): + # Required fields: author, title, institution, year + # Optional fields: type, number, address, month, note, key + return toplevel[ + sentence(sep=' ')[ + self.format_names('author', as_sentence=False), + join["(", date, ")"] + ], + self.format_btitle(e, 'title'), + sentence[field('institution')], + sentence[optional_field('note')], + ] + + def get_unpublished_template(self, e): + # Required fields: author, title, note + # Optional fields: month, year, key + template = toplevel[ + sentence(sep=' ')[ + self.format_names('author', as_sentence=False), + join["(", first_of[optional[date], "n.d."], ")"] + ], + self.format_btitle(e, 'title'), + sentence[field('note')], + ] + return template diff --git a/book/_ext/pybtexapastyle/formatting/pybtex/style/formatting/__init__.py b/book/_ext/pybtexapastyle/formatting/pybtex/style/formatting/__init__.py new file mode 100644 index 0000000..5ac42b8 --- /dev/null +++ b/book/_ext/pybtexapastyle/formatting/pybtex/style/formatting/__init__.py @@ -0,0 +1,69 @@ +from __future__ import unicode_literals + +from pybtex.style import FormattedEntry, FormattedBibliography +from pybtex.style.template import node, join +from pybtex.richtext import Symbol +from pybtex.plugin import Plugin, find_plugin + + +@node +def toplevel(children, data): + return join(sep=Symbol('newblock')) [children].format_data(data) + + +class BaseStyle(Plugin): + """ + The base class for pythonic formatting styles. + """ + + default_name_style = None + default_label_style = None + default_sorting_style = None + + def __init__(self, label_style=None, name_style=None, sorting_style=None, abbreviate_names=False, min_crossrefs=2, **kwargs): + self.name_style = find_plugin('pybtex.style.names', name_style or self.default_name_style)() + self.label_style = find_plugin('pybtex.style.labels', label_style or self.default_label_style)() + self.sorting_style = find_plugin('pybtex.style.sorting', sorting_style or self.default_sorting_style)() + self.format_name = self.name_style.format + self.format_labels = self.label_style.format_labels + self.sort = self.sorting_style.sort + self.abbreviate_names = abbreviate_names + self.min_crossrefs = min_crossrefs + + def format_entries(self, entries, bib_data=None): + sorted_entries = self.sort(entries) + labels = self.format_labels(sorted_entries) + for label, entry in zip(labels, sorted_entries): + yield self.format_entry(label, entry, bib_data=bib_data) + + def format_entry(self, label, entry, bib_data=None): + context = { + 'entry': entry, + 'style': self, + 'bib_data': bib_data, + } + try: + get_template = getattr(self, 'get_{}_template'.format(entry.type)) + except AttributeError: + format_method = getattr(self, "format_" + entry.type) + text = format_method(context) + else: + text = get_template(entry).format_data(context) + return FormattedEntry(entry.key, text, label) + + def format_bibliography(self, bib_data, citations=None): + """ + Format bibliography entries with the given keys and return a + ``FormattedBibliography`` object. + + :param bib_data: A :py:class:`pybtex.database.BibliographyData` object. + :param citations: A list of citation keys. + """ + + if citations is None: + citations = list(bib_data.entries.keys()) + citations = bib_data.add_extra_citations(citations, self.min_crossrefs) + entries = [bib_data.entries[key] for key in citations] + formatted_entries = self.format_entries(entries) + formatted_bibliography = FormattedBibliography(formatted_entries, style=self, preamble=bib_data.preamble) + return formatted_bibliography diff --git a/book/_ext/pybtexapastyle/formatting/pybtex/style/sorting/__init__.py b/book/_ext/pybtexapastyle/formatting/pybtex/style/sorting/__init__.py new file mode 100644 index 0000000..3430087 --- /dev/null +++ b/book/_ext/pybtexapastyle/formatting/pybtex/style/sorting/__init__.py @@ -0,0 +1,12 @@ +from __future__ import unicode_literals + + +from pybtex.plugin import Plugin + + +class BaseSortingStyle(Plugin): + def sorting_key(self, entry): + raise NotImplementedError + + def sort(self, entries): + return sorted(entries, key=self.sorting_key) \ No newline at end of file diff --git a/book/_ext/pybtexapastyle/formatting/pybtex/style/sorting/author_year_title.py b/book/_ext/pybtexapastyle/formatting/pybtex/style/sorting/author_year_title.py new file mode 100644 index 0000000..c315c0c --- /dev/null +++ b/book/_ext/pybtexapastyle/formatting/pybtex/style/sorting/author_year_title.py @@ -0,0 +1,39 @@ +from __future__ import unicode_literals + +from pybtex.style.sorting import BaseSortingStyle + +class SortingStyle(BaseSortingStyle): + + def sorting_key(self, entry): + if entry.type in ('book', 'inbook'): + author_key = self.author_editor_key(entry) + elif 'author' in entry.persons: + author_key = self.persons_key(entry.persons['author']) + else: + author_key = '' + return (author_key, entry.fields.get('year', ''), entry.fields.get('title', '')) + + def persons_key(self, persons): + return ' '.join(self.person_key(person) for person in persons) + + def person_key(self, person): + if person.prelast_names[0] != '{' and person.last_names[0] != '{' and person.first_names[0] != '{': + return ' '.join(( + ' '.join(person.prelast_names + person.last_names), + ' '.join(person.first_names + person.middle_names), + ' '.join(person.lineage_names), + )).lower() + else: + return ' '.join(( + ' '.join(person.first_names + person.middle_names), + ' '.join(person.prelast_names + person.last_names), + ' '.join(person.lineage_names), + )).lower() + + def author_editor_key(self, entry): + if entry.persons.get('author'): + return self.persons_key(entry.persons['author']) + elif entry.persons.get('editor'): + return self.persons_key(entry.persons['editor']) + else: + return '' diff --git a/book/_ext/pybtexapastyle/labels/__init__.py b/book/_ext/pybtexapastyle/labels/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/book/_ext/pybtexapastyle/labels/apa.py b/book/_ext/pybtexapastyle/labels/apa.py new file mode 100644 index 0000000..59176f3 --- /dev/null +++ b/book/_ext/pybtexapastyle/labels/apa.py @@ -0,0 +1,67 @@ +# -*- coding:Utf-8 -*- +from __future__ import unicode_literals + +from collections import Counter +import re +import unicodedata + +from pybtex.style.labels import BaseLabelStyle + + +_nonalnum_pattern = re.compile('[^A-Za-z0-9 \-]+', re.UNICODE) + + +def _strip_accents(s): + return "".join( + (c for c in unicodedata.normalize('NFD', s) + if not unicodedata.combining(c))) + + +def _strip_nonalnum(parts): + """Strip all non-alphanumerical characters from a list of strings. + + >>> print(_strip_nonalnum([u"ÅA. B. Testing 12+}[.@~_", u" 3%"])) + AABTesting123 + """ + s = "".join(parts) + return _nonalnum_pattern.sub("", _strip_accents(s)) + + +class LabelStyle(BaseLabelStyle): + def format_labels(self, sorted_entries): + labels = [self.format_label(entry) for entry in sorted_entries] + count = Counter(labels) + counted = Counter() + for label in labels: + if count[label] == 1: + yield label + else: + yield label # + chr(ord('a') + counted[label]) + # counted.update([label]) + + def format_label(self, entry): + label = "Anonymous" + if 'author' in entry.persons: + label = self.format_author_or_editor_names(entry.persons['author']) + elif 'editor' in entry.persons: + label = self.format_author_or_editor_names(entry.persons['editor']) + elif 'organization' in entry.fields: + label = entry.fields['organization'] + if label.startswith("The "): + label = label[4:] + return '' + # if 'year' in entry.fields: + # return "{}, {}".format(label, entry.fields['year']) + # else: + # return "{}, n.d.".format(label) + + def format_author_or_editor_names(self, persons): + if len(persons) is 1: + return _strip_nonalnum(persons[0].last_names) + elif len(persons) is 2: + return "{} & {}".format( + _strip_nonalnum(persons[0].last_names), + _strip_nonalnum(persons[1].last_names)) + else: + return "{} et al.".format( + _strip_nonalnum(persons[0].last_names)) diff --git a/book/_ext/pybtexapastyle/names/__init__.py b/book/_ext/pybtexapastyle/names/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/book/_ext/pybtexapastyle/names/firstlast.py b/book/_ext/pybtexapastyle/names/firstlast.py new file mode 100644 index 0000000..8f23263 --- /dev/null +++ b/book/_ext/pybtexapastyle/names/firstlast.py @@ -0,0 +1,39 @@ +# -*- coding:Utf-8 -*- +from __future__ import unicode_literals + +from pybtex.style.names import BaseNameStyle, name_part +from pybtex.style.template import join + + +class NameStyle(BaseNameStyle): + + def format(self, person, abbr=False): + r""" + Format names similarly to {vv~}{ll}{, jj}{, f.} in BibTeX. + + >>> from pybtex.database import Person + >>> name = Person(string=r"Charles Louis Xavier Joseph de la Vall{\'e}e Poussin") + >>> firstlast = NameStyle().format + + >>> print(firstlast(name).format().render_as('latex')) + Charles Louis Xavier~Joseph de~la Vall{é}e~Poussin + >>> print(firstlast(name).format().render_as('html')) + Charles Louis Xavier Joseph de la Vallée Poussin + + >>> print(firstlast(name, abbr=True).format().render_as('latex')) + C.~L. X.~J. de~la Vall{é}e~Poussin + >>> print(firstlast(name, abbr=True).format().render_as('html')) + C. L. X. J. de la Vallée Poussin + + >>> name = Person(first='First', last='Last', middle='Middle') + >>> print(firstlast(name).format().render_as('latex')) + First~Middle Last + >>> print(firstlast(name, abbr=True).format().render_as('latex')) + F.~M. Last + + """ + return join[ + name_part(abbr=abbr)[person.rich_first_names + person.rich_middle_names], + name_part(before=' ')[person.rich_prelast_names], + name_part(before=' ')[person.rich_last_names], + ] diff --git a/book/_ext/pybtexapastyle/setup.py b/book/_ext/pybtexapastyle/setup.py new file mode 100644 index 0000000..a62d122 --- /dev/null +++ b/book/_ext/pybtexapastyle/setup.py @@ -0,0 +1,27 @@ +import setuptools + + +setuptools.setup( + name='pybtex-apa-style', + version='1.3', + author='Naeka', + author_email='contact@naeka.fr', + description='Pybtex APA-like style', + url='https://github.com/naeka/pybtex-apa-style', + py_modules=['formatting.apa', 'labels.apa', 'names.firstlast'], + entry_points={ + 'pybtex.style.formatting': 'apa = formatting.apa:APAStyle', + 'pybtex.style.labels': 'apa = labels.apa:LabelStyle', + 'pybtex.style.names': 'firstlast = names.firstlast:NameStyle', + }, + classifiers=( + 'Operating System :: OS Independent', + 'Programming Language :: Python', + 'Programming Language :: Python :: 2.7', + 'Programming Language :: Python :: 3', + 'License :: OSI Approved :: MIT License', + 'Operating System :: OS Independent', + 'Topic :: Text Processing :: Markup', + 'Topic :: Utilities', + ), +) diff --git a/book/_toc.yml b/book/_toc.yml new file mode 100644 index 0000000..146f8d6 --- /dev/null +++ b/book/_toc.yml @@ -0,0 +1,10 @@ +format: jb-book +root: intro.md +parts: + - caption: Contents + chapters: + - file: reliability-component/overview.md + sections: + - file: reliability-component/contamination.ipynb + - file: references.md + - file: credits.md \ No newline at end of file diff --git a/book/code/cosinewave.py b/book/code/cosinewave.py new file mode 100644 index 0000000..744c2fe --- /dev/null +++ b/book/code/cosinewave.py @@ -0,0 +1,12 @@ +import numpy as np +import matplotlib.pyplot as plt + +x = np.linspace(0, 2*np.pi, endpoint=True) +y = np.cos(x) + +plt.figure() +plt.plot(x, y) +plt.title('$y=\cos(x)$') +plt.xlabel('$x$') +plt.ylabel('$y$') +plt.savefig('cosinewave.svg') \ No newline at end of file diff --git a/book/code/ex_FN_curve_step_01.py b/book/code/ex_FN_curve_step_01.py new file mode 100644 index 0000000..efc3ade --- /dev/null +++ b/book/code/ex_FN_curve_step_01.py @@ -0,0 +1,38 @@ +import numpy as np +import matplotlib.pyplot as plt +from mpl_toolkits.axisartist.axislines import AxesZero + +# Probability density/mass function + +fig = plt.figure(figsize=(8,6)) +ax = fig.add_subplot(axes_class=AxesZero) + +for direction in ["xzero", "yzero"]: + ax.axis[direction].set_axisline_style("-|>") # add arrows + ax.axis[direction].set_visible(True) # x and y from origin + +for direction in ["left", "right", "bottom", "top"]: + ax.axis[direction].set_visible(False) # hide borders + +N_fatalities = ['0', '10', '100'] +N_fatalities_loc = [0.05, 0.30, 0.66] + +pdf = ['0.989', '$10^{-2}$', '$10^{-3}$'] +pdf_loc = [0.99, 0.66, 0.33] + +ax.bar(N_fatalities_loc, pdf_loc, width=0.05, color= 'lightcyan', edgecolor='k') + +ax.set_xticks(N_fatalities_loc) +ax.set_xticklabels(N_fatalities) + +ax.set_yticks(pdf_loc) +ax.set_yticklabels(pdf) + +ax.set_title('Probability density/mass function, $f_{N}(n)$', x=0.6, y=1.0) +ax.set_xlabel('Fatalities') +ax.set_ylabel('Probability') + +ax.axhline(y=0.66, xmin= 0.01, xmax= 0.40, linewidth=1, linestyle='dashed', color='k') # add dashed horizontal lines +ax.axhline(y=0.33, xmin= 0.01, xmax= 0.90, linewidth=1, linestyle='dashed', color='k') + +plt.savefig('ex_FN_curve_step_01_py.svg') \ No newline at end of file diff --git a/book/code/ex_FN_curve_step_02.py b/book/code/ex_FN_curve_step_02.py new file mode 100644 index 0000000..d83d51e --- /dev/null +++ b/book/code/ex_FN_curve_step_02.py @@ -0,0 +1,38 @@ +import numpy as np +import matplotlib.pyplot as plt +from mpl_toolkits.axisartist.axislines import AxesZero + +# Cumulative Distribution Function + +fig = plt.figure(figsize=(8,6)) +ax = fig.add_subplot(axes_class=AxesZero) + +for direction in ["xzero", "yzero"]: + ax.axis[direction].set_axisline_style("-|>") # add arrows + ax.axis[direction].set_visible(True) # x and y from origin + +for direction in ["left", "right", "bottom", "top"]: + ax.axis[direction].set_visible(False) # hide borders + +N_fatalities = ['0', '10', '100', ''] +N_fatalities_loc = [0.03, 0.33, 0.76, 0.95] + +pdf = ['0', '0.989', '0.999', '1'] +pdf_loc = [0.03, 0.66, 0.86, 0.99] + +ax.step(N_fatalities_loc, pdf_loc, color= 'darkblue',linewidth=4) + +ax.set_xticks(N_fatalities_loc) +ax.set_xticklabels(N_fatalities) + +ax.set_yticks(pdf_loc) +ax.set_yticklabels(pdf) + +ax.set_title('Cumulative distribution function, $F_{N}(n) = P(N \leq n)$', x=0.55, y=1.0) +ax.set_xlabel('Fatalities') +ax.set_ylabel('Probability') + +ax.text(0.8, 0.9, r'} $10^{-3}$', fontsize=20) +ax.text(0.4, 0.725, r'} $10^{-2}$', fontsize=30) + +plt.savefig('ex_FN_curve_step_02_py.svg') \ No newline at end of file diff --git a/book/code/ex_FN_curve_step_03.py b/book/code/ex_FN_curve_step_03.py new file mode 100644 index 0000000..ec61816 --- /dev/null +++ b/book/code/ex_FN_curve_step_03.py @@ -0,0 +1,35 @@ +import numpy as np +import matplotlib.pyplot as plt +from mpl_toolkits.axisartist.axislines import AxesZero + +# FN curve + +fig = plt.figure(figsize=(8,6)) +ax = fig.add_subplot(axes_class=AxesZero) + +for direction in ["xzero", "yzero"]: + ax.axis[direction].set_axisline_style("-|>") # add arrows + ax.axis[direction].set_visible(True) # x and y from origin + +for direction in ["left", "right", "bottom", "top"]: + ax.axis[direction].set_visible(False) # hide borders + +N_fatalities = ['0', '10', '100','100'] +N_fatalities_loc = [0.03,0.33, 0.95, 0.95] + +pdf = ['0','$1.1 * 10^{-2}$', '$10^{-3}$','0'] +pdf_loc = [0.03,0.99, 0.66, 0.03] + +ax.step(N_fatalities_loc, pdf_loc, color= 'darkblue',linewidth=4) + +ax.set_xticks(N_fatalities_loc) +ax.set_xticklabels(N_fatalities) + +ax.set_yticks(pdf_loc) +ax.set_yticklabels(pdf) + +ax.set_title('FN curve, $1-F_{N}(n) = P(N > n)$', x=0.75, y=1.0) +ax.set_xlabel('Fatalities') +ax.set_ylabel('Probability') + +plt.savefig('ex_FN_curve_step_03_py.svg') \ No newline at end of file diff --git a/book/code/present_value.py b/book/code/present_value.py new file mode 100644 index 0000000..ffbd88e --- /dev/null +++ b/book/code/present_value.py @@ -0,0 +1,16 @@ +import numpy as np +import matplotlib.pyplot as plt + +t = np.linspace(0, 101) +y_2 = 1 / (1 + 0.02)**t +y_4 = 1 / (1 + 0.04)**t + +fig = plt.figure() +plt.plot(t, y_2, label='2%') +plt.plot(t, y_4, label='4%') +plt.grid() +plt.legend() +plt.xlabel('Year') +plt.ylabel('Normalized Present Value [$-$]') + +plt.savefig('present_value_py.svg') diff --git a/book/code/risk_types.py b/book/code/risk_types.py new file mode 100644 index 0000000..38f967f --- /dev/null +++ b/book/code/risk_types.py @@ -0,0 +1,54 @@ +import numpy as np +import matplotlib.pyplot as plt + +# Given Parameters + +N_fatalities = np.linspace(1,1000,1000) # fatalities + +P_df = 0.1; beta = 0.1 + +alpha = 2 +k = 3 +N_A = 100 + +r= 0.025 +I = 5*10**6 +B = 0.33 + +# Individual Risk + +Pf_ind_risk = (beta*(10**-4))/P_df # per year + +# print('Acceptable Failure Probability: ', Pf_ind_risk) + +# Societal Risk + +C = ((beta*100)/(k*np.sqrt(N_A)))**2 # binomial distribution + +Pf_SR = (C/(N_fatalities**alpha)) + +# Economic Risk + +D_damage = (5*10**7)*N_fatalities + +Pf_ER = (I*B*r)/(D_damage) + +# Visualize + +my_linewidth = 4 + +plt.figure(figsize=(8,6)) + +plt.yscale('log') +plt.xscale('log') +plt.plot(N_fatalities, Pf_SR, linewidth=my_linewidth, label='Societal Risk') +plt.plot(N_fatalities,Pf_ER, linewidth=my_linewidth, color='r', label='Economic Risk') +plt.axhline(Pf_ind_risk, linewidth=my_linewidth, color='g', label='Individual Risk') + +plt.ylabel('Probability of Exceedance, $1-F_N(n)$') +plt.xlabel('Fatalities, N') +plt.ylim(10**(-7),1) + +plt.legend(loc='upper right') + +plt.savefig('risk_types_py.svg') \ No newline at end of file diff --git a/book/code/sinewave.py b/book/code/sinewave.py new file mode 100644 index 0000000..74a1d42 --- /dev/null +++ b/book/code/sinewave.py @@ -0,0 +1,12 @@ +import numpy as np +import matplotlib.pyplot as plt + +x = np.linspace(0, 2*np.pi, endpoint=True) +y = np.sin(x) + +plt.figure() +plt.plot(x, y) +plt.title('$y=\sin(x)$') +plt.xlabel('$x$') +plt.ylabel('$y$') +plt.savefig('sinewave.svg') \ No newline at end of file diff --git a/book/code/test.py b/book/code/test.py new file mode 100644 index 0000000..21a9781 --- /dev/null +++ b/book/code/test.py @@ -0,0 +1,23 @@ +import modulefinder + +finder = modulefinder.ModuleFinder() +finder.run_script('cosinewave.py') + +moduleslist = {} +for name, mod in finder.modules.iteritems(): + filename = mod.__file__ + if filename is None: + continue + if '__' in name: + continue + #if "python" in filename.lower(): + # continue + moduleslist[name.split(".")[0]] = True + #print '%s: %s' % (name, filename) + #print ','.join(mod.globalnames.keys()[:3]) + +print('Loaded modules:') +for name, dummy in moduleslist.iteritems(): + print(name) + +input("Press Enter to continue...") diff --git a/book/credits.md b/book/credits.md new file mode 100644 index 0000000..d49744b --- /dev/null +++ b/book/credits.md @@ -0,0 +1,39 @@ +(credits)= +# Credits and License + +You can refer to this book as: + +> `` `` ``, TU Delft Open, ``, doi XXXXXXXX. + +The introduction, structure of the book and formatting of contents is done by the Editor, ``. Some chapters and pages have additional primary authors who are identified within the book either at the bottom of the first page in a chapter, or at the bottom of an individual page, as necessary. If an author is not listed on a particular page, it is ``. + +You can refer to individual chapters or pages within this book as: + +> `` `` ``. In `<Author>` (Ed.), `<Book Title>` TU Delft Open,`<Year>`, doi XXXXXXXX. + +Although content will be added over time, chapter titles and URL's in this book are expected to remain relatively static. However, we make no guarantee, so if it is important for you to reference a specific location within the book, we recommend including the complete URL and date of access in your reference. + +## How the book is made +<!-- edit $CI_PROJECT_NAME below accordingly --> +This book is created using open source tools: it is a Jupyter Book that is written using Markdown, Jupyter notebooks and Python files to generate some figures. The files are stored on a [public GitLab repository of TU Delft](https://gitlab.tudelft.nl/interactivetextbooks-citg/$CI_PROJECT_NAME/). The published version of this book is compiled from a special branch (`xxxxxxxx`). View the repository README file or contact the author for additional information. + +(editor)= +## About the Editor + +`<Author>` + +### Acknowledgements + + +--- + +This book is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0 International License</a>. + +<a rel="license" href="http://creativecommons.org/licenses/by/4.0/"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by/4.0/88x31.png"/></a> + +The following items referenced in the text are _not_ included in the license: + +{numref}`risk-curve-baecher` and {numref}`risk-curve-baecher-2` are from {cite:t}`baecher2003`, based on {cite:t}`baecher1982` and described in {cite:t}`baecher2021` + +{numref}`risk_matrix` is from an online PDF document (located [here](https://home.army.mil/lee/application/files/7815/3809/1878/Tables.pdf)). The formal definition for the risk matrix can be found in Engineering Manual EM 385-1-1 (located [here](https://www.publications.usace.army.mil/portals/76/publications/engineermanuals/em_385-1-1.pdf)). + diff --git a/book/figures/1.png b/book/figures/1.png new file mode 100644 index 0000000..5227771 Binary files /dev/null and b/book/figures/1.png differ diff --git a/book/figures/FN-simple.PNG b/book/figures/FN-simple.PNG new file mode 100644 index 0000000..7e8eea1 Binary files /dev/null and b/book/figures/FN-simple.PNG differ diff --git a/book/figures/combined_risk_criteria.png b/book/figures/combined_risk_criteria.png new file mode 100644 index 0000000..bb9f78e Binary files /dev/null and b/book/figures/combined_risk_criteria.png differ diff --git a/book/figures/cover.png b/book/figures/cover.png new file mode 100644 index 0000000..2a2bfb0 Binary files /dev/null and b/book/figures/cover.png differ diff --git a/book/figures/cover.svg b/book/figures/cover.svg new file mode 100644 index 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b/book/images/TUDelft_logo_rgb.png new file mode 100644 index 0000000..753f310 Binary files /dev/null and b/book/images/TUDelft_logo_rgb.png differ diff --git a/book/intro.md b/book/intro.md new file mode 100644 index 0000000..ff1502d --- /dev/null +++ b/book/intro.md @@ -0,0 +1,10 @@ +(intro)= +# INTRO PAGE + +_Write book intro here. This is the first page the student will see when opening the url._ + +--- + +This book is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0 International License</a>. + +<a rel="license" href="http://creativecommons.org/licenses/by/4.0/"><img alt="Creative Commons License" style="border-width:0" src="https://i.creativecommons.org/l/by/4.0/88x31.png"/></a> \ No newline at end of file diff --git a/book/notebooks/Untitled.ipynb b/book/notebooks/Untitled.ipynb new file mode 100644 index 0000000..b7f29e4 --- /dev/null +++ b/book/notebooks/Untitled.ipynb @@ -0,0 +1,153 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "9d7ffe9f-441f-4119-b5e4-0e872922a78d", + "metadata": {}, + "outputs": [], + "source": [ + "from sympy import *" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "406dc83e-b114-46be-baf8-073a72b47a36", + "metadata": {}, + "outputs": [], + "source": [ + "t, a = symbols('t a')\n", + "theta = Function('theta')(t)\n", + "r = Function('r')(t)\n", + "U_c = Function('U_c')(t)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "df8fe246-6986-4ffd-9c39-6bd259176e42", + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle - \\frac{a^{2} \\operatorname{U_{c}}{\\left(t \\right)} \\cos{\\left(\\theta{\\left(t \\right)} \\right)}}{r{\\left(t \\right)}}$" + ], + "text/plain": [ + "-a**2*U_c(t)*cos(theta(t))/r(t)" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "phi = - (a**2*U_c)/r * cos(theta)\n", + "phi" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "a6e55454-52c6-493b-a753-f901cee357bc", + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\frac{a^{2} \\operatorname{U_{c}}{\\left(t \\right)} \\sin{\\left(\\theta{\\left(t \\right)} \\right)} \\frac{d}{d t} \\theta{\\left(t \\right)}}{r{\\left(t \\right)}} + \\frac{a^{2} \\operatorname{U_{c}}{\\left(t \\right)} \\cos{\\left(\\theta{\\left(t \\right)} \\right)} \\frac{d}{d t} r{\\left(t \\right)}}{r^{2}{\\left(t \\right)}} - \\frac{a^{2} \\cos{\\left(\\theta{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{U_{c}}{\\left(t \\right)}}{r{\\left(t \\right)}}$" + ], + "text/plain": [ + "a**2*U_c(t)*sin(theta(t))*Derivative(theta(t), t)/r(t) + a**2*U_c(t)*cos(theta(t))*Derivative(r(t), t)/r(t)**2 - a**2*cos(theta(t))*Derivative(U_c(t), t)/r(t)" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "phi.diff(t)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "52970004-5d18-4905-a61c-01c5d9a7f81c", + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\frac{a^{2} \\operatorname{U_{c}}{\\left(t \\right)} \\cos{\\left(\\theta{\\left(t \\right)} \\right)}}{r^{2}{\\left(t \\right)}}$" + ], + "text/plain": [ + "a**2*U_c(t)*cos(theta(t))/r(t)**2" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "phi.diff(r)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "3bc6b6e8-cdba-4eb9-b754-e07cc74c6063", + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\frac{a^{2} \\operatorname{U_{c}}{\\left(t \\right)} \\sin{\\left(\\theta{\\left(t \\right)} \\right)}}{r^{2}{\\left(t \\right)}}$" + ], + "text/plain": [ + "a**2*U_c(t)*sin(theta(t))/r(t)**2" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "phi.diff(theta)/r" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "bcae9e54-d38d-4128-b872-e4bcb11d19c5", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.13" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/book/notebooks/contamination/Exercise_Contamination_Render.ipynb b/book/notebooks/contamination/Exercise_Contamination_Render.ipynb new file mode 100644 index 0000000..0bbed65 --- /dev/null +++ b/book/notebooks/contamination/Exercise_Contamination_Render.ipynb @@ -0,0 +1,689 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "id": "bcb1b890", + "metadata": {}, + "source": [ + "# Contaminant Transport" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "ab31a602", + "metadata": {}, + "source": [ + "````{note}\n", + "This page is generated from an `*.ipynb` file which requires several auxiliary files, all of which can be downloaded using the link below.\n", + "```{eval-rst}\n", + ":download:`Download zip file for this exercise.<exercise_contamination.zip>`\n", + "```\n", + "````" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "06fa7af4", + "metadata": {}, + "source": [ + "The purpose of this exercise is to:\n", + "- evaluate component reliability\n", + "- illustrate functions of random variables\n", + "- see the effect of random variable distributions on reliability\n", + "- consider 'sensitivity' as a functional and/or stochastic influence on the limit-state function\n", + "\n", + "You should accomplish this by playing with the code that is provided with the notebook and trying to answer the following questions:\n", + "1. Which random variables have the biggest influence on reliability?\n", + "2. How does the assumption of probability distribution influence reliability?\n", + "3. Do the random variables act as loads or resistances?\n", + "\n", + "## Introduction of Case Study\n", + "\n", + "The case study is a contaminant transport problem, illustrated in the figure below. A factory located near a town produces hazardous waste, which can threaten the drinking water supply of the town that is extracted from groundwater wells (C). The regional groundwater system has a gradient that causes water to flow in the direction of the town from the factory, thus any spilled hazardous waste that enters the ground will eventually be transported to the wells. In order to mitigate the consequences of a spill a ditch is constructed around the factory to collect it (A). Unfortunately, even with powerful pumps, there will still be some waste that reaches the groundwater table. Our task is to quantify the probability that the waste concentration exceeds the maximum exposure level to prevent the drinking water becoming unhealthy.\n", + "\n", + "```{figure} ./figures/sketch.png\n", + "---\n", + "width: 600px\n", + "name: sketch_contaminant\n", + "---\n", + "\n", + "```\n", + "\n", + "### Contaminant Transport\n", + "\n", + "Once the ditch becomes contaminated it is cleaned quickly, but unfortunately a 'pulse' of contamination enters the ground, after which the regional gradient carries it towards the town (advection). The pulse also disperses due to diffusion, which results in a classic advection-diffusion problem (see red shapes in diagram, at three different times, $t$). Because the ditch extends a long distance in the lateral direction and the contaminant is buoyant (it floats on the groundwater table and we neglect vertical dispersion), the problem can be analyzed in 1 dimension with the following analytic expression:\n", + "\n", + "$$\n", + "\\frac{C}{C_0} = \\frac{1}{2} \\mathrm{erf}\\left(\\frac{x-(q/n)t}{2\\sqrt{a(q/n)t}}\\right)\n", + "$$\n", + "\n", + "Where $C$ contaminant concentration (e.g., parts per million, ppm) at distance $x$ from the ditch at time $t$ after the spill, and $C_0$ is the concentration in the ditch (just prior to cleanup). $\\mathrm{erf}$ is the error function. There are three parameters in the equation which are related to soil properties and groundwater flow:\n", + "\n", + "- $q$ is the horizontal groundwater flow velocity (specific discharge) [m/day]\n", + "- $n$ is the soil porosity [$-$]\n", + "- $a$ is the longitudinal dispersivity, which describes dispersion in the left to right direction in the image [m]\n", + "\n", + "Unfortunately there is not a lot of soil information, so we have to take into account uncertainty in these three variables, using the following probability distributions with first and second moments (i.e., $\\mu$ and $\\sigma$).\n", + "\n", + "- $q\\sim\\mathrm{N}\\left(\\mu_q=1.00,\\sigma_q=0.10\\right)$\n", + "- $n\\sim\\mathrm{N}\\left(\\mu_n=0.20,\\sigma_n=0.02\\right)$\n", + "- $a\\sim\\mathrm{N}\\left(\\mu_a=10.0,\\sigma_a=1.00\\right)$\n", + "\n", + "It is important to check the sensitivity of the reliability analysis to the distribution type and moments. We will use the concentration ratio $C/C_0$ to evaluate this problem and compare it to a threshold defined by health regulations: $\\mathrm{threshold}=1e-4$.\n", + "\n", + "### Definition of Limit States\n", + "\n", + "As shown in the figure above, there are two locations of interest: the monitoring station ($x=100$ m from the ditch, point B) and the town well ($x=500$ m, point C). We are interested in evaluating two cases with a reliability analysis:\n", + "1. Whether the contamination can be detected at the monitoring station above the threshold level within 1 week of the spill, and \n", + "2. If the contamination level at the town groundwater well exceeds the threshold level within 1 month of the spill (30 days)\n", + "\n", + "Relating these descriptions to our variables of interest:\n", + "1. find the probability that $C/C_0$ > threshold \n", + "2. find the probability that $C/C_0$ < threshold\n", + "\n", + "We will refer to these values as 'failure probabilities', even though case 1 technically doesn't correspond to failure---it's just the way we refer to things in practice.\n", + "\n", + "Next we will convert these into functions that will allow us to quantify the 'failure' conditions. For convenience, it is often useful to define the limit state as a function, $Z$, such that failure occurs when $Z<0$. It follows from the descriptions above, that the limit state functions for both cases are:\n", + "\n", + "1. $Z=C/C_0 - \\mathrm{threshold}$\n", + "2. $Z=\\mathrm{threshold} - C/C_0$\n", + "\n", + "NB: *in the book another notation used for $Z$ is $g_X(X)$.*\n", + "\n", + "### Analysis Approach\n", + "\n", + "Our programming task is to create a function of random variables to represent these two limit-states, define the random variables, then evaluate the reliability with Monte Carlo simulation. In other words, we will numerically approximate the probability distribution of $Z$, then evaluate reliability as $P(Z<0)$.\n", + "\n", + "This is a lot of work, but fortunately a number of helper functions and a Class are provided in the auxiliary file `exercise_setup.py`!\n", + "\n", + "### References\n", + "\n", + "This example draws inspiration from Case 2 of the paper by {cite:t}`sitar1987`." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "8287dbcf", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy.special import erfc\n", + "from scipy import stats\n", + "import seaborn as sns\n", + "\n", + "from exercise_setup import process_negative_values\n", + "from exercise_setup import RandomVariableDistribution\n", + "from exercise_setup import pdf_of_function_of_RV\n", + "from exercise_setup import monte_carlo" + ] + }, + { + "cell_type": "markdown", + "id": "d104b4b2-4fa5-4b37-891d-39201281ed2f", + "metadata": {}, + "source": [ + "## Defining the Limit States\n", + "\n", + "We only define limit state Case 2 below, and will use a simple multiplying factor of $-1$ to switch to Case 1 using a multiplying factor `flip_LSF`." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "64c24956", + "metadata": {}, + "outputs": [], + "source": [ + "def C_C0(q, n, a, x, t):\n", + " \"\"\"Contaminant concentration ratio.\"\"\"\n", + " q, n, a = process_negative_values(q, n, a)\n", + " return 0.5*erfc((x - q/n*t)/(2*np.sqrt(a*(q/n)*t)))\n", + "\n", + "def limit_state_fun(q, n, a, x, t, threshold):\n", + " \"\"\"Limit state fxn, Case 2 (multiply by flip_LSF=-1 for Case 1).\"\"\"\n", + " return threshold - C_C0(q, n, a, x, t)" + ] + }, + { + "cell_type": "markdown", + "id": "d7410d16-14d4-45c6-9f93-81ae08de0594", + "metadata": {}, + "source": [ + "## Class `RandomVariableDistribution`\n", + "\n", + "The class `RandomVariableDistribution` makes it very easy to define Normal and Lognormal distributions for the random variables. See documentation and example below.\n", + "\n", + "NB: *you can use the code in `exercisesetup.py` and this notebook to confirm the result of the 2 random variable case in the Probabilistic Design chapter, and recreate the figures.*" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "8bbf80be-5124-40ba-b3de-0da3eaa12ef1", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Define a N or LN probability to use in MUDE week 2.7 exercise.\n", + " \n", + " Usage:\n", + " -----\n", + " Create an instance of the class\n", + " by default, the random variable is ~N(0,1)\n", + " Specify distribution using 1st and 2nd moments for N or LN:\n", + " --> use method define_distribution to change it!\n", + " (the method prints a summary of the change)\n", + " for example, copy/paste the following:\n", + " test = RandomVariableDistribution()\n", + " test.print_status()\n", + " test.define_distribution(mean=5, stddev=1, dist_type='LN')\n", + " An instance will include the following attributes:\n", + " - distribution moment and (scipy) parameters shape, location, scale\n", + " - dist_object: distribution object (scipy.stats)\n", + " - get_sample: method for getting random samples from the distribution\n", + " - plot_pdf_or_cdf:\n", + " \n" + ] + } + ], + "source": [ + "print(RandomVariableDistribution.__doc__)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "a9b93099-b1cb-458b-baf6-8ad5dd39c440", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The mean is 5.000e+00\n", + "The standard deviation is 1.000e+00\n", + "The distribution is Lognormal\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "example_random_variable = RandomVariableDistribution()\n", + "example_random_variable.define_distribution(mean=5,\n", + " dist_type='LN',\n", + " print_new_dist=True)\n", + "example_random_variable.plot_pdf_or_cdf()" + ] + }, + { + "cell_type": "markdown", + "id": "62617026-f251-462b-a93c-b7305cfd3fa4", + "metadata": {}, + "source": [ + "## Setting up the problem\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "4641ae3c", + "metadata": {}, + "outputs": [], + "source": [ + "N = 10000\n", + "\n", + "t = 7\n", + "x = 100\n", + "threshold = 1e-4\n", + "\n", + "flip_LSF = -1\n", + "\n", + "q_rv = RandomVariableDistribution()\n", + "q_rv.define_distribution(mean=1., stddev=.1)\n", + "n_rv = RandomVariableDistribution()\n", + "n_rv.define_distribution(mean=0.2, stddev=.02)\n", + "a_rv = RandomVariableDistribution()\n", + "a_rv.define_distribution(mean=10., stddev=1.)" + ] + }, + { + "cell_type": "markdown", + "id": "f3e0ffb1-6035-4f76-a550-4ff19c1b5946", + "metadata": {}, + "source": [ + "## Monte Carlo analysis\n", + "\n", + "The Monte Carlo procedure for estimating failure probability, $p_f$, is:\n", + "- For each random variable $X_i$ ($i = 1, …, n$) one simulates N realizations, $x_{i,1}, x_{i,1}, ..., x_{i,N}$. \n", + "- For each set of simulations $j$ ($j = 1, ..., N$) one calculates $g(x_{1,j}, x_{2,j}, …, x_{n,j})$\n", + "- In case $g(.) < 0$ a counter $N_f$ is increased by one. After $N$ simulations one calculates: $\\hat{p_f}=N_f/N$\n", + "- In case $N\\rightarrow+\\infty$ one obtains the failure probability $p_f$.\n", + "\n", + "The number of simulations $N$ directly influences the accuracy of $\\hat{p_f}$, which is an estimate of the 'true' value $p_f$. As an infinite number of simulations is not possible, one must choose a value for $N$ that balances total computation time, which increases linearly with $N$, and accuracy of the estimator $\\hat{p_f}$, which can be determined as the number of significant digits desired for $p_f$, or based on relative error (coefficient of variation, $V=\\sigma/\\mu$. The failure observations, $N_f$, within the Monte Carlo procedure are the result of a sequence of statistically independent and identically distributed random trials in a Bernoulli process. Using the binomial distribution, the standard deviation of of $\\hat{p_f}$ can be written\n", + "\n", + "$$\\sigma_\\hat{p_f}=\\sqrt{\\frac{p_f(1-p_f)}{N}}$$\n", + "\n", + "As $\\hat{p_f}\\rightarrow1$ this leads to the coefficient of variation, $V_\\hat{p_f}$:\n", + "\n", + "$$V_\\hat{p_f}=\\frac{\\sigma_\\hat{p_f}}{\\hat{p_f}}=\\frac{1}{\\sqrt{N\\hat{p_f}}}$$\n", + "\n", + "The coefficient of variation is a useful measure for gauging the accuracy of a Monte Carlo simulation: values of 0.01 are ideal, but 0.1 can be sufficient in many applications, depending on the need for accuracy. For example, consider $V=0.1$ for a target failure probability of $0.01$. Assuming the samples follow a Gaussian distribution implies a probability of 0.997 that the 'true' failure probability is within the interval 0.007-0.013. It is also useful to plot the calculated values of $V$ and $\\hat{p_f}$ for every realization $j = 1, ..., N$, as shown below. The figure clearly shows convergence to a stable value of $\\hat{p_f}$ after X simulations, indicating that for future analyses that are similar can use a lower number of simulations instead ($N\\sim X$).\n", + "\n", + "In case of a target coefficient of variation the number of required simulations $N$ increases as $p_f$ decreases. As an example, for $V = 0.01$ and $p_f=1e-5$ one has to execute $10^9$ simulations. As for this case on average only one of 10^5 simulations leads to an increase of $N_f$, the frequency of obtaining a 'success' (realization in the unsafe domain) is very low. In addition, for low failure probabilities the number of function evaluations is quite high, which may be practically impossible if there is a high function evaluation time, for example with a complex finite element model. To address this problem, variance reducing techniques have been developed which allow the simulations to be performed in a more effective way. In the following the so-called importance sampling or Latin hypercube sampling." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "ec7883de-544e-48d5-85f2-dfc7856e9028", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "MONTE CARLO RESULTS\n", + "--------------------------------------------------\n", + " N = 10000, number of samples\n", + " Nf = 18, number of failed realizations\n", + " pf = 1.800e-03, estimated failure probability\n", + " V = 0.236, c.o.v. of estimated pf\n", + "\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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h/UyXAnQ7RsPNqlWrlJubq6KiIk2YMEFLly5VZmamtmzZosGDBwfs/9hjj+mBBx7wvz5y5IguuOACXXPNNZ1ZNoBWDO8fryh7hBq8jfrW4zVdjlHferz6+8c1hBvAAKPhZtGiRcrOztaMGTMkSYWFhXrjjTe0ZMkSFRQUBOzfu3dv9e7d2/969erV+vrrr3XDDTd0Ws0AWnfewHhtvPsK7a/zmC7FqKfKduiZtz+Xj7sZAkYYCzcNDQ2qqKjQvHnzmm3PyMhQeXl5m9pYvny5rrjiCiUnJ7e6T319verr6/2v3W63JMnj8cjj6d6/gK3WdD45r91brF2K7eUwXYZRPaLskiRvYyN/H9DtBKsvaE97xsJNbW2tvF6vEhMTm21PTExUdXX1SY93uVz629/+pj/96U8n3K+goEALFiwI2L5mzRrFxcW1r2i0idPpNF0CYNT2yghJEfp81+cqKdlpuhzACKv7grq6ujbva3xB8XcftOfz+dr08L3i4mL16dNHV1999Qn3y8/PV15env+12+1WUlKSMjIyFB8f36Ga0TKPxyOn06nJkyfL4eje/3JH97btrc/0RtUODU5O1tSpI0yXA3SqYPUFTTMvbWEs3CQkJMhutweM0tTU1ASM5nyXz+fTihUrNG3aNEVFRZ1w3+joaEVHRwdsdzgcdMBBwrlFdxdhPzotZYuw8XcB3ZbVfUF72jJ2n5uoqCilpaUFDFs5nU6NHz/+hMeWlpbqs88+U3Z2djBLBIAO4V6GgFlGp6Xy8vI0bdo0jR07Vunp6Vq2bJkqKys1a9YsSUenlKqqqrRy5cpmxy1fvlzjxo1TamqqibIB4ISaZta5WAoww2i4ycrK0r59+7Rw4UK5XC6lpqaqpKTEf/WTy+VSZWVls2P279+vl19+WY899piJkgGgzcg2gBnGFxTn5OQoJyenxfeKi4sDtvXu3btdK6YBoLPZmJgCjOLZUgBgMaalALMINwBgsePjNqQbwATCDQAACCuEGwCwGNNSgFmEGwCwWNNd1gk3gBmEGwAIEh9rbgAjCDcAACCsEG4AwGKsuQHMItwAgMWabuJHtgHMINwAAICwQrgBAIsxLQWYRbgBAIs13aGYq6UAMwg3AAAgrBBuAMBituNDNwAMINwAgMW4Wgowy9Jwc9ddd+nGG2+0skkA6HKOLygm3gAmRFrZWFVVlXbv3m1lkwAAAO3SoXBTWlqqSy65JGD7M888c8oFAUC4YNwGMKND01KTJ0/W4MGDNW/ePH344YdW1wQAXRpPBQfM6lC42bNnj+bOnauysjKNGjVKo0aN0kMPPaQvvvjC6voAAADapUPhJiEhQbfccos2bNig7du3KysrSytXrlRKSoomTZpkdY0A0KVwJThg1ilfLTVkyBDNmzdPDzzwgM4//3yVlpZaURcAdFlcLQWYdUrhZsOGDcrJydGAAQN03XXXaeTIkfrLX/5iVW0A0CXZTr4LgCDq0NVSd911l55//nnt2bNHV1xxhQoLC3X11VcrLi7O6voAoMti3AYwo0PhZu3atbr99tuVlZWlhIQEq2sCgC7N5p+XMlsH0F11KNyUl5dbXQcAhI3j2YZ0A5hg6eMXXC6XKisrrWwSAACgXSwNN5MmTdKQIUOsbBIAuhz/peAM3ABGWPpsqZUrV6qurs7KJgGg6+EOxYBRloabCy+80MrmAKBL4lJwwKwOh5tvvvlGy5cv19atW2Wz2TRixAhlZ2erd+/eVtYHAF0WC4oBMzq05mbjxo0aOnSoFi9erK+++kq1tbVavHixhg4dqvfff9/qGgGgSzl+h2KzdQDdVYdGbubMmaOrrrpKTz75pCIjjzZx5MgRzZgxQ7m5uVq3bp2lRQJAV2JjYgowqsMjN3feeac/2EhSZGSk5s6dq40bN7arraKiIg0ZMkQxMTFKS0tTWVnZCfevr6/X/PnzlZycrOjoaA0dOlQrVqzoyNcAgKBi4AYwo0MjN/Hx8aqsrNTw4cObbd+9e7d69erV5nZWrVql3NxcFRUVacKECVq6dKkyMzO1ZcsWDR48uMVjrr32Wu3du1fLly/X2WefrZqaGh05cqQjXwMAgoJpKcCsDoWbrKwsZWdn65FHHtH48eNls9m0fv163XHHHfr5z3/e5nYWLVqk7OxszZgxQ5JUWFioN954Q0uWLFFBQUHA/q+//rpKS0u1Y8cOnX766ZKklJSUjnwFAAgaJqUAszoUbh555BHZbDZNnz7dP2ricDj0q1/9Sg888ECb2mhoaFBFRYXmzZvXbHtGRkarj3f485//rLFjx+qhhx7Ss88+qx49euiqq67Sfffdp9jY2BaPqa+vV319vf+12+2WJHk8Hnk8njbVirZpOp+cV3R3jY3eY//byN8HdDvB6gva016Hwk1UVJQee+wxFRQUaPv27fL5fDr77LPb9VTw2tpaeb1eJSYmNtuemJio6urqFo/ZsWOH1q9fr5iYGL366quqra1VTk6Ovvrqq1bX3RQUFGjBggUB29esWcNTzIPE6XSaLgEw6l97bZLs2luzVyUlJabLAYywui9oz02CT+kmfnFxcTr//PNPpYnjT889xufzBWxr0tjYKJvNpj/+8Y/+++ksWrRIP/3pT/XEE0+0OHqTn5+vvLw8/2u3262kpCRlZGQoPj7+lGpHcx6PR06nU5MnT5bD4TBdDmDMoYoqvbDjI/Xrd4amTh1juhygUwWrL2iaeWkLS+9QXFRUpNraWt1zzz0n3TchIUF2uz1glKampiZgNKfJgAEDdOaZZza7UeCIESPk8/n0xRdf6Jxzzgk4Jjo6WtHR0QHbHQ4HHXCQcG7R3UVG2iVJERER/F1At2V1X9Cetix9cObLL7+s4uLiNu0bFRWltLS0gGErp9Op8ePHt3jMhAkTtGfPHh08eNC/7dNPP1VERIQGDRrU4boBIBh8XC4FGGFpuHnrrbe0Y8eONu+fl5enp556SitWrNDWrVs1Z84cVVZWatasWZKOTilNnz7dv/91112nvn376oYbbtCWLVu0bt063XHHHbrxxhtbXVAMAJ3N/1Rwo1UA3VeHpqUKCgqUmJioG2+8sdn2FStW6Msvv9Sdd97ZpnaysrK0b98+LVy4UC6XS6mpqSopKVFycrIkyeVyqbKy0r9/z5495XQ6deutt2rs2LHq27evrr32Wt1///0d+RoAEBStrRsE0Dk6FG6WLl2qP/3pTwHbR44cqZ/97GdtDjeSlJOTo5ycnBbfa2mKa/jw4VyNAyCk+UduGLoBjOjQtFR1dbUGDBgQsL1fv35yuVynXBQAhAOyDWBGh8JNUlKSNmzYELB9w4YNGjhw4CkXBQBdGbNSgFkdmpZqevq3x+PRpEmTJB1dTDx37lzddtttlhYIAF1NU7h5e3ut0u5rfRq9f+8Yrbzx++rbM/B2FQA6rkPhZu7cufrqq6+Uk5OjhoYGSVJMTIzuvPNO5efnW1ogAHQ1Z/frJXuETR6vT/sONbS6375DDar4/GtljOzfidUB4a9D4cZms+nBBx/U3Xffra1btyo2NlbnnHNOizfLA4Du5vxBvfVO/uX6uq71YJP7wmZtcblZlwMEwSndobhnz5668MILraoFAMJGv17R6ter9X/wxUUdvYsxN/oDrGfpTfwAAG3TtC6HbANYj3ADAAbYjt0Nh2wDWI9wAwAmMHIDBA3hBgAMOP78KdINYDXCDQAYwJobIHgINwBgAGtugOAh3ACAAcdHbog3gNUINwBgQMSxdEO2AaxHuAEAA/wjN0xMAZYj3ACAQYzcANYj3ACAATampYCgIdwAgAHH73MDwGqEGwAwgKulgOAh3ACAAYzcAMFDuAEAA2zHL5cCYDHCDQAYEHEs2zQyLQVYjnADAEbw+AUgWAg3AGAAD84EgodwAwAGHF9QTLoBrEa4AQADGLkBgodwAwAG2FhzAwQN4QYADLD556WIN4DVCDcAYAC3uQGCh3ADAAY0TUs1NhJvAKsRbgDAAEZugOAh3ACAAU2PX2DJDWA9wg0AGMCDM4HgMR5uioqKNGTIEMXExCgtLU1lZWWt7rt27VrZbLaAn48//rgTKwaAU3f8PjfEG8BqRsPNqlWrlJubq/nz52vTpk2aOHGiMjMzVVlZecLjPvnkE7lcLv/POeec00kVA4A1bCffBUAHGQ03ixYtUnZ2tmbMmKERI0aosLBQSUlJWrJkyQmPO+OMM9S/f3//j91u76SKAcAarLkBgifS1Ac3NDSooqJC8+bNa7Y9IyND5eXlJzx29OjROnz4sM477zz95je/0WWXXdbqvvX19aqvr/e/drvdkiSPxyOPx3MK3wDf1XQ+Oa/AyfkaGyVJi9/8VH8o3d7qfpF2m+7IGKYfXzCgs0oDTkmw+oL2tGcs3NTW1srr9SoxMbHZ9sTERFVXV7d4zIABA7Rs2TKlpaWpvr5ezz77rC6//HKtXbtWF198cYvHFBQUaMGCBQHb16xZo7i4uFP/IgjgdDpNlwCEPN83Nkl21TV4VdfgPeG+K978pxxVmzqnMMAiVvcFdXV1bd7X5jO0mm3Pnj0688wzVV5ervT0dP/23/72t3r22WfbvEj4yiuvlM1m05///OcW329p5CYpKUm1tbWKj48/tS+BZjwej5xOpyZPniyHw2G6HCDkff5Vneo9rQebN7d+qcVvfaaLz+mr5dPTOrEyoOOC1Re43W4lJCRo//79J+2/jY3cJCQkyG63B4zS1NTUBIzmnMhFF12k5557rtX3o6OjFR0dHbDd4XDQAQcJ5xZom7MTe5/w/Y/3HvuXqi2Cv1PocqzuC9rTlrEFxVFRUUpLSwsYtnI6nRo/fnyb29m0aZMGDGAuGkD4iTj2G5rLxYH2MTZyI0l5eXmaNm2axo4dq/T0dC1btkyVlZWaNWuWJCk/P19VVVVauXKlJKmwsFApKSkaOXKkGhoa9Nxzz+nll1/Wyy+/bPJrAEBQRHBFFdAhRsNNVlaW9u3bp4ULF8rlcik1NVUlJSVKTk6WJLlcrmb3vGloaNDtt9+uqqoqxcbGauTIkfrrX/+qqVOnmvoKABB0jaQboF2MhhtJysnJUU5OTovvFRcXN3s9d+5czZ07txOqAgDzmkZuCDdA+xh//AIAoGXHH9Fgtg6gqyHcAECIYs0N0DGEGwAIUcefHE66AdqDcAMAIcrmX3NjuBCgiyHcAECIivCvuSHdAO1BuAGAEMXIDdAxhBsACFH+kRuzZQBdDuEGAEKUjWkpoEMINwAQomxcCg50COEGAEJU06Xg3KEYaB/CDQCEKG7iB3QM4QYAQhTPlgI6hnADACGqaUExgPYh3ABAiGoKN4zcAO1DuAGAEGUTN/EDOiLSdAEAgJY13cRvzzff6sbi9yxpM9Zh15zJ5+jsM3pZ0h4Qigg3ABCi+vWKliTVNXj1/z6usazdM+Kj9b9XjrSsPSDUEG4AIESd1a+nXvjlRar8qs6S9t7csldrtuxVw5FGS9oDQhXhBgBC2EVn9dVFZ/W1pK29+w9rzZa9rOFB2GNBMQB0E8cvLSfdILwRbgCgm2h6VlUjs1IIc4QbAOgmuOMxugvCDQB0ExH+mwKarQMINsINAHQTxx/ESbpBeCPcAEA3weMc0F0QbgCgmzi+5sZwIUCQEW4AoJtg5AbdBeEGALoJ/5obw3UAwUa4AYBuoulqKRYUI9wRbgCgm+AmfuguCDcA0E1wEz90F4QbAOgmuIkfugueCg4A3UTTyM1Wl1v/+9qHhqtpnx7RkbphwhD16xVtuhR0AcbDTVFRkR5++GG5XC6NHDlShYWFmjhx4kmP27Bhgy655BKlpqZq8+bNwS8UALq4+Nijv/KrvvlWz7z9ueFq2i/GYdfsy88xXQa6AKPhZtWqVcrNzVVRUZEmTJigpUuXKjMzU1u2bNHgwYNbPW7//v2aPn26Lr/8cu3du7cTKwaAruuy4Wdo4Y9HqvZAvelS2qXss1ptqvxGh+qPmC4FXYTRcLNo0SJlZ2drxowZkqTCwkK98cYbWrJkiQoKClo9bubMmbruuutkt9u1evXqTqoWALq26Ei7pqenmC6j3eq9jdpU+Y28LBZCGxkLNw0NDaqoqNC8efOabc/IyFB5eXmrxz399NPavn27nnvuOd1///0n/Zz6+nrV1x//V4rb7ZYkeTweeTyeDlaPljSdT84rAEsdCzVHvF5+v3QBweoL2tOesXBTW1srr9erxMTEZtsTExNVXV3d4jHbtm3TvHnzVFZWpsjItpVeUFCgBQsWBGxfs2aN4uLi2l84TsrpdJouAUAY2VkZISlCO3buUknJDtPloI2s7gvq6uravK/xBcVNN5Vq4vP5ArZJktfr1XXXXacFCxZo2LBhbW4/Pz9feXl5/tdut1tJSUnKyMhQfHx8xwtHAI/HI6fTqcmTJ8vhcJguB0CY+PStz7SmaocGJydr6tQRpsvBSQSrL2iaeWkLY+EmISFBdrs9YJSmpqYmYDRHkg4cOKCNGzdq06ZNuuWWWyRJjY2N8vl8ioyM1Jo1azRp0qSA46KjoxUdHXjpoMPhoAMOEs4tACtF2u1H/4/Nxu+WLsTqvqA9bRm7iV9UVJTS0tIChq2cTqfGjx8fsH98fLw++OADbd682f8za9YsnXvuudq8ebPGjRvXWaUDADqR/djdB708NgJtZHRaKi8vT9OmTdPYsWOVnp6uZcuWqbKyUrNmzZJ0dEqpqqpKK1euVEREhFJTU5sdf8YZZygmJiZgOwAgfPDAT7SX0XCTlZWlffv2aeHChXK5XEpNTVVJSYmSk5MlSS6XS5WVlSZLBAAYFuEfuSHcoG2MLyjOyclRTk5Oi+8VFxef8Nh7771X9957r/VFAQBCxvEHfhouBF0GD84EAIQ0O08zRzsZH7kBAOBEmu4Ostd9WBs+q7W8/aH9eqp/7xjL24U5hBsAQEhz2I9OMpRv36fy7fssbz8uyq5351+hntF0ieGC/5IAgJA2afgZ+tuHLn19yPpHL3xac0B1DV7tO1hPuAkj/JcEAIS0pNPj9MIv04PS9vn/+4YO1B9hsXKYYUExAKDb4jLz8ES4AQB0W9wgMDwRbgAA3Zb/0Q6Em7BCuAEAdFtNNwhkWiq8EG4AAN1WU7hh4Ca8EG4AAN2WnQXFYYlwAwDotiKO9YI82iG8cJ8bAEC31TQt9ezbn2vNlr3N3usd69D/XJTMzf26IP6LAQC6rV4xR7vBVzZVtfh+j+hITbsouTNLggUINwCAbuv+q8/XX/+1J+AOxWXbvtSnew/K/a31j3xA8BFuAADd1veS+uh7SX0Ctue/8oE+3XuQhcZdFAuKAQD4jshjV1EdIdx0SYQbAAC+4/gl4o2GK0FHEG4AAPgORm66NsINAADfYbcfDTeNhJsuiXADAMB3MHLTtXG1FAAA32E/duvi0k++VO6hTS2+/z8XDdbowad1dmloA8INAADf0bdHlCRpR+0h7ag91OI+Xx6s18obv9+ZZaGNCDcAAHzHtWOTFOuwy3048CZ+H1cf0EsVX6iu/oiBytAWhBsAAL4jNsquay9MavG9N7fs1UsVX7AeJ4SxoBgAgHZoupLqCPfACVmEGwAA2sFxbLHxES8jN6GKcAMAQDvYuUw85LHmBgCAdog8Ni112OPVF1/XBbzfPz5GkXbGDkwi3AAA0A5NIzdffP2tfvDg3wPeP29AvP46+wey2WydXRqOIVoCANAOI/rHa8SAeEVHRjT7iYo82qVucbnV4GWxsUmM3AAA0A6xUXb97dcTA7Z/2+DViHtel3R0sXE0PawxjNwAAGCBpukqiSupTDMeboqKijRkyBDFxMQoLS1NZWVlre67fv16TZgwQX379lVsbKyGDx+uxYsXd2K1AAC0zGE/Hm483APHKKODZqtWrVJubq6Kioo0YcIELV26VJmZmdqyZYsGDx4csH+PHj10yy23aNSoUerRo4fWr1+vmTNnqkePHvrlL39p4BsAAHCUzWaTPcImb6OPkRvDjIabRYsWKTs7WzNmzJAkFRYW6o033tCSJUtUUFAQsP/o0aM1evRo/+uUlBS98sorKisrI9wAAIyLPBZufrP6Q8VF2U+6v80m/deYQbp4WL9OqK77MBZuGhoaVFFRoXnz5jXbnpGRofLy8ja1sWnTJpWXl+v+++9vdZ/6+nrV19f7X7vdbkmSx+ORxxP4QDR0XNP55LwC6K4Sekap6pvDenPr3jYfs3WPW3+9dXwQq+pcweoL2tOesXBTW1srr9erxMTEZtsTExNVXV19wmMHDRqkL7/8UkeOHNG9997rH/lpSUFBgRYsWBCwfc2aNYqLi+tY8Tghp9NpugQAMOJ/kqVP+7Tt/jZf19u01hWh2v0HVFJSEuTKOp/VfUFdXeANE1tj/EK1797kyOfznfTGR2VlZTp48KDeeecdzZs3T2effbZ+/vOft7hvfn6+8vLy/K/dbreSkpKUkZGh+Pj4U/8C8PN4PHI6nZo8ebIcDofpcgAgpH20x621S96RIzpGU6deYrocywSrL2iaeWkLY+EmISFBdrs9YJSmpqYmYDTnu4YMGSJJOv/887V3717de++9rYab6OhoRUdHB2x3OBx0wEHCuQWAk4uJPvp70tvoC8vfmVb3Be1py9il4FFRUUpLSwsYtnI6nRo/vu1zjz6fr9maGgAAuoLIY08XbzjSqMZGX7MfnBqj01J5eXmaNm2axo4dq/T0dC1btkyVlZWaNWuWpKNTSlVVVVq5cqUk6YknntDgwYM1fPhwSUfve/PII4/o1ltvNfYdAADoiKb74rgPH9FZdx1fcxNhk+784XDNvGSoqdK6PKPhJisrS/v27dPChQvlcrmUmpqqkpISJScnS5JcLpcqKyv9+zc2Nio/P187d+5UZGSkhg4dqgceeEAzZ8409RUAAOiQ/r1jlNI3Trv2NV8o2+iT3ty6l3BzCmw+n69bjX+53W717t1b+/fvZ0GxxTwej0pKSjR16tSwnD8GAKsd8TbqwOEj/teln36p3FWb9b2kPlp98wSDlXVcsPqC9vTfxq+WAgCgu4q0R+i0HlH+133ijoYBD08VPyWEGwAAQoTDfnyRcf0Rb4v72G02RdqNPxoypBFuAAAIEU3hZlvNQZ37m9db3CfWYdey6WmaeA6PbGgN0Q8AgBBxbmIvndEr8N5s/+5bj1dvb9/XSRV1TYzcAAAQInrHOVQ+b5K+9bQ8JbXI+ame3rBLDUdYk3MihBsAAEJIpD1CvVpZU9Mr+mi33cCC4xMi3AAA0EVEO+ySpA2f1equVz+wrN2M8xJ16blnWNaeaYQbAAC6iL7HLhvf/uUhbf/ykGXtOrfs1Xvzr7CsPdMINwAAdBE//t6ZavA26ps6jyXtub/16Kn1O+X+1pr2QgXhBgCALiI2yq7p6SmWtVdz4LCeWr9TDd5G+Xw+2Ww2y9o2iUvBAQDopqLtR9fw+HzSgv/boq8ONRiuyBqEGwAAuqnYKLtijy1SLi7fpZcrvjBckTUINwAAdFNRkREqvuFC/+sDh8Nj7Q3hBgCAbmzcWX31y4vPkiQdPnJ07U1LP10JC4oBAOjmoiOPjnUsW7dDy9btCHg/xhGhwqzR+mFq/84urUMYuQEAoJtLSz5NDnvrV0od9jSq9NMvO7GiU8PIDQAA3dyl556hzfdkqL6FZ1atfHuXCt/cpvpWnncVihi5AQAA6hEdqdN7RAX8NN0Ved22WuWt2qz9XeCGf4QbAADQqjNPi5Uk1R6s1yubqvT/Pt5ruKKTI9wAAIBWXTrsDK288fu6IKmPJOng4SNmC2oD1twAAIBWRUTYdPGwflq9qUr/3P2Nni7fJefWmlb39zU26tDXEZo6tROL/A7CDQAAOKlBx6andnx5SDtO8kTyeIfZZ1QRbgAAwEn96tKzNWJAvL49yVVTXq9XWz74ZydV1TLCDQAAOKnYKLsyzx9w0v08Ho+i9mwOfkEnwIJiAAAQVgg3AAAgrBBuAABAWCHcAACAsEK4AQAAYYVwAwAAwgrhBgAAhBXCDQAACCuEGwAAEFaMh5uioiINGTJEMTExSktLU1lZWav7vvLKK5o8ebL69eun+Ph4paen64033ujEagEAQKgzGm5WrVql3NxczZ8/X5s2bdLEiROVmZmpysrKFvdft26dJk+erJKSElVUVOiyyy7TlVdeqU2bNnVy5QAAIFTZfD6fz9SHjxs3TmPGjNGSJUv820aMGKGrr75aBQUFbWpj5MiRysrK0j333NOm/d1ut3r37q39+/crPj6+Q3WjZR6PRyUlJZo6daocDofpcgAABgSrL2hP/23swZkNDQ2qqKjQvHnzmm3PyMhQeXl5m9pobGzUgQMHdPrpp7e6T319verr6/2v3W63pKMn3+PxdKBytKbpfHJeAaD7ClZf0J72jIWb2tpaeb1eJSYmNtuemJio6urqNrXx6KOP6tChQ7r22mtb3aegoEALFiwI2L569WrFxcW1r2i0yWuvvWa6BACAYVb3BXV1dZKktkw4GQs3TWw2W7PXPp8vYFtLnn/+ed1777167bXXdMYZZ7S6X35+vvLy8vyvq6qqdN5552nGjBkdLxoAABhx4MAB9e7d+4T7GAs3CQkJstvtAaM0NTU1AaM537Vq1SplZ2frxRdf1BVXXHHCfaOjoxUdHe1/3bNnT+3evVuTJk3Sxo0bO/4F2ujCCy/Ue++91yXaPtX23G63kpKStHv3btYzhZFg/hnuirr6+QjF+k3W1FmfHazPCbV+QApeX+Dz+XTgwAENHDjwpPsaCzdRUVFKS0uT0+nUf/7nf/q3O51O/fjHP271uOeff1433nijnn/+ef3oRz9q9+dGRERo0KBBioyM7JQO2G63B+1zrG7bqvbi4+MJN2EkmH+Gu6Kufj5CsX6TNXXWZwfrc0K1H5CC0xecbMSmidFpqby8PE2bNk1jx45Venq6li1bpsrKSs2aNUvS0SmlqqoqrVy5UtLRYDN9+nQ99thjuuiii/yjPrGxsW3+wk1uvvlma7+Mgc+xuu3OOifoWvhz0VxXPx+hWL/Jmrp6X0A/0DKjl4JLR2/i99BDD8nlcik1NVWLFy/WxRdfLEm6/vrrtWvXLq1du1aSdOmll6q0tDSgjV/84hcqLi7uxKrREi6zBwCEQl9gPNwgfNTX16ugoED5+fnN1jkBALqPUOgLCDcAACCsGH+2FAAAgJUINwAAIKwQbgAAQFgh3AAAgLBCuAEAAGGFcINOceDAAV144YX63ve+p/PPP19PPvmk6ZIAAAbU1dUpOTlZt99+e9A+w/iDM9E9xMXFqbS0VHFxcaqrq1Nqaqp+8pOfqG/fvqZLAwB0ot/+9rcaN25cUD+DkRt0Crvdrri4OEnS4cOH5fV62/TYegBA+Ni2bZs+/vhjTZ06NaifQ7hBm6xbt05XXnmlBg4cKJvNptWrVwfsU1RUpCFDhigmJkZpaWkqKytr9v4333yjCy64QIMGDdLcuXOVkJDQSdUDAE6VFf3A7bffroKCgqDXSrhBmxw6dEgXXHCBHn/88RbfX7VqlXJzczV//nxt2rRJEydOVGZmpiorK/379OnTR//85z+1c+dO/elPf9LevXs7q3wAwCk61X7gtdde07BhwzRs2LCg18rjF9BuNptNr776qq6++mr/tnHjxmnMmDFasmSJf9uIESN09dVXt5jSf/WrX2nSpEm65pprOqNkAICFOtIP5Ofn67nnnpPdbtfBgwfl8Xh022236Z577rG8PkZucMoaGhpUUVGhjIyMZtszMjJUXl4uSdq7d6/cbreko0+MXbdunc4999xOrxUAYL229AMFBQXavXu3du3apUceeUQ33XRTUIKNxNVSsEBtba28Xq8SExObbU9MTFR1dbUk6YsvvlB2drZ8Pp98Pp9uueUWjRo1ykS5AACLtaUf6EyEG1jGZrM1e+3z+fzb0tLStHnzZgNVAQA6y4n6gX93/fXXB7UOpqVwyhISEmS32wPSeU1NTUCKBwCEn1DrBwg3OGVRUVFKS0uT0+lstt3pdGr8+PGGqgIAdJZQ6weYlkKbHDx4UJ999pn/9c6dO7V582adfvrpGjx4sPLy8jRt2jSNHTtW6enpWrZsmSorKzVr1iyDVQMArNKl+gEf0AZ///vffZICfn7xi1/493niiSd8ycnJvqioKN+YMWN8paWl5goGAFiqK/UD3OcGAACEFdbcAACAsEK4AQAAYYVwAwAAwgrhBgAAhBXCDQAACCuEGwAAEFYINwAAIKwQbgAAQFgh3ADoFGvXrpXNZtM333xjuhQAYY5wA8Byl156qXJzc5ttGz9+vFwul3r37m2mqFakpKSosLDQdBkALMSDMwF0iqioKPXv3990GQC6AUZuAFjq+uuvV2lpqR577DHZbDbZbDbt2rUrYFqquLhYffr00V/+8hede+65iouL009/+lMdOnRIzzzzjFJSUnTaaafp1ltvldfr9bff0NCguXPn6swzz1SPHj00btw4rV279oQ13XvvvRo8eLCio6M1cOBAzZ49W9LREabPP/9cc+bM8dfapLy8XBdffLFiY2OVlJSk2bNn69ChQ/73U1JSdN999+m6665Tz549NXDgQP3+97+37kQC6DDCDQBLPfbYY0pPT9dNN90kl8sll8ulpKSkFvetq6vT7373O73wwgt6/fXXtXbtWv3kJz9RSUmJSkpK9Oyzz2rZsmV66aWX/MfccMMN2rBhg1544QX961//0jXXXKMf/vCH2rZtW4uf8dJLL2nx4sVaunSptm3bptWrV+v888+XJL3yyisaNGiQFi5c6K9Vkj744ANNmTJFP/nJT/Svf/1Lq1at0vr163XLLbc0a/vhhx/WqFGj9P777ys/P19z5syR0+m04jQCOBVGnkUOIKxdcsklvl//+tfNtv3973/3SfJ9/fXXPp/P53v66ad9knyfffaZf5+ZM2f64uLifAcOHPBvmzJlim/mzJk+n8/n++yzz3w2m81XVVXVrO3LL7/cl5+f32Itjz76qG/YsGG+hoaGFt9PTk72LV68uNm2adOm+X75y18221ZWVuaLiIjwffvtt/7jfvjDHzbbJysry5eZmdni5wDoPIzcADAmLi5OQ4cO9b9OTExUSkqKevbs2WxbTU2NJOn999+Xz+fTsGHD1LNnT/9PaWmptm/f3uJnXHPNNfr222911lln6aabbtKrr76qI0eOnLCuiooKFRcXN/uMKVOmqLGxUTt37vTvl56e3uy49PR0bd26td3nAYC1WFAMwBiHw9Hstc1ma3FbY2OjJKmxsVF2u10VFRWy2+3N9vv3QPTvkpKS9Mknn8jpdOrNN99UTk6OHn74YZWWlgZ8VpPGxkbNnDnTvzbn3w0ePPiE3+nf1+0AMINwA8ByUVFRzRYBW2X06NHyer2qqanRxIkT23xcbGysrrrqKl111VW6+eabNXz4cH3wwQcaM2ZMi7WOGTNGH330kc4+++wTtvvOO+8EvB4+fHjbvxCAoGBaCoDlUlJS9I9//EO7du1SbW2tf+TlVA0bNkz//d//renTp+uVV17Rzp079d577+nBBx9USUlJi8cUFxdr+fLl+vDDD7Vjxw49++yzio2NVXJysr/WdevWqaqqSrW1tZKkO++8U2+//bZuvvlmbd68Wdu2bdOf//xn3Xrrrc3a3rBhgx566CF9+umneuKJJ/Tiiy/q17/+tSXfFUDHEW4AWO7222+X3W7Xeeedp379+qmystKytp9++mlNnz5dt912m84991xdddVV+sc//tHqFVl9+vTRk08+qQkTJmjUqFF666239H//93/q27evJGnhwoXatWuXhg4dqn79+kmSRo0apdLSUm3btk0TJ07U6NGjdffdd2vAgAHN2r7ttttUUVGh0aNH67777tOjjz6qKVOmWPZdAXSMzefz+UwXAQBdTUpKinJzcwPuxAzAPEZuAABAWCHcAACAsMK0FAAACCuM3AAAgLBCuAEAAGGFcAMAAMIK4QYAAIQVwg0AAAgrhBsAABBWCDcAACCsEG4AAEBYIdwAAICw8v8BsLfbFNO1CGMAAAAASUVORK5CYII=", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "sample_q = q_rv.get_sample(N)\n", + "sample_n = n_rv.get_sample(N)\n", + "sample_a = a_rv.get_sample(N)\n", + "sample_C_C0 = C_C0(sample_q, sample_n, sample_a, x, t)\n", + "sample_Z = flip_LSF*limit_state_fun(sample_q,\n", + " sample_n,\n", + " sample_a,\n", + " x, t, threshold)\n", + "\n", + "monte_carlo(sample_Z);" + ] + }, + { + "cell_type": "markdown", + "id": "d00e1316-c4ac-474d-93ad-18abcda30cfc", + "metadata": {}, + "source": [ + "The method `pdf_of_function_of_RV` makes it easy to see what the distribution of $C/C_0$ and the limit state function for different distributions of q, n or a. Below a second distribution of a is considered:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "c08e0e56-8a6b-45a2-ad3f-abe3ce869513", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a has 61 negative values that have been set to 1.0e-03.\n", + "a has 54 negative values that have been set to 1.0e-03.\n", + "The mean is 1.000e+01\n", + "The standard deviation is 1.000e+00\n", + "The distribution is Normal\n", + "The mean is 1.000e+01\n", + "The standard deviation is 4.000e+00\n", + "The distribution is Normal\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "C_C0_cases = []\n", + "Z_cases = []\n", + "C_C0_cases.append(sample_C_C0)\n", + "Z_cases.append(sample_Z)\n", + "\n", + "a_2 = RandomVariableDistribution()\n", + "a_2.define_distribution(mean=10, stddev=4, dist_type='N')\n", + "C_C0_cases.append(C_C0(sample_q, sample_n, a_2.get_sample(N), x, t))\n", + "Z_cases.append(flip_LSF*limit_state_fun(sample_q,\n", + " sample_n,\n", + " a_2.get_sample(N),\n", + " x, t, threshold))\n", + "\n", + "a_rv.print_status()\n", + "a_2.print_status()\n", + "\n", + "pdf_of_function_of_RV(C_C0_cases)\n", + "pdf_of_function_of_RV(Z_cases, case_C=False)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "695f1336-8d3e-4503-9196-9969d181ae10", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "8c197ae8-3a6c-45fe-b304-75f601dbb9ac", + "metadata": {}, + "source": [ + "This is the density of the function of random variables, $C/C_0$, two values of $\\sigma_a$, and a third with the uniform distribution (not using the `RandomVariableDistribution` class)." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "53273645-453b-48b9-85c0-e69eb1ac579e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Joint density of 2 RVs with failure realizations\n" + ] + }, + { + "data": { + "image/png": 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C2tpaFBQUYMCAAZ0eXFegG4jcDORKFbamluGbI3koqBUDUBcpndUvEA8ODUaEF03qNwKpQol/LlRi/elCpBY36r4+vqcXHh8Vjv4hbt03OEK6AM2Z5kWJ9IR0I4VShW1p5Vh9MBsl9W0AABc7IRYODcEDQ0LgZm/VzSMkXJKLGvDTiXz8c7FSt/U4KNQNT4+PxJAwdzr1SG5KNGeal8lBV3Fxsd7vX7v12N3oBiI3IpZlsf9SFVb+exl5NeqVLQ8HKzwyIgzzBwfDwZo6dN0s8mpa8MOxfGxJKdW1VRoU6oYX7+yBfsG08kVuLjRnmpfJQRePx9P7CU6pVHJ+rzvQDURuNKnFDXhn1yWkaLanXO2EeHxUOBYMCYadFQVbN6vyxjZ8dzQPG8+WQKZUNw0f3cMTL90ZjZ6+9LeH3BxozjQvk4Ou9PT0q/5bLpcjNTUVn332Gd577z3MmDGjSwfYWXQDkRtFdbMEH/5zGX+nlgEAbIV8PDw8BI+NCoeTDZV8uFWUN7bhi4M5+Cu5FAoVC4YB7knwx4t3RMPHmU47khsbzZnm1WU5Xbt378bHH3+MI0eOdMXTdRm6gUh3kytVWH+qEKsO5Ogqn9/bLwAv3NED3k40Cd+qCmvF+HhfFnafrwCgDrIfGRmGx0eF0YomuWHRnGleXRZ05eTkID4+HmKxuCuersvQDUS6U3pJI17ach6XK0UAgLhAF7w9tRfiAl26d2DEYtJKGvHOrktILmoAAPi72OK1u3vijl4+lGxPbjg0Z5qXyUFXc/PVjWJZlkVFRQXefPNNXL58GWlpaV05vk6jG4h0hzaZEp/uy8LPJwugYtV5Wy9P6ol7+wWAR3W2bjssy+Kfi5V4b3cmyhrVp1RHRnni7am9qD8muaHQnGleXZJIz7IsAgMDsWnTJgwZMqRLB9hZdAMRS0sqrMcLf53X1duaHu+H1+6OgbuDdTePjHS3NpkSXx/JxXdH8yFTqmAl4OGp0RF4YnQ4rATUWoh0P5ozzcvkoOvo0aNX/TePx4OnpyciIiIgENx4eQp0AxFLkSlU+PxANr49mgeWBXycbPDBjFiMifbq7qGRG0x+TQve2JGB4zm1AIAe3o74cGYsEoJcu3lk5HZHc6Z5UXFUQrpAfk0Llm1K1bXuubdfAF67O+a2aUStUKrQ2CZHg1iGZokCLVIF2mQKSOQqyJQqqFQsVCzAYwAej4G1gAdrAQ+2VgI4WPPhaCOEi50QLrZWt82KD8uy2Hm+Am/tyECdWAYeAzwyIgzPTIiCjZDf3cMjtymaM82rQ0FXXl4eVq1ahczMTDAMg549e+Lpp59GeHi4OcbYKXQDEXPbnlaGV/6+ALFMCRc7IT6cEYs7e/t297C6lEKpQnF9KwpqxSisa0VJfStKG1pR3ihBtUiCOrEMXfXxzcVOCC9Ha/g628Lf1RaBrnYIdrdDkJsdwjztb7mTf/ViGd7ZdQlbNaVEwj3t8fl98egT4NK9AyO3JZozzcvkoGvv3r2YOnUq4uPjMWzYMLAsi1OnTiE9PR07d+7EhAkTzDXWDqEbiJiLTKHC27sy8NsZdZeGQaFu+GJuwk1fBqJVpsCF0iZcKGtCRnkzMiuakV8j1hX85MIwgLOtEE42QthbC2BnxYeNkAcrPg98HgOGYcCygFKlglzJQiJXolWmRItUgWaJHE1tcqMCN38XW0R5OyDa1wm9/JzQx98FgW62N/1JwAOXqvDy1guoEUnB5zFYOjYCT42JgJB/e6z8kRsDzZnmZXLQlZCQgDvuuAMffvjhVV9fsWIF9u3bh5SUlC4dYGfRDUTMobJJgid+T0ZqcSMYBlgyJgJPj4uE4CacIFukCpzJq8OZ/DokFtTjUkUzlKrr/yzYCvkI8bBHqIcdAt3sEOhqB38XW3g72cDLyRoutsJO/fwqFYvGNjlqRFJUNUtQ0dSGsoY2FNW3ori+FUV1ragXy9p9rJu9FfoGuWJAiCsGh7mjl5/TTfm7aGyV4dVtF3W1vRKCXPDFnAQEutl188jI7YLmTPMyOeiysbHBhQsXEBkZedXXs7Oz0adPH0gkki4dYGfRDUS6WmpxAx79NRk1IimcbARYPSfhpkqWZ1kWlyqacfhyNY5k1SCtpBGKa4IsbydrxAe6oLefM2L8nBDl7Qh/F9tuL3fRIJYht6YFlytFyKxoxsWyJlyuEF23CudgLcDAUDcMi/DAqChPhHva31QrYdvTyvC/bRchkijgaC3A+zNiMSXOr7uHRW4DNGeal8nJEZ6enkhLS7su6EpLS4OX180z8RDSEdtSy/DilvOQKVTo4e2I7x/oh2D3G7/OEsuySC1pxO7zFfj3YqWuVpRWsLsdhoZ7YHCYGwaEuMHPxbabRqqfq70VBtirx6glVSiRUd6M5MIGJBbUI7GgDiKJAocuV+PQ5Wq8AyDIzQ4TYrxxZ28f9A1yBf8Gr5U2Ld4f/YJd8fSmNCQXNWDpxlQkFtThf3fFUJI9ITcxk1e63n77bXz++edYsWIFhg4dCoZhcOLECaxcuRLPPfcc/ve//5lrrB1CUTvpCizLYvXBHKw6kAMAGN/TG6vmxMPB+sZO6i6qE2NLcim2p5ejqK5V93VbIR/DIjwwJtoTIyM9b6ntK6WKRWZFM07m1uJ4Ti3OFtRftRLm5WiNSb19cFcfP/QPdu321Tt9FEoVVh3IwZeHcwEAvf2d8M38frfU74vcWGjONC+Tgy6WZbFq1Sp8+umnKC8vBwD4+fnhhRdewLJly264JXy6gUhnyZUqvLr1AjYnlQIAHh8Vjhfv6HHDTtYyhQr/ZlTi9zNFSCyo133dzoqPCTHemBzri1FRnrfNiolYqsDxnFrsy6jE/swqiCQK3fcCXG0xPd4fs/sHIsj9xg1kjmRV45k/0tDQKoezrRCr7ou/qba0yc2D5kzz6lSdLpFI3U/O0dGxywbU1egGIp0hkSvx1O8pOHi5GjwGeGd6b8wfFNzdw2pXXYsUv50pxm+JRagRSQGoTxSOiPTEzL7+mBDjfcuVWzCVTKHCidwa7DpfgX0ZVboG5AAwItID8wYGYXyM9w15YrCssQ1P/p6C9JJGAMBzE6KwZGzEDfdBl9zcaM40L5ODrjfffBMPPfQQgoM7P/EcO3YMH3/8MZKTk1FRUYGtW7di+vTpAAC5XI7//e9/2LNnD/Lz8+Hs7Izx48fjww8/hJ+f8QmldAORjhJJ5Fi0PglnC+phLeDhq3l9MT7Gu7uHdZ3iulZ8czQPW1JKIVOot9E8Ha0xb2AQ7hsQeMPmZ3W3NpkS+zOr8GdSCU7k1urKVXg7WWPuwCDcPzgYHjdY6yapQol3dl3SlSmZHOuDT2bF3fbBNOk6NGeal8lBV79+/ZCeno5Ro0Zh0aJFmDFjBmxsOlaX6J9//sHJkyfRt29fzJw586qgq6mpCffeey8eeeQRxMXFoaGhAcuXL4dCoUBSUpLRr0E3EOmIplY5Hlh7FukljXC0FuCnhQMwMNTN8AMtqLiuFasP5mBbWpmuxEOfAGcsGh6KSb19b5vK7l2hpL4Vm84V449zJahtUZelsBLwMLOvPx4dGY7QG6wp9aazxXht+0XIlSx6+Tnhxwf7w9eZgmvSeTRnmleHthfPnz+PtWvXYsOGDZDJZJgzZw4efvhhDBgwoOMDYZirgq72nDt3DgMHDkRRURGCgoKMel66gYipmlrluP+nRFwoa4KrnRC/PDwIsQHO3T0snapmCVYfzMHmcyW6Ug8jozyxZEwEBoS40nZTJ2jz4X46no/00iYA6i3ayb19sWRsBHr63jh/Q5IK6/HYr8moE8vg7WSNnx4cgN7+N859Sm5ONGeaV6dyuhQKBXbu3Im1a9fi33//RY8ePbB48WIsXLgQzs6m/eM3Jug6cOAAJk6ciMbGRs6bQSqVQiqV6v67ubkZgYGBdAMRozS1yXH/j+qAy93eCr8/MgjRPjfGfdMmU+KH4/n49mgeWmVKAOpg69kJUYgPdOnewd1iWJbFucIGfHMkF4ezanRfn9TbB89MiEKU942Rx1pS34qH151DTnUL7Kz4+Hp+X4zuQQn2xHg0Z1pWp4IumUyGrVu34ueff8ahQ4cwdOhQVFVVoby8HD/88APuu+8+4wdiIOiSSCQYPnw4oqOj8dtvv3E+z5tvvom33nrruq/TDUQMEUsVWPBTIlKKG+Fmb4WNjwxGD5/un1xZlsXejEq8sytTV1+rb5ALVkzq2e1bnjKFCuWNbShrbENVswTVIikaxDI0tMrQIlWgRaqERK6EXKmCQqn+U8MwgIDHwErAg62QD3trARxthHC1E8LN3gpeTjbwdrSGv6stfJxsur2yfGZFM748nIs9FyrAapp235MQgGcmRCLAtftPPDZL5HjytxScyK0Fn8fgwxmxmNU/sLuHRW4SNGdaVoeCruTkZKxduxYbN26EtbU1HnjgASxevBgREREAgE8//RQfffQRqqqqjB+InqBLLpdj1qxZKC4uxpEjR/TeCBS1k46QKpRYvD4Jx3Nq4WwrxMZHBiPGr/vvl5L6Vry67SKOZatXW/xdbLFiUjTu7uNr0W1EpYpFTrUIl8qbcam8GTnVLciraUFZY1uXNbpuD5/HIMDVFmEe9gj3VPdbjPZxRA8fR4ufMMyqFOGz/VnYm6H+u2Yl4GHR8FA8OTocjjZCi47lWjKFCiu2nMffmqbZr0yOxqMjw7t1TOTmQHOmZZkcdPXp0weZmZmYOHEiHnnkEUyZMgV8/tX1fmpqauDt7Q2VSn+D3KsGwhF0yeVyzJ49G/n5+Th06BDc3d1NGS7tTxODVCoWSzelYvf5CthZ8fH74kFICHLt9jGtO1WIj/dmoU2uhBWfh8dGheHJ0RGwtTJ/fa1WmQJJhQ04V1iPpMIGnC9thFizpXktGyEP/i628HG2gZejDdzsreBqJ4SjpvG1rZAPIZ+BgM+AAQMWLORKFjKFCm1XNLxubJWjTixDdbMEVc0SlDdKOJtsWwl4iPF1QkKQi6bnoht8nC3TaDytpBEr/7mM0/l1AAAPB2u8PCka9yT4d2vtNpZl8eE/l/HdsXwAwBOj1fXkKMePmILmTPMyOeh655138PDDD8Pf379rB9JO0KUNuHJycnD48GF4enqa/Lx0AxFD3t11CT+eKICQz+DnhQMwItL0+6wrlTa04rnN6brCpgND3fDhjFiEeTqY9XVzq1twILMKR7NqkFRUD7ny6j8N9lZ89LqiF2OElwNCPezh4WBlloldpWJRLZKioFaM/NoW5FS14HKleqWt+YoCp1qhHvYYEu6OUVGeGBbhYdZuASzLYv+lKry/JxOFmkr/fYNc8N49sd2ebP/NkTys/PcyAGDh0BC8MSWGAi9iNJozzatTOV2d1dLSgtxcdXuLhIQEfPbZZxgzZgzc3Nzg5+eHmTNnIiUlBbt27YK393/1kdzc3GBlZWXUa9ANRPRZf6oQb+zIAACsnhOPafFd+2HCVNtS1Y2OW6QK2Fnx8fLknpg/MMhsKyjZVSLsOl+BXefLkV8jvup7/i62GBTqhgGhbugb5IoIL4cbomchy7IorGtFekkjUosbkFzcgEvlzbiyZ7eQz2BIuAcmxnhjYi9veDmaZxVMplDhpxMFWHMoB60yJQQ8Bo+ODMOycZHdWvH/98QivLr1IgBg3qAgvDut9w3bQYHcWGjONK9uDbqOHDmCMWPGXPf1Bx98EG+++SZCQ0Pbfdzhw4cxevRoo16DbiDC5Wh2DR5aexYqFnjhjh54akxEt42lVabA69sz8FeyutVQv2BXfDY7zizNtBvEMmxLK8NfyaXIKG/WfV0bqIyL9sLIKE+EuNvdNCskTW1ynCuox/GcGhzJrrmqzyTDAAND3DAt3h93xfrC2a7r868qmyR4c0cG/s2oBACEedjj41l90C+4+w46/JlUghe3nAfLAnMHBuG96RR4EcNozjSvbg26LIFuINKe/JoWTPvqJEQSBWb1C8BH9/bptgAjv6YFj/+WjOyqFvAYYNm4SCwdG9nlq0oXSpuw/nQhdqSX6yrXC/kMRkZ6YkqcH8b29IJTNyeEd5Xc6hbsu1SJvRcrdfW2AHUu2IQYb8wbGIQhYe5dHoTszajEa9suolokBcMAi4eH4rmJPbpt1Wtbahme3ZwGFQs8MCQYb03tddME0qR70JxpXhR0kdtOi1SBaV+eQF6NGP2CXbHhkUGwFnTPpHjochWe3pQGkUQBT0drfDEnAUPCTTssoo9KxeLQ5Wp8fzwfZ69oft3Lzwmz+wdiapwfXO2N26q/WZXUt2L3hQpsTSlDVpVI9/VgdzssGByMWf0D4WzbdcFmU6scb++6hC0p6lXLaB9HrJ6T0G3lR7Ykl+L5v9LBssAjI0LxyuSeFHgRTjRnmhcFXeS2wrIslmxUn1T0cbLBjqXDzJbvY2gcP50owHt7MsGyQP9gV3w9vy+8nLpmLCoVi32XqrD6YA4yK9RbiAIeg7v7+OKBoSFICHS57SZelmWRUd6MP86VYFtqGUSaZte2Qj7uGxCIxSNCu7Tu1oFLVXhpy3nUiWWwEvDw5pRemDswsFve9z/OFeOlLRcAdP9WOrmx0ZxpXiYHXSEhIXj44YexcOFCo1vxdCe6gciV1p4swFs7L0HAY/DHY0PQL9jypSEUShXe2JGB3xPVTYvnDgzEW1N7d1mvxBM5tVj572VcKFNvq9lb8XH/4GAsHBZC/fk0WmUKbE8rx/pThbhcqV794vMYTIvzw1NjIxDeRSdFq0USvPjXeRzRVLWfGueHD2bEwt6MJyu5/Hg8H+/uzgQAvH9PLOYNuvH/fhPLoznTvEwOutasWYN169YhPT0dY8aMwaJFi3DPPffA2traXGPsFLqBiNb50kbM/OYU5EoWb0yJwUPD2j+oYU4SuRLLNqZi36UqMAzw6uSeWDQ8tEtWP/JqWvD2zks4qimkam/Fx0PDQrFoeKhZtxAbW2XIqxGjtKEVpQ3qyvRVzRI0tMrR1CpHi1QBiVwJqUIFFcuCZdWrbgI+o6tI72QrhKudFTwcrODtZANfZxsEutkh2N0Ofs62ZksAZ1kWJ3Pr8O3RPJzIrQWgTryfGueHZydEdclBBpWKxQ/H8/Hx3iwoVCyivB3w3YL+3dJE+5O9WfjycC54DPDDA/0xrqe34QeR2wrNmebV4e3F9PR0/Pzzz9i4cSMUCgXmzZuHhx9+GH379u3qMXYK3UAEAEQSOe5ecwJFda24s5cPvrm/r8W3eZolcixel4SzhfWwEvDwxZwE3Nnbp9PP2ypTYPXBHPx8ogByJQshn8H8QcFYMjYCHg5d+2GoskmC5KIGXChrQkZ5EzIrRKhtkRp+YCfYCHmI8HJAtI8Tevs5ITbAGb38nLs8OT29pBFrDuXiQKa64ryAx2DeoCA8PS4S7l3wPiYV1uOJ31NQI5LC0UaAL+YmYIyF+ySyLIsX/zqPP5NLYSvk44/HBqNPgItFx0BubDRnmlenc7rkcjm+/vprvPTSS5DL5ejduzeefvppPPTQQzdEzgjdQAQAXvwrHZuTSuHvYos9y0aYpWyAPk2tciz4ORHnS5vgaC3ADw/2x+CwzifMH82uwf+2XUBJvbon47hoL/zv7pguW0WpF8twLLsGJ3NrcSqvTtf78VralalAVzv4OtvAy8kabvZWcLYVwsFaAFsrPqwFfPAZBgwDKFQs5Ep1RXqxpiJ9vViOGpEUlc0SlDe2oaS+FSUNrdcVaQXUpy5j/JwxOMwNQ8LcMSjUvcsq9V8sa8LHe7N0K4aO1gIsGRuBhcNCOn3gorpZgid+T0FyUQN4DPDqXTF4eFiIRf9WypUqLFqfhGPZNfBytMaOJcMtVs2f3PhozjSvDgddcrkcW7duxdq1a7F//34MHjwYixYtQnl5Ob788kuMGTMGGzZs6OrxmoxuILIvoxKP/poMhgH+eHSIxZtEN4hlmP9jIi5VNMPN3gq/LhqIXn7OnXpOkUSOd3dl4o+kEgDqQqZvT+vVJdtF5Y1t2HOhAnszKpFc1HBV0VEeA/T0dUJcoAt6+Tmhl58zIrwczFb9XaFUoai+FTlV6r6PGeXNSC9tum51zUrAw5Awd4zr6YWJMT5dEkScyqvFe7szdbXMwjzt8c603hgW4dGp55UpVHh9+0VsOqf+3c0bFIS3p/ayaGNvkUSOmd+cQnZVC2L9nbH5sSEWaS9Fbnw0Z5qXyUFXSkqKrtk1n8/HggULsHjxYkRHR+uuOXfuHEaOHIm2tvY/FVsS3UC3twaxDBM+P4raFhkeGxmGlyf3tOjrN7XJMe+HM8gob4aHgxV+Xzy406UDkosa8PSmVJQ2tIFhgIeGhuK5iVGdSs5ukSqw+3w5/kouxbnChqu+19PXCSOjPDAs3AP9gl27JQn8SizLorShDecK63E6rw4nc2tR3iS56pr4QBdMi/fD3X384OnY8a1BlYrFlpRSrPw3SxfozUjwx2t3x3QqT+7a06vjor3w5by+Fg18SupbMfXLE2holWN6vB8+vy/+htidIN2L5kzzMjno4vP5mDBhAhYtWoTp06dDKLx+m0YsFmPJkiVYu3Ztlw20o+gGur09/2c6/kouRYSXA3YvG27RelxiqQILfkpESnEj3O2t8MdjgxHh1fGAS5uQ/dHeLChVLAJcbfHprDgM6sQ2ZU6VCOtOFWJrahlaNQ2tGQYYEOyGybE+mNDLB/4uN/aJR5ZlkVvdgkOXq7E3oxIpxY267/EYYEwPL9w3IBBjo706vJrU1CbHZ/uy8OuZIqhYwN3eCu9M743Jsb6dGvvejEos25gKqUKFvkEu+HnhALjYWa5u2pn8Osz/MRFKFYu3pvbCg0NDLPba5MZEc6Z5mRx0FRUVITg42Fzj6XJ0A92+TubWYv6PiWAY4K/Hh1q0PIRMocLD687hRG4tnG2F2PTo4E41QhZJ5Hjmj3RdkveUOD+8f09vOHaggjzLskgsqMe3R/N0pQwAdeuaWf0DcU+C/02d41PdLMGeCxXYnl6O1CsCMF9nG8wfFIQ5A4M6fMAgtbgBL205j+yqFgDAtHg/vD2td6eKqyYV1mPR+iQ0tckR7eOIXxcN6tTqnKm0pSQEPAZ/Pj4ECUGWL6NCbhw0Z5pXh3O6kpKSkJmZCYZhEB0djf79+3f12LoE3UC3J4lciUmrj6OgVowHhgTj7Wm9LfbaKhWLZzenYVtaOeys+NjwyGDEB7p0+Pnya1rwyC9JyKsRd7rI5pn8Ony6L0u3hchjgAkx3nhwaAiGhLnfcttLeTUt2HyuBH8ll6JOLAMAWAt4uLdfAB4dGdahkhBShRJfHsrFV4dzoWIBP2cbrJmX0Kk+i1mVItz/UyJqRFKEe9pj4yODu6xQriEsy+KpDSnYc6ESgW622L1sxC3TDoqYjuZM8zI56CotLcXcuXNx8uRJuLi4AAAaGxsxdOhQbNy4EYGBgeYYZ4fRDXR7+nx/NlYfzIGXozUOPDfKopPIh/9cxrdH8yDgMfh54QCMjPLs8HOdyqvF478mo1migK+zDb5b0K9DR/yzKkV4b08mjmlO5FkJeJjVicBDnzaZEmWNbagWSVDXIkNjmxxiqQKtMiXkShWUKhY8hoGQz8BGyIe9FR+ONkK4O1jBw8Eafi62cLUTdmkAKFUosedCBdadLNT1YuTzGEyP98fSsREI6cBpz+SiBjy7OQ1Fda3g8xi8cEcPPDoirMM1xQpqxZj/wxmUN0kQ5mGPTY9aLvBqapNj8urjKGtsw9Q4P3wxN8Eir0tuPDRnmpfJQdfEiRPR3NyM9evXo0ePHgCArKwsPPzww7C3t8e+ffvMMtCOohvo9lPa0Ipxnx6FVKHCV/P64q4+ncu7McWfSSV44a/zAIBPZsXh3n4BHX6u7WlleP7PdMiVLPoFu+Lb+/uZvO3U2CrDJ/uysCGxGCpNUdI5AwOxdGwkvDs5oUsVSlyuEOFCWRMyK5qRU92C/JoW1LbIOvW8gLo1T7C7HcI9HRDp7YAYXyf09neGr7NNp4Kx9rZW+TwG9w0IxPLxkSa3hGqRKvDK3xewI70cAHBHL298Oju+w6c5S+pbMef7MyhrbEOUtwM2PToEbhbqjZlc1IDZ352GUsXii7kJmBrnZ5HXJTcWmjPNy+Sgy9bWFqdOnUJCwtWfhFJSUjBs2LAb4sTilegGuv0s2ZCCXecrMDjMDRsfGWyxLbPkonrM/T4RMqUKy8ZG4NmJPTr8XFe2bLkr1hefzo4zqRgoy7LYnlaOd3Zd0m2rTertgxWToju8sqVQqpBW0ohjObVIzK9DWkkjpApVu9c6WAvg7WQNDwdruNgJ4WAthJ0VHwI+AwGPgYpVP1+bXAmxVImmNjnqxDLUiCR6gzZvJ2v0C3bFkDB3DAl3R7inQ4d/v+kljVh1IBuHNcGXnRUfj48Kx6Mjw0x+rzeeLcGbOzIgU6oQ6eWAHx7o36HVMwAoqhNj9nenUdUsRW9/J2x8ZHCHcvc6QrtC7GQjwL5nRt3UuX2kY2jONC+Tg64ePXrg119/xcCBA6/6+tmzZzFv3jzk5uZ26QA7i26g20tyUT1mfnMaPAbYtXQEYvws8zuvapbg7jUnUCOSYlJvH3w1r2+HtplYlsWaQ7n4bH82AODhYaH43109TXquapEEK7ZcwKHL1QCASC8HvDO9d4eKsUrkShzNrsHei5U4kFmFZoniqu+72gnR298Zvf2dEeXtgHBPBwS72cPJVtDhYEgiV6K8sQ2FdWLkVYtxuVKESxXNyK4SQam6+s+Vv4stxkR7YkKMD4aGu0PYgdOJZwvq8f6eTKSVNAIAAt1s8eYU02uepRQ34PFfk1EtksLVTogfHuiP/iEdy/PKrW7Bfd+dRp1YhmER7li7cGCX9ebUR65UYeY3p3C+tAljo73w04P9b7k8P6IfzZnmZXLQtX37drz//vv46quv0K9fPzAMg6SkJCxduhQvvfQSpk+fbqahdgzdQLcPlmUx69vTSCpqwH39A7Hy3j4WeV25UoV5P5zBucIG9PB2xNanhsLOyvTtJZZl8fn+bHxxSP3B5bkJUVgyNsKkSe/fixV4+e8LaGiVw4rPw7JxEXh0ZLjJE3Z6SSM2J5VgZ3r5VYGWs60QwyM9MDzCAwND3RDmYW+xSblVpsCF0iacLajH6fw6JBU1QHbFSpuLnRB39vLBjL4BGBDiatK4WJbFzvMVeH93Jiqb1TW/7or1xRtTY0zacqxulmDxL0k4X9oEKwEPn86Kw5QObtNdLGvCfd+dhlimxLR4P3w+O95sPSivlFMlwuQvjkOuZLF6Tjymxfub/TXJjYPmTPMyKuhydb36D5hYLIZCoYBAoJ5YtP/f3t4e9fX15httB9ANdPs4mFmFReuTYCPk4cjzYyy2NfLBP5n47mg+HK0F2LF0eIdb8HxxMEe3wvXK5Gg8OjLc6MdKFUq8tzsTv5wuAgD08nPCZ7PjTSrEKlOosDO9HOtPF+K8JtkcAHycbDA51hd39vZBv2BX8C0w8RujTabE6fxaHMisxr6Myqu2JYPd7TBvYBBm9Q80KSdKLFXgi0M5+PF4AZQqFi52Qrw3PdakvMBWmQJPb0rD/kvq8h5vT+uFB4aEGP34Kx3LrsHD685BoWLx9LhIPDMhqkPPYyrtvehmb4XDz422eNss0n1ozjQvo4Ku9evXG/2EDz74YKcG1NXoBro9qFQspnx5AhnlzXh8VDhWTIo2/KAucCy7Bg/8fBYA8O39fXFn744l7f90ogDv7LoEAHh1ck88MjLM6MeWN7bh8d+SdYHS46PC8eyEKKNXtyRyJTYkFuPH4/m6yu5WfB4mx/pgVv9ADA5zv2ECLS5KFYvEgjpsTSnDngsVEGsKvVoJeLgn3h+PjAw1qTDtxbImvLTlvK4F0PR4P7w9vbfRp2CVKhZv78zAek0Q/MIdPfDUmAgTfyq1zedK8OIW9eEMSx0MkStVuOuL48iuasGDQ4LxlgVLrpDuRXOmeXW64fWNjm6g28O/Fyvw+G8pcLAW4PiLYzrVosVY9WIZ7lh1DDUiKeYPCsJ798R26Hm2pZZh+R9pAIBnJ0Rh2bhIox+bXNSAx35NQm2LDC52Qnw+Ox5jor2MeqxcqcIf50rwxcEcVIvULW48Ha2xcGgI5gwIhHsHC4h2t1aZAjvTy/HbmWJcKPtvxe6OXt54elyU0Xl+cqUKaw7m4EtNPa5AN1t8Pa8fYgOM65vJsiw+P5CDLw7mAACWjYvEsx1cqXpn1yX8dKIANkIetj45rFOFdo11Kq8W835ItHh+JOleNGeaFwVd5KbHsizuXqNe5ersqUFTXnPJhlTsvlCBSC8H7Fw63KQTb1qn8mrx4M9nIVeyeHhYKF67u6fRuUi7z1fgmc1pkClUiPZxxA8P9Eegm51Rjz2eU4O3dl5CbrW6srq/iy2eGhOBGX39O/RzXEmpYlHa0IqyhjZUNElQ2yJFY5sczW1ySBUqyJUqMAB4PAa2Qj4crAVwshXC08Eank7WCHS1RYCrXafHAairvX9/LB/7M6ug/Us3OdYHL9wRbfQ28JW9Lq34PLw1rRfmDgwyegzfH8vD+3suA1Dn6S01IajWUihVeHh9Eo5l1yDE3Q47lg63SO25pzakYHc3nAQm3YfmTPOioIvc9A5frsZD687BzoqPky+Ntcgq1470cizbmAoBj8HWJ4cZvfpxpdzqFtzz9UmIJArc1ccXa+YkGJ0ove5kAd7adQksq64ov+q+eKMaUVc3S/D69gz8m1EJAHCzt8KysRGYOyioQ30pFUoVMsqbkVTUgItlTbhU3oyCWjFkyvZLSZgi0M0WPbwd0cvPGfGBLogPdOnw7za3WoTVB3Ox63w5WE29svsHB+OZCVFGtfBpapXjuT//a8O0YHAwXp8SY/Rpye+O5uGDf9SBl6nbx1oNYhnuXnMCZY1tmNTbB1/P72v2IKi0oRVjPz0KmUKF7xb0wx29fMz6eqT70ZxpXhR0kZvenO9P40x+PR4ZEYpX74ox++vVi2UY/9lR1ItlWD4+EsvHm75l1CyRY/qXJ5FfK0a/YFf8vniQ0Ss7aw7m4FNNwv0DQ4LxxpReBnOuWJbFX8mleHvXJYgkCvB5DB4cEoKnx0ea3DewoqkNBzOrcfhyNc7k1+nyp65kJeAh0NUWvs628HK0houdFRxtBLAW8mClCVQUKhYSuRItEgUa2+SobZGiskmC0oY2tEgV1z0nwwDRPk4YGu6OsdFeGBDiZvKpzKxKET78J1NXm8vDwQqvTO6JexL8DQYwLMviq8O5+HR/NlgWGB7hgW/u72t0Da0vD+Xgk33q39vn98XhngTTC+emlTRi1renIFeyeO+e3pg/yPx9cD/eexlfHc5DhJcD9i4fecPn95HOoTnTvCjoIje186WNmPrlSQh4DI6/NAa+zrZmf83lm1KxLa0c0T6O2LFkuMkTv0rF4pFfknDwcjV8nW2wc+lwoxowX1tS4pnxUVg2znBJiQaxDCv+Po+9GepVmlh/Z3x0bx+T8oIaW2XYnlaOnenlSCpquOp7TjYCDAhxQ58AF/T2d0KUtyP8XWw7XN6AZVnUiWXIrhIhu1KE82VNSCtpRH6N+KrrHK0FGNfTC1Pi/DAyytOkGl0ncmrxxo6LyNM85/AID3wwI9ao7dn9l6rw9KZUtMqU6OnrhHUPDTC6ur82N6szLaK0hXNthDzsWjrcpAMCHdEskWPEysNoapPjs9lxmNG3410WyI2P5kzzoqCL3NSWbkzFzvRyzEjwx2f3xZv99U7m1mL+j+rk4q1PDkNcBxpZf3U4Fx/vzYKVgIe/Hh9idC/FVQeyseqAOinb2JISqcUNePL3FFQ0SSDkM3hmQhQeHREGgZEBSnpJI9adKsTuCxW6mlgMA/QNcsXYaC+MivJET18ni6x+1IikOJNfh+M5NTh0uQa1LVLd9zwcrDCzbwDuGxCIME8Ho55PplDhxxP5WH0gB1KFCg7WArwxJQb39gswGMheKG3CQ+vOobZFikA3W2xYPNiogE2lYrH8jzTsSC+Ho7UAW58ahggv48Z75XM8uPYsjufUok+AM/5+YqjRv8+O+vpILj76NwtBbnY49Nwos78e6T40Z5qXyUGXWCzGhx9+iIMHD6K6uhoq1dW5G/n5+V06wM6iG+jWVdUswbAPD0GhYrFr6XD09jc9r8oUcqUKk1YfR251CxYODcGbU3uZ/ByJ+XWY+8MZqFhg5cxY3DfAuITsn08U4G1NSYn/3dUTi0cYzgnadLYYr29Xt6YJ87DHF3MTjHqPWJbFkewafHMkD2cL/qu719PXCTP7+uPuPn7d3h5GpWKRWtKAXecrsDO94qoAbGy0FxYPD8WQcHejcp4KasV44c903QretHg/vDu9t8Ftw5L6Vtz/UyKK6lrh52yDDY8MNqr1j1ShxP0/JuJcYQNCPeyx7clhJtfBqmqWYMJnR9EsUeClO6PxxGjja7p1RKtMgeErD6NeLKPVrlsczZnmZXLQNXfuXBw9ehQLFiyAr6/vdX/Unn766S4dYGfRDXTr0q789A92xV9PDDX762m3ddztrXDo+dEm50I1tspw56rjqGyWYEaCPz6dHWdUULA9rQxPb0oDYFxJCaWKxbu7L2HtyUIA6lIJn8yKMyr3KDG/Dh/tzUKyJgAR8hlMifPDg0NC0CfA+YY8vSZXqnD4cjU2ni3Gkewa3SnFhCAXLB8fhZGRHgbHrVSx+PZoHj7bnw2likWohz2+X9APkd76t+6qmiWY98MZ5NWI4e1kjc2PDTGqt2VtixTTvjyJssY2jIryxNqFA0zejtU2V7cS8LB3+cgOF+U1lna1K9zTHvufGWWR6vjE8mjONC+Tgy4XFxfs3r0bw4YNM9eYuhTdQLcmpYrFiJWHUN4ksUirknqxDKM+PgyRRGHSCtWVtI24wzzssXPpcKNOG54tqMf8H89ArmTx0LAQvH53jN4AQiJX4pk/0vDPRfXpxOcnRuHJ0REGJ8iyxja8vzsTuy9UAACsBTzcPzgYi0eEWiRPrqsU1Iqx9mQB/jhXomvGPSjUDa/e1dOobdzkogYs25iKssY2OFgL8Pl98ZgQo78HY41Iivk/nkF2VQsC3Wzx1+NDjcrxyihvwsxvTkEiV3WoeCrLsnjgZ/U248goT6x/aIBZg2KRRI6hHxyCSKrA2ocGYEwP4+rBkZsLzZnmZXLQFRoaij179qBnz57mGlOXohvo1nQ4qxoPrT0HZ1shEl8Z1yU1nfR5c0cG1p0qRE9fJ+xaOtzkHCZtiQk+j8HfTww1KhesuK4V0746gYZWuVFNtFukCjy87hzOFtTDis/Dp7MN9/1Tqlj8fKIAn+7PgkSuAo8B5gwMwtPjIo1ODr9WXYsUGeXNyK9pQWFdK8ob21DTIkWDWIZWmRISufq045V1ulzshPBysoGfsw1CPRwQ7mmPnn5OHa5FVS2S4Luj+fj1TJEuF21m3wC8MjnaYNHXuhYpnvg9BWcL6sEw6hIPhrZzq0USzPr2NIrqWhHl7YA/Hxtq1Jahtto8jwE2PjIYg0xsSl5QK8Ydnx+DTKnCN/P7YlKseavVv7vrEn48UYDhER74bfEgs74W6R40Z5qXyUHXb7/9hu3bt2P9+vWwszOuEGN3ohvo1vTEb8n452Jlh3OrTFFS34qxnx6BXMnit0WDMDzSw6THX1liwtj+ea0yBWZ8fQqXK0XoE+CMPx4dAlsr7sBSJJFj4dpzSC5qgKONAD880B+DDUzgBbViPP9num4rcWCoG96c0svkyuNljW04ll2DM/l1OFdQr2sl1BVCPezRN8gVg8PcMCzCA34upq26lTW24dO9Wfg7tQyAuin2K5N7YpaBZHm5UoW3dmbgtzPFAIDHRobhpTuj9Qa9JfWtuPfbU6hqlmJImDt+WTTQ4IlKlmXx3J/p+DulDP4utvhn+QiTA83P9mXhi0O5CHC1xYFnR5n1A0hJfStGfXwYKhY48OxIs5+cJJZHc6Z5mRx0JSQkIC8vDyzLIiQkBELh1X8gUlJSunSAnUU30K2nrkWKwR8chFzJ4p+nR5i9Jcrzf6bjr+RSDItwx++LB5v8+Gf/SMPfqWXo4e2InUsNl5hgWRbPbk7H1tQyeDhYY9fS4XoT18VSBRb8lIiU4kY42Qjw2+JBBrfStqWW4dWtFyCWKeFgLcD/7uqJ+wYEGr09VVLfim2pZfjnYiUuVTRf9/0wD3tEejsgxMMeAS628HS0hpu9Neys+LC14oMBoGJZtMlUEEnkqG+VoapZirKGNuTXtiCnqgVljW3XPW+0jyMm9vLBtHg/hBt5ShEAUoob8MrfF3C5UgRAnWy/cmYfeDpyr3qxLIvvjuXjQ01R09n9A/DhjD56A69L5c2Y9e0piGVKzBkQiA9mxBp8T1ukCkxefRzF9a2Y2TcAn86OM/rnAtQB+phPjqCqWWqRpPpHf0nCvktVeGBIMN6mnoy3HJozzctwUsk1pk+fboZhEGK8XecrIFey6O3vZPaAq7BWjL9TSgEAz3egvdDpvDr8nVoGhgE+nBlrVE2vP5NLsTW1DHweg6/mJegNuGQKFR7/LRkpxY1wthXi98WD9J5QvHYFZ1CoGz67Lx7+RqwgKVUs9l+qwi+nC3Eqr073dZ6mhMTQCA8MDnVDbICz0QVD9akXy3C+tBFnC+pxOr8O6SWNuFwpwuVKEb44mIO4QBfMGxiIqXH+elcBAfX4di4djh+PF+Dz/dk4dLkad646hi/mJmBYRPsrlwzD4PFR4XC3t8JLW85jc1IpGDD4YEYsZ+AV4+eENfMSsHh9EjadK0Evf2csGKy/gKmDtQCfzo7D7O9OY0tKKabG+2GUCfW77KwEePGOaDz3Zzq+PpKLeYOCTD7kYYoHhoRg36UqbE0pwyuTe5p9a5+QWwnV6SI3nXu/OYWkogajSyd0xot/pWNzUinG9PDE2ocGmvRYuVKFu744juyqFtw/OAjvTjfcEDu/pgV3rzmBVpnSYHK1SsXi2c1p2JZWDlshHxsfHYx4PbliDWIZnvw9Bafz68AwwNKxkXh6XKTB/DSZQoXNSSX47lgeSurVq08MAwwNd8e0eH+M7+kNNws1GD98uRq7L1TgaHYNlCr1ny5nWyHmDAzEouGh8HI0nIeWVSnC05tScblSBB6jPhFq6LDBzvRyPL0pFSoWmD8oCO9O7613Bevbo3n48J/LEPIZ/PW4cTl8b+3MwNqThQh0s8W+5aMMBpJXUqlY3Ln6GLKrWjrVWNvY1xrx0WGUNbZZ5BALsSyaM82rQxXuGhsb8eOPP+Lll19Gfb26jk9KSgrKysq6dHCEXKu8sQ1JRQ1gGODuPvqTxLvitf5OUd/THWlS/PuZImRXtcDVTmjUKplCqcIzm9PRKlNiaLg7Hh+lf5to9cEcbEsrh4DH4Jv7++oNuMoa2zDzm1M4nV8Heys+fnygP56dEKU34GJZFttSyzDmkyP437aLKKlvg6udEE+ODseJl8bi98WDMbt/oEUCLkDdJ3JmvwD8vHAAEl8Zh1cmRyPIzQ5NbXJ8dzQfI1Yexru7LqGxVab3eXr4OGLbU8NwX/9AqFjgk33ZWLYpVZfg354pcX74bHY8GAb4PbEYqw/m6H2Nx0aG4Y5e3pArWSzZmNJuW6NrPTexB/ycbVBS34avDucavP5KPB6DZzTtqH4+UYCmVrlJjzf1tWb2VQdaW1Ppbz4hpjA56Dp//jyioqKwcuVKfPLJJ2hsbAQAbN26FS+//HJXj4+Qq/yrKYXQP9jV7AU6150qhELFYnCYG/oGuZr02GaJXNeu57mJPeBiZzgw+fFEAdJLGuFoo95u0hcQ/XuxQjfxvz8jFqP1HN8vqBVj1jenkF8rhr+LLf5+chjG9dRfBuFiWRPu/fY0lv+RhrLGNng6WuONKTE4tWIcXrwz2qjtSHPycLDGoyPDceT50fjhgf6ID3SBVKHCjycKMPKjw/jxeD7keppu2wj5WHlvH6ycGQshn8Gu8xVY8FMiGsTcAdv0BH+8o8lhWnUgB38ll3JeyzAMPp4VB38XW5TUt+HNHRkGfyYHawHe0BwK+f54PorrWg0+5kp39PJBD29HtEgV+OV0oUmPNdX0BHXQdSKnFvV63jNCyNVMDrqeffZZLFy4EDk5ObCx+W/SmzRpEo4dO9algyPkWns0daTu7G3eo/EiiRwbEtV5T4+ONH0L85sjeagXyxDh5YA5AwINXp9X04LPNE2sX787Rm9trJwqEZ7dnA4AeHhYKGb3537+vJoWzPr2NMqbJAjztMefjw9BDx/uE2cyhQqf7svCtK9OIrmoAbZCPp6fGIVjL4zBQ8NCTdrysgQej8GEGG9sfXIo1j00ANE+jmiWKPDu7kzc/cUJpJU06n38fQOCsP6hgXC0FuBcYQPu+/70VdXtr3X/4GBdovrLf59HUmE957VONkJ8fl88eAzwV3Ip9mVUGvx5JsZ4Y3iEB2QKFT74J9Pg9Vfi8Rg8OUY9tp9PFqCtnUbkXSXM0wGx/s5QqFjsPl9uttch5FZjciL9uXPn8N133133dX9/f1RWGv6jQkhHVYskSC5WlzeYHOtj1tfaklyKFqkC4Z72GB1lWhHI2hYp1mmqwb90Z7TBPnUsy+L17RchU6gwMsoT9/bjbrEikSuxZIO62fKwCHe8Mjma89rShlbc/2Mialuk6OnrhF8XDdTbWLuwVowlG1NwsUx9GvGuWF/87+6eHS6O2iJVIKuyGfk1YpQ1tqGqWQqRRA6xVAEVq84Ls7Piw8lGCA8HawS42iLIzQ49fBwN1tK6FsMwGN3DCyMiPbEluRQf/nsZWVUizPj6JB4fFY5nJkRxlm8YGuGBv54Yigd+TkR2VQvmfn8GGx4ZzHmy8YWJPVBc14rdFyrw1IYU7Fo6gvPagaFueGRkGL47mo/Xt2dgSLi73kMGDMPgtbtjcOfqY/jnYiXSSxpN6u95V6wvPtmXhZL6NmxPK8OcgaYX8TXW1Dg/XChrwj8XK7FgSIjZXoeQW4nJQZeNjQ2am68/Ip6VlQVPT+NP3BBiqoOZ1WBZIC7A2axV0lmWxS9nigAADw4NMbndyXdH89AmVyIuwBnjexoO2HZfqMDJ3DpYCXh4Z1ovvQna7+3ORFaVCB4O1lh1XwJnQFfXIsWCn86iokmCcE97/LZooN5AZm9GJZ7bnI4WqQIudkK8O723yTlzLVIFjmbV4ERuLRLz65BfKzbp8VfycbJBvxBXDAv3wOgenkbX5+LzGMweEIjxMd54Z9clbE0tw9dH8nAytxZfzuvL2ZS6h48jNj06BHO/P4Oc6hbM++EM/nx8SLvbwjweg4/u7YOsKhFyq1uwbGMqfls8iHM7+JnxUfj3YiWK6lrxyd4svGWgzEIPH0fcE++Pv1PL8Mm+LPy6yPgipAI+Dw8MDsF7ezKx7lShSWVATHVHLx+8tycTiQX1aBDL4Gqh3D5CbmYmB13Tpk3D22+/jc2bNwNQfzIrLi7GihUrMHPmzC4fICFaBzOrAcBgW5bOOltQj/waMeyt+CY39m0Qy3TlGJZPiDI44UnkSnywR10H6snR4Xr79h3LrsGvmmDws9lxnKsr2jISBZocrt8WD+IMuFiWxbdH87HyX/UYBoS4Ys3cvkbny8mVKhy4VIUtKWU4llOjq/6u5eNkg0hvB/i72MLbyQbOtkI42AjAYxiwLItWmRJNbXLUiKQobWhFfq0YRXWtqGyWYPf5Cuw+r95Ojgt0wZQ+vrgnwd+oVTA3eyt8fl88JsZ4Y8XfF5Be2oSpX57At/f346z6Huphj02PDsYcTeD16C/J+GXRwHZLIthbC/Dt/X0x7cuTOJ1fhx+O53MefLAR8vH+PbGY/2Mifj1ThDkDgwyWOlk+Pgo70stxPKcWqcUNSDAhp3B2/0B8uj8LlytFSC1pNDkf0VhB7naI9nHE5UoRjuXU0ClGQoxgctD1ySefYPLkyfDy8kJbWxtGjRqFyspKDBkyBO+99545xkgIpAolTuXVAoDepPGusDlJnSB9dx8/OBjRH/FK604Vok2uRIyvE0YbUWtp/alClDW2wcfJBo+N5D6tKJLIsWLLeQDAwqEhGMnx3CzL4rVtF3GusAGO1gKsf3gA56qgUsXizR0ZukBu4dAQvHpXT4NV1AGgqVWOn08WYMPZYtSI/suBCvOwx+geXhga7o6+wa4dOtnYIlXgYlkTzuTX4UROLZKLG5Be0oj0kkas/PcyJsb44NGRYUZtu02K9UWfQBc8/msyLpQ1Yf6PiXj/nljM5sizC/Gwx/qHB+Leb07hbGE9XvjrPL6YE99u8Bzh5YjXp8TgpS0X8Nm+bIyK8uQMpoZFeGByrA/2XKjEu7sv4bdFg/QG5EHudpie4I+/kkvx9ZE8/PBAf4M/q5aznRCTe/vi79QybDpbbLagC1D/W7xcKcLRLAq6CDGGyUGXk5MTTpw4gUOHDiElJQUqlQp9+/bF+PHjzTE+QgAAyYUNaJUp4eFgjV4mtqkxhViq0CXrzx5g2iqXRK7UnRp7YnS4wVWupja5rjTAcxOj9Capf74/B+VNEgS52eHFO7nLT/xxrgR/JJWAxwBfzEvgbNOiVLF44c90XeHW1+6KwcPDQw38hOrq598fy8dPxwsg0pRB8HCwxqz+AZgW74ce3o6d3s5ysBZgcJg7Boe5Y/n4KFSLJNh7sRJ/JZcivbQJuy9UYPeFCoyM8sQLE3sgNoC7GCwA+LvYYvNjQ/D8X+nYfb4CL245j2aJnLPGWw8fR3y7oB8e/PksdqaXo7efEx7jWMWa3T8Q+y9V4UBmNV7ach5bnxzGuc348qSeOHCpGidz63RNqvV5fFQ4tqSUYv+lKuTXtCDMhAr8cwYG4e/UMuw6X4E3p/aCnZXJf+qNMjLKA98ezcOxnFqwLGvWhtuE3Ao6VKcLAMaOHYvnn38eL774Ivr3N/5TGLk5NLXKkFfdgtTiBuTVtKDJQO0jc9NWQB8e4W7WP+z/XqxEm1yp6/lnih1p5WholcPfxRaTehtO9P/5RAGaJQpEejno3ca8XNmM9Zpg7p3pvTkn0OwqEd7QlCZ4bmIPjOFYEVSpWLz893n8ral6v2ZugsGAi2VZ7Ewvx7hPj2LVgRyIpAr08HbEmrkJOLViLF66MxrRPk5m+d14OdpgwZAQbF8yHHuWjcCMvv7g8xgcy67B1K9O4LnN6ahq1t/v0daKjy/nJui2AN/dnYmvj3DXwhoW4YG3pqnLN3y0NwtnC9o/pcgwDN6/JxaO1gKcL23C74lFnM8Z6GaH+zXV6T/bnw1DdakjvBwwVvM7/OU09/O2Z0CIKwLdbNEqU+KAZlveHPoFu8JawENtixS51S1mex1CbhUmB10rV67EH3/8ofvv2bNnw93dHf7+/khPT+/SwZHuUd7YhiUbUzHus6O45+tTGPfpUSzdmIrydnrhWcpJzdbiUI6WLV1lW5q62OOMBH+TAgiWZXWB0QNDgg2eWGyWyPHziQIAwDN6ipSyrHoLUKliMam3D2d7GLlSheWb0iDVnIB8Qk9h1ff3ZGJzUil4DLB6TrzBhPkGsQyP/ZqMpRtTUdEkgb+LLdbMTcA/T4/AlDg/o1obdZUYPyd8Njseh54bhWnxfmBZYEtKKcZ/dhTbUsv0BjIMw+ClO3tg+Xh1oduP/s3CupMFnNfPGxiE6fF+UKpYLN2Ywll01cvJBi9oVh8/3pult9bX46PDYCPkIa2kEUezawz+vA8ODQGgLjnRKjNcYFWLYRhMi1Nv9+1IM19JB2sBHwNC3AAAJ3NrzfY6hNwqTP5r+d133yEwUJ0PsX//fuzfvx///PMPJk2ahBdeeKHLB0gsq6lVhpe2nMfxnKv/gB7LqcWKLee7ZcVLJJHjfGkTAHXrGXNpEMt0K2pT4kw7uXexrBkZ5c2w4vP01s3S2pBYDJFUvcp1Zy/uVbEjWTU4k18PKwEPr97Vk/O6rw/n4VJFM1zthPhkFndT5g2JxfhRE+x9MivOYMB1Jr8Od64+hn2XqiDkM1g+PhIHnxuFKXF+Jp/q7ErB7vZYPScB254ahrgAZ4gkCiz/Iw1LNqZCJOGuxs4wDJaPj9JVb39r1yXs5aifxTAM3p8RizAPe1Q1S/H2zkuczzt/UDCifRwhkij0VpP3crTB/EHq1a7vj+Ub/DlHRHog2N0OLVIF9lwwrSTP5Fh1LbvjOTVmrdk1OEwddJ3VU7OMEKJmctBVUVGhC7p27dqF2bNnY+LEiXjxxRdx7ty5Lh8gsazaFtl1AZfWsZxa1LZYPug6V1gPpYpFsLsdAlzbP/LfEdduoe5IL4NSxSLG1wkhHtynCNuz6Zz6xOIdvX0MHp2XK1VYq1lheWRkGGfwolKxulOFDw0N4fzZc6tF+PKwujr9m1N7cfYfTMyvw+vbLwIAnpsQZfBk5m9nijD/x0RUNUsR7mmPrU8Ow/LxUTdUg+P4QBdseWIonp0QBQGPwe7zFZj65Unk1+jf6lo2LgJzBwaBZYFlG1Nxsayp3evsrAT4ZHYceAzwd2oZDme1v1XH5zF4ebI6KP7ldBFKG7iryT80LAR8HoNTeXWcr6vFMIwuiN98rkTvtdfq6esIfxdbSBUqHM8xvKrWUdqVrnOFDQa3TAm53ZkcdLm6uqKkRP2P/99//9Ul0LMsC6XSfJ+miGU061klAKB3FcFczhaoC6IOCnXrsudsbwv1i4PqFYo79Kw8tUemUGGXprTBfUascv17sRJVzVJ4OlpjWjz3StO+S5W4XCmCo7VAVwX9WizL4q2dlyBXshgX7YWpHCt0dS1SLN2YCoWKxdQ4PywZy91Im2VZfLz3Mv637SKUKhbT4/2wa+kI9PbXn7Cuj1LForShFekljTiSVY3Dl9X/SyqsR2GtWG/fQ0MEfB6WjYvEX08MhZ+zDQpqxbjn61NILuJeeWEYBu9M64XRPTwhVajw1IYUznu7b5ArHh6mznl7a0cGpIr2xzoy0gNDwtwhU6rw3VHuVawAVzvdKtRvZwznas3o6w+GUa8kVTQZv8XPMIyuvMoRI7YyOyou0AUCHoMakRRl3ZiCQMjNwOQjLTNmzMC8efMQGRmJuro6TJo0CQCQlpaGiAjuP+Tk5uCkp1o2AL3VtM1F22pF+4m6s7i2UOs0uTgDQ0xLoD+SVY2mNjm8nawxxIjtz181SdFzBwbBWtD+qhHLsvhSs021cFgIZ+/GA5nVOJ5TCys+D69PiWk3D41lWbz413lUi6SI9HLAhzNjOfPVWJbFO7sy8bNmJe7ZCVFYOjbC5AT5VpkCp3LrcCS7GmkljcipaoFUwd0LkccAIe726OnnhJGRHhjdwwveTqb11owPdMH2JcPx6K9JSC1uxP0/nsUPD/TH8Mj28wAFfB5W35eAyV8cR1FdK17++wLWzE1o92ddPiEK29PLUVjXip9PFLYbBDMMg2XjInE6vw5/JJVg6bgIzlXH+YOCsDO9HDvSy/HqXT31/rvydbZF/2BXnCtswJ4LlVhkxClTrVE9PLHuVCGOZtWY7XShjZCPHj6OyChvxoXSpi5djSbkVmPyStfnn3+OJUuWICYmBvv374eDg/oYc0VFBZ588skuHyCxLA8HK4zkmKRGRnrAw8GyVaflShXOa7Zg+gV3Tb0hfVuoAODBUXSUi3aVa0ofP71NqgF1L8SzhfXg8xjM09Oi5XR+HS6WNcNWyMdDw9qfZJVXbD8uHhHKWVh1a2oZDl6uhhWfhy/mJugtH/DZ/mxdwPXu9N5YNi7S6ImaZVmcLajHc5vT0e+dA1j8SxJ+O1OMi2XNkCpUEPIZ+DrboKevE2L9ndHLzwlBbnaws+JDxQL5tWLsPl+Bl7ZcwKD3D+K+707j75RSk1bBPB2tsWHxYIyK8kSbXInFv5zT2x/R2U6INfMSIOCpm15z5U05WAuw4k51y6VvjuSiqa39VbHBYW5ICHKBTKHS9e5sz6BQN4R52qNVpsQ/Fw3namlXxrjyz7gMDnWHlYCHssY2FHSiQ4AhfTRlOy4Y2C4l5HZn8kqXUCjE888/f93Xly9f3hXjId3M2c4KH87sgxVbzuPYFYHJyEgPrJzZB84cKy7mklUpgkyhgpONAKEm5llxMbSFKpYaf0pMplDh8GV1ns+kWMNNuP9OURdeHRnpobfq+1pN78aZ/fw5C4zuSC9DbnULnG2FeJxj+7GuRYq3d6kTwJ8eH6m3EvrGs8VYc0i9uvbO9N668gaGsCyLI1k1WH0w56oG0wGuthjTwwvDItwR7eOEQDe7doNSlmVR0yJFVqUIyUUNOJJVg/TSRiQW1COxoB7v7c7E4hFheHBosFH1pmyt+Pjhgf547NckHM6qweJfkvDX40MR4dV+nau+Qa54cnQ4vjiUizd2ZGB4pAecba9feZqe4I9vj+Yhp7oFa08WYLkmGf9KDMPgoWGhSC1OxYbEYjw1JqLdYrMMw+CeeH98uj8bO9PLDR6+GN/TG2/tvITkogY0tcnbHR/XexEf6IKzBfU4W1BvUq0vU2jvq6xKkVmen5BbRYfOeufl5WHp0qUYP348JkyYgGXLliE/3/BJHHJz8NOUBDj47Chse3IoDj47CmvmJsDXyP53XSm9tBGAOm+kq7ZGunILNbGgDiKpAp6O1kgwUCGdZVlsS1Uf35+pp6l1eWMbDmRWAVBXiW+PSsXiS02A9OjIMM6f6ZN92WhslaOnrxMeHdl+MVAASC5qwGvb1En2T4+LxAIjA67yxjY8vO4cHlp3DmkljbAR8nBf/0BseWIojr84Bu9M7407e/sixMOecxWQYRh4OdpgRKQnlo+PwranhuHkS2Px3IQo+LvYok4sw8p/L2PsJ0dxUPO+GGIl4OHr+f2QEOSCxlY5Hv0lSW8+4lNjIxDmaY/aFilWH8hp9xo+j8HTmnITP58o4CzhcGcvH3g4WKNaJNW1rmrPVE0+38ncWtS1SDmvA9Q1viK9HKBUsSYnxWtzIc15urCHt7oI72UKugjRy+Sga+/evYiJicHZs2fRp08f9O7dG4mJibrtRnJrcLazQriXA+KDXBHu5WDxFS6tS+Xq5uq9/P5L4u5s4VZ9W6iDQl1N2kI9mqWeAMf08DRYQuFCWRPKGttgK+RjXDR3/8gtyaVgWfVWFVdF+aPZNcirEcPRWoAHhrQfIOVWi7A5SX3o5e1pvTjb+zSIZVi6IQUKFYu7Yn11daz0YVkWm5NKMPHzYzicVQMrPg+PjgzD8RfHYuW9fdAv2LVTQbKfiy2WjovEkRdG45NZcQhwtUVlswSL1idh+aZUzu29K9la8fHjA/3h62yD/FoxXv77AufpOmsBH29MURdD/e1MEUrq2z99OLm3L4Ld7dAsUWBralm711gJeJjRV10ja3ta+9cA6rIXMb5OULHA4SzDgdSISHWNNm1ZE2Npi/ymX7EK2dW0q4hljW1mLU9ByM3O5KBrxYoVeOaZZ5CYmIjPPvsMn3/+ORITE7F8+XK89NJL5hgjuY1dqlAHXTGa1j9dUbhVu4V6beBlI+Bh1X0JJgWY2gKXhlq6AOpTiwAwJtqTs+UPy7LYotmCnNWPe8tJm3c1Z2Ag58rcp/uyoVSxmBDjrfcQwus7MlDeJEGoh73eJHstpYrFGzsy8OJf59EiVSAhyAV7nh6OVyb35GzC3VFCPg/39gvA/mdG4dGRYeAxwLa0ctzz1UkU13GXZdByd7DGV/P76nK2dqRzFwodGemBYRHq04erOFa7eDwGDw4JAaDum8kVxGlPpR68XK13hW285nShMSt42hp1p00MurT5Vnk1YoNb6x3lZm8FFzv1fWjO3DFCbnYmB12ZmZlYtGjRdV9/+OGHcekSd/FAQkzFsixyqtT1lqJ9HLu0cOuVW6hzNc2Px/b0MmkLtUYkRU51CxgGGBZuuFL+IU3ul76SFBnlzSisa4WNkIc7OVoJldS34nhOLRgGeEATAFwrt1qkS9B+4Q7uXo3Hc2qwM71c3atxToLBrVWpQoknfkvGL6eLwDDq51bnS7W/ItdVbK34eGVyT2zRlIXIrxXjnq9PGqxzBahXepaNU6/evbMrk3OVjGEYvHCHOll+e1oZKpvaby10b/8AWAt4yK5qwcWy5navifF1QpiHPWQKFY5lcx/aGN1DHayfzq+DSqW/xpU2cC6oFeuten8tdwdr+GryB7PNtP3HMIzuIEcxxyohIaQDQZenpyfS0tKu+3paWhq8vNrv9UZIR5Q2tKFFqoCQzyDUw77LC7dqt1CrRep8GlNLUiQWqFccon2cDBZErWhqw+VKERgGGBnJvSr2z0X1SchRUZ6wt24/afzPZPVK2LBwDwS6tX88X1vtfGKMN6K82w+IZAqVLo/rwaEhBhtHK1Usnvo9FfsuVcFKwMNX8/riqTERBk9sdqWEIFdsfWoYYnydUCeWYf6PiUYlbz82KkyXs/XZvizO6+IDXTAw1A0K1X9tna7lZCPU1b/6O7W03WsYhtGtYh3Qs4oV6+8Meys+GlvlulVdLs52QoRpDpOkaXIdjdXDx/w5V0Gae7G4nla6COFictD1yCOP4NFHH8XKlStx/PhxnDhxAh9++CEee+wxPProo+YYI7lNZVepJ4hwTwcI+TyzFW7VTnaxJhb/TC5SF201pq7XqVx1gNYnwEVvgHbosnq7clLv9k9CsiyLXZotsns5kvGb2uTYrum3py95/o9zxSisa4WnozWenXD9Sbxrvbc7Ewcyq2At4GHdwgG6MgaW5u1kgz8eG4y+QS5oapNj0fpzBhPRrQV8vDOtNwDg98RivUU8Hx4WAkDd71ChbL+22LR4dc7Wvowqzi1GbcPxE7m1nNcI+Tz00wT7KcUNen8G4L+twgwTSzNEanKu8gxU6u+MIDf1KjGtdBHCzeSg67XXXsPrr7+ONWvWYNSoURg5ciS+/PJLvPnmm3j11VfNMUZym8qtVk8Q2iRdcxRubWyVoUKzjaRdDTCWNjE5Ichw0HW2QH1yTNunrj1VzRJkVjSrV8M4csSyq1qQXyuGFZ+HcT3bX1nekV4OqUKFKG8HztpmUoUSXx/JAwAsHRth8L37M6lEl0f2+X3xZm88boijjRA/PTgAwe52KG1ow5O/p0BpYHtuWIQHBoepV7F+0NP3cGy0N1zthKgRSXGSI39qeIQHrDX1r7Kr2g9kEoJcYCXgoUYkRb6ePKd4zanX9BLDgVS0pjSDqStW2rZWhWbMt/J3Ua90VTS2vy1LCOlA0MUwDJ555hmUlpaiqakJTU1NKC0txdNPP22Wasfk9pVfo54gwjW1hcxRuDVHE9j5u9iaFLQpVSwyNCcrDW3LAUCSpiXNQD1bmKfy1Funsf7OnLW5tFtVwyM9OMe7TXOqbnb/QM5/k3suVKCiSQJvJ2uDNaKqmiV4S9Psefn4yG5b4bqWq70VfnqwP+yt+EgsqMfviYZb6iwZo87t2pxUghaOemxWAp6u4fkujsR7Wyu+LrH9GEeLHRshXxdQJRdyr2L10aywZpQbDrqivNX/FrQfSIwVqsm3KjLi8EFH+bqo88bKOXLhCCEdrNOl5ejoCEdH8ybQkttXYZ066NIWReU6ddiZwq3axshhnqYVXi2qE0OqUMFGyEMIRyV4rRapQrfS0SfAhfO6pELtdiV3YHZCk9OmTcC+VnWzRLdNdVcf7uDo9zPqaunzBwUbbGD9zq5LaJEqEBfogqVjDZeTsKQIL0e8NEmd/P7x3izUGthmHBbhjjAPdSX4PZpOAu2ZGKM+xHAku4YzwX1wmDroOqen/lVcgOGASrvCml8r5tzO1Aq5IlndlObS2tY8ZY1tZmtK7aU5uVoj0v87IOR2ZnLQVVVVhQULFsDPzw8CgQB8Pv+q/xHSVbS5IUHu/yWLd3Xh1mtX04ylzTeL9HI0mEh+qbwZLAv4ONnoLamQUtwIAOjPkSMmkSt1eWTDOLb3Dl6uBsuqJ3tf5/bfk/yaFiQVNYDPY3DfAP2rXEmF9dh1vgI8Bnhvem+LJs0ba/6gYPTyc4JIosAXB9sv9aDFMAxmaVb2/kppPwkeAAaGusHeio8akRSZle0nuPfXBMfJRQ2cgUxv3SoWd5K8v4stbIQ8yBQqlDToL30S4GoHHgO0ypSoMRBgXsnH2QYMA0gVKtSbcPLRFNp7u04sNbjVS8jtyuQ2QAsXLkRxcTFee+01+Pr60pYiMQu5UoWqZvU2RYDr1cGDs51VlxVrLWnQBHYcpwC5FNSqHxduxAqZditIX86YVKFEjiaQi+VYDcusaIZMqYK7vZXuFNu1tDWcRvfgPkm8N0O9RTk03N1gU+lvNHlfs/sH6gKIGw2fx+DVyT0x78dEbE4qwbMTojgbhAPA3X18sfLfy+qWOq1yONtdv01rJeChb7ArjufUIrW48arivFq9/JzAY9SN0mtapO02t9YG8/pyung8BkFudsiuakFJfavedldWAp6u2n11c/uvyfU4Vzsr1ItlqG2Rwd2ha+upAYCr5j1nWaC5TW7wRC8htyOTg64TJ07g+PHjiI+PN8NwCFGrapZAxQJCPgMP+66fIABtZXv1ZCjkM2hqlRkdzP23Cmc46NKeGOPq/QcAedViKFQsnGwE8OPoyahN3NfXEklbxmKQnoT9/ZfU9bv01QsD1FuoBzW1xfSdgrwRDAl3R4yvEy5VNOOv5FIsHsE93kA3O0R4OSC3ugUn82o5c9TiA11wPKcWaSWN7fahtBHyEeJuj/xaMbIqRe0GQNoE9nqxTG/PxABXddBVamClC1Cf3qwWSVHZJDEpEHa31wZdUvRA16eFCPk8OFoLIJIq0NAqo6CLkHaYvL0YGBhotpwAQrSqmtVbJ16ONgbb63SEtrJ9lmZ16bXtGSZVttdeF2DEtqY2QAtx515N01bxjvBy4AyosjSn5GI4mlbXiKSoapaCYYCEwPa3KNtkSpwvVecXceWFaWmLqw6P8DBbo+SuwjD/bZXuyzBc3V17ijRdT70r7fucoydpXbsqxVUmwcFaAFfNSlpFE/e9pV1xNCYfyl1zYKTexPZX2pUoY1oodZSjjfpzvEhifNN4Qm4nJgddq1atwooVK1BYWGiG4RCipp18urqtDIAuqWyv3fr05liVulKZZvXC35U7QNNO2sF6Vs60Sf/hXu1fc1mTexTibs/ZZuhieRMUKhZejtbwNxAw7stQB11clfFvNGOj1VuqycXqbUN9tNuFl/TkWhlTZsFP8x7qK5OgXQHTF1C52asDs3qx4aBLu1pm6Ge8loMuIDJf0KUt6CvmOBlKyO3OqKDL1dUVbm5ucHNzw5w5c3DkyBGEh4fD0dFR93Xt/0xx7NgxTJkyBX5+fmAYBtu2bbvq+yzL4s0334Sfnx9sbW0xevRoZGRkmPQa5OZUp5l8OlIGwpCuqGyvvcaY8VWL1BOyjxN3kKNdOdMXCJUYCMy0hwL0bWNmagrB9glw1puP2SZTIk2znakNZm50gW52CHG3g1LF6l3BAqCr0p+nZxVLm+fX1CbnLC/h7aT+UKD9HbdHW/5DXwK7i63xq1COHQye7DSBuFhqvobUdtqgi5peE9Iuo3K6Vq1aZZYXF4vFiIuLw0MPPYSZM2de9/2PPvoIn332GdatW4eoqCi8++67mDBhArKysqhUxS2uUfMp3rWLEuav1NnK9izLoqlNPYEaGp9KxaJB87O46wnQDAWZLMvqTqtxJb+XNxkO3LR1mgyVubhc2QwVC3g4WOtWc24G0T5OKKxrRW51i94m5NpehDUtUqhUbLtb2HZWfFgJ1KcKG8QyOLTTlklbK03fdpp29adVTyBiowmI2uSGgxUbgfpaqYHyEteyEqg/Y8tNfJwprDWvIVOY7zUIuZkZFXQ9+OCDZnnxSZMmYdKkSe1+j2VZrFq1Cq+++ipmzJgBAFi/fj28vb2xYcMGPPbYY2YZE7Gsplb1aapmiRxOtkJ42KtPJmo/8bu0c7LMmMfr09nK9m1yJeRKdV6jE0ditJZIqtAdn+dKogaAOs3KmRvHqbKmNrnuNT05rqnW5MH56Nny1G51Xnsi9FraRuM9fW+uDzfaemvaGm9ctNvWciWLJo6TdgzDwNlWXZm+qU2O9opraAMxrpUwALqtXr1BlyZYkcgNByva4ElqxLVXPY5vuaBLqqCVLkLaY/LpxT179oDP5+OOO+646uv79u2DUqnkDKJMVVBQgMrKSkycOFH3NWtra4waNQqnTp3iDLqkUimk0v/yIpqb9TeRJd2nvLHtutyqkZEe+HBmH90k5mDNHajoe7y+1RltZftj7WwxGlPZ/sqJ0c5AYVGJZuWCx/w3IbVHu8Jhz5GLpd2usRLwdJPutbTvmXb7Sd817ZVJuJI2SZsrwLtRaQNmfQEOoD5px2MAFas/CBFqVsBUHIeHtHXL9J0tugFLm5kNX/d+dfNAiNFozrQskxPpV6xYAaXy+j9oKpUKK1as6JJBAUBlpTqJ19vb+6qve3t7677Xng8++ADOzs66/wUG6i/+SLqHoWT2Rs2kb8cRhHQmGV5b2T7W7+pTgMZWttd+ihfyGYMnK7VBl42QrzeH6srr2tOmCSJs9AVummu43jMAEMsUmmv0f97SbrEaWsm70VjrVowMr7RoAwSlnohJ+zvrTBBhzGFv7SXGlD005dr2xmHO2oo87ftFUddNg+ZMyzI56MrJyUFMTMx1X4+OjkZubm6XDOpK1/6BYFlW7x+Nl19+WdcTsqmpCSUlJV0+JtJ5hpLZRW3q4MCGI4DobDK8n4stnhgdDkC9JWVKZXuVCZOXdqLjGbj2vwmR8wr18+gJ8oyZS7WXGAoEhBbYijIH7UqevYGgUq5U6bZrbfWsVmpXILmuaTMQLANXBtTcf26lmhwobb6WPtptRWsjrr2STPO7FPLNF3RpVwSpZvbNg+ZMyzJ5e9HZ2Rn5+fkICQm56uu5ubmwtzetf50+Pj7qY+qVlZXw9f2veGF1dfV1q19Xsra2hrX1zbUlcjsylMyuncysOCaIzibDA/+dtLKz4iNcz4m/a+lGZMSHed0nfwNRjqFtKgFPPWErldzPowuUFNzXaIMDQzk32m265pus3pK296KhUiPanEGG4c7hY1n2ihW/9v9UtkiM39JtLxFfq1VzjZ214UBK+29D34pme7S/c0O9NjtDm794I7aLIu2jOdOyTF7pmjp1KpYvX468vDzd13Jzc/Hcc89h6tSpXTaw0NBQ+Pj4YP/+/bqvyWQyHD16FEOHDu2y1yHdw1Ayu/aTMp/X/i3a2WR49XOrX0ShJ5Bpjy64UakMFgoWCtSvIVPov1a7LdbGkYuknShb5UrO59FOwiI9Sd3aZH5D/fe0pRC4in7eqLQHAAwdFNCW6PBwsOYMEBpb/zu8wHVKtVZz6lTfgQ/t6VV9W7XaINDQfQ3894FCXxDXnhap/lW7rqBdGRXwTZ5aCLktmPwv4+OPP4a9vT2io6MRGhqK0NBQ9OzZE+7u7vjkk09Meq6WlhakpaUhLS0NgDp5Pi0tDcXFxWAYBsuXL8f777+PrVu34uLFi1i4cCHs7Owwb948U4dNbjDaZPb2jIz00J204vq8bOjxxtTP0r6GzMQtNO1pNJb9b1uIi3ZiVKhYvddqJ2SRtP0VOu2krlSxnEGVhybpvVZPI2RtOYkyA+1mtNXYL1c0Q3GTbDFeWZ8rIaj9ivxa2n6Y+npnagNOL0drztUhbVFUP47m4gBQo6nh5a2nT6L2d2bMfdugyVfUV4KkPc2awE7fKdrO+m+blIIuQtrToe3FU6dOYf/+/UhPT4etrS369OmDkSNHmvziSUlJGDNmjO6/n332WQDqEhXr1q3Diy++iLa2Njz55JNoaGjAoEGDsG/fPqrRdQvQJrOv2HL+qlOE2mT2FX9fAMC9LWfo8cb0UNROpBITCznaCflgGHXQJZIo9G7X2FsJdKfkmtvknNc66Vag2g+6bIR82FvxIZYpUSuStrsioq3fVaGnlVGQphWRvgbMgLqOl6ONACKJAufLmtDXQBBzI0gpbkCrTAlHG4HeArHAf5Xo9V2XX6sOzIL1tG/SNkznOi0rkStRp1lV1FfKQ9v2ypgODLUi42rEXUt7OMWcQZfuwIcZV9MIuZmZHHQB6gTiiRMnXlXOoSNGjx6td8uFYRi8+eabePPNNzv1OuTG5OdiizVzE1DbIoNIIoejjRAeDuo6W9otPIWeU1D6Hm8M3eqSiXlLPB4DF1shGlrlaGiV6Z0oeTwG7g7WqBFJUdMihRdHYVMfzde17YXaE+Bqh6wqEYrrW9vthaitUZVbw11lXdsg+Xxpo95DKTwegzE9vLAjvRx7L1beFEHXzvRyAMDEGB+DOUXnCusBAP2DubtoXChVB2balkHXYllWt50Z6d1+8FZU1wqWBZxs/uvB2B5t8Bboyh3gaWmL4Poa0YLqSto2RFz3YFfQ5a/pyXEj5HZm1Brwpk2bjH7CkpISnDx5ssMDIrcXZzsrhHs5ID7IFeFeDrqAydjK1lyPN4aTtp2KVGHyFpq2tYu+rTwtba0rfQGVdgLVt+2nXaXSVpW/VqRm1Sa3uoXz1GGMrxOEfAa1LTLO59HS9lzckV5+w59iFEsVuqDr7jhfvdfWi2W4UKZu+j0wlDvo0m5VagPVa5U2tKFFqoCQz3BW+M/TBMChHvacAa5CqUJpvfr3HuimP+gSSeS6DwnGnLTVapEqdLXezNHPVEs7NkcT880IuV0YFXR98803iI6OxsqVK5GZmXnd95uamrBnzx7MmzcP/fr1Q319fZcPlNxetHlT2rpS5sDgv8KV6ibJhnsuavlqcngqm7gDKa1AN/W1+oKcUE1z5Tw9q1Q9NP0CuZo0h7jbw8lGAIlcpeuxeC0bIV+3unMgs0rvuMdGe8HDwQoVTRLsPl+h99rutu5UIRpa5Qhxt8OIiPZz/bT+uVgBFQv08nPi3BYUSeS63pODOAKz5KIGAECMnzNnwdqLmuCup69Tu98HgKL6VsiUKtgIeQabkGvvIXd7K5MS6bXBvLOt0OQEfGMpVazuVHF7Ff4JIUYGXUePHsUnn3yCQ4cOoXfv3nByckJkZCRiY2MREBAAd3d3LFq0CCEhIbh48SKmTJli7nGTW5y9rjmveYKu8sY2PP1Hmq7m1n3fncHSjam6U22GGLMypaVtUK0v6Ir0UgdU+bVizlW3XppirtpVmmvxeAz6h6gDhMR87g8+E3upS67suaA/kLIR8vHQsFAAwOqDOUYVHO0ONSIpvjuqPk39zIQogyfntqeqV8SmxvlxXnMytw5KFYtQD3vO1SftFmU/PVuv2t9VL47VMgDIqhQBUDfhNlRsV5uLpw3SjaVtlm7oVGdnNLbKdCVPXG6yorqEWIrRR0zuvvtu7N27F9XV1fj111+xZMkSzJ8/H2+++SYSExNRVlaG999/H15eXuYcL7lNaJN9tUfpu1JnqtlraZOrCwz0+AOACE3+VXaViPOaAFdbOFoLIFOokF3V/mqX9kTe5cpmzvdlmGaV5+Bl7lWsybG+4PMYpBQ36iZ8Lg8MCYanozUKasVYcyhH77Xd5Y0dF9EsUaCXnxPu7sMdSAFARnkTzhbWg89jMDWe+9rdmoB0TI/2/56xLIuj2TUAgMFh7a+EKZQqpGhWwxICXThf63ypOjCL0bMappVVafgAQHu0vSgNNTrvDG1Ddjd7KyoZQQgHk/9luLu7Y9q0aXj66aexYsUKLF68GP369QOPo54SIR2h3Z7Q1jjqSp2tZg9Al8ieV829Hail3VrKrGjmPDjC4zHoE6heDUktaWj3Gh9nG4R52EPFAmcL2l/JmhijXsU6W1DPWYvL28kG43uqg4nfzhTpHbujjRDvTOsNAPj2aD7SNVtuN4q/kkux50IlBDwGH93bx2AC/c8nCgEAk3r76LaIr9UqU+DAJXXQyhWY5dW0oLShDVZ8ni7QvdbF8maIZUo42wr1BlRpmt93QpCL3rEDQGaFOkiO8TMcoF09XnXQFaanREZnaU9gepkxZ4yQmx1FSuSG5K5JPteeuOpKXVHNXpu0nl3VoqvCzXmttwOEfAYNrXKU1HNvR2q3qfRtDWon+EMcK1mBbnbo7e8EFQtsTyvjfJ4Hh4QAADYnlehN8AfUCfV3xfpCqWKx+Jck3VZVdzuRU4uX/z4PAFgyNoLzlKFWbrUI2zTvyaLhoZzXbUstR5tciRB3O8QFtP+cey6o+78OCXeHPUeO1JGsagDqlTCubUOpQqnLHTN0QpRlWV3Q28vEoCtHs8oa3s6p166i3ZrXVxqDkNsdBV3khqTNmTIUEHREV1SzD/N0gK2Qjza5EgW1+le7bIR8xGpyepKKuAOq4ZGeAICTubWcDYPv6KU+Ubgvo4oz2JvdX92wdtPZEs6VtSHh7ugf7AqpQoXVBw1vG34wMxbRPo6oEUnxwM9nzRIMmyK9pBGP/5YMuZLFlDg/LBsbafAx7+3OhFLFYnxPb87iqSzL4pfThQCA+wcHt3vikGVZXfCmLy/sYKY66BrXk7ttWUpRIyRyFTwdrQ1uGRbXt6JOLIMVn8d5orI9KhWrO1hh6gqZKbTBuDFlLwi5XVHQRW5IPrpCnxLOAKSjuqKaPZ/H6FYbUosbDV4/QJPgfia/jvOahCAXOFgLUCeW6coVXGtQmBtc7ISoE8twMrf9LdJp8f6wEfKQVSXC6bz2X49hGLxwRw8AwKazxbrVFi5ONkKsf3gg/F1sUVArxr3fntKtnljavxcrcN/3p9EiVWBImDs+mdXHYAL67vMVOJxVAwGPwSuTozmvO5JVg8uVItgK+ZjVL7Dda1KKG5BfI4a1gKc7lHCtkvpWXChrAsOoT4Fy0eaFDQ13N9hAPVGzpRwb4GxSs+vCOjHEMiWsBDyEmZiAbwptBX/taV1CyPUo6CI3JF9nGwh4DGRKFSq7eLVLW83+2sBrQIir0dXsAehOCmpPsekzXPNaR7NrOFefhHwexmgm6H8uVnJeo11d+eNcSbvXONsKdQHDl4dzOcc0KMwd0+P9oGKBF/9KN1gTzdvJBr8tHgR/F1sU1bXinq9P6XKfLEGpYrH6QA4e/y0FErkKI6M88f0D/QwGIHUtUry2/SIA4InR4e0WlgXUK1if7MsCoD5A4MxRzHT9KXUe3LR4P85V0W2p6pWwoeHuuvZM7dl3Sf17Hq9nNUzrhCYPcWi4u8Frr6T9UBDr72zWBHdLJOsTcrOjoIvckAR8nu6ofqGBljUdoa1mf/DZUbr+e7P6BZhUcFJbv+mMnhwsrQEhbrAV8lHVLMUljhpaADBZU5B09/kKzhW++waoA6p9lyo5t18fHx0OIZ/Bqbw6nOJYEQOA16f0gru9FbKrWvDx3ssGf45QD3vsWDIMA0Pd0CJVYPEvSXjmjzRUi7p+G/hKF8uaMP2rk/j8QDYAYOHQEPz8YH+DW8EKpQrL/0hDvViGHt6OWDI2gvPaHenlyChvhr0VH4+NCm/3mvLGNvxzUX2y8QFNXty1VCoWWzVB1z0JAZyvl10lQn6NGEI+g9E9PPX+HEoVixOa3+NwA3XIrpVSrE7U72tEon5HsSyLwlr1Spep5SwIuZ2YFHS1tbXhxIkTuHTp0nXfk0gk+OWXX7psYIRok35zjDgh2BHaavba5PRMA+UTrjUg1A1CPoPi+lYUGAgMbYR8jIxSv46++lhjor3gaCNAWWMbTnFsDfbyc0b/YFfIlSzWnixs9xp/F1vMHRgEAHh71yXO/C83eyu8d08sAOCH4wXYmlqq9+cA1Iccfls0CA8NCwHDAFtTyzDuk6NYfSDH4CEFUxXWirFsYyruXnMCF8qa4GQjwKez4vDm1F5Grdq8v+cyjufUwlbIx6o58ZyrYmKpAu/vURd+fmxUuK7jwLW+PZoHuZLFkDB3zryqk3m1yK8Vw8FaoKvq3x7tQYdRUZ4Gg8e0kgbUi2VwtBGgb7BpLZm0W8wDQ01bITNFRZMELVIFBDxGV5eOEHI9o4Ou7Oxs9OzZEyNHjkRsbCxGjx6Nior/Jo+mpiY89NBDZhkkuT318FEHXZdNDIZMZco24ZUcrAW6NjKHLlcbvH5yrLo9ze7zFZxbjDZCPqbH+wMANp4r5nyuxzUrMb+fKUITR1mNZ8ZHwdlWiMuVIvyeyF0a4s7ePnhqjPr5Xtpywaj3wUrAwxtTemHbk8PQJ8AZIqkCnx/IxrAPD+F/29TP0dFcPLFUgd3nK7Bw7VmM/fQIdqT/V8z0wHOjMLMf9+rRldafKsTPJwsAAJ/NjtNbFf7jvVmoapYi2N0Oj44Ma/eaiqY2bNJs6S4dx71ipt1+nNnXn7P6u0rFYnua+ueapvl967P/kvr+GtPDS9eX1BgVTW3IrxWDx+hvedRZ2hp0oR72nNX5CSEmBF0vvfQSYmNjUV1djaysLDg5OWHYsGEoLuaeGAjpjBhf9UpCRnn7Fdi7inabMKO8mbO2FZex0epcnH0Z7edgXWlcT2/YCvkorGtFip7ke+0K1b8XK1HGUSF/bLQXon0cIZIq8I2mGvu1XO2t8NzEKADAB3su692mfW5CD4zv6Q2ZQoWH1p7TtbgxJC7QBVufHIY1cxMQ6eUAkUSB384UY9a3pzHw/QNYsiEF608V4nReHapFkutW3CRyJYrqxDh0uQqrD+Tg/h8TkfD2fjy1IQVHsmqgYoExPTyxa+lwfDE3AV6OxpUj+OV0Id7YkQFAHXxOiuXux3gsuwbrThUCAN6a2gs2wvZXwz76NwsyhQoDQ90wJKz9VaOcKhEOZFaBYYAFHNuPAHA8txalDW1wtBEYzOdiWRa7L2iaeXMk7nM5kqVO1O8T4KIrOGwOGZrWVNFGFHgl5HZmdBOuU6dO4cCBA/Dw8ICHhwd27NiBp556CiNGjMDhw4dhb09Lyre6plYZaltkaJbI4WQrhIe9lUkNpk3VR1MjKbOiGRK5knMy7CxvJxtE+zjicqUIJ3Jr9ZYBuNYdvbzxzq5LOFdYj9oWqd6kaQdrASbH+mJLSik2nytBP45tohg/JwyLcMfJ3Dr8fKIAr90dc901PB6D5yf2wOJfkrD2ZAEWDAlut2/f/YOC8c+FSpzOr8Ozm9Pwx2ND2l0p4fEYrJmbgIfWncWZ/Ho88FMiflo4AIM5gosr8XkMpsT54a5YX5zMq8X2tHL8e7EStS0y7DpfgV1X9G1kGPX7wABQqFi0ytpvLRToZoupcX64t1+gSTlCLMvipxMFeHe3dqswDMv0rErVtUjx/J/pAIAFg4MxmqMCfWpxA7amloFhgNfuiuE8afj1EXUAPDHGW28JCG1R2pl9A3R9RrmkljSipL4NdlZ8jIs2LejSrsCO03OCsitc0FTVj/WnoIsQfYxe6Wpra4NAcHWM9tVXX2Hq1KkYNWoUsrOzu3xw5MZR3tiGJRtTMe6zo7jn61MY9+lRk3oVdkSAqy3c7a0gV7J6k8+7wqgodSLzQQNNoK8V4KouoKligV2abTB9tEnwO9LL0ain3dAjI9RbXL8nFnEmqY/r6YVBoW6QKlR4S7Oqcy0ej8Ens+PgaCNASnEjPvyHO1ne1oqPtQsHYmi4O8QyJR746Sw2nTV+JZvHYzAi0hOfzIpDymsTsPmxIXh6XCTGRnsh0M0WDAOwLCCSKNAsUegCLhshD1HeDpiR4I83psTg4HOjcOyFMXjhjmiTAi6pQokVWy7oAq7HR4VjxZ3RnAGSTKHCk7+noFokRbinPV6Z3LPd6+RKFV7++wIAdZAUy1EwNatSpMvTWjKGu25YYa1Y12x8/qAggz/XX8nqPLuJMd4GA7QrtcmUuhOPY8wYdLEsq+uiEOvvYrbXIeRWYPRKV3R0NJKSktCz59V/mNasWQOWZTF16tQuHxy5MRjqVbhmboJZVrwYhkFCkCsOZFYhpajBYMXuzpjYyxvfHcvHocxqyBQqk/JS7knwR3ppE/5KKcXCYdyVzgF1WYqevk7IrGjGhrPFeHJ0+6swo6I8ER/ogrSSRnxzJA9vTOl13TUMw+Dtab1x1xfHse9SFfZmVOqKp17J38UWH98bh8d/S8ZPJwoQ7eOIWf3br0Fla8XHzwsH4Jk/0vDPxUqs+PsCzpc14fW7Y0xaabQS8DAw1O2qPCKFUoWmNjka2+RgoF4hc7G1gpOtwGCNKkNKG1qxbGMqUoobwWOAlyf1xOIRoZzPy7Is3thxEYkF9XCwFuDb+/txBjTfHc3D5UoRXO2EeHkSd42vj/69DBWrbjHEFZgBwA/H88GywOgenoj0dtT7c4mlCmzXnIS8b4DhAO1KR7Nr0CZXwt/F1uQK9qYobWhDVbMUAh6DeD09JgkhJqx03XPPPdi4cWO73/vyyy8xd+5czuRgcnPril6FHaXdguPqNdhVEgJd4eloDZFUgZN53CUW2jM13h9CPoOLZc24WKY//4xhGF0LmnUnCyGRt7+9xjDq7UMA+P1MMWc+Vg8fR13i9/+2XURdS/uV4u/s7YNlmnIJL/99Qdeipj02Qj6+mtcXz0+MAsMAGxKLMfmL40gy8aDBtQR8HtwdrBHu6YAwTwcEu9vD2U7YqYBLpWKx8Wwx7vj8GFKKG+FoI8DPCwfgkZFhep931YEcbDxbAh4DdT4aR/CTVtKIVQfUFfvfmNJL157qWsdzanDwcjX4vP+KzranoqkNf2pWrh7nKEtxpW1pZRDLlAj1sOdsrM1F27T7zt4+nQ5q9dH+2+zl72zSShwhtyOjg66XX34Ze/bs4fz+119/DZVKf3FFcnNqrwyAnRUfS8ZG4KcH+6NOLENeTQua9GyXddQQTSHI0/l1BnscdgaPx+hqZO1MM7xNeCU3eytM6q1O1F6vScjWZ2qcH/ycbVAtkmJzUvsFTgFgWIQ7RkZ5QqZU4Z1d15dp0Vo2LhKRXg6oEanzk7g+/CwfH4Vp8X5QqFg8/lsyEvVUx+fxGCwZG4mfFw6Ap6M18mvEmPXdabz89wXOwM7SLpY16cYklinRP9gVu5eO4MzL0vr6SK6u9dEbU3pxbr01tcmxZEMKFCoWd8X6YhpH82uJXInXt6u3dxcMDuYsvgoAXx7KVSfjh7jpDnBwYVkW6zQlQbhaEnFplsh1hzumG3E6sjO09cOGmVi0lZDbEZ3tJQZd26vQzoqPL+YmILW4AYvWJ2H2d6fNluMV6+8MRxsBRBIFZ2ucrjJVM6nuzahEq0xh0mMfHBoCQJ2rZSgosRLw8MQY9arT14fz0MaRTM4wDF6/OwYCHoODl6s5T0jaCPlYMy8BVgIeDmfV4Ltj+e1ex+Mx+GRWHMb08IRErsLCtedwTNOGhsuYHl448MwozOoXAJYFNp4txqiPj+CzfVndFnxlVjRjyYYUTPnyBJKLGmBnxcf/7uqJPx4bgiB37r5/LKuuaP/Rv+qq8y/c0UP3e7uWUsXiuc3pKG1oQ6CbLT6YGcsZ9Hx1OBcFtWJ4OVrjWc1p0fYU1Ip1XQSev6OHwSDqaHYNcqpbYG/Fx6z+xpXJ0Np9vgJShQqRXg7obcbkdpa9omgrR2stQsh/KOgiBl3bq/Dh4aFYe7IAJ3OvXinR5nh15YoXn8dgZGTHktxN1TfIFSHudhDLlNiVzl3AtP3HuiAuwBlShcqo1a7Z/QPg72KLymYJfjrRfpAEABFeDlisSap/ddtFzuT7aB8nvK455fjRv5dxmGP7UMjn4Zv7+2FUlCfa5EosWn9Ol/zNxdlOiI9nxeGPRwejt78TWqQKfHEoF8NWHsKrWy+YvaQHoA6CDlyqwoM/n8Wk1cex63wFWBaYEueHg8+NwuIRYeDr6b+oTYbXVrR/bkIUnhrDfarxo38v40BmFawEPHw5ty9nk/S0kkbdicU3p/bS20z9vd2ZUKhYjO7habBmFsuyWHNI3cJpzsAgg03ar7UhUX0AYlb/ALNuLWZWiFAjksJWyOc8jUsI+Q8FXcSga3sVJgS6XBdwaZkjx2tCjPqY/H4z9/ljGAZzNDWyfjfh1J72sdocnXWnCiEyUJndWsDHi3eqc3++OZKHaj39JZePj0S4pz1qRFK8tZN7m3H+oCDMGRAIFQss3ZCKS+Xtn/i0EfLxwwP9cXcfX8iVLJ7elIZP92UZ3L4dFOaOHU8Nx9fz+yLW3xkSuQq/Jxbjri9O4K4vjmPNwRxcKm/ustxOiVyJk7m1eGP7RQz98CAW/5KEo9k1YBjgrj6+2LNsBNbMTYCvs/7WTQ1iGR5edw6bzqlzuN6e1gtLx3GfLtyQWKxbLfz43j6I40gOF0sVeHZzGpQqFlPi/HTFb9tzNLsGBzKrIOAx+N9d7Z+SvNKpvDokFzXASsDDYxzFWrlcKG3ChbImWPF5uJejaXdXOZKtDu6Hhrub1ISbkNuV0acXye1N26uwtkWGOgMFRA0FHKZSV+FmkF3VgpwqkcETX51xb78AfLYvG+kljUgraTTpNNbEXj4I87RHfo0YP58oxNPjuSd2QJ3btfZkIdJKGvHu7kx8MTeh3etshHx8PCsO935zCltTyzAswgP3tlOVXXuasbBOrK619fNZ/PX4EIS0U3bBSsDDF3MS4O9ii++O5WPNoVyklTTi09lxeguQ8ngMJsf6YlJvH5zOr8PvicXYl1GJjPJmZJQ349P92XC3t0L/EFfEB7oi2scREV4O8Hay0XsitFWmQEl9G/JqWnCxrAnppY1IKmyA9Iom3C52QszuH4h5A4Pa/Znac66wHss2pqKiSQJbIR9r5iZgfAx3ravtaWV4dZu6PMTT4yI5q8WzLItXtl5Afo0Y3k7WeGfa9adLr/zZ/qd5zgeGhCDCS//9y7IsPtqr3gKdOyAQXk7GFYTVWqupwj8p1oeznVFX0X4QGm3mOmCE3Coo6CJGc7bTFEM10AvRUB85019XiJGRnjh4uRq7zlfgmQnmC7o8HKwxJc4PW1JKsfZkAVbPaT8Qag+fx+DZCVFYsiEVPxzPx4IhwXonPYZh8O703pj65QnsSC/Hvf0CMDKq/cbHfYNcsXx8FD7bn43Xtl1EnwBnRLUTfFoJePhuQX/M+f4MMiuaMf/HRGx6dLCuefiVeDwGL0/uiWhfR7z89wUcz6nFpFXHsXJmH72BiXbsQ8M9MDTcA/ViGfZmVOJgZhVO5NaiTizD3owq7M2ouuJ6wN3eCo42QthZ8cEwgFKlXi1qbJWhWdJ+Dp2nozVGRXlicqwPhkV4GL2aIlUo8fXhPHx5OBdKFYswD3t8Nb+v3lZAey5U4NnN6WBZ9arhcj1B82+JxdieVg4+j8GX8/rCRU/JlFUHclBS3wY/Zxu9OV9aezOqkF7SCFshH0/padDdnqpmCXaeVx8E0Z6SNZeKpjakFjeCYYA7DNwvhBC1Dm0v/vrrrxg2bBj8/PxQVKSurLxq1Sps3769SwdHbkzX5nhdaWSkBzwcuv7TtXbrZmd6udlLkzw0LASAOhm5pL7VpMdO7u2LXn7qvKfVBwwXDO7t74wHNO1iXv77gt5VwqfGRGB4hAfa5Eo88ksSZ36Xs60Qvzw8EGGe9ihrbMOsb08jV0+gfE9CAHYtHY5oH0fUiWVY/EsSnvgtGZVN3FueV3Kzt8LcgUH48cEBSH9jIrY8MQQv3RmNu/v4ItLLAVYCHlhWXXqkoFaMjPJmXCxrRmZFM4rrW3UBl7OtEH0CnDF3YCDeu6c39j8zEmdfGYdPZsVhbLS30QHXucJ63P3FCaw+mAOlisU9Cf7YuXS43oDrz6QSLN2YCqWKxb39AvDOtN6cuVCn8mp1xWhfurMHBoRw52edLajHD8fVW5XvTO/N2YtRSyJX4oN/1MVdFw0PNbrtkdaPx/MhV7IYEOKKPgEuJj3WVLs1nQb6BrmavBpHyO2KYU2cwb755hu8/vrrWL58Od577z1cvHgRYWFhWLduHdavX4/Dhw+ba6wd0tzcDGdnZzQ1NcHJiVpUdJXyxjas2HIex66o3zUy0gMrZ/aBbzvtaDqrRarAgHcPoE2uxNYnhyLBjIVSAeD+HxNxIrcW9w8OwrvTY0167KncWsz7MRF8HoN/nx5hcDu0RarApNXHUFLfhtn9A/DRvXGc19a1SDH1y5Moa2zDkDB3rH94IOe2XVWzBPN/TERudQtc7YT4aeEAvQVmJXIlPt+fjR9PFECpYmFvxccTo8OxaHhYp+ovsSyLOrEM1c1StEgVEGtOhvIYBg7WfDjbWsHTwRrOdp1bIS1rbMPKfy7rGmR7OFjhzam9cHcf7rZOLMvim6N5uhONs/oF4MOZfTiT8nOrWzDj65Nolihwdx9frJmbwBmcNUvkmLTqOMoa23BvvwB8Mov796r11eFcfLw3C16O1jj0/GiDQdqV6lqkGL7yMNrkSqx9aADGGCid0VmTVx/HpYpmvDO9NxYMDjbraxHLoTnTvEwOumJiYvD+++9j+vTpcHR0RHp6OsLCwnDx4kWMHj0atbWmFZY0N7qBzEfbi1EkkcPRRggPB/P2YnzmjzRsTS3D3IFB+GCGaYHQlYzpIXk6rw5zfzgDKz4Ph18Y3W5fQ30e/SUJ+y5VYWi4O35fPMjgCbKzBfW47/vTYFl1sc4pevo/ZlY0495vTkEsU2JqnB9W3RcPHkeQUNcixUPrzuF8aROsBTx8MitO73Nrn//VrRd0Tbk9Ha3x6IgwzBsUBHsTggBLKW1oxTdH8vBnUilkShUYBpgzIBAv3Rmtd9tPIlfije0Z+ENTK+3xUeF46U7uUg6VTRLM/OYUyhrb0DfIBRseGcxZpZ9lWSzblIad6eUIdLPFnmUjDG67F9e1YuKqo5DIVVh1XzymJ5hWX+uDfzLx3dF8xPo7Y8eSYWY+tdiMSauPQ8hncPaV8XA1c+4YsRyaM83L5O3FgoICJCRcn+dibW0Nsbj9qtnk1uRsZ4VwLwfEB7ki3MvBrAEX8F/fwm2pZWhqu3obrqlVhrzqFqQWN+gt1GpsD8nBYerilTKlCms0hTRN8b+7YmAt4OFUXh3+TtFfkgEABoa64cnR6tOPK7acR34N93ZgT18nfDW/LwQ8BjvSy/HmzgzOLVd3B2tsfGQwxkV7QapQYenGVLy3+xIUSu5Cxj19nfDX40Oxek48AlxtUSOS4r09mRi28hA++vcyShtM23I1B5ZlkVzUgKUbUzH64yP4PbEYMqUKQ8LcsXPJcHwwo4/egKuiqQ33fX8GfySpTzS+fncMVkzi7tNYI5Ji3o9nUNbYhlAPe3z/QH+9bZHWnyrEzvRyCHgMVt2XYDDgYlkWr267AIlchcFhbpyFWLlUNkl0hVSXj480a8AFAH8mqavqj+/pTQEXISYwOegKDQ1FWlradV//559/EBMT0xVjIrcRY4MlABgU6oYobwe0yZW6JsCA8YGUoR6SV742wzC6kg5/JpciT08Q1J4gdzssH69Omn539yXUiAwXEn1mfBQGhrpBLFPiid9S0CLlLtA6uocXPp0dB4YBfjldhHd2ZXIGXvbWAnz/QH88NkpdeuCH4wWY8/0ZvflqPB6DafH+OPTcaKycGYtQD3s0tsrx9ZE8jPjoMBb8lIjNSSXXBb/mVlKvXtWa+PkxzPzmFHaml0OhYjEswh1/PDoYGx8djN7+3H0PAeDfi5WYvPo40ksa4WInxPqHB+JhPUnnNSIp5v94Bvk1Yvi72OLXRQPhwdEOCADO5Nfpmm6/MrmnUfWr/kwuxfGcWlgJePhgxv/bu+/oqKotDsC/KZn03hsppBNSINRIBwUBRUCq0oKKKAj4LE99FBURCygIKi0g0quAdKRDIAkJNSGkkZDeM2lTz/sjZkwkZSaZmRT2txZrmXvnzux7c52zc+45+wSonDT9eC4BIqkc3V3MMVjDMwlFUhkO/13bTdWirYQ861R+vBgeHo7//e9/+P777xEWFoZNmzYhKSkJK1aswKZNmzBp0iRNxdos1FXadmUWVz6VBPX3tMLX4wLg0MDjvN8jHuOzw/fQycIA5/8zEGVVEry7K6betSH7e1rVWYw7KbcMQ1ZdbDCec4sGoLNN3SVcZm+LxNm4XAz2scGWGT1UOj+JTI6Xf7qKB1mlGOprg43TQppsTHNKqzBq7RXkCUUY4mODDdNCGi36ufNGGj45VF2O4LXenfD5S/4NPmoEgJP3svCffXdQJpLCUMDD/0b5YWIP5ybjkskZzjzIwfaI1Do12nR4HPRwtcBAb2v0cbeCr70x+Dz1lf+rkshw63ERribl46/4PMRl/VN7TMDn4uVAB8wIdUUXh8YTLaB6WZ8vjz1QrH3YxcEEv7zWvd6ZnTWeFFXg9c03kZJfXRpiz5v1l+CokZpfjjHrr6K4QoKXAh3w46SgJq9temEFRvx4GWUiKT4a7oO3Bza9JmNtDzJLMWrtZcgZsG9On0YH9qvDwVtPsGjvbdiZ6OHKR4PU+vsmrY/aTM1SeYDGzJkzIZVK8eGHH6KiogJTpkyBo6MjfvzxxzaXcJG2q6lep9rJUm1juzni21MPkVZYgXNxOehsbdTkYtw171PfGpK11Tdz8L8v+uLCwzz8FZ+LCw9zm1zXrzYdHherJgbipbVXcTYuF3si0xXFVxtia6KHjdNCMPHX6zgXn4sVx+Pw2aiGe5Cn9OoEHhf4+OBd/B6RhpJKKb57NaDBmX7D/e3hZ2+K9/fFIjK1CB8fvItjd7Kw7OUu6NzImoE8LgfD/e0w3N8OjwvKcSQ2E0duZ+JRbhmuJRXgWlJ1Imaky0cXBxP42pvA09YILhaGcDTXh5WRAEa6/HoTEMYYSiolyCkVIaO4Asl55UjMLcO9zBI8zBZCIvvn70Iup/pR7JggR4zoag9T/aYH3zPGcOp+NpYcuY+cUhE4HOCt/p2xaJhXo7XDHmYLMX3LTWSXVsHRTB87ZvdqNOGqGT9XXCFBoLMZvhnfdI+VVCbHwj2x1RNFXM0Vi5crizGGL449gJxVF4zVdMLFGEP4348xX+/jQgkXISpSuaertvz8fMjlctjYtN3CeJS1t03N6XWqsfJkPH6+kIQgZzMsHuWLsT9fb/B9Ds/ti6C/Z+w19zO/PPYAm66kwNXSACcX9G90LE99fr2YhBUn4qGnw8Uf7zwHb7um64wduZ2J+btiAAD/HeGDtwY03vvxR2wG3t97G1I5Q083C/z6WvdGx9rI5AybryTju9MJEEvl0OFxMCvUDXMHeSiVyNRIzS/HX/G5uPQoD9GpRRA28khUwOPCQJcHPX51nS45Y6gUy1AmkqKxYvi2Jrro29kKoR5WGOxjo1LBz7isUnz55wNF75yblSFWjgtochme8/G5mLcrBmUiKTxsjPB7WC/YmTZcFkFYJcGUjTdwN6MEjmb6OPROX6XKPdTcy0a6fJx4r1+jvW71ORyTgQV7YqHL5+LsogEqH6+qmgkmunwurv93iMaLrxLtozZTs1o0FcnKihY4Jc3TnF6nGrNCq9d+jE0vxiMVCrXW1Be71MCjyIbqi7031BNH72QitaB6PNHCYU0XuKztjX7uuJpUgEsJeZi7IxpH3n2uyVmALwU6IKu4EitOxGPFiXiYGwgwoUfDS7q8HOQIS0NdvP17NG6mFOKldVewcVoIfOzq/9LkcTl4s39nvNDFDkuO3MeFvxfK3hOVjncGemBq704wEDT99eBqZYhZz7lh1nNukMkZEnKEeJBZigdZpUjNL0dqQTmySqpQIZZBLJNDXCEHUP/v1sxAB3YmenC3NoSblSH8HUzh72gKJ3N9lcc4pRdWYM25Rzhw6wnkDIrldN4Z5NFo0swYw6bLKVhxIg5yVt2rtuH17o0Oyq8UyzB7WxTuZpTA0lCA38J6KpVwnYvLwc9/r9u4clyAyglTcYUYXxyrXhZq/hBPjSdcALDhUnW8r4Y4UcJFSDMo1dMVHNxwLZp/u3XrVouDUifK2tumlvR0AcCyo/cRfjUVAY6mMNXn43I9a0H+e0wX0Pz6YsfuZOLdnTHQ4XFwbF4/pXqrassvE+HFHy8jVyjCi13tsG5KN6X+n1pxPA6/XkoGhwN8My4Ar4Y0vpZeQo4Qs7dFIa2wAvo6PCx/xR9juzU+2JkxhvMPc7HieLwiibUwFCDsOTdM6dlJLbPTKsRSFFVIUCmWolJcPXOSwwH0BTwY6/Jhoq+jcg9ifeKzS7HxUgr+iM2A9O/us5Fd7fHxCJ8mk5KSSgk+2n8HJ+9nA6guO/H5y/5NLl80a2skIpILYazLx843eqOrU9PjyxJzhXhl3TUIRVJM7+OCZS/7q3CW1RbtjcXBWxnwtDHCn/P7NRqnOtzPLMHINVfA4QDn3x+o9FJMpH2hNlOzlEq6li1bpvQbLlmypEUBqRvdQG1TSYUY83bFNNjr1NCYrhq5pVXo/+15VEnk+P7VQPwRm6F0ItWc+mKMMbzxWxTOxuXC39EEh+aGQkfF8SxRqYWYvDECEhnD+8O8Gl10ufbn/u+Pe/g9Ig0cDrDila5NjgsrKhdj/u5/Jhe8EuyoVDV0qUyOg7cy8NP5RKT9PbNRT4eLV4IdMaWnC/wdTTReiqA5JDI5zsXlYMeNtLqTMryssWCoZ6MFYWvcSivCe7tjkF5YCR0eB5+N9MO0Pi6Nnq+wSoKwrVG4mVoII10+ts3qge4uTY+pKq4QY8y6q0gtqEBPVwv8PruXygnTubgchG2LApcD7JvTV6kZki311vYonLqfg9GBDljbwDqhpP2jNlOzWjSmqz2gG6jtamlV++V/PsDGyyno4mCC38N6orBcotFCrbmlVRi2+hJKKiWYP9gDi573Vvk9dt9Mw8cHq2cbrpvSDSMD7Js8hjGGpUfuY9v16iW3Pn3RF280MeBaJmdYfz4Rq88mQM4ARzN9fDM+AKEeTQ8JkMrkOHonE5sup+B+5j+zBX3sjPFykCNe7GoHF8vW7eWQyxlinxTjSGwmjt3JQn5ZdUkOLgcY7m+HN/q5K7VqgUgqw49nH+GXi0mQM8DZQh/rpnRrcgmdPKEIM7fexL2MUhjr8rEtrKdSyV2VRIZpW27iZkohHM30ceTdUFg2Un6iPgVlIgz/8TLyhCK82d8dn7zoq9LxzXEvowSj1lb3cp1e0F+ji86T1kVtpmY1O+mKiopCXFwcOBwOfH190b17d3XHphZ0A7VtLalqX1AmwsBvL0AokuLb8U0/elOHP2Iz8N7uWHA5wO43+zQ5ILs+S4/cx9ZrqRDwufg9rJdS78EYw1fH47DxcgqA6nX5Pn3Rt9HyEEB179qCPbF4UlRds2xyz6Yrtdf+zMjUImyPeIxT97Mhlv5TUNXHzhiDfGwwwMsaQc5mank02JTiCjEikgtwMSEP5+JykVur9pmVkS5eDXHClJ6dlB7bdCO5AJ8cuoukvOqizmOCHLDsZf8mJxIk55VhRngk0gorYGkowLZZPZusDQZUJ8Lzdt3C8bvZMNblY++cPo2uB1mf2j2uHjZGODbvOa1c+9c338DlR/l4OchBpUXgSftDbaZmqZx0PXnyBJMnT8bVq1dhZmYGACguLkbfvn2xa9cuODtrvuFTBd1AHVvNzEAbY12c/89ArSxTUzOWxsFUD3/O76fymCeZnGHO79E48yAHJnp87HlL+cZ346VkLD9eXXjzhS62WDUhqMlzLhdJsfJkPH77u6fMwlCAD17wxoQQ50ZrgNVWUiHBn3ez8OfdTFxPKqgz21DA4yLAyRQBTmbo6mQCL1tjuFsZtWi9xpJKCR7lCPEwR4i7T0oQm16MhzlC1P62MhTwMNTPFi8HOaCfp7XSj3tzSqvwzcmHOHCrul6XlZEAX7zsjxFdm+51vJaYj7d33EJJpQTOFvr4bVYvuCkxtqn2Y2IBj4uts3qgb2fVJyJtvZqCpUcfQMDj4tA7fZWqT9ZSNWuJ8rkc/PX+QHSy1PyAfdJ6qM3ULJWTrueffx6lpaXYtm0bvL2rH688fPgQs2bNgqGhIU6fPq2RQJuLbqCOTSSVYdiqS0grrMDcgZ3x4XCfel+nzHqLyioTSTFqzWWkFlRgoLc1tkzv0WSP079VSWR4bdMNRD0ugpWRLva81bvROlm1/RGbgQ/23YFYJoePnTE2TgtRqnfnZkohPjt8Fwk51YPlfeyM8fEIHwzwslZprFZhuRiXEvJw4WEuriYVNFht39ZEFw5m+rA11oO5oQ5M9HWgr8NT9MwwVn0dKsRSlFRKUFAmRo6wCumFlQ1Wuve0MULfzpYY7GuL3u4WDdYjq0+ZSIrNl1Pw66UkVIhlAKp7/j4e7tvkYts19amWH4+DTM4Q5GyGTdNDGq1MX/vYL/+Mw+YrKeBwgDWTGl9bsyG30oow8dfrkMgYFo/ya7SKvrrI5Awj11xGfLaw2QP+SftCbaZmqZx06evr49q1a0+tv3jr1i2EhoaisrKygSNbB91AHd+ZBzl447coCHhcnF7Y/6lZVc2pfN+UB5mleGX9VYikciwa5oX5SgyK/7eSSgkmb4jAg6xS2JroYvebfZTqNQGA6MdFeGt7NPLLRDDV18GqCYEY4mvb5HESmRzbrqVizblHKK2qrqnVw9Uc7w3xQqiHpcoD5RljSC2oQPTjItzLKMH9zBIk5pahqKLlywPZm+rB09YY/g4mCHQ2Q3AnM6VKMfxbuUiKnTfS8PPFJBSWVy/11K2TGf43yk+pcV9lIin+e/Aujt7OBFA9MWHF2K5KPdZjjGHlyYf45WJNaYiumNij8YkQ9ckvE2H02ivIKqlSafZrS9WsAGGqr4ML/xlI6yw+A6jN1CyVky5vb29s374dPXv2rLP95s2bmDJlChITE9UaYEvRDdTxMcYwPTwSlxLyEOphid/DeikapJIKsdLLBKlqb1Q6Ptx/BwCw4fXueL6LncrvUVguxqQN15GQUwYbY13sfKMXPGyUG6ScVVKJOb/fwu30YgDA7Ofc8MFwb6V6f4orxFh3PhHbrj9WjNUKdDLFG/3dMbyLXYsrjReWi/GkqAKZxZXIFYpQVC5BSaUEVVIZRJJ/Skbo6XBhKODDWI8PKyNdWBnpwslCH07mBk3OtmxKfpkI268/xrbrqSj+Owl0szLEomFeGBVgr1TSEptejPd2x+BxQQX4XA4+HemLGX1dlTpWLmf4/NgDbL2WCgD44uUueL2Pq8rnIZJW94pGphbB3coQf7wb2uQC2upQWC7GoO8uoKRSgqWj/TAjVPM9a6T1UZupWSonXX/88Qe++uorrFu3Dt27dweHw0FUVBTmzZuHjz76CGPGjNFQqM1DN9Cz4XFBOZ5ffQkiqRzfvRqI8d2ra1M1VQ/s1IJ+8G6ggKgy/nf4HrZHPIaBgIcDb/dVeWA0UJ0cTN14Aw9zhLAwFOA3JQdmA9UN8tcn4hVLs/jYGeOHSUENFkX9t+ySKvxyMQk7b6Ypki8HUz1M7NEJE3s4N1qFvS1ijCH6cRF23EjDn3eyIJZVn5OrpQHmDvTA2G6OSiWUEpkcv1xIwo/nHkEqZ3A008ePk4IQouQyO1KZHJ8euoc9UekAmp9wMcbw0YE72Bv1BMZ6fByaGwqPRurXqdPHB+5gd2Q6fO1NcPTdUFry5xlBbaZmKZV0mZub1/nLrry8HFKpFHx+9V+iNf9taGiIwsJCzUXbDHQDPTt+uZiEr0/Ew1RfB2cW9oeNiR5i0orwyvprDR6zeXoIQlzMm93bJZHJMSP8Jq4mFsDeVA+H5oY2K1EpLBdj+pabuJtRAiNdPn59vbtS5R1qnHmQg48P3EFBuRg6PA7eGeSBtwd2VnrMU02v0PaIx4pHcFwOEOphhbHdHDHU11YrvSvNlZpfjmN3MnHwVgaS88sV2wOdzfBmP3cM97dTetLAg8xSfHjgNu5lVJfLGB3ogC/HND2rsUaFWIr5u2JwNi4XXA7wzfh//ghQ1brzifj21ENwOcCWGT1UWvuzJW4kF2DihggAwP45fZRONkn7R22mZimVdG3btk3pN5w+fXqLAlI3uoGeHRKZHGPXX8PdjBIM8bHBpukhSM4rb7Sna/P0ELhaGjZa/b4pxRVijP35GpLzyuFrb4I9b/WGSTMSFGGVBG/8FoWI5ELwuRx8PS5ApcY6TyjCfw/exdm4HADVg86/HOOPXu6WSr9HlUSGE/eysOtGOm6m/vMHlIDHRaiHJYb42mKAl7VWlpxpjEzOcDejBH/F5+Lsgxw8yPqnnpiBgIeRXe3xWm8XBDqbKf2e5SIpfjz3CJuvpEAmZzDV18HSl/wwJshR6fFT+WUihG2Lwu30Ygj4XKyZFITh/k3PiqzPoZgnWLjnNgBo9fFelUSG4T9cQmpBBSb3dMaKsQFa+VzSNlCbqVlUHJV0KA+zhRi99grEMjlWjuuK4V3sGhzTFephieBO5hjqY6NYFLu50gsr8Mr6a8gvE6G3uwW2zuzZrPpJVRIZPth/RzFo+51BnfH+MG+lZ0cyxnDsThaWHb2P/LLqHquXAh3w3xd9YG+q2qSBxwXlOBSTgSO3M5GcV15nn4ulAXq5WaCHqwWCnM3gbm2kdE9Sc1RJZLifWYqYtCJEphYiIrmwzgxHHpeDvp0tMTrQASO72qtUOkQuZzhyOxMrT8Yjq6QKADC8ix0+H9NFpYH7DzJL8cZvUcgoroSZgQ42TQtpdg/RxYQ8zN4WCYmMaa0Aao2aosN2Jno4vah/s/6AIO0XtZma1aKkq7KyEhJJ3VlKbe2XRDfQs6fmMaOBgIcT7/UDY8Cnh+/iaq31GUM9LDEz1A3zd8Xg6LvPtainq8a9jBJM2hCBMpEUQ3xs8PNr3Zu1Hp5czvDd6YdY//diyIN9bLB6YpDSj7eA6t63b049xK6baWAM0OVzMTPUDW8P7KzS+9RIzBXi1P0cXHyYh+i0Isjkdb82DAQ8eNoaw8vGCK5WhnCxNIC9qT5sTaoHxzeVgDLGIBRJUVgmRlZJFTKLK/G4oBzJ+eV4mC1Ecn75U59prMtHPy8rDPK2wWAfG5UruwNARHIBVpyIV0xGcDLXx+cvd8Fgn6Zngtb2550s/GffbVRKZHC1NMDmGT2ULgHybzeSCzA9/CaqJHKMDnTAjxODVC5J0lwRyQWYvDECjAFbZoSofB1I+0dtpmapnHSVl5fjo48+wt69e1FQ8PQiwzKZTG3BqQPdQM8emZxhysYI3EgprK6nNK07zsTlwsZYFyKpHLp8LmLSi7HlSgpCXMxbNIPx324kF2DalpsQSeUY4W+HNZODVV6jscbhmAx8dOAORFI5XC0NsG5qN5WLYd7LKMGyo/cRmVoEADDR4+ONfu6YEera7DFawioJolKLEJFSgJi0YtzLKFHUvWqIgM+FsS4fejo8RSLKGINIKkelRIayKqligeqGWBoKENzJHN1czNDH3RJdHU2bPbg7+nEhVp95hCuJ1T2ghgIe5g7yQNhzbir1UIqlcqw8GY/NV6pXCujnaYWfJndrsu5XQ2LTi/HaphsoE0kx2McGvzQzcW+O0ioJRvxwGRnFlZjUwxlfj6PHis8iajM1S+Wk65133sH58+fx+eefY9q0aVi3bh0yMjLw66+/4uuvv8bUqVM1FWuz0A30bMoorsTwHy5BWCXFG/3cMDPUrUXrPKriwsNcvPlbNMQyOUZ2tccPk4KanXjdyyjBW9ujkVFcCQGfiyWj/TClZyeVajQxxnAuLhcrT8bjUW51YVQTPT5e7+OC6X1dm1X7qjaZnCElvwwJOWVIyBEiraACjwsrkF1ShTyhSDGDUBkGAh7sTPVgb6qHThaGcLMygKetMXztTGBrotui2lSMMVx+lI/1FxIRkVw9Xk2Hx8HEHs6YP8RT5evwuKAc7+2ORezfvWRvDXDHB897NzsRvJVWhOmbb0IokrboEXVzMMYwf3csjt7ORCcLAxx/r1+LS3aQ9onaTM1SOenq1KkTfvvtNwwcOBAmJia4desWPDw8sH37duzatQvHjx/XVKzNQjfQs+vkvWzM+T0aALBpWgh6uJo3e51HVZ2Ly8Hbv9+CWCbH8362WDslWKXq6bUVlYvx/r7b+Cs+F0D18j8rxgbAohnLD/15Nws/nk1QrDco4HMxOsAB0/qoNuhcWYwxlImkKK2SorRSArFUrkjCOAB0+TzoC7gw1OXD3ECgkSSjXCTFH7GZCL+aokg6dXgcjA12wruDPVSeFMAYw8FbGVj8xz2Ui2Uw0ePju1cDm1WnrUZUaiFmhEeiTCRFTzcLhM/ooZUlrWrsi0rHB/vvgM/lYN+cPkoVjSUdE7WZmqVy0mVkZIT79+/DxcUFTk5OOHjwIHr27ImUlBR07doVZWVlmoq1WegGerYtO3of4VdTYazHx9F3n3uqWr0mnY/PxVu/R0MslaOfpxV+fb07DATNa0jlcoZNV5Lx7amHkMgYrIx0sWJsVwzzU33MjUzOcOZBDjZcSsKttGLFdn9HE0wIccZLgQ5KLYjdljHGEJtejH3RT/BHTAbK/378aSjg4dUQZ7zZ371ZqxHkCqvwycF7ihmiPV0tsHpSEBxb0Ft6/mEu3v49GlUSOfq4W2LzjJBm3yfNEZ9dijHrrqJKIscHL3jjnUEeWvts0vZQm6lZKiddAQEBWLt2LQYMGIDnn38eAQEB+O6777BmzRp88803ePLkiaZibRa6gZ5tYqkckzdGIPpxEbxsjXBobqhWexCuJubjjd+iUCGWIcjZDFtm9FC5h6q2exklWLAnFol/99iMCrDH0pe6KLUGYH1i0oqw/fpjHKtVSFSHx0F/T2uMCrTHYG/bZo9P0jbGGOKyhDh5LwtHbmcitaBCsc/V0gCv9XbBhB7OzZqNxxjDgVsZ+PLPByiukECHx8F7Qzzx9kCPFs3a/CM2A+/vvQ2pnGGgtzV+ntq9RQuFq0pYJcFLP11FSn45+ntZI3xGD43OQiVtH7WZmqVy0rV69WrweDzMnz8f58+fx8iRIyGTySCVSrFq1Sq89957moq1WegGIrmlVRi59gryhCK80MUWP0/trrXZYED1WJ1ZWyNRXCGBu5Uhts7siU6Wza9zVSWRYfXZBGy8lAw5A0z1dfDhcG9M7tGp2edVWC7GH7EZ2Bv1BHG1al7xuRz0drfEQG9rDPCyhoeNkVbW/FNWhViKyNQinI/PxV/xuUgr/CfR0tfh4fkutpgY4ow+nVVfV7JGYm4ZPjt8VzEOzN/RBN+OD2zW6gM1GGP45WIyVp6MBwCMCXLAt68GNnvsX3PI5Qxzfo/G6Qc5cDDVw7H5/Vr0BwHpGKjN1KwW1+lKS0tDVFQUOnfujMDAQHXFpTZ0AxGgeoHoyRsiIJbJMXdgZ3w43Eern5+YK8T0LZHIKK6EhaEAG6d1R3eXllX5vvOkGB8fuKsoDBrobIbFo/zQ3aVl43Ee5Qhx9HYmTt7PRkJO3eECVka66OVmge4u5gh0NkUXB1OtDvbOFYpwO70Yt9KKEf24ELHpxZDI/vkKE/C5GOBljZFd7THMz7ZFvZollRKsOfcI266lQipn0NPhYsFQL4Q959ai5Egik2PxH/ew62b1EkGzQt3w2Uhfrf4hAACrzyTgx3OPIOBxseet3jSOiwCgNlPTqDgqeWYcvPUEi/ZWV/j+dnwAXg1x1urn55RWYfa2KNzNKIGAx8WKsV0xrpnLw9SQyuT47fpjrDqTgDKRFED1sjUfPO/dot60Gin55TgXl4NLj/JxI7kAImndmYhcDuBubQRvO2N0tjaCu5UhnC304WCmD2sj3WbN5CsXSZFTWoX0okqkF1YgKa8MiblliMsqVRR8rc3RTB/9PK0wyMcGz3lYtfjxsVgqx+8Rj7H2r0co+nuh7KG+NlgyukuLK/EXlYvx7q5buJpYAC4H+N8oP8xshYWk/7yThXd23gLQOv8vkLaL2kzNUirpWrNmDd58803o6elhzZo1jb52/vz5agtOHegGIrV9eyoe684ngc/lYMuMHujvZa3Vz68QS7FwTyxO3a8eiD2jrys+Henb4sdKuaVV+O70Q+yLfgLGqsdlTe7ZCe8M8oCtiXoWra6SyHDnSQluphQgNr0YseklyC8TNfh6DgcwNxDAzEAHxrp8GOryIeBzFefKGCCWyVEllqFMJEVJpQTFFWLFoPf6cDmAh40Rgp2r63X1drdEJwsDtTzylMrkOBiTgbV/PUJ6YSWA6s9aPMpPLfdJfHYp3vwtGmmFFTAQ8PDjpOBmTYRoqVtp1b2+Iqkcs0LdsHi0n9ZjIG0XtZmapVTS5ebmhqioKFhaWsLNreG/yjgcDpKTk9UaYEvRDURqk8sZFuyJxZHbmTDS5WPPW71VLjiqjhh+OJuANX8lAqieAbd2SrBakqP7mSVYefIhLiXkAah+3DaphzPeGtC5RTPs6lPzuO9BVikSsoVIya+uIJ9ZXInskqomi502xkDAg5O5PpzNDeBubQgPGyN42RrDx85E7QPNRVIZDt3KwM8Xk/D478H31sa6WDTMC692d2p23a3aDsU8wScH76FSIkMnCwNsnBYCbzvjFr+vqqqXq7qK/DIxhvjYYMO0EBo4T+qgNlOz6PEieeaIpDJM33ITEcmFsDLSxf45fbRaSqLG6fvZWLT3NspEUlgZCfDjpGCEelip5b2vJeVj1ekERD2urkTP53LwUqAD3ujv3qIB4MqSyRmKKsQoKBOjqEKMcpEUZSIpxFK5YgwWh1O9kLaeDg+GujyY6uvAzEAAG2NdrcwwLamQYHdkGsKvpiK7tHrNRUtDAd4a4I7XeruopWxDpViGz489wK6baQCqK9avmRQM81YYsF5QJsL4X64jJb8cfvYm2Denj1Zn8pL2gdpMzVIp6ZJIJPD29saxY8fg59c+uqTpBiL1KamUYNKGCMRllcLJXB8H3u6rtsdwqkjOK8PcHbcQny0EhwPMHdgZC4Z6qWUWG2MM15MLsPZcIq4n/7NkV09XC7zexwUvdLHT2hIzbcn9zBLsuJGGQ7cyUCmpfpRpa6KLN/q5Y3LPTmpLROKySjF/Vwwe5ZaBwwHmD/bE/CGerdKzVC6SYsrGCNx+UgJHM30cmtsXNq1wv5O2j9pMzVK5p8vR0RFnz56Fr6/2Vr1vCbqBSENyhVV49ZfreFxQAQ8bI+x+s3ez6121RJVEhqVH7mN3ZPVstkBnM/wwMQgWBjrILxOjtEoCE30dWBk2v4L+nSfF+PVSMk7ey1YsHG1pKMD47k4Y190JXrbaf9SlTSWVEhy7k4n90U8QU6sgrI+dMWaGumJMsGOzVwz4N5mcYdPlZHx/OgFimRzWxrpYPSEIz3mqpxdTVVUSGWZvi8KVxHyYG+hg/9t9m70YN+n4qM3ULJWTrq+//hrx8fHYtGkT+Py23zVNNxBpTHphBSb8eh1ZJVXwsTPGrjd6t8qjHwA4dicTnxy8i9IqKXT5XDia6SM5v1yxv7+nFb4eF9CsSuo1skuqsPPGY+yOTEeu8J9B8L72JhgdaI8X/e1b5VGrJpSJpDgXl4M/72ThQkIexH/PvORzOXjB3w6v9XJBb3cLtdYdS8kvx4f7bysWGB/iY4NvxgfAshWSeaB6csDcHbdw+kEODAQ87Jjdi0pDkEZRm6lZKiddr7zyCs6dOwcjIyN07doVhoZ1v6APHjyo1gBbim4g0pTkvDJM3BCBPKEIXRxM8HtYr1ZLvDKKK7FoTyxupBTWu7+/pxXWTg5u8ZqRUpkcf8XnYm/UE1xMyK1T68rX3gRDfW0w2McGAU5m7WqgdWZxJS48zMPZuBxceZRfZ7FtL1sjvNrdGS8HO7R4ke9/k8rk2HwlBavOJEAklcNIl4/Fo/zwaohTqxWTlcrkWLT3No7czoSAz8XWmT3Qt3Pr9LaR9oPaTM1SOemaOXNmo/vDw8NbFJC60Q1ElPEoR4jJGyOQXyaGj50xdszu1Wq9E4k5QgxdfanB/ecWDUBnG/U9HioqF+PEvWycuJeFa0kFisePQHW1+z7ulujlboEerhbwsTNWy2w+dcksrsSttCJEJBcgIrlQsTxSDTcrQ4zsao+RAfbwsTPWSAIU/bgI/zt8T1Gktp+nFb56pWuLa3q1hEzO8P7eWByOzQSfy8HPr3VvlfIUpP2hNlOz2vTsRalUiqVLl2LHjh3Izs6Gvb09ZsyYgc8++wxcrnJf/HQDEWUl5goxeeMN5AlF8LI1wu9hvVplsHFMWhFeWX+twf2H5/ZFkIYeERWVi3H+YS7OxuXg8qN8CKukdfbr6/DQ1ckUgU6m8HMwgbetCdytDTVelZ4xhoziSiTkCPEgsxR3M0pw50kJskqq6ryOywGCO5ljoJc1XvC3g6cGly3KE4rw7al47I2qXm/WRI+Pz0b54dXurde7BVT3cH2w/w4OxWSAz+XgpyndMNzfrtXiIe0LtZma1aaTruXLl2P16tXYtm0bunTpgqioKMycORNffvml0ms80g1EVJGUV4YpGyOQUyqCi6UBfg/rpfUei6TcMgxZdbHB/X3cLbH8FX+4a3gwtFQmx52MElxPKsDNlELcelwEoUj61Os4nOqq8J0sDOBsbgA7Uz3YmujB0kgAcwMBTPT5MBTwYSDggc/jgv/340oGQCKVQySVo1wsRWmlBCWVEhSUiZFfJkJWSRUyiyuRVliB1IJyVEnkT302j8uBj50xerpZoLe7JXq5WcCshY9em1IlkeG366lYey5RcT1e7e6Ej0f4tFrvaA2xVI73dsfgxL1s8Lgc/DQ5GCO62rdqTKR9oTZTs5qVdO3fvx979+5FWloaxOK6y3LcunVLbcGNGjUKtra22Lx5s2LbuHHjYGBggO3btyv1HnQDEVWlFVTgtc03kFZYAVsTXWwP66XV2X0lFWLM2xWDS4/yG3wNn8vB1F6dMG+Ip9ZmXMrlDEl5ZYhJL8aDzFLczyxBQk4ZSiolWvl8HR4Hna2ri6R2dTSFv6MpAp1N1VJPSxkyOcOR2xn47lQCMoqrK9Z3dTTF0pf8WryOpjpUSWR4Z8ctnIvPhYDHxU9TgvF8F+rhIqqhNlOzVP62WrNmDT799FNMnz4df/zxB2bOnImkpCRERkbinXfeUWtwzz33HH755RckJCTAy8sLt2/fxpUrV/DDDz80eIxIJIJI9M+srNLSUrXGRDq+TpYG2DenD17ffAMJOWUY//M1bJreAz3d1NOwllSIGy0FYWogwNfjAvDxgTt1Eq/+nlZ4e2BnbLycgr/ic7Ht+mPsj36CsH7uCHvODab6OmqJryFcLgeetsbwrJWAMsZQUC5Gcl450gsrkF5UgZxSEXJLq1BQLkZxhRilVVJUiKX19lQB1cmUvg4Pxno61dfDSABLQwHsTPXhYKYHZwsDuFoawslcXy31y1TFGMOp+9lYdSZBsQC4nYkeFj3vhfHdnLS+UHV9SioleGNbFG6mFkKXz8WGaSEYoOUlrkj7RG2mdqnc0+Xj44MlS5Zg8uTJMDY2xu3bt+Hu7o7FixejsLAQP/30k9qCY4zhk08+wcqVK8Hj8SCTybB8+XL897//bfCYpUuXYtmyZU9tp6ydqKq4QoywbVGIflwEAZ+LNZOCMNy/eY9qahKtogoxJDI5riYVYMuVFFSIZQ2Wgqg5RlglgbFedTJSk5xdS8zH1yfjcedJCQDAWI+PWaFumBnqqvHHa80llzNI5QxSuRwccMDhADo8bpudHSmTM/x5NwvrzyciPlsIoHrc1lsDOmNWqJvalyNqrtzSKkwPj0RcVimMdfnYND0EvdwtWzss0k5Qm6ldKiddBgYGiIuLg4uLC2xsbHDmzBkEBgbi0aNH6N27NwoKCpp+EyXt3r0bH3zwAb799lt06dIFsbGxWLBgAVatWoXp06fXe0x9WbuzszPdQKRZqiQyvLszBmfjcsDhAJ++6Iuw59xUGiidWVyJjw7cweVavVahHpaYGeqG+btiFImXqqUg5HKGE/ey8eO5f3pgDAU8vNbHBTP7usHOlCqON0eVRIb90U+w+UoKUv6uk2Yo4CHsOTeE9XPXeI+iKh7lCDEjPBIZxZWwMtLFb7N6ws+BvueI8qjN1C6VHy/a2dmhoKAALi4ucHFxQUREBAIDA5GSkgJ1j8n/4IMP8PHHH2PSpEkAgK5du+Lx48dYsWJFg0mXrq4udHVbdzAr6Tj0dHj45bVuWHr0Pn6PSMOXf8bhcUEFloz2U6p0QkmF+KmECwCuJlb/cTLrOTf89FciLj3KR36ZWKWki8vlYGSAPUb42+HEvWz8dD4RcVml+PViMjZfTsGoAHtM7+tKxTCV9KSoAjtupGFPZDoKy6vHqprq62BWqBtm9HWFqUHbSbYA4HpSAd7aHoXSKincrAyxdWYPuFh2jMK2RHuozdQulZOuwYMH4+jRo+jWrRvCwsKwcOFC7N+/H1FRURg7dqxag6uoqHiqNASPx4NcXv/YEEI0gc/j4ouX/eFiYYivTsRhe8RjpOSXY92Ubk02xPll4qcSrhpXEwswK9RN8bOwqnkD0muSrxe72uFcXC42XE7GzZRCHI7NxOHYTAQ6mWJqbxeMCrDX2qDz9kImZ7iUkIcdNx7jr/hc1JQoczTTx+x+bpgQ4twmF4XeE5mGzw7fg0TG0N3FHBunhcCilQr6EkKUp/S3yeHDhzF69Ghs2LBBkfTMmTMHFhYWuHLlCkaPHo05c+aoNbjRo0dj+fLl6NSpE7p06YKYmBisWrUKs2bNUuvnENIUDoeDN/q7o5OlARbuicWVxHyMWX8VG17vXmdg+b+VNpFIiaT//AFhrNeynhQOh4OhfrYY6meLO0+KsfVqKo7dycLtJyW4vf8OPj/6AKMD7TEmyBE9XC3axADw1sAYQ3y2EIdjM3A4JgM5pf88Wgn1sMS0Pq4Y4mPTporA1pDK5PjqeDy2XE0BAIwKsMd3rwZqvE4aIUQ9lB7TxefzYWVlhenTp2PWrFnw9vbWdGwQCoX43//+h0OHDiE3NxcODg6YPHkyFi9eDIFAub/qaPorUbe4rFLM3haFjOJKGAh4+P7VwAZrITVVc2vz9BCEbYtS2/I+/1ZQJsLuyHTsiUxHWmGFYruDqR5GBtjjpUBH+DuatGoxT21JzBXi+N1sHL2diUe1KtebGehgfDcnTO7VqU0vBF1YLsa7O2/hWlL1o+kFQz3x3hDPZ+J3R7SH2kzNUjrpyszMRHh4OLZt24akpCT06dMHYWFhmDBhwlPrL7YldAMRTSgoE+HdnTG4nlzdAL7Z3x0fvOD9VEmDxmpuhXpYIriTOe6kF2PluADYt2Ah66bI5QwRKQU4dCsDJ+9l1yly6mimj2F+thjkY4NebhYdptdEIpMj+nERzsfn4lx8bp0lggQ8LgZ4W2NcN0cM8rGBLr9tn3NMWhHe3RmjVKJPSEtQm6lZzSqOevHiRWzZsgUHDx4Eh8PBhAkTEBYWhj59+mgixhahG4hoilQmx8qT8dh4ufpRT4iLOdZOCYa9ad3kKbO48qmaW/08rbDspS4AAMt/1enStCqJDBce5uHonUyci8upUz9Ll89FTzcL9O1shb6dLdHFwaRNPmarj0zOEJdViojkAlxNzMeNlEJUiGWK/To8Dp7zsMKLXe3xgr8dTFr4OFcbGGPYdi0Vy4/HQSJjcLU0wK+vh8DbTnvFesmzhdpMzWrRMkBlZWXYvXs3wsPDERERAR8fH9y/f1+d8bUY3UBE007czcKH++9AKJLC3EAH370aiCG+dRcXbqzmVmuqFMtwJTEfZx/k4GJCHrJL665laCDgIbiTGYKczRDgZIYuDiZwNNNv9UdajDFkl1bhXkb1OowxaUWITSt+apkiC0MBBnhZY5CPDQZ4Wbepcg9NKf575uup+zkAgBH+dlg5PqBdJIuk/aI2U7NavPZiUlISwsPD8fPPP6O0tBQSiXaWBFEW3UBEG1Lzy/Hurlu4l1FdzXlWqBs+GuHd5h9b1cYYw6PcMlxLzMeVxALcTClAadXTay0a6/HhbWsMd2tDuFkZoZOFAVwsDeBgpg9zAx21JWSMMZRUSvCkqBLphRVILahAan45kvPL8DBbWG9sRrp89HSzQB93S/T1sISvnUm7nDBwI7kAC/fEIrOkCjo8Dv47whczQ11bPdklHR+1mZrVrKSroqIC+/btw5YtW3DlyhW4u7tjxowZmDFjBhwdHTURZ7PRDUS0RSSVYcXxeGy9lgoA8LU3wZpJQY3ObmzL5HKGhFwholKLcOdJMe48KUFibhmk8oa/MvR0uLA21oWVkS4sDAQw0deBkS4f+gIe9Phc8GtVoGeMQSxjEEllqBDJUCaqXvS6sEKMgjIxcoVVDS4dBFQvdu1pYwQ/BxMEO5shuJM5fOyM283j0PqIpXKsPpuAXy4mgTHA1dIAayd3Q1cn09YOjTwjqM3ULJWSrqtXr2LLli3Yt28fpFIpxo4di7CwMAwaNEiTMbYI3UBE284+yMGHB+6gsFwMXT4XH7zgjZmhbm12uRtViKVyJOaWITGvDEm5ZXhcUI7UggqkF1ag4O+CoupmZSSAk3l1b5qrpSHcrQ3haVPd09ZRBv0DwIPMUvxn3208yKruLR3f3QlLX+oCozZYJ4x0XNRmapbSSZeXlxeSkpIQHByMsLAwTJkyBaambf+vL7qBSGvIFVbhg313cDEhDwDQ09UC374a0KErhldJZMgprUKeUIT8MhFKKiUoqZSgrEqKSokMlRIZZHJAVmvtRQGfC10+F3o6PBjr8WGspwMLQwEsDAWwNdaDjYluh0qs6iOWyrH+QiJ++isRUjmDmYEOVrzSlWYnklZBbaZmKZ10zZ8/H2FhYQgMDNR0TGpFNxBpLYwx7LqZjuV/PkC5WAY9HS7+83zH6fUiLRf9uAj/PXhHsXbmC11s8cUYf9gY07qZpHVQm6lZLR5I39bRDURaW3phBT46cEdR1DLQyRQrxgbQwsTPsJIKCb45FY+dN9PAWHXZkCUvdcHoAHsaLE9aFbWZmkVJFyFawBjD7sh0fPVnHIQiKfhcDmb3c8e8wR5tcm0/ohlyOcOBW0+w8uRD5JdVLz80rpsTPhvpC3NaO5G0AdRmahYlXYRoUU5pFZb8cR8n72cDAOxM9PDpSF+Moh6ODi/6cSGWHX2AO09KAACdrQ2x/JWu6O1u2cqREfIPajM1i5IuQlrB2Qc5WHbsPtILKwEAvd0tsPSlLvCxo3u0o8korsTXJ+Jx9HYmgOpaYvMGe2BGqGu7quNGng3UZmoWJV2EtJIqiQy/XkzG+guJEEnl4HKACSHOWDjMC7YmNJC6vSsoE2Hd+ST8HvEYYpkcHA4wobsz/vOCN6yNdVs7PELqRW2mZjUr6bp58yYuXLiA3NxcyOV1ixeuWrVKbcGpA91ApK17UlSBr47H4fjd6keO+jo8zO7nhjf6u9OSL+1QaZUEmy6nYMuVFJT9vSxRb3cLfDbSD/6Obb/MDnm2UZupWSonXV999RU+++wzeHt7w9bWts44FA6Hg7/++kvtQbYE3UCkvYhKLcRXx+NwK60YAGBuoIM5Azrj9T4uMBDQYPu2rqRCgm3XU7HlagqKK6qXQ/N3NMGHL/ign6cVjdkj7QK1mZqlctJla2uLlStXYsaMGRoKSb3oBiLtCWMMp+5n49tTD5GUVw6gupzAWwPcMbWXC810bIPyhCJsuZqC7dcfK3q2PGyM8P4wLwz3t6Nki7Qr1GZqlspJl729PS5dugRPT09NxaRWdAOR9kgqk+NgTAbWnU/E44IKANU9X7NC3fBabxcqL9AGJOYKEX41Ffujn0AkrR5m4WNnjLmDPDCyqz0VwCXtErWZmqVy0vXNN98gMzMTP/zwg4ZCUi+6gUh7VpN8rT+fiNS/ky89HS5e7e6MWc+5wc2q4y4r1BbJ5QwXE/Kw5WoKLj/KV2wPcjbDO4M8MNTXhnq2SLtGbaZmqZx0yeVyjBw5EgkJCfDz84OOTt2BvgcPHlRrgC1FNxDpCKQyOf68m4VfLyYrFkTmcIAhPjaY1scVz3lYgUs9KxpTWC7GwVtPsPNGGpLzqx/7cjjAUF9bzAp1Q293C0q2SIdAbaZmqTxAZN68eTh//jwGDRoES0tL+qIhRAv4PC5eDnLES4EOuJ5cgI2XknH+YR7OxuXibFwunC30MalHJ4zv7kTlJtREJme4lJCHfdHpOPsgF2JZ9SNEYz0+JoY4Y1ofV3SyNGjlKAkh7YnKPV3GxsbYvXs3Ro4cqamY1IqydtJRJeWV4bdrqTgYkwFhVfUAbh6Xg0He1hjbzQmDfWygp0PFN1XBGENclhCHYzPwR2wGckpFin0BTqaY1KMTXg5yoAkNpMOiNlOzVE66XFxccOrUKfj4+GgqJrWiG4h0dJViGf68m4W9kem4mVqo2G6sx8cwP1uM8LdHP08rSsAawBjDvYxSnLqfjeN3sxSPD4HqyQtjgh0xvrsTujhQjS3S8VGbqVkqJ13h4eE4efIkwsPDYWDQ9rvW6QYiz5LEXCEO3MrAHzEZyCypUmw3EPAwyMcGw7vYob+XNUz1n+2iqxKZHJEphTgTl4MzD3LwpKhSsU/A5yp6Cwd520DA57ZipIRoF7WZmqVy0hUcHIykpCQwxuDq6vrUQPpbt26pNcCWohuIPIvkcoaox0U4cS8LJ+9lI6tWAsbjctDdxRz9PKzQ18MKAU6m0OF17MRCLmd4lFuGGykFuJSQj+tJ+SgXyxT79XV4GOBljRFd7TDYxwbGtBIAeUZRm6lZKiddy5Yta3T/kiVLWhSQutENRJ51jDHcflKCE3ezcC4+F4m5ZXX26+vwEOJqjp6uFghxtUCQsxn0Be37UaREJkd8lhBRjwtxI7kQN1MLUVgurvMaS0MBBvvYYKifLfp7Wrf7cyZEHajN1Cxa8JqQZ0xaQQUuJ+bhamI+riUVKJasqcHjcuBpY4QAJ1P42ZvA194EnrbGsGijBVkrxFI8yinDw2whHmSV4m5GCe5nlqBKUnddWH0dHrq7mKNPZ0v097RGFwcTKrNByL9Qm6lZzU66oqOjERcXBw6HAz8/PwQHB6s7NrWgG4iQhtU8dotILkBkaiEiUwvrzNirzcJQADcrQ7haGsLF0gCdLAzgbKEPO1N92Brrgq+hR5RyOUNRhRhZJVV4UlSBtMIKpBZUIK2gAsl5ZXXGrtVmosdHcCdz9HK3QC83C3R1NKPxWYQ0gdpMzVI56crNzcWkSZNw4cIFmJmZgTGGkpISDBo0CLt374a1tbWmYm0WuoEIUU12SRVi04txP7MEcVmliM8W1hloXh8OB7AwEMDKSBfmhjow0xfARJ8PQ10+DAQ86PF5EPC54HE5iuVxGKuuhSWRy1ElkaNSLEW5WAZhlRQllRIUlotQWCZGXpkIElnjX1NWRgJ42xnDx84EXR1N4e9oCncrQ+rJIkRF1GZqlspJ18SJE5GUlITt27fD19cXAPDgwQNMnz4dHh4e2LVrl0YCbS66gQhpuQqxFMl55UgtKEdqfjnSCqt7nJ4UVSKntKrJpEgdrIx04WSuDydzfUVvm7u1IdytjGgtSkLUhNpMzVI56TI1NcXZs2fRo0ePOttv3ryJ559/HsXFxeqMr8XoBiJEs+RyhvxyEfKFYuSXiVBcKUFxhRjCKinKRFJUimUQSWUQSeSQMQapvPorhwNAh8eFDo8DAZ8LQwEf+gIeTPR0YKzHh6WRABaGurAx1oWVkS49GiREC6jN1CyVyyrL5fKnykQAgI6ODuRyeT1HEEI6Mi6XAxtjPdgY0/JDhBDSGJX/dBw8eDDee+89ZGZmKrZlZGRg4cKFGDJkiFqDI4QQQgjpKFROun766ScIhUK4urqic+fO8PDwgJubG4RCIdauXauJGAkhhBBC2j2VHy86Ozvj1q1bOHPmDOLj48EYg5+fH4YOHaqJ+AghhBBCOgQqjkoIIYQQANRmappSPV1r1qxR+g3nz5/f7GAIIYQQQjoqpXq63Nzc6vycl5eHiooKmJmZAQCKi4thYGAAGxsbJCcnayTQ5qKsnRBCCFEOtZmapdRA+pSUFMW/5cuXIygoCHFxcSgsLERhYSHi4uLQrVs3fPHFF5qOlxBCCCGkXVJ5TFfnzp2xf//+p9ZajI6Oxvjx45GSkqLWAFuKsnZCCCFEOdRmapbKJSOysrIgkUie2i6TyZCTk6OWoAghhBBCOhqVk64hQ4bgjTfeQFRUFGo6yaKiovDWW29R2QhCCCGEkAaonHRt2bIFjo6O6NmzJ/T09KCrq4tevXrB3t4emzZt0kSMhBBCCCHtnsrFUa2trXH8+HEkJCQoiqP6+vrCy8tLE/ERQgghhHQIKiddNby8vCjRIoQQQghRkspJl0wmw9atW3Hu3Dnk5uZCLpfX2f/XX3+pLThCCCGEkI5C5aTrvffew9atWzFy5Ej4+/uDw+FoIi5CCCGEkA5F5aRr9+7d2Lt3L1588UVNxEMIIYQQ0iGpPHtRIBDAw8NDE7EQQgghhHRYKidd77//Pn788UeoWMieEEIIIeSZpvLjxStXruD8+fM4ceIEunTpAh0dnTr7Dx48qLbgCCGEEEI6CpWTLjMzM7zyyiuaiIUQQgghpMNSOekKDw/XRByEEEIIIR2aymO6CCGEEEKI6ppVkX7//v3Yu3cv0tLSIBaL6+y7deuWWgIjhBBCCOlIVO7pWrNmDWbOnAkbGxvExMSgZ8+esLS0RHJyMkaMGKGJGAkhhBBC2j2Vk67169djw4YN+OmnnyAQCPDhhx/izJkzmD9/PkpKSjQRIyGEEEJIu6dy0pWWloa+ffsCAPT19SEUCgEAr7/+Onbt2qXe6AghhBBCOgiVky47OzsUFBQAAFxcXBAREQEASElJoYKphBBCCCENUDnpGjx4MI4ePQoACAsLw8KFCzFs2DBMnDiR6ncRQgghhDSAw1TsnpLL5ZDL5eDzqyc+7t27F1euXIGHhwfmzJkDgUCgkUCbq7S0FKampigpKYGJiUlrh0MIIYS0WdRmapbKSVdjMjIy4OjoqK63Uwu6gQghhBDlUJupWWopjpqdnY158+bBw8NDHW9HCCGEENLhKJ10FRcXY+rUqbC2toaDgwPWrFkDuVyOxYsXw93dHREREdiyZYsmYyWEEEIIabeUTro++eQTXLp0CdOnT4eFhQUWLlyIUaNG4cqVKzhx4gQiIyMxefJktQeYkZGB1157DZaWljAwMEBQUBCio6PV/jmEEEIIIZqk9DJAf/75J8LDwzF06FDMnTsXHh4e8PLywg8//KCx4IqKihAaGopBgwbhxIkTsLGxQVJSEszMzDT2mYQQQgghmqB00pWZmQk/Pz8AgLu7O/T09DB79myNBQYAK1euhLOzM8LDwxXbXF1dNfqZhBBCCCGaoPTjRblcDh0dHcXPPB4PhoaGGgmqxpEjRxASEoJXX30VNjY2CA4OxsaNGxs9RiQSobS0tM4/QgghhDyN2kztUrqnizGGGTNmQFdXFwBQVVWFOXPmPJV4HTx4UG3BJScn4+eff8aiRYvwySef4ObNm5g/fz50dXUxbdq0eo9ZsWIFli1bprYYCCGEkI6K2kztUrpO18yZM5V6w9qPAltKIBAgJCQE165dU2ybP38+IiMjcf369XqPEYlEEIlEip9LS0vh7OxMNUcIIYSQf6E2U7uU7ulSZzKlLHt7e8U4shq+vr44cOBAg8fo6uoqeuMIIYQQ0jBqM7VLLcVRNSU0NBQPHz6ssy0hIQEuLi6tFBEhhBBCSPO06aRr4cKFiIiIwFdffYXExETs3LkTGzZswDvvvNPaoRFCCCGEqKRNJ109evTAoUOHsGvXLvj7++OLL77ADz/8gKlTp7Z2aIQQQgghKlHrgtdtES3eSQghhCiH2kzNatM9XYQQQgghHQUlXYQQQgghWkBJFyGEEEKIFlDSRQghhBCiBZR0EUIIIYRoASVdhBBCCCFaQEkXIYQQQogWUNJFCCGEEKIFlHQRQgghhGgBJV2EEEIIIVpASRchhBBCiBZQ0kUIIYQQogWUdBFCCCGEaAElXYQQQgghWkBJFyGEEEKIFlDSRQghhBCiBZR0EUIIIYRoASVdhBBCCCFaQEkXIYQQQogWUNJFCCGEEKIFlHQRQgghhGgBJV2EEEIIIVrAb+0ACCHtS0mFGPllYpRWSWCirwMrQwFMDQStHRYhhLR5lHQRQpSWWVyJjw7cweVH+Ypt/T2t8PW4ADiY6bdiZIQQ0vbR40VCiFJKKsRPJVwAcOlRPj4+cAclFeJWiowQQtoHSroIIUrJLxM/lXDVuPQoH/lllHQRQkhjKOkihCiltErS6H5hE/sJIeRZR0kXIUQpJno6je43bmI/IYQ86yjpIoQoxcpIgP6eVvXu6+9pBSsjmsFICCGNoaSLEKIUUwMBvh4X8FTi1d/TCivHBVDZCEIIaQKVjCCEKM3BTB9rJwcjv0wMYZUExno6sDKiOl2EEKIMSroIISoxNaAkixBCmoMeLxJCCCGEaAElXYQQQgghWkBJFyGEEEKIFlDSRQghhBCiBZR0EUIIIYRoASVdhBBCCCFaQEkXIYQQQogWUNJFCCGEEKIFlHQRQgghhGgBJV2EEEIIIVpASRchhBBCiBZQ0kUIIYQQogWUdBFCCCGEaAElXYQQQgghWkBJFyGEEEKIFlDSRQghhBCiBZR0EUIIIYRoASVdhBBCCCFaQEkXIYQQQogWUNJFCCGEEKIFlHQRQgghhGgBJV2EEEIIIVpASRchhBBCiBZQ0kUIIYQQogWUdBFCCCGEaAElXYQQQgghWkBJFyGEEEKIFlDSRQghhBCiBZR0EUIIIYRoQbtKulasWAEOh4MFCxa0diiEEEIIISppN0lXZGQkNmzYgICAgNYOhRBCCCFEZe0i6SorK8PUqVOxceNGmJubt3Y4hBBCCCEqaxdJ1zvvvIORI0di6NChTb5WJBKhtLS0zj9CCCGEPI3aTO1q80nX7t27ER0djRUrVij1+hUrVsDU1FTxz9nZWcMREkIIIe0TtZnaxWGMsdYOoiHp6ekICQnB6dOnERgYCAAYOHAggoKC8MMPP9R7jEgkgkgkUvxcWloKZ2dnlJSUwMTERBthE0IIIe0CtZna1aaTrsOHD+OVV14Bj8dTbJPJZOBwOOByuRCJRHX21ae0tBSmpqZ0AxFCCCFNoDZTs/itHUBjhgwZgrt379bZNnPmTPj4+OCjjz5qMuEihBBCCGkr2nTSZWxsDH9//zrbDA0NYWlp+dR2QgghhJC2rM0PpCeEEEII6QjadE9XfS5cuNDaIRBCCCGEqIx6ugghhBBCtICSLkIIIYQQLaCkixBCCCFECyjpIoQQQgjRAkq6CCGEEEK0gJIuQgghhBAtoKSLEEIIIUQLKOkihBBCCNECSroIIYQQQrSAki5CCCGEEC2gpIsQQgghRAso6SKEEEII0QJKugghhBBCtICSLkIIIYQQLaCkixBCCCFECyjpIoQQQgjRAkq6CCGEEEK0gJIuQgghhBAtoKSLEEIIIUQLKOkihBBCCNECSroIIYQQQrSAki5CCCGEEC2gpIsQQgghRAso6SKEEEII0QJ+awegaYwxAEBpaWkrR0IIIYRoj7GxMTgcTmuHQWrp8EmXUCgEADg7O7dyJIQQQoj2lJSUwMTEpLXDILVwWE1XUAcll8uRmZlJGT+qe/ucnZ2Rnp5O/yM2E11D9aDr2HJ0DVuuo1/D5rR7jDEIhUJqMzWkw/d0cblcODk5tXYYbYqJiUmH/ILRJrqG6kHXseXoGrYcXcN/cDgcuhYaRAPpCSGEEEK0gJIuQgghhBAtoKTrGaKrq4slS5ZAV1e3tUNpt+gaqgddx5aja9hydA2JtnX4gfSEEEIIIW0B9XQRQgghhGgBJV2EEEIIIVpASRchhBBCiBZQ0kUIIYQQogWUdHUw69evh5ubG/T09NC9e3dcvny50deLRCJ8+umncHFxga6uLjp37owtW7ZoKdq2SdVruGPHDgQGBsLAwAD29vaYOXMmCgoKtBRt23Pp0iWMHj0aDg4O4HA4OHz4cJPHXLx4Ed27d4eenh7c3d3xyy+/aD7QNk7V63jw4EEMGzYM1tbWMDExQZ8+fXDq1CntBNtGNederHH16lXw+XwEBQVpLD7y7KGkqwPZs2cPFixYgE8//RQxMTHo168fRowYgbS0tAaPmTBhAs6dO4fNmzfj4cOH2LVrF3x8fLQYddui6jW8cuUKpk2bhrCwMNy/fx/79u1DZGQkZs+ereXI247y8nIEBgbip59+Uur1KSkpePHFF9GvXz/ExMTgk08+wfz583HgwAENR9q2qXodL126hGHDhuH48eOIjo7GoEGDMHr0aMTExGg40rZL1WtYo6SkBNOmTcOQIUM0FBl5ZjHSYfTs2ZPNmTOnzjYfHx/28ccf1/v6EydOMFNTU1ZQUKCN8NoFVa/ht99+y9zd3etsW7NmDXNyctJYjO0JAHbo0KFGX/Phhx8yHx+fOtveeust1rt3bw1G1r4ocx3r4+fnx5YtW6b+gNohVa7hxIkT2WeffcaWLFnCAgMDNRoXebZQT1cHIRaLER0djeeff77O9ueffx7Xrl2r95gjR44gJCQE33zzDRwdHeHl5YX//Oc/qKys1EbIbU5zrmHfvn3x5MkTHD9+HIwx5OTkYP/+/Rg5cqQ2Qu4Qrl+//tQ1f+GFFxAVFQWJRNJKUbV/crkcQqEQFhYWrR1KuxIeHo6kpCQsWbKktUMhHVCHX/D6WZGfnw+ZTAZbW9s6221tbZGdnV3vMcnJybhy5Qr09PRw6NAh5OfnY+7cuSgsLHwmx3U15xr27dsXO3bswMSJE1FVVQWpVIqXXnoJa9eu1UbIHUJ2dna911wqlSI/Px/29vatFFn79v3336O8vBwTJkxo7VDajUePHuHjjz/G5cuXwedT80jUj3q6OhgOh1PnZ8bYU9tqyOVycDgc7NixAz179sSLL76IVatWYevWrc9sbxeg2jV88OAB5s+fj8WLFyM6OhonT55ESkoK5syZo41QO4z6rnl924lydu3ahaVLl2LPnj2wsbFp7XDaBZlMhilTpmDZsmXw8vJq7XBIB0WpfAdhZWUFHo/3VI9Mbm7uU70INezt7eHo6AhTU1PFNl9fXzDG8OTJE3h6emo05ramOddwxYoVCA0NxQcffAAACAgIgKGhIfr164cvv/ySemmUYGdnV+815/P5sLS0bKWo2q89e/YgLCwM+/btw9ChQ1s7nHZDKBQiKioKMTExePfddwFU/2HKGAOfz8fp06cxePDgVo6StHfU09VBCAQCdO/eHWfOnKmz/cyZM+jbt2+9x4SGhiIzMxNlZWWKbQkJCeByuXByctJovG1Rc65hRUUFuNy6/xvxeDwA//TWkMb16dPnqWt++vRphISEQEdHp5Wiap927dqFGTNmYOfOnTSuUEUmJia4e/cuYmNjFf/mzJkDb29vxMbGolevXq0dIukIWnEQP1Gz3bt3Mx0dHbZ582b24MEDtmDBAmZoaMhSU1MZY4x9/PHH7PXXX1e8XigUMicnJzZ+/Hh2//59dvHiRebp6clmz57dWqfQ6lS9huHh4YzP57P169ezpKQkduXKFRYSEsJ69uzZWqfQ6oRCIYuJiWExMTEMAFu1ahWLiYlhjx8/Zow9fQ2Tk5OZgYEBW7hwIXvw4AHbvHkz09HRYfv372+tU2gTVL2OO3fuZHw+n61bt45lZWUp/hUXF7fWKbQ6Va/hv9HsRaJulHR1MOvWrWMuLi5MIBCwbt26sYsXLyr2TZ8+nQ0YMKDO6+Pi4tjQoUOZvr4+c3JyYosWLWIVFRVajrptUfUarlmzhvn5+TF9fX1mb2/Ppk6dyp48eaLlqNuO8+fPMwBP/Zs+fTpjrP5reOHCBRYcHMwEAgFzdXVlP//8s/YDb2NUvY4DBgxo9PXPoubci7VR0kXUjcMYPQMhhBBCCNE0GtNFCCGEEKIFlHQRQgghhGgBJV2EEEIIIVpASRchhBBCiBZQ0kUIIYQQogWUdBFCCCGEaAElXYQQQgghWkBJFyGEEEKIFlDSRZ45rq6u+OGHH1o7DLVS9Zy2bt0KMzOzRl+zdOlSBAUFtSiulujfvz927typ1GuVOZ+2qL3GDQDHjh1DcHAw5HJ5a4dCSLtBSRfRuhkzZoDD4YDD4YDP56NTp054++23UVRU1Nqhacy8efPg6elZ776MjAzweDwcPHiw2e8fGRmJN998s9nHa8qlS5cwevRoODg4gMPh4PDhw0odd+zYMWRnZ2PSpEmaDZA026hRo8DhcJROjAkhlHSRVjJ8+HBkZWUhNTUVmzZtwtGjRzF37tzWDktjwsLCkJiYiMuXLz+1b+vWrbC0tMTo0aNVfl+xWAwAsLa2hoGBQYvjVLfy8nIEBgbip59+Uum4NWvWYObMmeBy6SuqLZs5cybWrl3b2mEQ0m7QNxppFbq6urCzs4OTkxOef/55TJw4EadPn1bsl8lkCAsLg5ubG/T19eHt7Y0ff/yxznvMmDEDY8aMwXfffQd7e3tYWlrinXfegUQiUbwmNzcXo0ePhr6+Ptzc3LBjx46nYklLS8PLL78MIyMjmJiYYMKECcjJyVHsr3nMtmXLFnTq1AlGRkZ4++23IZPJ8M0338DOzg42NjZYvnx5g+cbFBSEbt26YcuWLU/t27p1K6ZNmwYul6v0Oa9YsQIODg7w8vIC8PTjxVWrVqFr164wNDSEs7Mz5s6di7Kysqc++/Dhw/Dy8oKenh6GDRuG9PT0Bs8BAMLDw+Hr6ws9PT34+Phg/fr1jb5+xIgR+PLLLzF27NhGX1dbfn4+zp49i5deeqnO9uLiYrz55puwtbWFnp4e/P39cezYsTqvOXXqFHx9fWFkZKRI7GvI5XJ8/vnncHJygq6uLoKCgnDy5EnFfrFYjHfffRf29vbQ09ODq6srVqxYodhfUlKCN998EzY2NjAxMcHgwYNx+/Ztxf6a+2T79u1wdXWFqakpJk2aBKFQ2OQ5N/R7SE1NBZfLRVRUVJ3Xr127Fi4uLqhv6dzPP/8cXbt2fWp79+7dsXjxYqWuxYULF8DhcFBcXKzYFhsbCw6Hg9TUVMW2l156CTdv3kRycnKT50gIAdDKC26TZ9D06dPZyy+/rPg5KSmJ+fn5MVtbW8U2sVjMFi9ezG7evMmSk5PZ77//zgwMDNiePXvqvI+JiQmbM2cOi4uLY0ePHmUGBgZsw4YNiteMGDGC+fv7s2vXrrGoqCjWt29fpq+vz1avXs0YY0wul7Pg4GD23HPPsaioKBYREcG6devGBgwYoHiPJUuWMCMjIzZ+/Hh2//59duTIESYQCNgLL7zA5s2bx+Lj49mWLVsYAHb9+vUGz3vdunXM0NCQCYVCxbYLFy4wAOz+/ftKn7ORkRF7/fXX2b1799jdu3cZY4y5uLgozokxxlavXs3++usvlpyczM6dO8e8vb3Z22+/rdgfHh7OdHR0WEhIiOLa9OzZk/Xt27fOeQcGBip+3rBhA7O3t2cHDhxgycnJ7MCBA8zCwoJt3bq1wXOuDQA7dOhQk687dOgQMzQ0ZDKZTLFNJpOx3r17sy5durDTp0+zpKQkdvToUXb8+PE65zN06FAWGRnJoqOjma+vL5syZYriPVatWsVMTEzYrl27WHx8PPvwww+Zjo4OS0hIYIwx9u233zJnZ2d26dIllpqayi5fvsx27tzJGKu+T0JDQ9no0aNZZGQkS0hIYO+//z6ztLRkBQUFiutlZGTExo4dy+7evcsuXbrE7Ozs2CeffNLguSrzexg2bBibO3duneOCg4PZ4sWL633P9PR0xuVy2c2bNxXbbt++zTgcDktKSlLqWpw/f54BYEVFRYr3iImJYQBYSkpKnc+zsbFR+h4g5FlHSRfRuunTpzMej8cMDQ2Znp4eA8AAsFWrVjV63Ny5c9m4cePqvI+LiwuTSqWKba+++iqbOHEiY4yxhw8fMgAsIiJCsT8uLo4BUCQop0+fZjwej6WlpSlec//+fQZA0WgtWbKEGRgYsNLSUsVrXnjhBebq6lonMfD29mYrVqxoMP6ioiKmp6fHtmzZotg2bdo01qdPH5XO2dbWlolEojqv+3fS9W979+5llpaWip/Dw8MbvDY3btxQnHftpMvZ2VmRhNT44osvGo2/NmWTrtWrVzN3d/c6206dOsW4XC57+PBhvcfUnE9iYqJi27p16+ok8g4ODmz58uV1juvRo4cioZk3bx4bPHgwk8vlT73/uXPnmImJCauqqqqzvXPnzuzXX39ljNV/n3zwwQesV69eDZ6rMr+HPXv2MHNzc8Vnx8bGMg6H81TyU9uIESPqJNkLFixgAwcOVPpaqJJ0BQcHs6VLlzYYCyHkH/R4kbSKQYMGITY2Fjdu3MC8efPwwgsvYN68eXVe88svvyAkJATW1tYwMjLCxo0bkZaWVuc1Xbp0AY/HU/xsb2+P3NxcAEBcXBz4fD5CQkIU+318fOrMFouLi4OzszOcnZ0V2/z8/GBmZoa4uDjFNldXVxgbGyt+trW1hZ+fX50xR7a2torPro+ZmRnGjh2reMQoFApx4MABzJo1S6Vz7tq1KwQCQYOfAwDnz5/HsGHD4OjoCGNjY0ybNg0FBQUoLy9XvKaha1P7vGvk5eUhPT0dYWFhMDIyUvz78ssvkZSU1GgsqqqsrISenl6dbbGxsXByclI8Tq2PgYEBOnfurPi59r1QWlqKzMxMhIaG1jkmNDRUcb4zZsxAbGwsvL29MX/+/DqPu6Ojo1FWVgZLS8s655+SklLn/P99n9SOoSFN/R7GjBkDPp+PQ4cOAQC2bNmCQYMGwdXVtcH3fOONN7Br1y5UVVVBIpFgx44divtMmWuhCn19fVRUVKh8HCHPIn5rB0CeTYaGhvDw8ABQPWh60KBBWLZsGb744gsAwN69e7Fw4UJ8//336NOnD4yNjfHtt9/ixo0bdd5HR0enzs8cDkcxhZ39Pd6Fw+E0GAdjrN79/95e3+c09tkNCQsLw5AhQ/Do0SNcvHgRADBx4kSVztnQ0LDRz3j8+DFefPFFzJkzB1988QUsLCxw5coVhIWF1RnvVhPzv9W3rea8Nm7ciF69etXZVzvpVQcrK6unZrLq6+s3eVx9vw/2rzFP/z632r/nbt26ISUlBSdOnMDZs2cxYcIEDB06FPv374dcLoe9vT0uXLjw1OfWTuKbc0/UF1ftbQKBAK+//jrCw8MxduxY7Ny5s8nyIKNHj4auri4OHToEXV1diEQijBs3rtHPrH0tav6YqH39/n3v1CgsLIS1tXXjJ0gIAUBJF2kjlixZghEjRuDtt9+Gg4MDLl++jL59+9aZ0ahqj4qvry+kUimioqLQs2dPAMDDhw/rDA728/NDWloa0tPTFb1dDx48QElJCXx9fVt+Yv8yaNAguLu7Y+vWrTh//jwmTJig6BlRxzkDQFRUFKRSKb7//ntF47l3796nXtfQtfHx8Xnqtba2tnB0dERycjKmTp2qckyqCA4ORnZ2NoqKimBubg4ACAgIwJMnT5CQkNBob1dDTExM4ODggCtXrqB///6K7deuXVOcf83rJk6ciIkTJ2L8+PEYPnw4CgsL0a1bN2RnZ4PP5zfaw9QcyvweZs+eDX9/f6xfvx4SiaTJiQl8Ph/Tp09HeHg4dHV1MWnSJMXsVmWuRU0SlZWVpfgdxMbGPvU5VVVVSEpKQnBwcPMvACHPEEq6SJswcOBAdOnSBV999RV++ukneHh44LfffsOpU6fg5uaG7du3IzIyEm5ubkq/p7e3N4YPH4433ngDGzZsAJ/Px4IFC+r0mgwdOhQBAQGYOnUqfvjhB0ilUsydOxcDBgyo88hHXTgcDmbOnIlVq1ahqKgI3377rWKfOs4ZADp37gypVIq1a9di9OjRuHr1Kn755ZenXqejo4N58+ZhzZo10NHRwbvvvovevXvXSUJqW7p0KebPnw8TExOMGDECIpEIUVFRKCoqwqJFi+o9pqysDImJiYqfU1JSEBsbCwsLC3Tq1KneY4KDg2FtbY2rV69i1KhRAIABAwagf//+GDduHFatWgUPDw/Ex8eDw+Fg+PDhSl2XDz74AEuWLEHnzp0RFBSE8PBwxMbGKma0rl69Gvb29ggKCgKXy8W+fftgZ2cHMzMzDB06FH369MGYMWOwcuVKeHt7IzMzE8ePH8eYMWNadK8o83vw9fVF79698dFHH2HWrFlK9fzNnj1b8YfD1atXVboWHh4ecHZ2xtKlS/Hll1/i0aNH+P7775/6jIiICOjq6qJPnz7NPn9CniU0pou0GYsWLcLGjRuRnp6OOXPmYOzYsZg4cSJ69eqFgoKCZtXxCg8Ph7OzMwYMGICxY8cqpvzXqCnYaW5ujv79+2Po0KFwd3fHnj171HlqdcyYMQMlJSXw9vauM65GXeccFBSEVatWYeXKlfD398eOHTvqlD6oYWBggI8++ghTpkxBnz59oK+vj927dzf4vrNnz8amTZuwdetWdO3aFQMGDMDWrVsbTQqjoqIQHBys6AlZtGgRgoODFaUL6sPj8TBr1qynynscOHAAPXr0wOTJk+Hn54cPP/wQMpmsqcuhMH/+fLz//vt4//330bVrV5w8eRJHjhxRFK01MjLCypUrERISgh49eiA1NRXHjx8Hl8sFh8PB8ePH0b9/f8yaNQteXl6YNGkSUlNTYWtrq3QM9VH29xAWFgaxWFxnDGBjPD090bdvX3h7ez/1SLipa6Gjo4Ndu3YhPj4egYGBWLlyJb788sunPmPXrl2YOnVqm6wRR0hbxGH/HvRACCGtLCcnB126dEF0dDRcXFxaO5w2Yfny5di9ezfu3r2r1OsZY/Dx8cFbb73VYE9kS+Tl5cHHxwdRUVEq98YS8qyini5CSJtja2uLzZs3PzVz81lUVlaGyMhIrF27FvPnz1fqmNzcXKxatQoZGRmYOXOmRuJKSUnB+vXrKeEiRAXU00UIIW3YjBkzsGvXLowZMwY7d+5UarYoh8OBlZUVfvzxR0yZMkULURJClEFJFyGEEEKIFtDjRUIIIYQQLaCkixBCCCFECyjpIoQQQgjRAkq6CCGEEEK0gJIuQgghhBAtoKSLEEIIIUQLKOkihBBCCNECSroIIYQQQrTg/4czlhltpiXBAAAAAElFTkSuQmCC", + "text/plain": [ + "<Figure size 600x600 with 3 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "values_of_RV_1 = sample_q\n", + "values_of_RV_2 = sample_a\n", + "\n", + "g = sns.JointGrid()\n", + "sns.kdeplot(x=values_of_RV_1,\n", + " y=values_of_RV_2, ax=g.ax_joint, bw_adjust=3)\n", + "sns.scatterplot(x=values_of_RV_1[sample_Z<0],\n", + " y=values_of_RV_2[sample_Z<0], ax=g.ax_joint)\n", + "g.ax_joint.set_xlabel('Random Variable 1 (chosen by you)')\n", + "g.ax_joint.set_ylabel('Random Variable 2 (chosen by you)')\n", + "print('Joint density of 2 RVs with failure realizations')" + ] + }, + { + "cell_type": "markdown", + "id": "75f127f7-c40b-425d-91cf-6c6ecad207a2", + "metadata": {}, + "source": [ + "## Case 2: exceeding the health threshold\n", + "\n", + "Now we return to the failure definition of exceeding the threshold (`flip_LSF` = 1)." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "3ee884a7-16fb-46bf-9766-9899e662a9bc", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "MONTE CARLO RESULTS\n", + "--------------------------------------------------\n", + " N = 100000, number of samples\n", + " Nf = 65, number of failed realizations\n", + " pf = 6.500e-04, estimated failure probability\n", + " V = 0.124, c.o.v. of estimated pf\n", + "\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "N = 100000\n", + "\n", + "t = 30\n", + "x = 500\n", + "threshold = 1e-4\n", + "\n", + "flip_LSF = 1\n", + "\n", + "sample_q = q_rv.get_sample(N)\n", + "sample_n = n_rv.get_sample(N)\n", + "sample_a = a_rv.get_sample(N)\n", + "\n", + "sample_C_C0 = C_C0(sample_q, sample_n, sample_a, x, t)\n", + "sample_Z = flip_LSF*limit_state_fun(sample_q,\n", + " sample_n,\n", + " sample_a,\n", + " x, t, threshold)\n", + "\n", + "monte_carlo(sample_Z);" + ] + }, + { + "cell_type": "markdown", + "id": "d1d693c6-df03-442f-a100-a065355b2c12", + "metadata": {}, + "source": [ + "NB: *the joint density and failure point plot is commented out here to prevent slowing down the kernel. When N=100000 (1e5) or higher, it will take around a minute to run.*" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "19a0f38a-f4e2-4dc0-8ade-0094f2a3cc91", + "metadata": {}, + "outputs": [], + "source": [ + "# values_of_RV_1 = sample_q\n", + "# values_of_RV_2 = sample_a\n", + "\n", + "# g = sns.JointGrid()\n", + "# sns.kdeplot(x=values_of_RV_1,\n", + "# y=values_of_RV_2, ax=g.ax_joint, bw_adjust=3)\n", + "# sns.scatterplot(x=values_of_RV_1[sample_Z<0],\n", + "# y=values_of_RV_2[sample_Z<0], ax=g.ax_joint)\n", + "# g.ax_joint.set_xlabel('Random Variable 1 (chosen by you)')\n", + "# g.ax_joint.set_ylabel('Random Variable 2 (chosen by you)')\n", + "# print('Joint density of 2 RVs with failure realizations')" + ] + }, + { + "cell_type": "markdown", + "id": "3e7d0cc4", + "metadata": {}, + "source": [ + "### Gradient Vector\n", + "\n", + "Partial derivatives will be useful for evaluating the functional influence of the variables on the limit states. The gradient vector is defined as:\n", + "\n", + "$\\nabla_{\\mathbf{y}} G(\\mathbf{y})=\\left(\\frac{\\partial G(\\mathbf{y})}{\\partial \\mathbf{y}_1}, \\cdots, \\frac{\\partial G(\\mathbf{y})}{\\partial \\mathbf{y}_n}\\right) $\n", + "\n", + "To find the gradient vector we need to find the partial derivatives of $\\frac{C}{C_0}$\n", + "\n", + "$\\frac{C}{C_0} = \\frac{1}{2} \\mathrm{erfc}\\left(\\frac{x-(q/n)t}{2\\sqrt{a(q/n)t}}\\right)=\\frac{1}{2} \\left(1-\\mathrm{erf}\\frac{x-(q/n)t}{2\\sqrt{a(q/n)t}}\\right)$\n", + "\n", + "Using $\\frac{\\partial}{\\partial x} (\\mathrm{erf} x) = \\frac{2}{\\sqrt{\\pi}}e^{-x^2} $ and $\\Omega = \\frac{1}{\\sqrt{\\pi}}e^{-\\left(\\frac{x-(q/n)t}{2\\sqrt{a(q/n)t}}\\right)^2} $, the derivatives are:\n", + "\n", + "$\\frac{\\partial (C/C_0)}{\\partial x} = \\Omega\\left(-\\frac{1}{2\\sqrt{a(q/n)t}}\\right)$\n", + "\n", + "$\\frac{\\partial (C/C_0)}{\\partial t} =\\Omega\\left(\\frac{x}{4\\sqrt{a(q/n)t^3}}+\\frac{q}{4n\\sqrt{a(q/n)t}}\\right)$\n", + "\n", + "$\\frac{\\partial (C/C_0)}{\\partial q} = \\Omega\\left(\\frac{x}{4\\sqrt{a(1/n)tq^3}}+\\frac{t}{4n\\sqrt{a(q/n)t}}\\right)$\n", + "\n", + "$\\frac{\\partial (C/C_0)}{\\partial n} = \\Omega\\left(-\\frac{x}{4\\sqrt{aqtn}}-\\frac{qt}{4\\sqrt{qatn^3}}\\right)$\n", + "\n", + "$\\frac{\\partial (C/C_0)}{\\partial a} = \\Omega\\left(\\frac{x-q/nt}{4\\sqrt{(q/n)ta^3}}\\right)$" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "a761d424", + "metadata": {}, + "outputs": [], + "source": [ + "def gradient(q, n, a, x, t):\n", + " Om = 1/np.sqrt(np.pi)*np.exp(-((x - q/n*t)/(2*np.sqrt(a*q/n*t)))**2)\n", + " dx = Om*(-1/(2*np.sqrt(a*q/n*t)))\n", + " dt = Om*(x/(4*np.sqrt(a*q/n*t**3)) + (q)/(4*n*np.sqrt(a*q/n*t)))\n", + " dq = Om*(x/(4*np.sqrt(a*q**3/n*t)) + (t)/(4*n*np.sqrt(a*q/n*t)))\n", + " dn = Om*(-x/(4*np.sqrt(a*q*n*t)) - (q*t)/(4*np.sqrt(a*q*n**3*t)))\n", + " da = Om*((x - q/n*t)/(4*np.sqrt(a**3 *q/n*t)))\n", + " return np.array([dq,dn,da,dx,dt])" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "d6492f20", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 2.84464056e-01 -3.55580070e+00 1.01594306e-02 -1.62550889e-03\n", + " 2.37053380e-02]\n" + ] + } + ], + "source": [ + "print(gradient(2.5, 0.2, 10, x, t))" + ] + }, + { + "cell_type": "markdown", + "id": "18ae1605-4c60-4c65-be4f-ce9cef2e40fd", + "metadata": {}, + "source": [ + "## Your turn!\n", + "\n", + "Now try and use the code to answer the questions posed at the beginning of the notebook, which are repeated here:\n", + "1. Which random variables have the biggest influence on reliability?\n", + "2. How does the assumption of probability distribution influence reliability?\n", + "3. Do the random variables act as loads or resistances?\n", + "\n", + "In particular, to evaluate sensitivity, you can consider two quantitative aspects:\n", + "1. What is the functional influence of the random variables and x and t on the limit-state function?\n", + "2. What is the stochastic influence of the random variables, \n", + "3. What is the combined influence of the two aspects above?\n", + "\n", + "<!-- \n", + "Hint: note the striking similarity of these terms to the material you have already seen in the variance propagation part of MUDE, where the variance of a function of random variables is proportional to $\\sigma_x\\cdot \\frac{\\partial Z}{\\partial x}$. The variable with the biggest influence on reliability will have the highest value of this term. Also, the sign of the partial derivative will indicate whether a variable acts as a load or resistance. -->" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "base", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.13 (main, Aug 25 2022, 23:51:50) [MSC v.1916 64 bit (AMD64)]" + }, + "vscode": { + "interpreter": { + "hash": "85471ad55176ca86192ed6be6d105faaef73891404cad6bd910e89e8513744d9" + } + }, + "widgets": { + "application/vnd.jupyter.widget-state+json": { + "state": {}, + "version_major": 2, + "version_minor": 0 + } + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/book/notebooks/contamination/exercise_contamination.zip b/book/notebooks/contamination/exercise_contamination.zip new file mode 100644 index 0000000..105f3ac Binary files /dev/null and b/book/notebooks/contamination/exercise_contamination.zip differ diff --git a/book/notebooks/contamination/exercise_setup.py b/book/notebooks/contamination/exercise_setup.py new file mode 100644 index 0000000..51a9470 --- /dev/null +++ b/book/notebooks/contamination/exercise_setup.py @@ -0,0 +1,247 @@ +import numpy as np +import matplotlib.pyplot as plt +from scipy.special import erfc +from scipy import stats +import seaborn as sns + +def process_negative_values(q, n, a): + """Prevents problems with negative values in sqrt of C_C0 function.""" + N_q = sum(q<0) + N_n = sum(n<0) + N_a = sum(a<0) + set_value = 0.001 + if N_q > 0: + for i in range(len(q)): + if q[i]<0: + q[i] = set_value + print(f'q has {N_q} negative values that have been set to {set_value:.1e}.') + if N_n > 0: + for i in range(len(n)): + if n[i]<0: + n[i] = set_value + print(f'n has {N_n} negative values that have been set to {set_value:.1e}.') + if N_a > 0: + for i in range(len(a)): + if a[i]<0: + a[i] = set_value + print(f'a has {N_a} negative values that have been set to {set_value:.1e}.') + return q, n, a + +class RandomVariableDistribution(): + """Define a N or LN probability to use in MUDE week 2.7 exercise. + + Usage: + ----- + Create an instance of the class + by default, the random variable is ~N(0,1) + Specify distribution using 1st and 2nd moments for N or LN: + --> use method define_distribution to change it! + (the method prints a summary of the change) + for example, copy/paste the following: + test = RandomVariableDistribution() + test.print_status() + test.define_distribution(mean=5, stddev=1, dist_type='LN') + An instance will include the following attributes: + - distribution moment and (scipy) parameters shape, location, scale + - dist_object: distribution object (scipy.stats) + - get_sample: method for getting random samples from the distribution + - plot_pdf_or_cdf: + """ + + def __init__(self): + self.mean = 0. + self.stddev = 1. + self.dist_type = 'N' + + def print_status(self): + """Returns current parameter values and distribution type.""" + print(f'The mean is {self.mean:.3e}') + print(f'The standard deviation is {self.stddev:.3e}') + if self.dist_type == 'N': + distribution_name = 'Normal' + elif self.dist_type == 'LN': + distribution_name = 'Lognormal' + print('The distribution is ' + distribution_name) + + def define_distribution(self, + mean=None, + stddev=None, + dist_type=None, + print_new_dist=False): + """Compute distribution parameters and RV object from moments. + + Usage: + ----- + Optional arguments will override current dist: + --> default distribution is standard normal, ~N(0,1) + mean: float + stddev: float + dist_type: 'N' or 'LN' + print_new_dist=True to print distribution changes. + """ + if mean is None: + mean = self.mean + if stddev is None: + stddev = self.stddev + if dist_type is None: + dist_type = self.dist_type + if dist_type == 'N': + shape = None + location = mean + scale = stddev + dist_object = stats.norm(loc=location, scale=scale) + elif dist_type == 'LN': + """ + Finds distribution parameters of LN-distributed X, + which are equivalent to the mean and standard deviation + of the log of X: Y = ln(X), then converts to the + parameterization used by scipy.stats.lognorm. + """ + stddev_y = np.sqrt(np.log(1 + (stddev/mean)**2)) + mean_y = np.log(mean) - 0.5*stddev_y**2 + + shape = stddev_y + location = 0 + scale = np.exp(mean_y) + dist_object = stats.lognorm(s=shape, + loc=location, + scale=scale) + else: + raise ValueError("You can only use N or LN for self.dist_type.") + self.mean = mean + self.stddev = stddev + self.dist_type = dist_type + self.shape = shape + self.location = location + self.scale = scale + self.dist_object = dist_object + self.get_sample = lambda size : self.dist_object.rvs(size=size) + if print_new_dist: + self.print_status() + + def plot_pdf_or_cdf(self, plot_type='pdf', plot_limits=None): + """Plots the pdf or cdf (specify choice with plot_type). + + Usage: + ----- + No inputs required, but there are optional inputs: + plot_type='cdf' to plot cdf (pdf is default value) + plot_limits: list with 2 values for x-axis + """ + if plot_limits is None: + if self.dist_type == 'N': + plot_limits = [self.mean - 3*self.stddev, + self.mean + 3*self.stddev] + elif self.dist_type == 'LN': + 'Avoid negative or zero value for lognormal dist.' + lower_value = self.mean - 3*self.stddev + if lower_value <= 0: + lower_value = 0.01 + plot_limits = [lower_value, + self.mean + 4*self.stddev] + else: + raise ValueError("You can only use N or LN for self.dist_type.") + + plot_x = np.linspace(plot_limits[0], plot_limits[1], 1000) + if plot_type == 'pdf': + plot_y = self.dist_object.pdf(plot_x) + y_label = 'PDF [-]' + elif plot_type == 'cdf': + plot_y = self.dist_object.cdf(plot_x) + y_label = 'CDF [-]' + else: + raise ValueError("You must specify pdf or cdf for plot_type.") + fontsize = 15 + plt.figure() + plt.plot(plot_x, plot_y, 'k-', linewidth=3) + plt.xlabel('Random Variable, X', fontsize=fontsize) + plt.ylabel(y_label, fontsize=fontsize) + plt.show() + +def pdf_of_function_of_RV(cases, case_C=True, case_name=None, plot_limits=None): + """Plot the PDF of a sampled function of random variables (C_C0 or Z). + + Usage: + ----- + cases: a list of arrays + case_C=True (default) assumes C_C0 is given. False is for Z. + case_name: list of strings with the labels for each array. + e.g., ['Original', 'High sigma_a', 'Low sigma_a'] + (default will return Case i for all arrays) + plot_limits: list of two values that override default limits + for x-axis. + """ + bw_adjust = 3 # adjusts smoothness of Seaborn kernel density contours + labels = [] + + plt.figure() + + for i in range(len(cases)): + if case_name == None: + labels.append(f'Case {i+1}') + else: + labels.append(case_name[i]) + sns.kdeplot(cases[i], label=labels[i], ax=plt.gca(), bw_adjust=bw_adjust) + plt.legend() + if case_C: + plt.xlabel('Concentration ratio, $C/C_0$ [$-$]') + if plot_limits == None: + plt.xlim(0,1) + else: + plt.xlim(plot_limits) + else: + plt.xlabel('Limit-state function, $Z=\mathrm{threshold}-C/C_0$ [$-$]') + if plot_limits == None: + plt.xlim(-2,1) + else: + plt.xlim(plot_limits) + plt.ylabel('PDF [$]$') + plt.grid() + plt.show() + +def monte_carlo(Z): + """Monte Carlo analysis for sampled function of random variables. + + Returns a summary of the analysis and a plot of pf and c.o.v.. + The only input is an array of the sampled limit state-function. + Assumes that failure is when the limit-state function Z<0. + """ + N = len(Z) + Nf = np.sum(Z<0) + + if Nf == 0: + raise ValueError('No failure realizations in the sample!') + elif Nf == N: + raise ValueError('All realizations in the sample failed!') + + pf = Nf/N + + N_f_c = np.cumsum(Z<0) + N_i = np.arange(1,len(N_f_c)+1,1) + p_f_c = N_f_c / N_i + with np.errstate(divide='ignore'): + V = 1/(np.sqrt(N_i*p_f_c)) + + print(f'MONTE CARLO RESULTS\n' + f'--------------------------------------------------\n' + f' N = {N}, number of samples\n' + f' Nf = {Nf}, number of failed realizations\n' + f' pf = {pf:.3e}, estimated failure probability\n' + f' V = {V[-1]:.3f}, c.o.v. of estimated pf\n') + + plt.loglog(N_i,p_f_c) + plt.xlim(10,N) + plt.ylim(10**(np.floor(np.log10(pf)) - 1),1) + plt.grid() + plt.xlabel('Realization No.') + plt.ylabel('Estimated failure probability, $\hat{p}_f$') + plt.show() + + plt.plot(N_i,V) + plt.xscale('log') + plt.grid() + plt.xlabel('time step') + plt.ylabel('c.o.v.') + plt.show() + + return Nf,pf \ No newline at end of file diff --git a/book/notebooks/contamination/figures/sketch.png b/book/notebooks/contamination/figures/sketch.png new file mode 100644 index 0000000..d2fd2b4 Binary files /dev/null and b/book/notebooks/contamination/figures/sketch.png differ diff --git a/book/notebooks/flood-risk/Exercise_Flood_Risk_Render.ipynb b/book/notebooks/flood-risk/Exercise_Flood_Risk_Render.ipynb new file mode 100644 index 0000000..09ce9bd --- /dev/null +++ b/book/notebooks/flood-risk/Exercise_Flood_Risk_Render.ipynb @@ -0,0 +1,792 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "e228e52d", + "metadata": {}, + "source": [ + "# Flood Risk\n", + "## Dike Ring 14" + ] + }, + { + "cell_type": "markdown", + "id": "6f028272-206c-4474-9083-43d7b52352f1", + "metadata": {}, + "source": [ + "````{note}\n", + "This page is generated from an `*.ipynb` file which requires several auxiliary files, all of which can be downloaded using the link below.\n", + "```{eval-rst}\n", + ":download:`Download zip file for this exercise.<exercise_flood_risk.zip>`\n", + "```\n", + "````" + ] + }, + { + "cell_type": "markdown", + "id": "6897cbb0-6e59-4ed3-a346-ae684e115bbc", + "metadata": {}, + "source": [ + "The overall objective of this assignment is to make a step from the simple FN/FD curves we have in the book to work on something 'real' and to make 'real' engineering decisions about how to modify a dike ring to meet safety standards. This exercise is based on a risk assessment of the Netherlands from around 10 years ago called VNK (veiligheid Nederland in kaart, or mapping Dutch (flood) safety. It was done in the runup to changing the safety standards in 2017. You can find more about the project [here](https://www.helpdeskwater.nl/onderwerpen/waterveiligheid/programma-projecten/veiligheid-nederland/publicaties/), and a report specifically about the case [here](https://www.helpdeskwater.nl/onderwerpen/waterveiligheid/programma-projecten/veiligheid-nederland/publicaties/dijkringrapporten/dijkringrapporten/fase-1a/14-zuid-holland/). The first website has some English reports, but unfortunately the Dike Ring 14 report is only in Dutch.\n", + "\n", + "*First the case is introduced, then some examples using the pre-prepared code are given to show you how to use it. Then you are asked to use the code to decide which repairs to specific dike segments should be done to see if you can meet the safety criteria!*\n", + "\n", + "*Our apologies in advance that the code does not meet the Golden Rules. Although it might not look pretty, we trust that it is clear enough to be able to learn about risk!*" + ] + }, + { + "cell_type": "markdown", + "id": "9b9e2b82-d018-4188-95ff-d75c290ec1d4", + "metadata": {}, + "source": [ + "## Overview of the case study\n", + "\n", + "The entire dike ring that protects South Holland is divided into 13 segments, which have been chosen such that the flooding that occurs after a breach is not dependent on the location of the breach itself. This results in significantly fewer flooding analyses that must be carried out. In addition, all possible breach locations within a single segment do not have to be considered. For South Holland, 7 segments are defined along the Nieuwe Waterweg (i.e., the river, behind the Maeslant Barrier) and 6 segments are defined along the coast.\n", + "\n", + "```{figure} ./figures/map-dike-segments.PNG\n", + "---\n", + "width: 500px\n", + "name: map_segments\n", + "---\n", + "```\n", + "All segments along the river are dikes and segments along the sea are dunes, with the following exceptions:\n", + "- Segment 3: Park Sluices in Rotterdam\n", + "- Segment 10: Scheveningen outlet sluice\n", + "- Segment 11: Scheveningen Bouldevard\n", + " \n", + "### How does a flood risk analysis work?\n", + " \n", + "We are essentially creating a probability mass function, where the random variable is fatalities or economic damage. Since we can't wait a few million years watch the dike ring fail to get a good estimate of the actual distribution, we try to simulate all possible combinations of floods. However, the actual flooding process is complicated: due to the river or sea conditions a dike or dune is broken (this is called a breach), water rushes into the protected area, depending on the flooding depth people may die and infrastructure is damaged. Sometimes we are able to warn and evacuate people, but there is a chance these systems do not work. Reality is extremely complex, so we simplify the process in our flood modeling studies, using the following steps:\n", + "a. assume a levee or dune is breached\n", + "b. estimate the resulting flood depth in the (formerly) protected area\n", + "c. calculated economic damage and fatalities as a function of water depth\n", + "d. modify the above value depending on the status of warning and evacuation systems\n", + "e. repeat this for many breach locations\n", + " \n", + "As such, each scenario returns a finite number of fatalities or damage, which is why the distribution is discrete. Of course, we need to also quantify the probability of each scenario. Although it sounds complex, it is actually simple to represent using conditional probability if we can assume:\n", + "$$\\textrm{P}(x_i)=\\textrm{P}(x_i|D,W,E)\\cdot\\textrm{P}(D)\\cdot\\textrm{P}(W)\\cdot\\textrm{P}(E)$$\n", + "\n", + "where $x_i$ is our risk metric of choice (i.e., economic damage or fatalities) and $D$, $W$ and $E$ represnt water depth, warning and evacuation status, respectively. Given the scenario-based approach where a fixed value is determined for $x_i$, it is clear that this type of analysis creates a descrete random variable. Furthermore, the equation above indicates that single values of $D$, $W$ and $E$ are used, but in theory one could integrate over each of these variables.\n", + " \n", + "An example of the flood depth analysis is shown below for a breach in segment 12:\n", + "```{figure} ./figures/flood-depth-12.PNG\n", + "---\n", + "width: 500px\n", + "name: flood_depth_12\n", + "---\n", + "```" + ] + }, + { + "cell_type": "markdown", + "id": "14231f96-55e5-44f1-baea-1f8a0e7e0e46", + "metadata": {}, + "source": [ + "## Exercise Instructions\n", + "\n", + "An Excel file has been prepared that includes the results from the risk analysis. Each row is a scenario, with a `Scenario_ID` and associated probability of occurrence (`scenario_probability`). The column `failed_segments` lists which dike segments are assumed to have failed in the particular scenario. Consequences are specifies in the last 8 columns (described below).\n", + "\n", + "Your task is to determine which **dike segments** you should repair to improve the safety of Dike Ring 14. Unfortunately due to the available budget, **you can only afford to repair 3 segments.** Thus, your task is to identify 3 segments to repair and justify your decision for doing so (there are some cells below where you can type your answer). You are free to consider both life loss and economic damage in your evaluation.\n", + "\n", + "The next set of cells will get you started with the helper functions, then you are free to use them to work on the assignment. First, start by importing the required packages:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "5362403f", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import pandas as pd" + ] + }, + { + "cell_type": "markdown", + "id": "940f2cff-4c61-4cef-81fa-73b701f8b43a", + "metadata": {}, + "source": [ + "Import special functions created to help with this assignment:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "1a4624ba-f457-4bf6-8848-713e6aa5ccfe", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "from functions import find_scenarios_with_segment_i\n", + "from functions import assemble_analysis_cases\n", + "from functions import exceedance_prob\n", + "from functions import plot_curves\n", + "from functions import sensitivity_analysis\n", + "from functions import compute_benefit\n", + "from functions import set_TUDstyle" + ] + }, + { + "cell_type": "markdown", + "id": "79bc6385", + "metadata": {}, + "source": [ + "Load data and take a look at it:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "771b9c7f", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "<div>\n", + "<style scoped>\n", + " .dataframe tbody tr th:only-of-type {\n", + " vertical-align: middle;\n", + " }\n", + "\n", + " .dataframe tbody tr th {\n", + " vertical-align: top;\n", + " }\n", + "\n", + " .dataframe thead th {\n", + " text-align: right;\n", + " }\n", + "</style>\n", + "<table border=\"1\" class=\"dataframe\">\n", + " <thead>\n", + " <tr style=\"text-align: right;\">\n", + " <th></th>\n", + " <th>Scenario_ID</th>\n", + " <th>scenario_probability</th>\n", + " <th>failed_segments</th>\n", + " <th>case_1_d</th>\n", + " <th>case_1_n</th>\n", + " <th>case_2_d</th>\n", + " <th>case_2_n</th>\n", + " <th>case_3_d</th>\n", + " <th>case_3_n</th>\n", + " <th>case_4_d</th>\n", + " <th>case_4_n</th>\n", + " </tr>\n", + " </thead>\n", + " <tbody>\n", + " <tr>\n", + " <th>0</th>\n", + " <td>1</td>\n", + " <td>0.000021</td>\n", + " <td>12</td>\n", + " <td>5700</td>\n", + " <td>600</td>\n", + " <td>5700</td>\n", + " <td>460</td>\n", + " <td>5700</td>\n", + " <td>420</td>\n", + " <td>5700</td>\n", + " <td>300</td>\n", + " </tr>\n", + " <tr>\n", + " <th>1</th>\n", + " <td>2</td>\n", + " <td>0.000016</td>\n", + " <td>2</td>\n", + " <td>1400</td>\n", + " <td>200</td>\n", + " <td>1400</td>\n", + " <td>150</td>\n", + " <td>1400</td>\n", + " <td>140</td>\n", + " <td>1400</td>\n", + " <td>99</td>\n", + " </tr>\n", + " <tr>\n", + " <th>2</th>\n", + " <td>3</td>\n", + " <td>0.000005</td>\n", + " <td>2,7</td>\n", + " <td>1800</td>\n", + " <td>210</td>\n", + " <td>1800</td>\n", + " <td>160</td>\n", + " <td>1800</td>\n", + " <td>150</td>\n", + " <td>1800</td>\n", + " <td>110</td>\n", + " </tr>\n", + " <tr>\n", + " <th>3</th>\n", + " <td>4</td>\n", + " <td>0.000004</td>\n", + " <td>5</td>\n", + " <td>1600</td>\n", + " <td>3700</td>\n", + " <td>1600</td>\n", + " <td>2800</td>\n", + " <td>1600</td>\n", + " <td>2600</td>\n", + " <td>1600</td>\n", + " <td>1800</td>\n", + " </tr>\n", + " <tr>\n", + " <th>4</th>\n", + " <td>5</td>\n", + " <td>0.000004</td>\n", + " <td>6</td>\n", + " <td>720</td>\n", + " <td>40</td>\n", + " <td>720</td>\n", + " <td>30</td>\n", + " <td>720</td>\n", + " <td>30</td>\n", + " <td>710</td>\n", + " <td>20</td>\n", + " </tr>\n", + " </tbody>\n", + "</table>\n", + "</div>" + ], + "text/plain": [ + " Scenario_ID scenario_probability failed_segments case_1_d case_1_n \\\n", + "0 1 0.000021 12 5700 600 \n", + "1 2 0.000016 2 1400 200 \n", + "2 3 0.000005 2,7 1800 210 \n", + "3 4 0.000004 5 1600 3700 \n", + "4 5 0.000004 6 720 40 \n", + "\n", + " case_2_d case_2_n case_3_d case_3_n case_4_d case_4_n \n", + "0 5700 460 5700 420 5700 300 \n", + "1 1400 150 1400 140 1400 99 \n", + "2 1800 160 1800 150 1800 110 \n", + "3 1600 2800 1600 2600 1600 1800 \n", + "4 720 30 720 30 710 20 " + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df = pd.read_excel(r'Prob_Cons.xlsx')\n", + "df.head()" + ] + }, + { + "cell_type": "markdown", + "id": "11d5077c-d8fa-4898-a68e-d3f6e6a96f9f", + "metadata": {}, + "source": [ + "### Evacuations (labeled Case 1-4)\n", + "\n", + "*As you can see above, the dataframe has 8 columns labeled `case_*_*`. The last character denotes either fatalities or damage with `n` or `d`, respectively.*\n", + "\n", + "The consequences in each scenario are dependent on whether or not there is a flood warning and time for an ordered evacuation or not. To account for this, 4 sub-scenarios are considered, and the probability of each is weighted equally in the total FN curve (cases are combined in `exceedance_prob`). For the response to a dike breach there are 4 conditions considered (in order of table on Page 139, Bijlage I):\n", + "- flood unexpected and no evacuation\n", + "- flood unexpected with an unorganized evacuation\n", + "- flood expected with an unorganized evacuation\n", + "- flood expected with an organized evacuation\n", + "\n", + "It is interesting to know how this is incorporated in the analysis, but you can ignore this when going through the exercise, since it becomes unecessarily complicated." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "5507ede2-4f44-413b-9f02-42a3adc81c8c", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "<div>\n", + "<style scoped>\n", + " .dataframe tbody tr th:only-of-type {\n", + " vertical-align: middle;\n", + " }\n", + "\n", + " .dataframe tbody tr th {\n", + " vertical-align: top;\n", + " }\n", + "\n", + " .dataframe thead th {\n", + " text-align: right;\n", + " }\n", + "</style>\n", + "<table border=\"1\" class=\"dataframe\">\n", + " <thead>\n", + " <tr style=\"text-align: right;\">\n", + " <th></th>\n", + " <th>Scenario_ID</th>\n", + " <th>scenario_probability</th>\n", + " <th>case_1_d</th>\n", + " <th>case_1_n</th>\n", + " <th>case_2_d</th>\n", + " <th>case_2_n</th>\n", + " <th>case_3_d</th>\n", + " <th>case_3_n</th>\n", + " <th>case_4_d</th>\n", + " <th>case_4_n</th>\n", + " </tr>\n", + " </thead>\n", + " <tbody>\n", + " <tr>\n", + " <th>count</th>\n", + " <td>50.00000</td>\n", + " <td>5.000000e+01</td>\n", + " <td>50.000000</td>\n", + " <td>50.000000</td>\n", + " <td>50.000000</td>\n", + " <td>50.000000</td>\n", + " <td>50.000000</td>\n", + " <td>50.00000</td>\n", + " <td>50.000000</td>\n", + " <td>50.000000</td>\n", + " </tr>\n", + " <tr>\n", + " <th>mean</th>\n", + " <td>25.50000</td>\n", + " <td>1.290931e-06</td>\n", + " <td>12549.780000</td>\n", + " <td>8603.360000</td>\n", + " <td>12493.000000</td>\n", + " <td>6631.500000</td>\n", + " <td>12491.000000</td>\n", + " <td>5988.66000</td>\n", + " <td>12471.100000</td>\n", + " <td>4269.280000</td>\n", + " </tr>\n", + " <tr>\n", + " <th>std</th>\n", + " <td>14.57738</td>\n", + " <td>3.822669e-06</td>\n", + " <td>8887.756677</td>\n", + " <td>8037.445146</td>\n", + " <td>8839.023921</td>\n", + " <td>6213.314184</td>\n", + " <td>8839.795512</td>\n", + " <td>5578.15815</td>\n", + " <td>8835.288088</td>\n", + " <td>3965.545056</td>\n", + " </tr>\n", + " <tr>\n", + " <th>min</th>\n", + " <td>1.00000</td>\n", + " <td>8.830000e-09</td>\n", + " <td>230.000000</td>\n", + " <td>8.000000</td>\n", + " <td>230.000000</td>\n", + " <td>6.000000</td>\n", + " <td>230.000000</td>\n", + " <td>6.00000</td>\n", + " <td>230.000000</td>\n", + " <td>4.000000</td>\n", + " </tr>\n", + " <tr>\n", + " <th>25%</th>\n", + " <td>13.25000</td>\n", + " <td>4.402500e-08</td>\n", + " <td>5475.000000</td>\n", + " <td>2225.000000</td>\n", + " <td>5475.000000</td>\n", + " <td>1700.000000</td>\n", + " <td>5475.000000</td>\n", + " <td>1600.00000</td>\n", + " <td>5475.000000</td>\n", + " <td>1100.000000</td>\n", + " </tr>\n", + " <tr>\n", + " <th>50%</th>\n", + " <td>25.50000</td>\n", + " <td>1.125000e-07</td>\n", + " <td>11000.000000</td>\n", + " <td>3800.000000</td>\n", + " <td>11000.000000</td>\n", + " <td>2950.000000</td>\n", + " <td>11000.000000</td>\n", + " <td>2700.00000</td>\n", + " <td>11000.000000</td>\n", + " <td>1900.000000</td>\n", + " </tr>\n", + " <tr>\n", + " <th>75%</th>\n", + " <td>37.75000</td>\n", + " <td>4.797500e-07</td>\n", + " <td>17000.000000</td>\n", + " <td>15750.000000</td>\n", + " <td>17000.000000</td>\n", + " <td>11750.000000</td>\n", + " <td>17000.000000</td>\n", + " <td>10750.00000</td>\n", + " <td>17000.000000</td>\n", + " <td>7775.000000</td>\n", + " </tr>\n", + " <tr>\n", + " <th>max</th>\n", + " <td>50.00000</td>\n", + " <td>2.140000e-05</td>\n", + " <td>33000.000000</td>\n", + " <td>29000.000000</td>\n", + " <td>33000.000000</td>\n", + " <td>22000.000000</td>\n", + " <td>33000.000000</td>\n", + " <td>20000.00000</td>\n", + " <td>33000.000000</td>\n", + " <td>14000.000000</td>\n", + " </tr>\n", + " </tbody>\n", + "</table>\n", + "</div>" + ], + "text/plain": [ + " Scenario_ID scenario_probability case_1_d case_1_n \\\n", + "count 50.00000 5.000000e+01 50.000000 50.000000 \n", + "mean 25.50000 1.290931e-06 12549.780000 8603.360000 \n", + "std 14.57738 3.822669e-06 8887.756677 8037.445146 \n", + "min 1.00000 8.830000e-09 230.000000 8.000000 \n", + "25% 13.25000 4.402500e-08 5475.000000 2225.000000 \n", + "50% 25.50000 1.125000e-07 11000.000000 3800.000000 \n", + "75% 37.75000 4.797500e-07 17000.000000 15750.000000 \n", + "max 50.00000 2.140000e-05 33000.000000 29000.000000 \n", + "\n", + " case_2_d case_2_n case_3_d case_3_n case_4_d \\\n", + "count 50.000000 50.000000 50.000000 50.00000 50.000000 \n", + "mean 12493.000000 6631.500000 12491.000000 5988.66000 12471.100000 \n", + "std 8839.023921 6213.314184 8839.795512 5578.15815 8835.288088 \n", + "min 230.000000 6.000000 230.000000 6.00000 230.000000 \n", + "25% 5475.000000 1700.000000 5475.000000 1600.00000 5475.000000 \n", + "50% 11000.000000 2950.000000 11000.000000 2700.00000 11000.000000 \n", + "75% 17000.000000 11750.000000 17000.000000 10750.00000 17000.000000 \n", + "max 33000.000000 22000.000000 33000.000000 20000.00000 33000.000000 \n", + "\n", + " case_4_n \n", + "count 50.000000 \n", + "mean 4269.280000 \n", + "std 3965.545056 \n", + "min 4.000000 \n", + "25% 1100.000000 \n", + "50% 1900.000000 \n", + "75% 7775.000000 \n", + "max 14000.000000 " + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df.describe()" + ] + }, + { + "cell_type": "markdown", + "id": "021ad4a5", + "metadata": {}, + "source": [ + "The function `find_scenarios_with_segment_i` will ask for the dike segment(s) of interest (as a list) and return all of the scenarios where a breach in this segment is considered." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "096d2419-9467-4505-898e-36a670dd46ce", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Given a list of segments, return set of dependent scenarios.\n" + ] + }, + { + "data": { + "text/html": [ + "<div>\n", + "<style scoped>\n", + " .dataframe tbody tr th:only-of-type {\n", + " vertical-align: middle;\n", + " }\n", + "\n", + " .dataframe tbody tr th {\n", + " vertical-align: top;\n", + " }\n", + "\n", + " .dataframe thead th {\n", + " text-align: right;\n", + " }\n", + "</style>\n", + "<table border=\"1\" class=\"dataframe\">\n", + " <thead>\n", + " <tr style=\"text-align: right;\">\n", + " <th></th>\n", + " <th>Scenario_ID</th>\n", + " <th>scenario_probability</th>\n", + " <th>failed_segments</th>\n", + " <th>case_1_d</th>\n", + " <th>case_1_n</th>\n", + " <th>case_2_d</th>\n", + " <th>case_2_n</th>\n", + " <th>case_3_d</th>\n", + " <th>case_3_n</th>\n", + " <th>case_4_d</th>\n", + " <th>case_4_n</th>\n", + " </tr>\n", + " </thead>\n", + " <tbody>\n", + " <tr>\n", + " <th>0</th>\n", + " <td>1</td>\n", + " <td>2.140000e-05</td>\n", + " <td>12</td>\n", + " <td>5700</td>\n", + " <td>600</td>\n", + " <td>5700</td>\n", + " <td>460</td>\n", + " <td>5700</td>\n", + " <td>420</td>\n", + " <td>5700</td>\n", + " <td>300</td>\n", + " </tr>\n", + " <tr>\n", + " <th>8</th>\n", + " <td>9</td>\n", + " <td>9.480000e-07</td>\n", + " <td>12,13</td>\n", + " <td>11000</td>\n", + " <td>2000</td>\n", + " <td>11000</td>\n", + " <td>1600</td>\n", + " <td>11000</td>\n", + " <td>1400</td>\n", + " <td>11000</td>\n", + " <td>1000</td>\n", + " </tr>\n", + " <tr>\n", + " <th>49</th>\n", + " <td>50</td>\n", + " <td>2.450000e-08</td>\n", + " <td>8,12,13</td>\n", + " <td>19000</td>\n", + " <td>2700</td>\n", + " <td>19000</td>\n", + " <td>2100</td>\n", + " <td>19000</td>\n", + " <td>1900</td>\n", + " <td>19000</td>\n", + " <td>1400</td>\n", + " </tr>\n", + " </tbody>\n", + "</table>\n", + "</div>" + ], + "text/plain": [ + " Scenario_ID scenario_probability failed_segments case_1_d case_1_n \\\n", + "0 1 2.140000e-05 12 5700 600 \n", + "8 9 9.480000e-07 12,13 11000 2000 \n", + "49 50 2.450000e-08 8,12,13 19000 2700 \n", + "\n", + " case_2_d case_2_n case_3_d case_3_n case_4_d case_4_n \n", + "0 5700 460 5700 420 5700 300 \n", + "8 11000 1600 11000 1400 11000 1000 \n", + "49 19000 2100 19000 1900 19000 1400 " + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "print(find_scenarios_with_segment_i.__doc__)\n", + "find_scenarios_with_segment_i([12], df)" + ] + }, + { + "cell_type": "markdown", + "id": "e4cdbb15-6659-4227-935c-cbeab4a5b927", + "metadata": {}, + "source": [ + "## Compute exceedance probabilities\n", + "\n", + "Now that we have explored the database of scenarios, let's move towards evaluating risk. Before assembling the risk curves, we will extract the probability associated with each scenario, and use a prepared function (`assemble_analysis_cases`) to make the process easier." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "f30a1a10", + "metadata": {}, + "outputs": [], + "source": [ + "scenario_prob = df.iloc[:,1]\n", + "damage_and_fatality_cases = assemble_analysis_cases(df)\n", + "\n", + "choose_damage_or_fatality = 'fatality'\n", + "case = damage_and_fatality_cases[choose_damage_or_fatality]" + ] + }, + { + "cell_type": "markdown", + "id": "984faaa2-c42c-4879-86df-6e25e4fe1f04", + "metadata": {}, + "source": [ + "The function `exceedance_prob` computes the FN or FD curve depending on the case that is provided. And the function `plot_curves` will plot them with the limit line." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "1b360ec0", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 1000x600 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "N_D_ordered_test, exceed_prob_test, complete_table = exceedance_prob(case, scenario_prob)\n", + "plot_curves(N_D_ordered_test, exceed_prob_test)" + ] + }, + { + "cell_type": "markdown", + "id": "7dce7a21-f338-40ce-ae1a-35ae357301ba", + "metadata": {}, + "source": [ + "## Modify the system and see how the FN (or FD) curve changes\n", + "\n", + "The function above allows the user to choose which dike segments to repair, then the relevant scenarios are removed from consideration. Play with the segments and see what the most important repairs should be to improve the system risk." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "f2a8ecf2", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Segment [12, 13] in scenarios [ 0 7 8 49]\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "<Figure size 1000x600 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Segment 12 (Katwijk scenarios) used at idx: [0,8,49]\n", + "segment_repaired = [12, 13]\n", + "segment_table = find_scenarios_with_segment_i(segment_repaired, df)\n", + "idx_segment = segment_table.index.values\n", + "print(f\"Segment {segment_repaired} in scenarios {idx_segment}\")\n", + "\n", + "# idx_segment = [0, 8, 49] # enter index of segment of interest\n", + "N_D_ordered_new, exceed_prob_new, complete_table_new = sensitivity_analysis(case, scenario_prob, idx_segment, N_D_ordered_test, exceed_prob_test, complete_table)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "a20111d8", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Old fatality: 3.04187862305\n", + "Old fatality: 2.6691130726399996\n", + "Difference: 0.3727655504100005\n" + ] + } + ], + "source": [ + "old_costs, new_costs, result = compute_benefit(complete_table, complete_table_new)\n", + "print(f\"Old {choose_damage_or_fatality}: {old_costs}\")\n", + "print(f\"Old {choose_damage_or_fatality}: {new_costs}\")\n", + "print(f\"Difference: {result}\")" + ] + }, + { + "cell_type": "markdown", + "id": "4ed2eff1-97dd-4df2-9e4e-a2fce6a6a360", + "metadata": { + "jp-MarkdownHeadingCollapsed": true, + "tags": [] + }, + "source": [ + "## Assignment Answers\n", + "\n", + "*You don't need to answer all of these questions, but they will probably help you arrive at a desicion.*\n", + "\n", + "\n", + "\n", + "1. Which scenario contributes the most to risk?\n", + "2. Which dike segment contributes the most to risk?\n", + "3. Is there a certain region that seems to contribute more to risk?\n", + "4. The above questions look at risk, but you can also consider probability and consequences separately. If you look through these details, do you notice any segments or scenarios that stand out as contributing a lot (or a little)?\n", + "5. Which dike segments do you choose to repair, and why?\n", + "6. What is the total reduction in expected damages?\n", + "7. Could you get the entire curve to satisfy the safety criteria? What is needed in order to do so?\n", + "8. Consider the dike segments you chose to repair. How might you actually go about repairing them: would you focus on reducing the probability or the consequences? Make a few suggestions for how you would do each improvement and comment on the feasibility." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.13" + }, + "vscode": { + "interpreter": { + "hash": "2f56e53acab938e533261baa35aac2c581caa9f2f4a01ed69448e50e809c0ddc" + } + }, + "widgets": { + "application/vnd.jupyter.widget-state+json": { + "state": {}, + "version_major": 2, + "version_minor": 0 + } + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/book/notebooks/flood-risk/Prob_Cons.xlsx b/book/notebooks/flood-risk/Prob_Cons.xlsx new file mode 100644 index 0000000..9d5f9c5 Binary files /dev/null and b/book/notebooks/flood-risk/Prob_Cons.xlsx differ diff --git a/book/notebooks/flood-risk/exercise_flood_risk.zip b/book/notebooks/flood-risk/exercise_flood_risk.zip new file mode 100644 index 0000000..992a414 Binary files /dev/null and b/book/notebooks/flood-risk/exercise_flood_risk.zip differ diff --git a/book/notebooks/flood-risk/figures/flood-depth-12.PNG b/book/notebooks/flood-risk/figures/flood-depth-12.PNG new file mode 100644 index 0000000..c3dc0c2 Binary files /dev/null and b/book/notebooks/flood-risk/figures/flood-depth-12.PNG differ diff --git a/book/notebooks/flood-risk/figures/map-dike-segments.PNG b/book/notebooks/flood-risk/figures/map-dike-segments.PNG new file mode 100644 index 0000000..a172d35 Binary files /dev/null and b/book/notebooks/flood-risk/figures/map-dike-segments.PNG differ diff --git a/book/notebooks/flood-risk/functions.py b/book/notebooks/flood-risk/functions.py new file mode 100644 index 0000000..7519bce --- /dev/null +++ b/book/notebooks/flood-risk/functions.py @@ -0,0 +1,163 @@ +import numpy as np +import matplotlib.pyplot as plt +import pandas as pd + +def find_scenarios_with_segment_i(segments_fixed, df): + """Given a list of segments, return set of dependent scenarios.""" + idx = [] + segments_fixed = set(segments_fixed) + for i, row in enumerate(df['failed_segments'].values): + segments_row = set([int(seg) for seg in row.split(",")]) + intersection = list(segments_fixed.intersection(segments_row)) + if len(intersection) > 0: + idx.append(True) + else: + idx.append(False) + segment_table = df.iloc[idx] + return segment_table + +def assemble_analysis_cases(df): + """From scenario dataframe collect damage and fatality information.""" + econ_damage_case_1 = df.iloc[:,3] # Unexpected, no evacuation + econ_damage_case_2 = df.iloc[:,5] # Unexpected, unorganised evacuation + econ_damage_case_3 = df.iloc[:,7] # Expected, unorganised evacuation + econ_damage_case_4 = df.iloc[:,9] # Expected, organised evacuation + + fatalities_case_1 = df.iloc[:,4] + fatalities_case_2 = df.iloc[:,6] + fatalities_case_3 = df.iloc[:,8] + fatalities_case_4 = df.iloc[:,10] + + scenario_prob = df.iloc[:,1] # scenario probability + + cases = {'damage': [econ_damage_case_1, econ_damage_case_2, econ_damage_case_3, econ_damage_case_4], + 'fatality': [fatalities_case_1, fatalities_case_2, fatalities_case_3, fatalities_case_4]} + return cases + +def exceedance_prob(cases, scenario_prob): + """Compute exceedance probability.""" + case_1 = cases[0] + case_2 = cases[1] + case_3 = cases[2] + case_4 = cases[3] + + key = case_1.index + + # Combine Evacuation Scenarios into new Dataframe + scenarios = [pd.DataFrame({'Nr': key, 'N/D': case_1}), + pd.DataFrame({'Nr': key, 'N/D': case_2}), + pd.DataFrame({'Nr': key, 'N/D': case_3}), + pd.DataFrame({'Nr': key, 'N/D': case_4})] + + scen_combi = pd.concat(scenarios, ignore_index=True) + + # Sort values by key ('Nr') + scen_combi_sorted = scen_combi.sort_values(by=['Nr']) # useful if scen_combi_nodup.sort_values(by=['Nr']) in case of no duplicates +# scen_combi_sorted = scen_combi.reset_index(drop=True) # Reset index starting from 0 + + # Create new Dataframe for scenario prob with corresponding key + prob = pd.DataFrame({'Nr': key, 'scen_prob':scenario_prob}) + + # Join both Dataframes based on common key + join_scen_prob = scen_combi_sorted.join(prob.set_index('Nr'), on='Nr') + + # Determine Exceedance Probability + sorted_N_D = scen_combi.sort_values(by=['N/D']) # Sort N/D based on ascending order + complete_table = sorted_N_D.join(prob.set_index('Nr'), on='Nr') + + N_D_prob_ordered = complete_table.iloc[:,2] + +# N_D = join_scen_prob.dropna(axis=0).iloc[:,1].reset_index(drop=True) # N/D +# N_D_prob = join_scen_prob.dropna(axis=0).iloc[:,2].reset_index(drop=True) # Corresponding scenario prob +# print('N_D', N_D) +# print('N_D_PROB', N_D_prob) +# order = N_D.argsort() # Sort N/D based on ascending order + +# N_D_prob_ordered = N_D_prob[order] + N_D_prob_cs = np.cumsum(N_D_prob_ordered[::-1]) # Take cumulative sum of reversed order + + exceed_prob = (1/4) * N_D_prob_cs[::-1] # Reverse result (1-FN(n)) and /4 as 4 evacuation scenarios are considered + complete_table = complete_table.join(exceed_prob, lsuffix='_orignal', rsuffix='_new') # complete resulting table +# N_D_ordered = N_D[order].reset_index(drop=True) + N_D_ordered = complete_table.iloc[:,1] + + return N_D_ordered, exceed_prob, complete_table + +def sensitivity_analysis(cases, scenario_prob, idx_segment, N_D_ordered_original, exceed_prob_original, complete_table): + """Docstring incomplete.""" + case_1 = cases[0] + case_2 = cases[1] + case_3 = cases[2] + case_4 = cases[3] + + # Dropping segment(s) + case_1_exc = case_1.drop(idx_segment, axis=0).reset_index(drop=True) + case_2_exc = case_2.drop(idx_segment, axis=0).reset_index(drop=True) + case_3_exc = case_3.drop(idx_segment, axis=0).reset_index(drop=True) + case_4_exc = case_4.drop(idx_segment, axis=0).reset_index(drop=True) + + scenario_prob_exc = scenario_prob.drop(idx_segment, axis=0).reset_index(drop=True) + + # Determine new exceedance probability - Excluding segment(s) + N_D_ordered_new, exceed_prob_new, complete_table_new = exceedance_prob([case_1_exc, case_2_exc, case_3_exc, case_4_exc], scenario_prob_exc) + + # Plotting + plot_curves(N_D_ordered_original, exceed_prob_original) + plt.plot(N_D_ordered_new.dropna(axis=0), exceed_prob_new.dropna(axis=0), marker="o", linewidth=2, markersize=5, color= 'darkblue', label='Excluding segment(s)', zorder=10) + + # Plot dropped points + x_point = [] + y_point = [] + for i in range(len(idx_segment)): + row_i = complete_table[complete_table['Nr']== (idx_segment[i] + 1)] + for j in range(len(row_i)): + x_point.append(row_i.iloc[j, 1]) + y_point.append(row_i.iloc[j, 3]) + plt.scatter(x_point, y_point, label='Dropped Points', s=45, color='darkred', zorder=15) # Plot the points corresponding to deleted segment + plt.legend() + plt.show() + return N_D_ordered_new, exceed_prob_new, complete_table_new + +def plot_curves(N_D, exceedance_prob): + """Plot FN or FD risk curve.""" + plt.figure(figsize=(10,6)) + set_TUDstyle() + + # Plot FN/FD curve + plt.plot(N_D, exceedance_prob, marker="o", linewidth=2, markersize=5, label='FN/D-curve',zorder=0) + + # Add acceptable limit line + ND = np.linspace(1,100000,100000) # fatalities + alpha = 1 + C = 0.010 + limit_line = (C/ND**alpha) + plt.plot(limit_line, linewidth=2, color='darkgreen', label='Acceptable Limit Line', zorder=5) + + # Styling + plt.yscale('log') + plt.xscale('log') + plt.grid(True, which="both", axis='x') + plt.grid(True, which="major", axis='y') + plt.title('FN/D-curve') + plt.ylabel('Probability of Exceedance, $1-F_N(n)$') + plt.xlabel('Economic damage [meuro] / Fatalities') + plt.xlim(1,100000) + plt.ylim(10**(-7),10**(-3)) + plt.legend() + +def compute_benefit(table_old, table_new): + """Compute new and old consequences and net benefit.""" + old_consequences = np.sum(table_old["N/D"].values * table_old["scen_prob_new"].values) + new_consequences = np.sum(table_new["N/D"].values * table_new["scen_prob_new"].values) + benefit = old_consequences - new_consequences + return old_consequences, new_consequences, benefit + +def set_TUDstyle(): + TUcolor = {"cyan": "#00A6D6", "darkgreen": "#009B77", "purple": "#6F1D77", + "darkred": "#A50034", "darkblue": "#0C2340", + "orange": "#EC6842", "green": "#6CC24A", + "lightcyan": "#00B8C8", "red": "#E03C31", "pink": "#EF60A3", + "yellow": "#FFB81C", "blue": "#0076C2"} + plt.rcParams.update({'axes.prop_cycle': plt.cycler(color=TUcolor.values()), + 'font.size': 16, "lines.linewidth": 4}) + return TUcolor \ No newline at end of file diff --git a/book/notebooks/overview.md b/book/notebooks/overview.md new file mode 100644 index 0000000..41cd6e9 --- /dev/null +++ b/book/notebooks/overview.md @@ -0,0 +1,3 @@ +# Notebooks + +This chapter contains notebooks that can be used to put your risk and reliability knowledge to the test in real life situations. They have been rendered as individual pages to show you their contents, and each page will have a download link near the top to allow you to download all files needed for the exercise directly in a zip file. diff --git a/book/notebooks/traffic/Exercise_Traffic_Render.ipynb b/book/notebooks/traffic/Exercise_Traffic_Render.ipynb new file mode 100644 index 0000000..a15a33b --- /dev/null +++ b/book/notebooks/traffic/Exercise_Traffic_Render.ipynb @@ -0,0 +1,2250 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Traffic and Transport Reliability" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "````{note}\n", + "This page is generated from an `*.ipynb` file which requires several auxiliary files, all of which can be downloaded using the link below.\n", + "```{eval-rst}\n", + ":download:`Download zip file for this exercise.<exercise_traffic.zip>`\n", + "```\n", + "````" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "Have you ever sat in a car during rush hour and been annoyed at the amount of traffic? Have you ever marvelled at the recklessness of fast drivers, watched rubber-neckers gawking at an accident or thought there must be a better way to design this highway? Today you will get a chance to give it a try on your own!\n", + "\n", + "One of the reasons traffic networks are difficult to design is that they must operate well under a wide range of difficult to predict conditions: think of severe weather events, a large number of vehicles on the road during a few key points per day and the unpredictable behavior of human drivers. This all suggests that a stochastic, or probabilistic approach can be well suited to traffic and transport evaluations.\n", + "\n", + "For this assignment you will consider a highway route between Dordrecht and The Hague (we will call this route the ‘trajectory’). You have data measuring travel time along this trajectory during two months, all measured between the hours of 5.00-11.00 (the morning commute), which we will use to estimate the probability that the travel time exceeds some critical threshold, and the threshold itself is determined based on travel time as a risk metric.\n", + "\n", + "## Estimating Traffic Patterns in Practice\n", + "\n", + "Before we begin, note that this exercise is a dramatic simplification of reality, as it uses simplified methods and a single dataset to evaluate one highway trajectory. In practice, this is done by setting up a complex network-based model and using stochastic processes and probability distributions to simulation things like vehicle flow rates, accidents, road closures, etc. Travel times are then described using probability distributions that are based on a large number of simulations.\n", + "\n", + "In other words: assume a distribution of flow rate or vehicles on the road, use stochastic processes to consider the range of highway conditions and the occurrence of accidents, then let the computer do the hard work. In the end you get a histogram of travel times for your trajectory of interest. You can then look at the database of simulations to try and make inference on what leads to undesirable conditions. For example, take the group of simulations with the longest travel times for a given trajectory and see if it is caused by insufficient flow capacity or emergency vehicle response rate (i.e., ability to clear accidents quickly).\n", + "\n", + "In this exercise we will not simulate an entire traffic network, but instead use two simplified methods for estimating travel time, each of which will give different insight into possible design decisions.\n", + "\n", + "## How does this link to MUDE Weeks 2.7-2.8 Risk and Reliability?\n", + "\n", + "This is in fact a relatively simple probabilistic design problem. Just as the simple example for computing dike height to withstand a river discharge with failure probability of 1% (a one random variable case), in this example we need to design the highway such that travel time on the highway only exceeds the threshold amount 5% of the time. In this case the only random variable is vehicle flow rate. As you continue reading, you will probably think the computational models and method for taking into account interventions is a bit complicated, but remember: you only need to design for one random variable!" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from ipywidgets import interact\n", + "import ipywidgets as widgets\n", + "import warnings\n", + "warnings.filterwarnings('ignore')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Traffic Variables\n", + "\n", + "We are interested in estimating tavel time, $t$ [minutes], measured along a single highway. Key variables that play a role in determining $t$ for the Dordrecht-Den Haag trajectory are:\n", + "\n", + "- Vehicle flow rate, $q$ [vehicles/hr]: typically measured per link, but for our purposes it will represent the entire highway trajectory. For the morning commute, the flow rate is typically 5500 veh/hr.\n", + "- Capacity, $C$ [veh/hr]: the maximum flow rate of a link. For our trajectory, the capacity is 5600 veh/hr.\n", + "- Delay, $t_{delay}$ [min]: additional time required to travel a trajectory for a single vehicle. Caused by an accident that lasts $t_{accident}$ minutes.\n", + "\n", + "A few other variables will be described below after we introduce two methods to calculate travel time, but first we will introduce you to the Python code that will be used to make it easy for you to solve this problem!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## `Trajectory` class\n", + "\n", + "As the objective of this exercise is to focus on the probabilistic design process (*not* to see how fast you can use Python), many key steps have been automated for you using a class, `Trajectory`, which is defined in `exercise_setup.py`. An instance of the class is initialized with default values already defined, and many of the methods can be used without the need to specify inputs (see examples below). Observations in the attached `csv` file are also initialized as a dataframe attribute of the class, so you don't even need to import the data. For most methods, making a user-specified input argument will allow you to quickly see how a design decision may modify the characteristics of our highway trajectory. \n", + "\n", + "An instance is created in the following cell, and the class is used repeatedly throughout this notebook to provide usage examples. We have tried to provide informative docstrings to help figure out what each method does, so you should not have to look in the `exercise_setup.py` file unless you are curious how the class is defined." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "from exercise_setup import Trajectory\n", + "t=Trajectory()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The class is initialized with a number of default values (explained later), which you can check using the following method:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Print current values used in Method 1 and 2.\n", + "Current parameter values are:\n", + " alpha = 0.15\n", + " beta = 4\n", + " t_0 = 28.5\n", + " C = 5600\n", + " rCf = 0.2\n", + " q = 5500\n" + ] + } + ], + "source": [ + "print(t.print_parameters.__doc__)\n", + "t.print_parameters()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It's easy to create a second instance of the class, which can be useful if you want to see what the affect of varying parameter values. For example, here we change $q$ from the default value of 5500 to 5000:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Current parameter values are:\n", + " alpha = 0.15\n", + " beta = 4\n", + " t_0 = 28.5\n", + " C = 5600\n", + " rCf = 0.2\n", + " q = 5000\n" + ] + } + ], + "source": [ + "t2=Trajectory()\n", + "t2.q = 5000\n", + "t2.print_parameters()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Part 1. Two Methods for Estimating Travel-Time\n", + "\n", + "We will introduce two methods for computing the travel time, one that focuses on *flow rate* and *capacity*, the other on *accident duration.*\n", + "\n", + "### Method 1: Bureau of Public Roads (BPR) Curve\n", + "\n", + "Method 1 computes travel time as a function of vehicle flow rate, $q$:\n", + "\n", + "$$t\\left(q\\right)=t^0\\left(1+\\alpha\\left(\\frac{q}{C}\\right)^\\beta\\right)$$\n", + "\n", + "where $t^0$ is the free flow travel time, which is the time it would take to travel the link if there were no other vehicles on the road ($q=0$).\n", + "\n", + "$\\alpha=0.15$ and $\\beta=4.0$ are constants, especially for our simple case.\n", + "\n", + "Later in the exercise we will make changes to the highway (interventions) that will influence the parameters $q$ and $C$ and $t^0$. For example, adding a lane to the highway will increase $C$.\n", + "\n", + "Method 1 has been implemented in the `Trajectory` class as `travel_time_method_1()`." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Compute travel time with Method 1.\n", + " \n", + " Keyword arguments: q, alpha, beta, t_0, C.\n", + " Returns: travel time as float or array, depending on input.\n", + " \n" + ] + } + ], + "source": [ + "print(t.travel_time_method_1.__doc__)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can use it to calculate the travel time for given variables." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Travel time computed with Method 1 = 32.5 minutes.\n" + ] + } + ], + "source": [ + "print(f'Travel time computed with Method 1 = '\n", + " f'{t.travel_time_method_1():.1f} minutes.')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You can use *keyword arguments* to change the default values for capacity, free-flow travel time and flow rate to see how the estimated travel-time changes!" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Travel time computed with Method 1 = 31.5 minutes.\n" + ] + } + ], + "source": [ + "print(f'Travel time computed with Method 1 = '\n", + " f'{t.travel_time_method_1(C=6000):.1f} minutes.')" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Travel time computed with Method 1 = 28.9 minutes.\n" + ] + } + ], + "source": [ + "print(f'Travel time computed with Method 1 = '\n", + " f'{t.travel_time_method_1(q=3000):.1f} minutes.')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Using sliders we can look at the effect of capacity and t_0 on the BPR curve." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{note}\n", + "The widgets displayed on this page will not work in the website version, only when you use the `*.ipynb` file with a Python kernel (e.g., in Jupyter Notebook or Jupyter Lab).\n", + "```" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "c0bdaad2190343f5b8c103bbd6bd9257", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "interactive(children=(FloatSlider(value=28.5, description='t_0', max=32.0, min=26.0, step=0.5), FloatSlider(va…" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from custom_widgets import method_1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Method 2: Delays Caused by Accidents\n", + "\n", + "This method takes into account accidents that may have occurred along our trajectory computing the delay experienced by a single vehicle, $t_\\mathrm{delay}$. The delay is related to the length of the accident itself, as well as the traffic flow and trajectory capacity:\n", + "\n", + "$$t_\\mathrm{delay}=t_{\\mathrm{accident}} \\cdot \\frac{(q - rC)}{2q}$$\n", + "\n", + "Where $rC$ is the remaining capacity of the link [veh/hr], approximated as a percentage of the link capacity:\n", + "\n", + "$$rC = rC_f \\cdot C$$\n", + "\n", + "In our case we assume $rC_f$=0.2.\n", + "\n", + "Total travel time along the trajectory can be estimated by adding $t_{delay}$ to the travel time without accidents. This is similar to the free flow travel time, $t^0$, except we must take into account the fact that accidents don't have a significant effect on travel time until traffic flow is already reaching the trajectory capacity. Thus, we introduce a cutoff time, $t_{cutoff}$, above which accidents affect $t$:\n", + "\n", + "$$t=t_{\\mathrm{cutoff}}+t_\\mathrm{delay}$$\n", + "\n", + "The value of $t_{cutoff}$ is estimated using Method 1 for a condition close to the capacity of the highway---100 veh/hr less---which returns 32.5 min, computed here:." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Travel time for q = 5500.0 and C = 5600.0 using Method 1: 32.50 min\n" + ] + } + ], + "source": [ + "print(f'Travel time for q = {t.q} and C = {t.C} using Method 1: '\n", + " f'{t.travel_time_method_1(q=t.q, C=t.C):.2f} min')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Method 2 has been implemented in the `Trajectory` class as `travel_time_method_2()`, which computes travel time for a single vehicle and a single accident. The class also assumes $t_{accident}=10$ min as a default value, which is close to the median accident length during the morning commute. " + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Compute travel time with Method 2 (delays).\n", + " \n", + " Keyword arguments: t_accident, q, C, rCf, t_cutoff.\n", + " Returns: travel time as float or array, depending on input.\n", + " \n" + ] + } + ], + "source": [ + "print(t.travel_time_method_2.__doc__)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can use it to calculate the travel time for given variables, which is set up to assume that a single 10 min accident has occured for a vehicle traveling the trajectory." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A single accident duration of 10 min is assumed by default. Include argument t_accident=? to override.\n", + "Travel time computed with Method 2 = 36.5 minutes.\n" + ] + } + ], + "source": [ + "print(f'Travel time computed with Method 2 = '\n", + " f'{t.travel_time_method_2():.1f} minutes.')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Investigating the effect of accident duration is easy because you can change the default argument values just like for Method 1 (see documentation for complete list of input arguments):" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Travel time computed with Method 2 = 44.4 minutes when accident time is 30 min.\n" + ] + } + ], + "source": [ + "try_t_accident = 30\n", + "print(f'Travel time computed with Method 2 = '\n", + " f'{t.travel_time_method_2(t_accident=try_t_accident):.1f} '\n", + " f'minutes when accident time is {try_t_accident} min.')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There is also a method to compute delay:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A single accident duration of 10 min is assumed by default. Include argument t_accident=? to override.\n", + "The delay for one vehicle is 3.98 min.\n", + "The delay for one vehicle due to a 30 min accident is 11.95 min.\n" + ] + } + ], + "source": [ + "print(f'The delay for one vehicle is '\n", + " f'{t.estimate_t_delay():.2f} min.')\n", + "print(f'The delay for one vehicle due to a {try_t_accident} min '\n", + " f'accident is {t.estimate_t_delay(t_accident=try_t_accident):.2f} min.')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Interesting, the previous calculation shows that if the accident time increases by 20 min, the delay is only increased by 8 min." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{note}\n", + "The widgets displayed on this page will not work in the website version, only when you use the `*.ipynb` file with a Python kernel (e.g., in Jupyter Notebook or Jupyter Lab).\n", + "```" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "d00800ac309946df9291756aa1ffcbc4", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "interactive(children=(FloatSlider(value=10.0, description='t_accident', max=60.0, min=5.0, step=5.0), FloatSli…" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from custom_widgets import method_2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Part 2. Importing the Data" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we do 'the usual': import data using pandas, clean it up and explore it with a few summary statistics and visualizations. Luckily we've already done this for you in the `process_observations` method in the `Trajectory` class, and class is initialized with the datafram as an attribute." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Create dataframe with observations.\n", + " \n", + " Steps:\n", + " - Import file defined by string attribute observations_filename.\n", + " - Extract all columns with observations.\n", + " - Set up and return new dataframe:\n", + " - travel_time_df\n", + " - Set up and return new arrays:\n", + " - travel_time\n", + " - flow_rate\n", + " - t_accident\n", + " - dataframe and arrays are added as attributes in init\n", + " \n" + ] + } + ], + "source": [ + "print(t.process_observations.__doc__)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "<div>\n", + "<style scoped>\n", + " .dataframe tbody tr th:only-of-type {\n", + " vertical-align: middle;\n", + " }\n", + "\n", + " .dataframe tbody tr th {\n", + " vertical-align: top;\n", + " }\n", + "\n", + " .dataframe thead th {\n", + " text-align: right;\n", + " }\n", + "</style>\n", + "<table border=\"1\" class=\"dataframe\">\n", + " <thead>\n", + " <tr style=\"text-align: right;\">\n", + " <th></th>\n", + " <th>Travel Time</th>\n", + " </tr>\n", + " </thead>\n", + " <tbody>\n", + " <tr>\n", + " <th>0</th>\n", + " <td>30.144795</td>\n", + " </tr>\n", + " <tr>\n", + " <th>1</th>\n", + " <td>30.064739</td>\n", + " </tr>\n", + " <tr>\n", + " <th>2</th>\n", + " <td>29.912339</td>\n", + " </tr>\n", + " <tr>\n", + " <th>3</th>\n", + " <td>29.972393</td>\n", + " </tr>\n", + " <tr>\n", + " <th>4</th>\n", + " <td>30.084815</td>\n", + " </tr>\n", + " </tbody>\n", + "</table>\n", + "</div>" + ], + "text/plain": [ + " Travel Time\n", + "0 30.144795\n", + "1 30.064739\n", + "2 29.912339\n", + "3 29.972393\n", + "4 30.084815" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "t.travel_time_df.head()" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "<div>\n", + "<style scoped>\n", + " .dataframe tbody tr th:only-of-type {\n", + " vertical-align: middle;\n", + " }\n", + "\n", + " .dataframe tbody tr th {\n", + " vertical-align: top;\n", + " }\n", + "\n", + " .dataframe thead th {\n", + " text-align: right;\n", + " }\n", + "</style>\n", + "<table border=\"1\" class=\"dataframe\">\n", + " <thead>\n", + " <tr style=\"text-align: right;\">\n", + " <th></th>\n", + " <th>Travel Time</th>\n", + " </tr>\n", + " </thead>\n", + " <tbody>\n", + " <tr>\n", + " <th>count</th>\n", + " <td>22021.000000</td>\n", + " </tr>\n", + " <tr>\n", + " <th>mean</th>\n", + " <td>34.344555</td>\n", + " </tr>\n", + " <tr>\n", + " <th>std</th>\n", + " <td>9.524935</td>\n", + " </tr>\n", + " <tr>\n", + " <th>min</th>\n", + " <td>28.524847</td>\n", + " </tr>\n", + " <tr>\n", + " <th>25%</th>\n", + " <td>30.146187</td>\n", + " </tr>\n", + " <tr>\n", + " <th>50%</th>\n", + " <td>31.284827</td>\n", + " </tr>\n", + " <tr>\n", + " <th>75%</th>\n", + " <td>34.625918</td>\n", + " </tr>\n", + " <tr>\n", + " <th>max</th>\n", + " <td>129.301866</td>\n", + " </tr>\n", + " </tbody>\n", + "</table>\n", + "</div>" + ], + "text/plain": [ + " Travel Time\n", + "count 22021.000000\n", + "mean 34.344555\n", + "std 9.524935\n", + "min 28.524847\n", + "25% 30.146187\n", + "50% 31.284827\n", + "75% 34.625918\n", + "max 129.301866" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "t.travel_time_df.describe()" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "hist = t.travel_time_df.hist(density=True,\n", + " bins = 25,\n", + " edgecolor='k',\n", + " linewidth=1.1)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "bin_count, bin_position = np.histogram(t.travel_time_df, bins=25)\n", + "travel_time_freq = bin_count / sum(bin_count)\n", + "travel_time_cdf = np.cumsum(travel_time_freq)\n", + "plt.plot(bin_position[1:], travel_time_freq, color=\"red\",\n", + " linewidth=3, label=\"Relative frequency\")\n", + "plt.plot(bin_position[1:], travel_time_cdf,\n", + " label=\"Cumulative empirical distribution\", linewidth=3)\n", + "plt.xlabel('Travel Times [min]')\n", + "plt.ylabel('Relative Frequency and Empirical CDF [$-$]')\n", + "plt.legend();" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0, 0.5, 'Empirical Exceedance CDF')" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(bin_position[1:], 1-travel_time_cdf, label=\"CDF\", linewidth=3)\n", + "plt.yscale('log')\n", + "plt.ylim([1e-4, 1]);\n", + "plt.xlabel('Travel Times [min]')\n", + "plt.ylabel('Empirical Exceedance CDF')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Part 3. Fitting a Burr-Distribution to the Data" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It turns out the Burr distribution often is a good fit for traffic flow rate data, and we can obtain the parameters using MLE incorporated in the `scipy.stats` method [`Burr12`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.burr12.html)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The standardized form of the Burr12 distribution (with location, `loc` = 0 and `scale` = 1) is:\n", + "\n", + "$$\n", + "f(x, c, d)=c d \\frac{x^{c-1}}{\\left(1+x^{c}\\right)^{d+1}}\n", + "$$\n", + "\n", + "The distribution has to be shifted and scaled to fit our data, which is done with the location and scale parameters that are returnd by the method in `scipy`. If the Burr distribution as shown in the introductory video is a two-parameter formulation, and if it is used with the location and scale parameters as follows, it is equivalent to the `scipy` formulation (four parameters):\n", + "\n", + "$$\n", + "f_{scipy}(x, c, d, \\mathrm{loc}, \\mathrm{scale}) = f_{video}(\\frac{x-\\mathrm{loc}}{\\mathrm{scale}}, c, d) \\cdot \\mathrm{scale}\n", + "$$\n", + "\n", + "The CDF of the Burr distribution is very easy to evaluate:\n", + "$$\n", + "F(x,c, d, \\mathrm{loc}, \\mathrm{scale})=1−(1+x^c)^{-k}\n", + "$$\n", + "\n", + "*NB:*\n", + "- *In the video the parameters loc and scale are a and b, respectively. c and k are used equivalently.*\n", + "- *You are asked to make a calculation with the CDF below, one of the few things you are required to code on your own in this notebook.*\n", + "- *There are actually twelve Burr distributions (yes, 12!). They were 'invented' in the 1940's to avoid tedious hand calculations easier. The scipy distribution is equation 12 from [Burr's 1942 paper \"Cumulative Frequency Functions,\"](https://doi.org/10.1093%2Fbiomet%2F64.1.129) hence the name*\n", + "\n", + "In `Trajectory`, the distribution is fit during initialization of the class with `fit_burr`, and the parameter values can be printed using `print_parameters_burr`. The example below illustrates the use of `scipy.stats.Burr12` without requiring to dig into the py file." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Parameters are:\n", + " c = 84.137\n", + " k = 6.421e-02\n", + " loc = 12.00\n", + " scale = 17.49\n" + ] + } + ], + "source": [ + "t.print_parameters_burr()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we will plot the distribution with the histogram to check the fit visually. The PDF is calculated two ways: one using the 4-parameter version provided by `scipy.stats`, the other using the shifted and scaled 2 parameter version. It is clear that the restuls are identical." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Plot the distribution and the histogram\n", + "from scipy import stats\n", + "from scipy.stats import burr12\n", + "c, k, loc, scale = t.burr_parameters\n", + "x = np.linspace(20,130, 100)\n", + "plt.plot(x, burr12.pdf(x, c, k, loc, scale),\n", + " 'b-', lw=3, label='PDF using 4 parameters')\n", + "plt.plot(x, burr12.pdf((x-loc)/scale, c, k, 0, 1)/scale,\n", + " 'r:', lw=3, label='PDF using 2 parameters')\n", + "plt.hist(t.travel_time_df,density=True, bins=25,\n", + " edgecolor='k', linewidth=1.1)\n", + "plt.legend(loc='best', frameon=False)\n", + "plt.xlabel('Travel time, $t$ [min]')\n", + "plt.ylabel('Probability density and histogram [$-$]')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#Burr fit on the data with 4 parameters (red) and with 2 parameters (blue)\n", + "fig, ax = plt.subplots(1, 1)\n", + "ax.plot(x, 1 - burr12.cdf(x, c, k, loc, scale),\n", + " 'b-', lw=3, label='Burr-fit 4 params')\n", + "ax.plot(x, 1 - burr12.cdf((x-loc)/scale, c, k, 0, 1),\n", + " 'r:', lw=3, label='Burr-fit 2 params')\n", + "ax.plot(bin_position[1:], 1 - travel_time_cdf,\n", + " 'k--', lw=3, label=\"CDF of data\")\n", + "ax.legend(loc='best', frameon=False)\n", + "plt.yscale('log')\n", + "plt.xlim([25, 60])\n", + "plt.ylim([1e-4, 1])\n", + "plt.xlabel('Travel time, $t$ [min]')\n", + "plt.ylabel('Exceedance probability, $1-F_t(t)\\:$ [$-$]')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "What do you think of the fit?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Part 4. Evaluating the Trajectory" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The requirement for the trajectory is that the 95 percentile value is no more than 10 minutes longer than the free-flow travel time:\n", + "\n", + "$$\n", + "t_{95} \\leq t_0 + 10\\: \\mathrm{min}\n", + "$$\n", + "\n", + "**Using the information provided above, compute the 95th percentile of the Burr distribution in the cell below.**" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [], + "source": [ + "burr_95th_percentile = None" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Use this cell to check whether the trajectory meets the requirement, after you compute the 95th percentile above.**" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Replace the variable in the cell above with your calculation!\n" + ] + } + ], + "source": [ + "if burr_95th_percentile is None:\n", + " print('Replace the variable in the cell above with your calculation!')\n", + "elif burr_95th_percentile > t.t_0 + 10:\n", + " print('The requirement is not met, interventions are needed.')\n", + "elif burr_95th_percentile < 0:\n", + " print('The trajectory meets the requirement.')\n", + "elif burr_95th_percentile < t.t_0 + 10:\n", + " print('The trajectory meets the requirement.')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Part 5. Effect of Interventions on Travel Time\n", + "\n", + "Now it's time for the fun part: let's look at a variety of interventions and see if we can improve the travel time on this highway trajectory! The following sections describe the interventions and illustrate the Python tools that are available for you to re-design the highway.\n", + "\n", + "## Description of Intervention Effects\n", + "\n", + "The following interventions can be considered for our trajectory:\n", + "\n", + "1. **Extra Lane:** widens existing road by one or two lanes \n", + "2. **Hard Shoulder:** adds a hard shoulder to the existing trajectory, providing extra capacity, especially during peak flow moments \n", + "3. **Max Speed:** sets the maximum allowed speed on trajectory (current value, 130 km/h; maximum value: 170km/h)\n", + "4. **Alternate Trajectory:** constructs one or two alternative trajectory options (e.g. a second highway or large road), decreasing peak flow rate on the original trajectory \n", + "5. **Incident Management:** speeds up towing and accident clean-up services by X% which reduces time duration of an accident \n", + "6. **Accident Risk Reduction:** employs cooperative intelligent transport systems, C-ITS (vehicle to vehicle communication), to reduce the number of incidents by X%. For our case it can also include a number of measures such as smart signs, lights and lane control. \n", + "7. **Modal Shift, Trucks:** decreases the number of trucks during the morning commute by X% by promoting alternative modes and commute times for truck transport \n", + "8. **Modal Shift, Cars:** equivalent to the above intervention, but for cars \n", + "\n", + "## Implementation of Intervention Effects\n", + "\n", + "The following table indicates which Method can take into account each intervention and how, as well as key information for using the Python tools:\n", + "\n", + "| No. | Intervention | Variable | Method 1 | Method 2 | Keyword Argument | Values |\n", + "| :---: | :---: | :---: | :---: | :---: | :---: | :---: |\n", + "| 1 | Extra Lane | $C$ | X | X | `extra_lane` | `None`, 1, 2 |\n", + "| 2 | Hard Shoulder | $C$ | | X | `hard_shoulder` | `True`/`False` |,\n", + "| 3 | Max. Speed | $t_0$ | X | X | `max_speed` | >0, 170 max |\n", + "| 4 | Alternate trajectory | $q$ | X | X | `alt_route` | `None`, 1, 2 |\n", + "| 5 | Incident Management | $t_{accident}$ | | X | `incident_management` | 1%$-$100% |\n", + "| 6 | Accident Risk Reduction | $t_{accident}$ | | X | `accident_risk_reduction` |1%$-$100% |\n", + "| 7 | Modal Shift, Trucks | $q$ | X | X | `modal_shift_trucks` | 0%$-$20% |\n", + "| 8 | Modal Shift, Cars | $q$ | X | X | `modal_shift_cars` | 0%$-$20% |\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Method 1: BPR" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The expected travel time changes when the free-flow travel time ($t_0$), flow ($q$) and capacity $C$ are modified. The interventions listed above have been implemented as keyword arguments in the method `intervention_method_1`, illustrated with an example below the docstring:" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Compute travel time with Method 1.\n", + " \n", + " Keyword arguments: q, alpha, beta, t_0, C.\n", + " Returns: travel time as float or array, depending on input.\n", + " \n" + ] + } + ], + "source": [ + "print(t.travel_time_method_1.__doc__)" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The baseline travel time is 32.50 min\n", + "The travel time with an intervention is 28.17 min\n", + " (the difference is -4.33 min)\n" + ] + } + ], + "source": [ + "travel_time_baseline = t.travel_time_method_1()\n", + "travel_time_with_intervention = t.intervention_method_1(max_speed=150)\n", + "print(f'The baseline travel time is '\n", + " f'{travel_time_baseline:0.2f} min')\n", + "print(f'The travel time with an intervention is '\n", + " f'{travel_time_with_intervention:0.2f} min'\n", + " f'\\n (the difference is '\n", + " f'{travel_time_with_intervention - travel_time_baseline:.2f} min)')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The Burr distribution can also be estimated for the same intervention using `plot_distribution_method_1`, which relies on `intervention_method_1`. Here it is set up with widgets to let you play with the effect of each intervention:" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{note}\n", + "The widgets displayed on this page will not work in the website version, only when you use the `*.ipynb` file with a Python kernel (e.g., in Jupyter Notebook or Jupyter Lab).\n", + "```" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "7974564f725f4bb1ba9a4b1d8a221aca", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "interactive(children=(Dropdown(description='1: Extra Lanes', options=(('None', None), ('1', 1), ('2', 2)), val…" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from custom_widgets import method_1_interv_dist" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This function will compute the 95th percentile for the baseline parameter values:" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "42.5\n" + ] + } + ], + "source": [ + "print(f'{t.burr_ppf_with_int_1(0.95):.3}')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The same function allows you to check out how the 95th percentile changes by applying interventions.\n", + "\n", + "*What interventions could you apply in order to meet the requirement for the trajectory?*\n" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "33.4\n" + ] + } + ], + "source": [ + "print(f'{t.burr_ppf_with_int_1(0.95,alt_route=1):.3}')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Method 2: Delays\n", + "\n", + "Interventions for Method two have been implemented as keyword arguments in the method `intervention_method_2`, and can be used the same as with those for Methods 1, although there are 8 possible interventions instead of 5:" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Compute travel time with Method 2 (delays).\n", + " \n", + " Keyword arguments: t_accident, q, C, rCf, t_cutoff.\n", + " Returns: travel time as float or array, depending on input.\n", + " \n" + ] + } + ], + "source": [ + "print(t.travel_time_method_2.__doc__)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{note}\n", + "The widgets displayed on this page will not work in the website version, only when you use the `*.ipynb` file with a Python kernel (e.g., in Jupyter Notebook or Jupyter Lab).\n", + "```" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "892aced71d0140a48243e07efbf54f4f", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "interactive(children=(Dropdown(description='1: Extra Lanes', options=(('None', None), ('1', 1), ('2', 2)), val…" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from custom_widgets import method_2_interv_dist" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Part 6. Cost-Benefit Analysis\n", + "\n", + "Now it's time for the fun part: coming up with an optimal design! It's easy to use the intervention functions introduced above to find a combination that gives a 95th percentile value that meets the requirement. However, in real life interventions cost money, and we will take that into account here using the costs specified in the table, which have also been implemented for you in the methods below, `benefit_cost_method_x`. These functions work with keyword arguments, just like the intervention functions above. With that, the assignment is simply:\n", + "\n", + "**Maximize the ratio of benefits to cost such that: 1) the maximum cost of 250 FCoins is not exceeded, and 2) the 95th percentile is less than $t_0+10$.** Your 'answer' should be in the form of a specific set of interventions (using keyword argument values), costs, benefit-cost ratio, and a short justification for how you came to the result.\n", + "\n", + "Although the assignment is simple, there are a few things to note, in particular: Method 1 and 2 are different, and *both* are simplified versions of reality. They will give you different results because they are different methods, not only because Method 2 includes more interventions. In addition, the costs are defined in terms of FCoins, which are not 'real' monetary units, and have not been scaled to reality; as such, the benefit-cost ratio will does not need to be greatere than 1 to be a viable project.\n", + "\n", + "| Intervention | Keyword Argument | Costs (FCoins) |\n", + "| :--- | :---: | :---: |\n", + "| New Alternative Route | `alt_trajectory` | --- |\n", + "| 1 lane | --- | 150 |\n", + "| 2 lanes | --- | 180 |\n", + "| New Lane | `extra_lane` | --- |\n", + "| 1 additional lane | --- | 70 |\n", + "| 2 additional lanes | --- | 100 |\n", + "| Create Hard Shoulder | `hard_shoulder` | 60 |\n", + "| Increase Max Speed | `max_speed` | 7/percent |\n", + "| Accident Risk Reduction | `accident_risk_reduction` | 5/percent |\n", + "| Incident Management | `incident_management` | 2/percent |\n", + "| Modal Shift Trucks | `modal_shift_trucks` | 5/percent |\n", + "| Modal Shift Cars | `modal_shift_cars` | 8/percent |\n", + "\n", + "NB: *the \"/percent\" cost is determined per percent change in the intervention basedo on the pre-intervention value. For example, changing the maximum speed from 130 to 140 km/hr is a +8% change, thus it would cost 56 FCoins*" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [], + "source": [ + "from benefit_cost import benefit_cost_method_1\n", + "from benefit_cost import benefit_cost_method_2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "These functions compute the benefit to cost ratio, which you need to maximize without exceeding the total cost." + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The benefit-cost ratio using Method 1 is: 0.095\n", + "Total cost for all interventions applied: 100.000 FCoins\n" + ] + } + ], + "source": [ + "BC1 = benefit_cost_method_1(modal_shift_trucks=20)" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The benefit-cost ratio using Method 2 is: -0.058\n", + "Total cost for all interventions applied: 100.000 FCoins\n" + ] + } + ], + "source": [ + "BC2 = benefit_cost_method_2(modal_shift_trucks=20)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Good luck!" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "base", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.13 (main, Aug 25 2022, 23:51:50) [MSC v.1916 64 bit (AMD64)]" + }, + "latex_envs": { + "LaTeX_envs_menu_present": true, + "autoclose": false, + "autocomplete": true, + "bibliofile": "biblio.bib", + "cite_by": "apalike", + "current_citInitial": 1, + "eqLabelWithNumbers": true, + "eqNumInitial": 1, + "hotkeys": { + "equation": "Ctrl-E", + "itemize": "Ctrl-I" + }, + "labels_anchors": false, + "latex_user_defs": false, + "report_style_numbering": false, + "user_envs_cfg": false + }, + "vscode": { + "interpreter": { + "hash": "85471ad55176ca86192ed6be6d105faaef73891404cad6bd910e89e8513744d9" + } + }, + "widgets": { + "application/vnd.jupyter.widget-state+json": { + "state": { + "0187e7214d8a445dbb5c831f13f34dd3": { + "model_module": "@jupyter-widgets/base", + "model_module_version": "1.2.0", + "model_name": "LayoutModel", + "state": {} + }, + "08f445fa1f7a42dab8956fa6ca209e16": { + "model_module": "@jupyter-widgets/base", + "model_module_version": "1.2.0", + "model_name": "LayoutModel", + "state": {} + }, + "0953d24691094e3d9b652d497901a09a": { + "model_module": "@jupyter-widgets/controls", + "model_module_version": "1.5.0", + "model_name": "SliderStyleModel", + "state": { + "description_width": "initial" + } + }, + "0bb275f5ec1542b5ae0ef636577f1b72": { + "model_module": "@jupyter-widgets/controls", + "model_module_version": "1.5.0", + "model_name": "DescriptionStyleModel", + "state": { + "description_width": "" + } + }, + "100c0581cfc747c8af541fc9d5145845": { + "model_module": "@jupyter-widgets/controls", + "model_module_version": "1.5.0", + "model_name": "DropdownModel", + "state": { + "_options_labels": [ + "No alternate routes", + "1 alternate route", + "2 alternate routes" + ], + "description": "4: Alt. 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\n", 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\n", 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"source": [ + "```{custom_download_link} exercise.zip\n", + ":text: \"Download Files\"\n", + ":replace_default: \"True\"\n", + "```" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "bcb1b890", + "metadata": {}, + "source": [ + "# Contaminant Transport" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0e18b539", + "metadata": { + "tags": [ + "thebe-remove-input-init", + "thebe-init" + ] + }, + "outputs": [], + "source": [ + "import micropip\n", + "await micropip.install(\"seaborn\")\n", + "\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy.special import erfc\n", + "from scipy import stats\n", + "import seaborn as sns\n", + "\n", + "from exercise_setup import process_negative_values\n", + "from exercise_setup import RandomVariableDistribution\n", + "from exercise_setup import pdf_of_function_of_RV\n", + "from exercise_setup import monte_carlo" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "06fa7af4", + "metadata": {}, + "source": [ + "`````{admonition} Interactive Python Page\n", + ":class: tip, dropdown\n", + "\n", + "The code on this page can be used interactively: click {fa}`rocket` --> {guilabel}`Live Code` in the top right corner, then wait until the message {guilabel}`Python interaction ready!` appears.\n", + "\n", + "When this page is activated:\n", + "- Several packages will be imported automatically\n", + "- Code cells will **not** be executed automatically (you do it!)\n", + "\n", + "The download button {fa}`download` provides a `*.zip` file with everything needed to run this analysis on your computer. \n", + "\n", + "````{admonition} Which packages are imported when this page is activated?\n", + ":class: note, dropdown\n", + "```\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy.special import erfc\n", + "from scipy import stats\n", + "import seaborn as sns\n", + "\n", + "from exercise_setup import process_negative_values\n", + "from exercise_setup import RandomVariableDistribution\n", + "from exercise_setup import pdf_of_function_of_RV\n", + "from exercise_setup import monte_carlo\n", + "```\n", + "````\n", + "`````\n", + "Here we use component reliability methods to evaluate the probability of a contaminant causing dangerous concentrations in a groundwater well. The contaminant plume is transported on the groundwater phreatic surface due to advection and diffusion.\n", + "\n", + "The purpose of this exercise is to:\n", + "- evaluate component reliability\n", + "- illustrate functions of random variables\n", + "- see the effect of random variable distributions on reliability\n", + "- consider 'sensitivity' as a functional and/or stochastic influence on the limit-state function\n", + "\n", + "### Instructions for Interactive Programming Exercise\n", + "\n", + "This page is designed to lead you through the analysis sequentially, so we recommend executing the cells one-by-one as you read through the page. Afterwards, you are welcome to use the \"run all\" button to execute all cells on the page.\n", + "\n", + "Once the interactive feature {fa}`rocket` is activated, you can use the code cells to answer the following questions:\n", + "1. Which random variables have the biggest influence on reliability?\n", + "2. How does the assumption of probability distribution influence reliability?\n", + "3. Do the random variables act as loads or resistances?\n", + "\n", + "## Introduction of Case Study\n", + "\n", + "The case study is a contaminant transport problem, illustrated in the figure below. A factory located near a town produces hazardous waste, which can threaten the drinking water supply of the town that is extracted from groundwater wells (C). The regional groundwater system has a gradient that causes water to flow in the direction of the town from the factory, thus any spilled hazardous waste that enters the ground will eventually be transported to the wells. In order to mitigate the consequences of a spill a ditch is constructed around the factory to collect it (A). Unfortunately, even with powerful pumps, there will still be some waste that reaches the groundwater table. Our task is to quantify the probability that the waste concentration exceeds the maximum exposure level to prevent the drinking water becoming unhealthy.\n", + "\n", + "```{figure} ../notebooks/contamination/figures/sketch.png\n", + "---\n", + "width: 600px\n", + "name: sketch_contaminant\n", + "---\n", + "\n", + "```\n", + "\n", + "### Contaminant Transport\n", + "\n", + "Once the ditch becomes contaminated it is cleaned quickly, but unfortunately a 'pulse' of contamination enters the ground, after which the regional gradient carries it towards the town (advection). The pulse also disperses due to diffusion, which results in a classic advection-diffusion problem (see red shapes in diagram, at three different times, $t$). Because the ditch extends a long distance in the lateral direction and the contaminant is buoyant (it floats on the groundwater table and we neglect vertical dispersion), the problem can be analyzed in 1 dimension with the following analytic expression:\n", + "\n", + "$$\n", + "\\frac{C}{C_0} = \\frac{1}{2} \\mathrm{erf}\\left(\\frac{x-(q/n)t}{2\\sqrt{a(q/n)t}}\\right)\n", + "$$\n", + "\n", + "Where $C$ contaminant concentration (e.g., parts per million, ppm) at distance $x$ from the ditch at time $t$ after the spill, and $C_0$ is the concentration in the ditch (just prior to cleanup). $\\mathrm{erf}$ is the error function. There are three parameters in the equation which are related to soil properties and groundwater flow:\n", + "\n", + "- $q$ is the horizontal groundwater flow velocity (specific discharge) [m/day]\n", + "- $n$ is the soil porosity [$-$]\n", + "- $a$ is the longitudinal dispersivity, which describes dispersion in the left to right direction in the image [m]\n", + "\n", + "Unfortunately there is not a lot of soil information, so we have to take into account uncertainty in these three variables, using the following probability distributions with first and second moments (i.e., $\\mu$ and $\\sigma$).\n", + "\n", + "- $q\\sim\\mathrm{N}\\left(\\mu_q=1.00,\\sigma_q=0.10\\right)$\n", + "- $n\\sim\\mathrm{N}\\left(\\mu_n=0.20,\\sigma_n=0.02\\right)$\n", + "- $a\\sim\\mathrm{N}\\left(\\mu_a=10.0,\\sigma_a=1.00\\right)$\n", + "\n", + "It is important to check the sensitivity of the reliability analysis to the distribution type and moments. We will use the concentration ratio $C/C_0$ to evaluate this problem and compare it to a threshold defined by health regulations: $\\mathrm{threshold}=1e-4$.\n", + "\n", + "### Definition of Limit States\n", + "\n", + "As shown in the figure above, there are two locations of interest: the monitoring station ($x=100$ m from the ditch, point B) and the town well ($x=500$ m, point C). We are interested in evaluating two cases with a reliability analysis:\n", + "1. Whether the contamination can be detected at the monitoring station above the threshold level within 1 week of the spill, and \n", + "2. If the contamination level at the town groundwater well exceeds the threshold level within 1 month of the spill (30 days)\n", + "\n", + "Relating these descriptions to our variables of interest:\n", + "1. find the probability that $C/C_0$ > threshold \n", + "2. find the probability that $C/C_0$ < threshold\n", + "\n", + "We will refer to these values as 'failure probabilities', even though case 1 technically doesn't correspond to failure---it's just the way we refer to things in practice.\n", + "\n", + "Next we will convert these into functions that will allow us to quantify the 'failure' conditions. For convenience, it is often useful to define the limit state as a function, $Z$, such that failure occurs when $Z<0$. It follows from the descriptions above, that the limit state functions for both cases are:\n", + "\n", + "1. $Z=C/C_0 - \\mathrm{threshold}$\n", + "2. $Z=\\mathrm{threshold} - C/C_0$\n", + "\n", + "NB: *in the book another notation used for $Z$ is $g_X(X)$.*\n", + "\n", + "### Analysis Approach\n", + "\n", + "Our programming task is to create a function of random variables to represent these two limit-states, define the random variables, then evaluate the reliability with Monte Carlo simulation. In other words, we will numerically approximate the probability distribution of $Z$, then evaluate reliability as $P(Z<0)$.\n", + "\n", + "This is a lot of work, but fortunately a number of helper functions and a Class are provided in the auxiliary file `exercise_setup.py`!\n", + "\n", + "### References\n", + "\n", + "This example draws inspiration from Case 2 of the paper by {cite:t}`sitar1987`." + ] + }, + { + "cell_type": "markdown", + "id": "d104b4b2-4fa5-4b37-891d-39201281ed2f", + "metadata": {}, + "source": [ + "## Defining the Limit States\n", + "\n", + "We only define limit state Case 2 below, and will use a simple multiplying factor of $-1$ to switch to Case 1 using a multiplying factor `flip_LSF`." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "64c24956", + "metadata": {}, + "outputs": [], + "source": [ + "def C_C0(q, n, a, x, t):\n", + " \"\"\"Contaminant concentration ratio.\"\"\"\n", + " q, n, a = process_negative_values(q, n, a)\n", + " return 0.5*erfc((x - q/n*t)/(2*np.sqrt(a*(q/n)*t)))\n", + "\n", + "def limit_state_fun(q, n, a, x, t, threshold):\n", + " \"\"\"Limit state fxn, Case 2 (multiply by flip_LSF=-1 for Case 1).\"\"\"\n", + " return threshold - C_C0(q, n, a, x, t)" + ] + }, + { + "cell_type": "markdown", + "id": "d7410d16-14d4-45c6-9f93-81ae08de0594", + "metadata": {}, + "source": [ + "## Class `RandomVariableDistribution`\n", + "\n", + "The class `RandomVariableDistribution` makes it very easy to define Normal and Lognormal distributions for the random variables. See documentation and example below.\n", + "\n", + "NB: *you can use the code in `exercisesetup.py` and this notebook to confirm the result of the 2 random variable case in the Probabilistic Design chapter, and recreate the figures.*" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8bbf80be-5124-40ba-b3de-0da3eaa12ef1", + "metadata": {}, + "outputs": [], + "source": [ + "print(RandomVariableDistribution.__doc__)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a9b93099-b1cb-458b-baf6-8ad5dd39c440", + "metadata": {}, + "outputs": [], + "source": [ + "example_random_variable = RandomVariableDistribution()\n", + "example_random_variable.define_distribution(mean=5,\n", + " dist_type='LN',\n", + " print_new_dist=True)\n", + "example_random_variable.plot_pdf_or_cdf()" + ] + }, + { + "cell_type": "markdown", + "id": "62617026-f251-462b-a93c-b7305cfd3fa4", + "metadata": {}, + "source": [ + "## Setting up the problem\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "4641ae3c", + "metadata": {}, + "outputs": [], + "source": [ + "N = 10000\n", + "\n", + "t = 7\n", + "x = 100\n", + "threshold = 1e-4\n", + "\n", + "flip_LSF = -1\n", + "\n", + "q_rv = RandomVariableDistribution()\n", + "q_rv.define_distribution(mean=1., stddev=.1)\n", + "n_rv = RandomVariableDistribution()\n", + "n_rv.define_distribution(mean=0.2, stddev=.02)\n", + "a_rv = RandomVariableDistribution()\n", + "a_rv.define_distribution(mean=10., stddev=1.)" + ] + }, + { + "cell_type": "markdown", + "id": "f3e0ffb1-6035-4f76-a550-4ff19c1b5946", + "metadata": {}, + "source": [ + "## Monte Carlo analysis\n", + "\n", + "The Monte Carlo procedure for estimating failure probability, $p_f$, is:\n", + "- For each random variable $X_i$ ($i = 1, …, n$) one simulates N realizations, $x_{i,1}, x_{i,1}, ..., x_{i,N}$. \n", + "- For each set of simulations $j$ ($j = 1, ..., N$) one calculates $g(x_{1,j}, x_{2,j}, …, x_{n,j})$\n", + "- In case $g(.) < 0$ a counter $N_f$ is increased by one. After $N$ simulations one calculates: $\\hat{p_f}=N_f/N$\n", + "- In case $N\\rightarrow+\\infty$ one obtains the failure probability $p_f$.\n", + "\n", + "The number of simulations $N$ directly influences the accuracy of $\\hat{p_f}$, which is an estimate of the 'true' value $p_f$. As an infinite number of simulations is not possible, one must choose a value for $N$ that balances total computation time, which increases linearly with $N$, and accuracy of the estimator $\\hat{p_f}$, which can be determined as the number of significant digits desired for $p_f$, or based on relative error (coefficient of variation, $V=\\sigma/\\mu$. The failure observations, $N_f$, within the Monte Carlo procedure are the result of a sequence of statistically independent and identically distributed random trials in a Bernoulli process. Using the binomial distribution, the standard deviation of of $\\hat{p_f}$ can be written\n", + "\n", + "$$\\sigma_\\hat{p_f}=\\sqrt{\\frac{p_f(1-p_f)}{N}}$$\n", + "\n", + "As $\\hat{p_f}\\rightarrow1$ this leads to the coefficient of variation, $V_\\hat{p_f}$:\n", + "\n", + "$$V_\\hat{p_f}=\\frac{\\sigma_\\hat{p_f}}{\\hat{p_f}}=\\frac{1}{\\sqrt{N\\hat{p_f}}}$$\n", + "\n", + "The coefficient of variation is a useful measure for gauging the accuracy of a Monte Carlo simulation: values of 0.01 are ideal, but 0.1 can be sufficient in many applications, depending on the need for accuracy. For example, consider $V=0.1$ for a target failure probability of $0.01$. Assuming the samples follow a Gaussian distribution implies a probability of 0.997 that the 'true' failure probability is within the interval 0.007-0.013. It is also useful to plot the calculated values of $V$ and $\\hat{p_f}$ for every realization $j = 1, ..., N$, as shown below. The figure clearly shows convergence to a stable value of $\\hat{p_f}$ after X simulations, indicating that for future analyses that are similar can use a lower number of simulations instead ($N\\sim X$).\n", + "\n", + "In case of a target coefficient of variation the number of required simulations $N$ increases as $p_f$ decreases. As an example, for $V = 0.01$ and $p_f=1e-5$ one has to execute $10^9$ simulations. As for this case on average only one of 10^5 simulations leads to an increase of $N_f$, the frequency of obtaining a 'success' (realization in the unsafe domain) is very low. In addition, for low failure probabilities the number of function evaluations is quite high, which may be practically impossible if there is a high function evaluation time, for example with a complex finite element model. To address this problem, variance reducing techniques have been developed which allow the simulations to be performed in a more effective way. In the following the so-called importance sampling or Latin hypercube sampling." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ec7883de-544e-48d5-85f2-dfc7856e9028", + "metadata": {}, + "outputs": [], + "source": [ + "sample_q = q_rv.get_sample(N)\n", + "sample_n = n_rv.get_sample(N)\n", + "sample_a = a_rv.get_sample(N)\n", + "sample_C_C0 = C_C0(sample_q, sample_n, sample_a, x, t)\n", + "sample_Z = flip_LSF*limit_state_fun(sample_q,\n", + " sample_n,\n", + " sample_a,\n", + " x, t, threshold)\n", + "\n", + "monte_carlo(sample_Z);" + ] + }, + { + "cell_type": "markdown", + "id": "d00e1316-c4ac-474d-93ad-18abcda30cfc", + "metadata": {}, + "source": [ + "The method `pdf_of_function_of_RV` makes it easy to see what the distribution of $C/C_0$ and the limit state function for different distributions of q, n or a. Below a second distribution of a is considered:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c08e0e56-8a6b-45a2-ad3f-abe3ce869513", + "metadata": {}, + "outputs": [], + "source": [ + "C_C0_cases = []\n", + "Z_cases = []\n", + "C_C0_cases.append(sample_C_C0)\n", + "Z_cases.append(sample_Z)\n", + "\n", + "a_2 = RandomVariableDistribution()\n", + "a_2.define_distribution(mean=10, stddev=4, dist_type='N')\n", + "C_C0_cases.append(C_C0(sample_q, sample_n, a_2.get_sample(N), x, t))\n", + "Z_cases.append(flip_LSF*limit_state_fun(sample_q,\n", + " sample_n,\n", + " a_2.get_sample(N),\n", + " x, t, threshold))\n", + "\n", + "a_rv.print_status()\n", + "a_2.print_status()\n", + "\n", + "pdf_of_function_of_RV(C_C0_cases)\n", + "pdf_of_function_of_RV(Z_cases, case_C=False)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "695f1336-8d3e-4503-9196-9969d181ae10", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "8c197ae8-3a6c-45fe-b304-75f601dbb9ac", + "metadata": {}, + "source": [ + "This is the density of the function of random variables, $C/C_0$, two values of $\\sigma_a$, and a third with the uniform distribution (not using the `RandomVariableDistribution` class)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "53273645-453b-48b9-85c0-e69eb1ac579e", + "metadata": {}, + "outputs": [], + "source": [ + "values_of_RV_1 = sample_q\n", + "values_of_RV_2 = sample_a\n", + "\n", + "g = sns.JointGrid()\n", + "sns.kdeplot(x=values_of_RV_1,\n", + " y=values_of_RV_2, ax=g.ax_joint, bw_adjust=3)\n", + "sns.scatterplot(x=values_of_RV_1[sample_Z<0],\n", + " y=values_of_RV_2[sample_Z<0], ax=g.ax_joint)\n", + "g.ax_joint.set_xlabel('Random Variable 1 (chosen by you)')\n", + "g.ax_joint.set_ylabel('Random Variable 2 (chosen by you)')\n", + "print('Joint density of 2 RVs with failure realizations')" + ] + }, + { + "cell_type": "markdown", + "id": "75f127f7-c40b-425d-91cf-6c6ecad207a2", + "metadata": {}, + "source": [ + "## Case 2: exceeding the health threshold\n", + "\n", + "Now we return to the failure definition of exceeding the threshold (`flip_LSF` = 1)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3ee884a7-16fb-46bf-9766-9899e662a9bc", + "metadata": {}, + "outputs": [], + "source": [ + "N = 100000\n", + "\n", + "t = 30\n", + "x = 500\n", + "threshold = 1e-4\n", + "\n", + "flip_LSF = 1\n", + "\n", + "sample_q = q_rv.get_sample(N)\n", + "sample_n = n_rv.get_sample(N)\n", + "sample_a = a_rv.get_sample(N)\n", + "\n", + "sample_C_C0 = C_C0(sample_q, sample_n, sample_a, x, t)\n", + "sample_Z = flip_LSF*limit_state_fun(sample_q,\n", + " sample_n,\n", + " sample_a,\n", + " x, t, threshold)\n", + "\n", + "monte_carlo(sample_Z);" + ] + }, + { + "cell_type": "markdown", + "id": "d1d693c6-df03-442f-a100-a065355b2c12", + "metadata": {}, + "source": [ + "NB: *the joint density and failure point plot is commented out here to prevent slowing down the kernel. When N=100000 (1e5) or higher, it will take around a minute to run.*" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "19a0f38a-f4e2-4dc0-8ade-0094f2a3cc91", + "metadata": {}, + "outputs": [], + "source": [ + "# values_of_RV_1 = sample_q\n", + "# values_of_RV_2 = sample_a\n", + "\n", + "# g = sns.JointGrid()\n", + "# sns.kdeplot(x=values_of_RV_1,\n", + "# y=values_of_RV_2, ax=g.ax_joint, bw_adjust=3)\n", + "# sns.scatterplot(x=values_of_RV_1[sample_Z<0],\n", + "# y=values_of_RV_2[sample_Z<0], ax=g.ax_joint)\n", + "# g.ax_joint.set_xlabel('Random Variable 1 (chosen by you)')\n", + "# g.ax_joint.set_ylabel('Random Variable 2 (chosen by you)')\n", + "# print('Joint density of 2 RVs with failure realizations')" + ] + }, + { + "cell_type": "markdown", + "id": "3e7d0cc4", + "metadata": {}, + "source": [ + "### Gradient Vector\n", + "\n", + "Partial derivatives will be useful for evaluating the functional influence of the variables on the limit states. The gradient vector is defined as:\n", + "\n", + "$\\nabla_{\\mathbf{y}} G(\\mathbf{y})=\\left(\\frac{\\partial G(\\mathbf{y})}{\\partial \\mathbf{y}_1}, \\cdots, \\frac{\\partial G(\\mathbf{y})}{\\partial \\mathbf{y}_n}\\right) $\n", + "\n", + "To find the gradient vector we need to find the partial derivatives of $\\frac{C}{C_0}$\n", + "\n", + "$\\frac{C}{C_0} = \\frac{1}{2} \\mathrm{erfc}\\left(\\frac{x-(q/n)t}{2\\sqrt{a(q/n)t}}\\right)=\\frac{1}{2} \\left(1-\\mathrm{erf}\\frac{x-(q/n)t}{2\\sqrt{a(q/n)t}}\\right)$\n", + "\n", + "Using $\\frac{\\partial}{\\partial x} (\\mathrm{erf} x) = \\frac{2}{\\sqrt{\\pi}}e^{-x^2} $ and $\\Omega = \\frac{1}{\\sqrt{\\pi}}e^{-\\left(\\frac{x-(q/n)t}{2\\sqrt{a(q/n)t}}\\right)^2} $, the derivatives are:\n", + "\n", + "$\\frac{\\partial (C/C_0)}{\\partial x} = \\Omega\\left(-\\frac{1}{2\\sqrt{a(q/n)t}}\\right)$\n", + "\n", + "$\\frac{\\partial (C/C_0)}{\\partial t} =\\Omega\\left(\\frac{x}{4\\sqrt{a(q/n)t^3}}+\\frac{q}{4n\\sqrt{a(q/n)t}}\\right)$\n", + "\n", + "$\\frac{\\partial (C/C_0)}{\\partial q} = \\Omega\\left(\\frac{x}{4\\sqrt{a(1/n)tq^3}}+\\frac{t}{4n\\sqrt{a(q/n)t}}\\right)$\n", + "\n", + "$\\frac{\\partial (C/C_0)}{\\partial n} = \\Omega\\left(-\\frac{x}{4\\sqrt{aqtn}}-\\frac{qt}{4\\sqrt{qatn^3}}\\right)$\n", + "\n", + "$\\frac{\\partial (C/C_0)}{\\partial a} = \\Omega\\left(\\frac{x-q/nt}{4\\sqrt{(q/n)ta^3}}\\right)$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a761d424", + "metadata": {}, + "outputs": [], + "source": [ + "def gradient(q, n, a, x, t):\n", + " Om = 1/np.sqrt(np.pi)*np.exp(-((x - q/n*t)/(2*np.sqrt(a*q/n*t)))**2)\n", + " dx = Om*(-1/(2*np.sqrt(a*q/n*t)))\n", + " dt = Om*(x/(4*np.sqrt(a*q/n*t**3)) + (q)/(4*n*np.sqrt(a*q/n*t)))\n", + " dq = Om*(x/(4*np.sqrt(a*q**3/n*t)) + (t)/(4*n*np.sqrt(a*q/n*t)))\n", + " dn = Om*(-x/(4*np.sqrt(a*q*n*t)) - (q*t)/(4*np.sqrt(a*q*n**3*t)))\n", + " da = Om*((x - q/n*t)/(4*np.sqrt(a**3 *q/n*t)))\n", + " return np.array([dq,dn,da,dx,dt])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d6492f20", + "metadata": {}, + "outputs": [], + "source": [ + "print(gradient(2.5, 0.2, 10, x, t))" + ] + }, + { + "cell_type": "markdown", + "id": "18ae1605-4c60-4c65-be4f-ce9cef2e40fd", + "metadata": {}, + "source": [ + "## Your turn!\n", + "\n", + "Now try and use the code to answer the questions posed at the beginning of the notebook, which are repeated here:\n", + "1. Which random variables have the biggest influence on reliability?\n", + "2. How does the assumption of probability distribution influence reliability?\n", + "3. Do the random variables act as loads or resistances?\n", + "\n", + "In particular, to evaluate sensitivity, you can consider two quantitative aspects:\n", + "1. What is the functional influence of the random variables and x and t on the limit-state function?\n", + "2. What is the stochastic influence of the random variables, \n", + "3. What is the combined influence of the two aspects above?\n", + "\n", + "<!-- \n", + "Hint: note the striking similarity of these terms to the material you have already seen in the variance propagation part of MUDE, where the variance of a function of random variables is proportional to $\\sigma_x\\cdot \\frac{\\partial Z}{\\partial x}$. The variable with the biggest influence on reliability will have the highest value of this term. Also, the sign of the partial derivative will indicate whether a variable acts as a load or resistance. -->" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "base", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.7" + }, + "vscode": { + "interpreter": { + "hash": "85471ad55176ca86192ed6be6d105faaef73891404cad6bd910e89e8513744d9" + } + }, + "widgets": { + "application/vnd.jupyter.widget-state+json": { + "state": {}, + "version_major": 2, + "version_minor": 0 + } + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/book/reliability-component/exercise.ipynb b/book/reliability-component/exercise.ipynb new file mode 100644 index 0000000..c0199aa --- /dev/null +++ b/book/reliability-component/exercise.ipynb @@ -0,0 +1,498 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "id": "bcb1b890", + "metadata": {}, + "source": [ + "# Contaminant Transport" + ] + }, + { + "cell_type": "markdown", + "id": "a05b1f14", + "metadata": {}, + "source": [ + "_This notebook and associated files were downloaded from the book [Risk and Reliability for Engineers](https://gitlab.tudelft.nl/interactivetextbooks-citg/risk-and-reliability/) (Lanzafame, 2024) under a CC-BY 4.0 License._\n", + "\n", + "Here we use component reliability methods to evaluate the probability of a contaminant causing dangerous concentrations in a groundwater well. The contaminant plume is transported on the groundwater phreatic surface due to advection and diffusion.\n", + "\n", + "The purpose of this exercise is to:\n", + "- evaluate component reliability\n", + "- illustrate functions of random variables\n", + "- see the effect of random variable distributions on reliability\n", + "- consider 'sensitivity' as a functional and/or stochastic influence on the limit-state function\n", + "\n", + "You can use the code to answer the following questions:\n", + "1. Which random variables have the biggest influence on reliability?\n", + "2. How does the assumption of probability distribution influence reliability?\n", + "3. Do the random variables act as loads or resistances?\n", + "\n", + "## Introduction of Case Study\n", + "\n", + "The case study is a contaminant transport problem, illustrated in the figure below. A factory located near a town produces hazardous waste, which can threaten the drinking water supply of the town that is extracted from groundwater wells (C). The regional groundwater system has a gradient that causes water to flow in the direction of the town from the factory, thus any spilled hazardous waste that enters the ground will eventually be transported to the wells. In order to mitigate the consequences of a spill a ditch is constructed around the factory to collect it (A). Unfortunately, even with powerful pumps, there will still be some waste that reaches the groundwater table. Our task is to quantify the probability that the waste concentration exceeds the maximum exposure level to prevent the drinking water becoming unhealthy.\n", + "\n", + "![sketch](./sketch.png)\n", + "\n", + "### Contaminant Transport\n", + "\n", + "Once the ditch becomes contaminated it is cleaned quickly, but unfortunately a 'pulse' of contamination enters the ground, after which the regional gradient carries it towards the town (advection). The pulse also disperses due to diffusion, which results in a classic advection-diffusion problem (see red shapes in diagram, at three different times, $t$). Because the ditch extends a long distance in the lateral direction and the contaminant is buoyant (it floats on the groundwater table and we neglect vertical dispersion), the problem can be analyzed in 1 dimension with the following analytic expression:\n", + "\n", + "$$\n", + "\\frac{C}{C_0} = \\frac{1}{2} \\mathrm{erf}\\left(\\frac{x-(q/n)t}{2\\sqrt{a(q/n)t}}\\right)\n", + "$$\n", + "\n", + "Where $C$ contaminant concentration (e.g., parts per million, ppm) at distance $x$ from the ditch at time $t$ after the spill, and $C_0$ is the concentration in the ditch (just prior to cleanup). $\\mathrm{erf}$ is the error function. There are three parameters in the equation which are related to soil properties and groundwater flow:\n", + "\n", + "- $q$ is the horizontal groundwater flow velocity (specific discharge) [m/day]\n", + "- $n$ is the soil porosity [$-$]\n", + "- $a$ is the longitudinal dispersivity, which describes dispersion in the left to right direction in the image [m]\n", + "\n", + "Unfortunately there is not a lot of soil information, so we have to take into account uncertainty in these three variables, using the following probability distributions with first and second moments (i.e., $\\mu$ and $\\sigma$).\n", + "\n", + "- $q\\sim\\mathrm{N}\\left(\\mu_q=1.00,\\sigma_q=0.10\\right)$\n", + "- $n\\sim\\mathrm{N}\\left(\\mu_n=0.20,\\sigma_n=0.02\\right)$\n", + "- $a\\sim\\mathrm{N}\\left(\\mu_a=10.0,\\sigma_a=1.00\\right)$\n", + "\n", + "It is important to check the sensitivity of the reliability analysis to the distribution type and moments. We will use the concentration ratio $C/C_0$ to evaluate this problem and compare it to a threshold defined by health regulations: $\\mathrm{threshold}=1e-4$.\n", + "\n", + "### Definition of Limit States\n", + "\n", + "As shown in the figure above, there are two locations of interest: the monitoring station ($x=100$ m from the ditch, point B) and the town well ($x=500$ m, point C). We are interested in evaluating two cases with a reliability analysis:\n", + "1. Whether the contamination can be detected at the monitoring station above the threshold level within 1 week of the spill, and \n", + "2. If the contamination level at the town groundwater well exceeds the threshold level within 1 month of the spill (30 days)\n", + "\n", + "Relating these descriptions to our variables of interest:\n", + "1. find the probability that $C/C_0$ > threshold \n", + "2. find the probability that $C/C_0$ < threshold\n", + "\n", + "We will refer to these values as 'failure probabilities', even though case 1 technically doesn't correspond to failure---it's just the way we refer to things in practice.\n", + "\n", + "Next we will convert these into functions that will allow us to quantify the 'failure' conditions. For convenience, it is often useful to define the limit state as a function, $Z$, such that failure occurs when $Z<0$. It follows from the descriptions above, that the limit state functions for both cases are:\n", + "\n", + "1. $Z=C/C_0 - \\mathrm{threshold}$\n", + "2. $Z=\\mathrm{threshold} - C/C_0$\n", + "\n", + "NB: *in the book another notation used for $Z$ is $g_X(X)$.*\n", + "\n", + "### Analysis Approach\n", + "\n", + "Our programming task is to create a function of random variables to represent these two limit-states, define the random variables, then evaluate the reliability with Monte Carlo simulation. In other words, we will numerically approximate the probability distribution of $Z$, then evaluate reliability as $P(Z<0)$.\n", + "\n", + "This is a lot of work, but fortunately a number of helper functions and a Class are provided in the auxiliary file `exercise_setup.py`!\n", + "\n", + "### References\n", + "\n", + "This example draws inspiration from Case 2 of the paper by {cite:t}`sitar1987`." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "0e18b539", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy.special import erfc\n", + "from scipy import stats\n", + "import seaborn as sns\n", + "\n", + "from exercise_setup import process_negative_values\n", + "from exercise_setup import RandomVariableDistribution\n", + "from exercise_setup import pdf_of_function_of_RV\n", + "from exercise_setup import monte_carlo" + ] + }, + { + "cell_type": "markdown", + "id": "d104b4b2-4fa5-4b37-891d-39201281ed2f", + "metadata": {}, + "source": [ + "## Defining the Limit States\n", + "\n", + "We only define limit state Case 2 below, and will use a simple multiplying factor of $-1$ to switch to Case 1 using a multiplying factor `flip_LSF`." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "64c24956", + "metadata": {}, + "outputs": [], + "source": [ + "def C_C0(q, n, a, x, t):\n", + " \"\"\"Contaminant concentration ratio.\"\"\"\n", + " q, n, a = process_negative_values(q, n, a)\n", + " return 0.5*erfc((x - q/n*t)/(2*np.sqrt(a*(q/n)*t)))\n", + "\n", + "def limit_state_fun(q, n, a, x, t, threshold):\n", + " \"\"\"Limit state fxn, Case 2 (multiply by flip_LSF=-1 for Case 1).\"\"\"\n", + " return threshold - C_C0(q, n, a, x, t)" + ] + }, + { + "cell_type": "markdown", + "id": "d7410d16-14d4-45c6-9f93-81ae08de0594", + "metadata": {}, + "source": [ + "## Class `RandomVariableDistribution`\n", + "\n", + "The class `RandomVariableDistribution` makes it very easy to define Normal and Lognormal distributions for the random variables. See documentation and example below.\n", + "\n", + "NB: *you can use the code in `exercisesetup.py` and this notebook to confirm the result of the 2 random variable case in the Probabilistic Design chapter, and recreate the figures.*" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8bbf80be-5124-40ba-b3de-0da3eaa12ef1", + "metadata": {}, + "outputs": [], + "source": [ + "print(RandomVariableDistribution.__doc__)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a9b93099-b1cb-458b-baf6-8ad5dd39c440", + "metadata": {}, + "outputs": [], + "source": [ + "example_random_variable = RandomVariableDistribution()\n", + "example_random_variable.define_distribution(mean=5,\n", + " dist_type='LN',\n", + " print_new_dist=True)\n", + "example_random_variable.plot_pdf_or_cdf()" + ] + }, + { + "cell_type": "markdown", + "id": "62617026-f251-462b-a93c-b7305cfd3fa4", + "metadata": {}, + "source": [ + "## Setting up the problem\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "4641ae3c", + "metadata": {}, + "outputs": [], + "source": [ + "N = 10000\n", + "\n", + "t = 7\n", + "x = 100\n", + "threshold = 1e-4\n", + "\n", + "flip_LSF = -1\n", + "\n", + "q_rv = RandomVariableDistribution()\n", + "q_rv.define_distribution(mean=1., stddev=.1)\n", + "n_rv = RandomVariableDistribution()\n", + "n_rv.define_distribution(mean=0.2, stddev=.02)\n", + "a_rv = RandomVariableDistribution()\n", + "a_rv.define_distribution(mean=10., stddev=1.)" + ] + }, + { + "cell_type": "markdown", + "id": "f3e0ffb1-6035-4f76-a550-4ff19c1b5946", + "metadata": {}, + "source": [ + "## Monte Carlo analysis\n", + "\n", + "The Monte Carlo procedure for estimating failure probability, $p_f$, is:\n", + "- For each random variable $X_i$ ($i = 1, …, n$) one simulates N realizations, $x_{i,1}, x_{i,1}, ..., x_{i,N}$. \n", + "- For each set of simulations $j$ ($j = 1, ..., N$) one calculates $g(x_{1,j}, x_{2,j}, …, x_{n,j})$\n", + "- In case $g(.) < 0$ a counter $N_f$ is increased by one. After $N$ simulations one calculates: $\\hat{p_f}=N_f/N$\n", + "- In case $N\\rightarrow+\\infty$ one obtains the failure probability $p_f$.\n", + "\n", + "The number of simulations $N$ directly influences the accuracy of $\\hat{p_f}$, which is an estimate of the 'true' value $p_f$. As an infinite number of simulations is not possible, one must choose a value for $N$ that balances total computation time, which increases linearly with $N$, and accuracy of the estimator $\\hat{p_f}$, which can be determined as the number of significant digits desired for $p_f$, or based on relative error (coefficient of variation, $V=\\sigma/\\mu$. The failure observations, $N_f$, within the Monte Carlo procedure are the result of a sequence of statistically independent and identically distributed random trials in a Bernoulli process. Using the binomial distribution, the standard deviation of of $\\hat{p_f}$ can be written\n", + "\n", + "$$\\sigma_\\hat{p_f}=\\sqrt{\\frac{p_f(1-p_f)}{N}}$$\n", + "\n", + "As $\\hat{p_f}\\rightarrow1$ this leads to the coefficient of variation, $V_\\hat{p_f}$:\n", + "\n", + "$$V_\\hat{p_f}=\\frac{\\sigma_\\hat{p_f}}{\\hat{p_f}}=\\frac{1}{\\sqrt{N\\hat{p_f}}}$$\n", + "\n", + "The coefficient of variation is a useful measure for gauging the accuracy of a Monte Carlo simulation: values of 0.01 are ideal, but 0.1 can be sufficient in many applications, depending on the need for accuracy. For example, consider $V=0.1$ for a target failure probability of $0.01$. Assuming the samples follow a Gaussian distribution implies a probability of 0.997 that the 'true' failure probability is within the interval 0.007-0.013. It is also useful to plot the calculated values of $V$ and $\\hat{p_f}$ for every realization $j = 1, ..., N$, as shown below. The figure clearly shows convergence to a stable value of $\\hat{p_f}$ after X simulations, indicating that for future analyses that are similar can use a lower number of simulations instead ($N\\sim X$).\n", + "\n", + "In case of a target coefficient of variation the number of required simulations $N$ increases as $p_f$ decreases. As an example, for $V = 0.01$ and $p_f=1e-5$ one has to execute $10^9$ simulations. As for this case on average only one of 10^5 simulations leads to an increase of $N_f$, the frequency of obtaining a 'success' (realization in the unsafe domain) is very low. In addition, for low failure probabilities the number of function evaluations is quite high, which may be practically impossible if there is a high function evaluation time, for example with a complex finite element model. To address this problem, variance reducing techniques have been developed which allow the simulations to be performed in a more effective way. In the following the so-called importance sampling or Latin hypercube sampling." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ec7883de-544e-48d5-85f2-dfc7856e9028", + "metadata": {}, + "outputs": [], + "source": [ + "sample_q = q_rv.get_sample(N)\n", + "sample_n = n_rv.get_sample(N)\n", + "sample_a = a_rv.get_sample(N)\n", + "sample_C_C0 = C_C0(sample_q, sample_n, sample_a, x, t)\n", + "sample_Z = flip_LSF*limit_state_fun(sample_q,\n", + " sample_n,\n", + " sample_a,\n", + " x, t, threshold)\n", + "\n", + "monte_carlo(sample_Z);" + ] + }, + { + "cell_type": "markdown", + "id": "d00e1316-c4ac-474d-93ad-18abcda30cfc", + "metadata": {}, + "source": [ + "The method `pdf_of_function_of_RV` makes it easy to see what the distribution of $C/C_0$ and the limit state function for different distributions of q, n or a. Below a second distribution of a is considered:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c08e0e56-8a6b-45a2-ad3f-abe3ce869513", + "metadata": {}, + "outputs": [], + "source": [ + "C_C0_cases = []\n", + "Z_cases = []\n", + "C_C0_cases.append(sample_C_C0)\n", + "Z_cases.append(sample_Z)\n", + "\n", + "a_2 = RandomVariableDistribution()\n", + "a_2.define_distribution(mean=10, stddev=4, dist_type='N')\n", + "C_C0_cases.append(C_C0(sample_q, sample_n, a_2.get_sample(N), x, t))\n", + "Z_cases.append(flip_LSF*limit_state_fun(sample_q,\n", + " sample_n,\n", + " a_2.get_sample(N),\n", + " x, t, threshold))\n", + "\n", + "a_rv.print_status()\n", + "a_2.print_status()\n", + "\n", + "pdf_of_function_of_RV(C_C0_cases)\n", + "pdf_of_function_of_RV(Z_cases, case_C=False)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "695f1336-8d3e-4503-9196-9969d181ae10", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "8c197ae8-3a6c-45fe-b304-75f601dbb9ac", + "metadata": {}, + "source": [ + "This is the density of the function of random variables, $C/C_0$, two values of $\\sigma_a$, and a third with the uniform distribution (not using the `RandomVariableDistribution` class)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "53273645-453b-48b9-85c0-e69eb1ac579e", + "metadata": {}, + "outputs": [], + "source": [ + "values_of_RV_1 = sample_q\n", + "values_of_RV_2 = sample_a\n", + "\n", + "g = sns.JointGrid()\n", + "sns.kdeplot(x=values_of_RV_1,\n", + " y=values_of_RV_2, ax=g.ax_joint, bw_adjust=3)\n", + "sns.scatterplot(x=values_of_RV_1[sample_Z<0],\n", + " y=values_of_RV_2[sample_Z<0], ax=g.ax_joint)\n", + "g.ax_joint.set_xlabel('Random Variable 1 (chosen by you)')\n", + "g.ax_joint.set_ylabel('Random Variable 2 (chosen by you)')\n", + "print('Joint density of 2 RVs with failure realizations')" + ] + }, + { + "cell_type": "markdown", + "id": "75f127f7-c40b-425d-91cf-6c6ecad207a2", + "metadata": {}, + "source": [ + "## Case 2: exceeding the health threshold\n", + "\n", + "Now we return to the failure definition of exceeding the threshold (`flip_LSF` = 1)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3ee884a7-16fb-46bf-9766-9899e662a9bc", + "metadata": {}, + "outputs": [], + "source": [ + "N = 100000\n", + "\n", + "t = 30\n", + "x = 500\n", + "threshold = 1e-4\n", + "\n", + "flip_LSF = 1\n", + "\n", + "sample_q = q_rv.get_sample(N)\n", + "sample_n = n_rv.get_sample(N)\n", + "sample_a = a_rv.get_sample(N)\n", + "\n", + "sample_C_C0 = C_C0(sample_q, sample_n, sample_a, x, t)\n", + "sample_Z = flip_LSF*limit_state_fun(sample_q,\n", + " sample_n,\n", + " sample_a,\n", + " x, t, threshold)\n", + "\n", + "monte_carlo(sample_Z);" + ] + }, + { + "cell_type": "markdown", + "id": "d1d693c6-df03-442f-a100-a065355b2c12", + "metadata": {}, + "source": [ + "NB: *the joint density and failure point plot is commented out here to prevent slowing down the kernel. When N=100000 (1e5) or higher, it will take around a minute to run.*" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "19a0f38a-f4e2-4dc0-8ade-0094f2a3cc91", + "metadata": {}, + "outputs": [], + "source": [ + "# values_of_RV_1 = sample_q\n", + "# values_of_RV_2 = sample_a\n", + "\n", + "# g = sns.JointGrid()\n", + "# sns.kdeplot(x=values_of_RV_1,\n", + "# y=values_of_RV_2, ax=g.ax_joint, bw_adjust=3)\n", + "# sns.scatterplot(x=values_of_RV_1[sample_Z<0],\n", + "# y=values_of_RV_2[sample_Z<0], ax=g.ax_joint)\n", + "# g.ax_joint.set_xlabel('Random Variable 1 (chosen by you)')\n", + "# g.ax_joint.set_ylabel('Random Variable 2 (chosen by you)')\n", + "# print('Joint density of 2 RVs with failure realizations')" + ] + }, + { + "cell_type": "markdown", + "id": "3e7d0cc4", + "metadata": {}, + "source": [ + "### Gradient Vector\n", + "\n", + "Partial derivatives will be useful for evaluating the functional influence of the variables on the limit states. The gradient vector is defined as:\n", + "\n", + "$\\nabla_{\\mathbf{y}} G(\\mathbf{y})=\\left(\\frac{\\partial G(\\mathbf{y})}{\\partial \\mathbf{y}_1}, \\cdots, \\frac{\\partial G(\\mathbf{y})}{\\partial \\mathbf{y}_n}\\right) $\n", + "\n", + "To find the gradient vector we need to find the partial derivatives of $\\frac{C}{C_0}$\n", + "\n", + "$\\frac{C}{C_0} = \\frac{1}{2} \\mathrm{erfc}\\left(\\frac{x-(q/n)t}{2\\sqrt{a(q/n)t}}\\right)=\\frac{1}{2} \\left(1-\\mathrm{erf}\\frac{x-(q/n)t}{2\\sqrt{a(q/n)t}}\\right)$\n", + "\n", + "Using $\\frac{\\partial}{\\partial x} (\\mathrm{erf} x) = \\frac{2}{\\sqrt{\\pi}}e^{-x^2} $ and $\\Omega = \\frac{1}{\\sqrt{\\pi}}e^{-\\left(\\frac{x-(q/n)t}{2\\sqrt{a(q/n)t}}\\right)^2} $, the derivatives are:\n", + "\n", + "$\\frac{\\partial (C/C_0)}{\\partial x} = \\Omega\\left(-\\frac{1}{2\\sqrt{a(q/n)t}}\\right)$\n", + "\n", + "$\\frac{\\partial (C/C_0)}{\\partial t} =\\Omega\\left(\\frac{x}{4\\sqrt{a(q/n)t^3}}+\\frac{q}{4n\\sqrt{a(q/n)t}}\\right)$\n", + "\n", + "$\\frac{\\partial (C/C_0)}{\\partial q} = \\Omega\\left(\\frac{x}{4\\sqrt{a(1/n)tq^3}}+\\frac{t}{4n\\sqrt{a(q/n)t}}\\right)$\n", + "\n", + "$\\frac{\\partial (C/C_0)}{\\partial n} = \\Omega\\left(-\\frac{x}{4\\sqrt{aqtn}}-\\frac{qt}{4\\sqrt{qatn^3}}\\right)$\n", + "\n", + "$\\frac{\\partial (C/C_0)}{\\partial a} = \\Omega\\left(\\frac{x-q/nt}{4\\sqrt{(q/n)ta^3}}\\right)$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a761d424", + "metadata": {}, + "outputs": [], + "source": [ + "def gradient(q, n, a, x, t):\n", + " Om = 1/np.sqrt(np.pi)*np.exp(-((x - q/n*t)/(2*np.sqrt(a*q/n*t)))**2)\n", + " dx = Om*(-1/(2*np.sqrt(a*q/n*t)))\n", + " dt = Om*(x/(4*np.sqrt(a*q/n*t**3)) + (q)/(4*n*np.sqrt(a*q/n*t)))\n", + " dq = Om*(x/(4*np.sqrt(a*q**3/n*t)) + (t)/(4*n*np.sqrt(a*q/n*t)))\n", + " dn = Om*(-x/(4*np.sqrt(a*q*n*t)) - (q*t)/(4*np.sqrt(a*q*n**3*t)))\n", + " da = Om*((x - q/n*t)/(4*np.sqrt(a**3 *q/n*t)))\n", + " return np.array([dq,dn,da,dx,dt])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d6492f20", + "metadata": {}, + "outputs": [], + "source": [ + "print(gradient(2.5, 0.2, 10, x, t))" + ] + }, + { + "cell_type": "markdown", + "id": "18ae1605-4c60-4c65-be4f-ce9cef2e40fd", + "metadata": {}, + "source": [ + "## Your turn!\n", + "\n", + "Now try and use the code to answer the questions posed at the beginning of the notebook, which are repeated here:\n", + "1. Which random variables have the biggest influence on reliability?\n", + "2. How does the assumption of probability distribution influence reliability?\n", + "3. Do the random variables act as loads or resistances?\n", + "\n", + "In particular, to evaluate sensitivity, you can consider two quantitative aspects:\n", + "1. What is the functional influence of the random variables and x and t on the limit-state function?\n", + "2. What is the stochastic influence of the random variables, \n", + "3. What is the combined influence of the two aspects above?\n", + "\n", + "<!-- \n", + "Hint: note the striking similarity of these terms to the material you have already seen in the variance propagation part of MUDE, where the variance of a function of random variables is proportional to $\\sigma_x\\cdot \\frac{\\partial Z}{\\partial x}$. The variable with the biggest influence on reliability will have the highest value of this term. Also, the sign of the partial derivative will indicate whether a variable acts as a load or resistance. -->" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "base", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.13 (main, Aug 25 2022, 23:51:50) [MSC v.1916 64 bit (AMD64)]" + }, + "vscode": { + "interpreter": { + "hash": "85471ad55176ca86192ed6be6d105faaef73891404cad6bd910e89e8513744d9" + } + }, + "widgets": { + "application/vnd.jupyter.widget-state+json": { + "state": {}, + "version_major": 2, + "version_minor": 0 + } + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/book/reliability-component/exercise.zip b/book/reliability-component/exercise.zip new file mode 100644 index 0000000..37314fa Binary files /dev/null and b/book/reliability-component/exercise.zip differ diff --git a/book/reliability-component/exercise_setup.py b/book/reliability-component/exercise_setup.py new file mode 100644 index 0000000..51a9470 --- /dev/null +++ b/book/reliability-component/exercise_setup.py @@ -0,0 +1,247 @@ +import numpy as np +import matplotlib.pyplot as plt +from scipy.special import erfc +from scipy import stats +import seaborn as sns + +def process_negative_values(q, n, a): + """Prevents problems with negative values in sqrt of C_C0 function.""" + N_q = sum(q<0) + N_n = sum(n<0) + N_a = sum(a<0) + set_value = 0.001 + if N_q > 0: + for i in range(len(q)): + if q[i]<0: + q[i] = set_value + print(f'q has {N_q} negative values that have been set to {set_value:.1e}.') + if N_n > 0: + for i in range(len(n)): + if n[i]<0: + n[i] = set_value + print(f'n has {N_n} negative values that have been set to {set_value:.1e}.') + if N_a > 0: + for i in range(len(a)): + if a[i]<0: + a[i] = set_value + print(f'a has {N_a} negative values that have been set to {set_value:.1e}.') + return q, n, a + +class RandomVariableDistribution(): + """Define a N or LN probability to use in MUDE week 2.7 exercise. + + Usage: + ----- + Create an instance of the class + by default, the random variable is ~N(0,1) + Specify distribution using 1st and 2nd moments for N or LN: + --> use method define_distribution to change it! + (the method prints a summary of the change) + for example, copy/paste the following: + test = RandomVariableDistribution() + test.print_status() + test.define_distribution(mean=5, stddev=1, dist_type='LN') + An instance will include the following attributes: + - distribution moment and (scipy) parameters shape, location, scale + - dist_object: distribution object (scipy.stats) + - get_sample: method for getting random samples from the distribution + - plot_pdf_or_cdf: + """ + + def __init__(self): + self.mean = 0. + self.stddev = 1. + self.dist_type = 'N' + + def print_status(self): + """Returns current parameter values and distribution type.""" + print(f'The mean is {self.mean:.3e}') + print(f'The standard deviation is {self.stddev:.3e}') + if self.dist_type == 'N': + distribution_name = 'Normal' + elif self.dist_type == 'LN': + distribution_name = 'Lognormal' + print('The distribution is ' + distribution_name) + + def define_distribution(self, + mean=None, + stddev=None, + dist_type=None, + print_new_dist=False): + """Compute distribution parameters and RV object from moments. + + Usage: + ----- + Optional arguments will override current dist: + --> default distribution is standard normal, ~N(0,1) + mean: float + stddev: float + dist_type: 'N' or 'LN' + print_new_dist=True to print distribution changes. + """ + if mean is None: + mean = self.mean + if stddev is None: + stddev = self.stddev + if dist_type is None: + dist_type = self.dist_type + if dist_type == 'N': + shape = None + location = mean + scale = stddev + dist_object = stats.norm(loc=location, scale=scale) + elif dist_type == 'LN': + """ + Finds distribution parameters of LN-distributed X, + which are equivalent to the mean and standard deviation + of the log of X: Y = ln(X), then converts to the + parameterization used by scipy.stats.lognorm. + """ + stddev_y = np.sqrt(np.log(1 + (stddev/mean)**2)) + mean_y = np.log(mean) - 0.5*stddev_y**2 + + shape = stddev_y + location = 0 + scale = np.exp(mean_y) + dist_object = stats.lognorm(s=shape, + loc=location, + scale=scale) + else: + raise ValueError("You can only use N or LN for self.dist_type.") + self.mean = mean + self.stddev = stddev + self.dist_type = dist_type + self.shape = shape + self.location = location + self.scale = scale + self.dist_object = dist_object + self.get_sample = lambda size : self.dist_object.rvs(size=size) + if print_new_dist: + self.print_status() + + def plot_pdf_or_cdf(self, plot_type='pdf', plot_limits=None): + """Plots the pdf or cdf (specify choice with plot_type). + + Usage: + ----- + No inputs required, but there are optional inputs: + plot_type='cdf' to plot cdf (pdf is default value) + plot_limits: list with 2 values for x-axis + """ + if plot_limits is None: + if self.dist_type == 'N': + plot_limits = [self.mean - 3*self.stddev, + self.mean + 3*self.stddev] + elif self.dist_type == 'LN': + 'Avoid negative or zero value for lognormal dist.' + lower_value = self.mean - 3*self.stddev + if lower_value <= 0: + lower_value = 0.01 + plot_limits = [lower_value, + self.mean + 4*self.stddev] + else: + raise ValueError("You can only use N or LN for self.dist_type.") + + plot_x = np.linspace(plot_limits[0], plot_limits[1], 1000) + if plot_type == 'pdf': + plot_y = self.dist_object.pdf(plot_x) + y_label = 'PDF [-]' + elif plot_type == 'cdf': + plot_y = self.dist_object.cdf(plot_x) + y_label = 'CDF [-]' + else: + raise ValueError("You must specify pdf or cdf for plot_type.") + fontsize = 15 + plt.figure() + plt.plot(plot_x, plot_y, 'k-', linewidth=3) + plt.xlabel('Random Variable, X', fontsize=fontsize) + plt.ylabel(y_label, fontsize=fontsize) + plt.show() + +def pdf_of_function_of_RV(cases, case_C=True, case_name=None, plot_limits=None): + """Plot the PDF of a sampled function of random variables (C_C0 or Z). + + Usage: + ----- + cases: a list of arrays + case_C=True (default) assumes C_C0 is given. False is for Z. + case_name: list of strings with the labels for each array. + e.g., ['Original', 'High sigma_a', 'Low sigma_a'] + (default will return Case i for all arrays) + plot_limits: list of two values that override default limits + for x-axis. + """ + bw_adjust = 3 # adjusts smoothness of Seaborn kernel density contours + labels = [] + + plt.figure() + + for i in range(len(cases)): + if case_name == None: + labels.append(f'Case {i+1}') + else: + labels.append(case_name[i]) + sns.kdeplot(cases[i], label=labels[i], ax=plt.gca(), bw_adjust=bw_adjust) + plt.legend() + if case_C: + plt.xlabel('Concentration ratio, $C/C_0$ [$-$]') + if plot_limits == None: + plt.xlim(0,1) + else: + plt.xlim(plot_limits) + else: + plt.xlabel('Limit-state function, $Z=\mathrm{threshold}-C/C_0$ [$-$]') + if plot_limits == None: + plt.xlim(-2,1) + else: + plt.xlim(plot_limits) + plt.ylabel('PDF [$]$') + plt.grid() + plt.show() + +def monte_carlo(Z): + """Monte Carlo analysis for sampled function of random variables. + + Returns a summary of the analysis and a plot of pf and c.o.v.. + The only input is an array of the sampled limit state-function. + Assumes that failure is when the limit-state function Z<0. + """ + N = len(Z) + Nf = np.sum(Z<0) + + if Nf == 0: + raise ValueError('No failure realizations in the sample!') + elif Nf == N: + raise ValueError('All realizations in the sample failed!') + + pf = Nf/N + + N_f_c = np.cumsum(Z<0) + N_i = np.arange(1,len(N_f_c)+1,1) + p_f_c = N_f_c / N_i + with np.errstate(divide='ignore'): + V = 1/(np.sqrt(N_i*p_f_c)) + + print(f'MONTE CARLO RESULTS\n' + f'--------------------------------------------------\n' + f' N = {N}, number of samples\n' + f' Nf = {Nf}, number of failed realizations\n' + f' pf = {pf:.3e}, estimated failure probability\n' + f' V = {V[-1]:.3f}, c.o.v. of estimated pf\n') + + plt.loglog(N_i,p_f_c) + plt.xlim(10,N) + plt.ylim(10**(np.floor(np.log10(pf)) - 1),1) + plt.grid() + plt.xlabel('Realization No.') + plt.ylabel('Estimated failure probability, $\hat{p}_f$') + plt.show() + + plt.plot(N_i,V) + plt.xscale('log') + plt.grid() + plt.xlabel('time step') + plt.ylabel('c.o.v.') + plt.show() + + return Nf,pf \ No newline at end of file diff --git a/book/reliability-component/overview.md b/book/reliability-component/overview.md new file mode 100644 index 0000000..4f4b4a5 --- /dev/null +++ b/book/reliability-component/overview.md @@ -0,0 +1,127 @@ +(rel_comp)= +# Component Reliability + +This Section gives a brief introduction to some of the mathematical foundations of component reliability theory, which is focused on determining the probability of a 'bad thing' happening (see {ref}`intro`). The topic has also been covered in the {ref}`prob_design` Section (especially the {ref}`prob_design_2_rv` example), and is a key part of Step 3 (quantitative analysis) in the {ref}`risk_steps`. + +## Definition + +In short, a component reliability analysis evaluates the reliability of a particular engineered object, where reliability is the complement of failure probability, $p_f$. The analysis is performed by defining a function of random variables, $g_X(x)$, and mathematically specifying a region of interest, $\Omega$, often called the failure region. The function of random variables implies a multivariate probability density function, $f_X(x)$, where integrating over the failure region $\Omega$ gives $p_f$. + +$$ +p_f=\int_\Omega f_X(x)\:\mathrm{d}x +$$ + +## A Simple Case + +The most simple reliability analysis is a univariate case with one random variable. Consider a water distribution *system* that relies on groundwater (i.e., one *component* within the system). Suppose we can model the groundwater elevation as a random variable with the normal distribution: + +$$ +h_w \: [\mathrm{m}] \sim \mathrm{N}(\mu=5,\sigma=1) +$$ + +If $h_w$ drops below 2 m, the pumps run dry, and our component fails. In this case our function of random variables is simply: + +$$ +g(X) \rightarrow g(h_w)=h_w +$$ + +and failure is defined as: + +$$ +\Omega: h_w < 2 \mathrm{m} +$$ + +The component reliability analysis is thus: + +$$ +p_f=\int_{-\infty}^{2} f_{h_w}(h_w)\:\mathrm{d}h_w +$$ + +Which is easily evaluated with the CDF of $h_w$: + +$$ +p_f=F_{h_w}(2)=\Phi\left[ \frac{2-\mu}{\sigma}\right] =\Phi[-3]=0.00135 +$$ + +This is nearly equivalent to the {ref}`prob_design_1_rv` example using river discharge from the {ref}`prob_design` Chapter, the only difference is there a load variable was considered and therefore evaluated with the complementary CDF. + +## Not Simple Cases + +The example above is 'simple' for three reasons, specifically. It has: +1. only one random variable, so the distribution of $g(X)$ is also univariate +2. the function of random variables, $g(X)$ is linear +3. the distribution of the random variables (variable, in this case) is Gaussian + +These three characteristics make component reliability problems very easy to solve. In fact, you should have already done this earlier probability courses with (co)variance propagation methods. For example, solving for the mean and standard deviation of a linear function of random variables that are each Gaussian is straightforward, as the function of random variables is also Gaussian. Unfortunately, as problems become more complex, so do the methods required for solving such problems. + +In this book we focus on simple situations with up to two variables (the 'bivariate' case) that can be solved analytically (linear functions and Gaussian random variables). Random variables are limited to continuous parametric distributions and linear measures of dependence (correlation coefficient, multivariate Gaussian). If these requirements are relaxed, we will use simulation to calculate the failure probability numerically (i.e., Monte Carlo simulation). + +With this in mind, a generic procedure for using component reliability analysis in a probabilistic design context is: + +1. determine probability distributions for each random variable (*marginal* distributions) +2. specify dependence between random variables (or independence) +3. define the function of random variables, $g_X(X)$, and region of interest, $\Omega$ +4. integrate multivariate PDF, $f_X(X)$, over $\Omega$ to evaluate probability of interest +5. check probability requirement, and if needed: +6. modify component (i.e., modify 1, 2 or 3) +7. repeat 4, 5 and 6 until the requirement is met + +```{note} +The term 'failure' here, widely used in civil engineering, is used here as a matter of convenience. Component reliability methods can also be used to find the probability of something that has nothing to do with failure, as long as it can be desribed with a function of random variables. +``` +## Two Random Variables + +The example with discharge from two rivers in the Probabilistic Design Chapter can be considered a component reliability problem with two random variables. The discharge of both tributary rivers act as loads because they both are proportional to the main design variable, $q$ or $h_{dike}$. The reliability integral is thus + +$$ +p_f=\int_\Omega f_{Q_1,Q_2}(q_1,q_2)\:\mathrm{d}x +$$ + +where the failure region $\Omega$ contains all values of $Q_1$ and $Q_2$ such that the river level exceeds the dike height: + +$$ +\Omega: h_{dike} \leq h_w(Q_1,Q_2) +$$ + +Note that if the dike were constructed to a height of 8.29 m, the component reliability would be 0.01 and the failure region would be equivalent to {numref}`design_2_rv_correct`. + +<!-- Component reliability Analysis: +- limit states (servicability, ultimate) and limit-state functions; failure definition +- Design frameworks +- A simple case +- Special page to illustrate partial safety factor approach. Start with univariate, then show bivariate (pointing out ‘choice’ that must be made for design point, reference it, then move along). + + +- other + - R-S + - Z = R + S + - non-linear + - most of these should probably go in the component reliability chapter + +Overview of non-linear problems (distribution and LSF); explanation of LSF; formulations of structural reliability. the area under the curve. Solution techniquest. Partial safety factor approach / LRFD / beta and reliability index. --> + +% save for later: compare Z=R-S to and/or and explicitly show how the generalized method can incorporate higher/lower together or values related to each other; lognormal case + +%To simple slope problem: *this example is borrowed from Moss, which is borrowed from Baecher and Christian. Both are excellent texts on risk and reliability analysis in civil and geotechnical engineering.* + +% THIS IS REMOVED FOR 2022-23 SINCE THE SEPARATE PAGES WERE NOT COMPLETED + +--- + +_The primary author for this chapter is Robert Lanzafame._ + +<!-- +```{admonition} Exam Information +:class: tip, dropdown +You are expected to recognize the role of random variables (e.g., loads and resistances) within the function of random variables for a component and visualize it on a bivariate plot. Component reliability problems will limited to linear functions of normally distributed random variables; although you will *not* be asked to compute reliability. +``` --> + +<!-- ```{admonition} Exam Information +:class: tip, dropdown +You are expected to recognize the role of random variables (e.g., loads and resistances) within the function of random variables for a component and visualize it on a bivariate plot. You may be asked to solve simple component reliability problems, limited to linear functions of normally distributed random variables, and evaluate the role of dependence between variables. You can produce a probabilistic design by modifying the component such that the probability of interest meets a specific criteria. +``` --> + +<!-- ```{admonition} Exam Information +:class: tip, dropdown +For the exam, you will be expected to be able to recognize and solve simple component reliability problems, and describe the influence that dependence between random variables may have on the calculated probability of interest. Given a specific problem of interest, you should be able to describe failure (or non-failure) analytically as a function of random variables and visually in a bivariate plot. Using these simple frameworks, you can modify the component such that the probability of interest meets a specific criteria. +``` --> \ No newline at end of file diff --git a/book/reliability-component/sketch.png b/book/reliability-component/sketch.png new file mode 100644 index 0000000..d2fd2b4 Binary files /dev/null and b/book/reliability-component/sketch.png differ diff --git a/figures/cover.ipynb b/figures/cover.ipynb new file mode 100644 index 0000000..bb44b64 --- /dev/null +++ b/figures/cover.ipynb @@ -0,0 +1,341 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "a4d8be0c", + "metadata": {}, + "source": [ + "Took code from Week 1.8 Project and axle data. helper and solution file are included here, but I did not clean out the unnecessary code. bivariate plotting function included here but other aspects (marginal, copula) are still included in `helper.py`. `solution.py` is not needed, but the model definition code uses a dictionary that is set up there. \n", + "\n", + "Not sure why the figure in this notebook is not rendered with transparent background, but the svg is transparent, so i ignored it.\n", + "\n", + "`pyvinecopulib` was added to virtual env using pip without any issue. not included in requirements file to avoid build issues on the server." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "7eeb37e0-aca0-4759-866f-f5ad09ea8d0b", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import scipy.stats as st\n", + "\n", + "from helper import plot_contour\n", + "from helper import Bivariate\n", + "from solution import *\n", + "\n", + "from matplotlib import rcParams\n", + "rcParams.update({'font.size': 16})\n", + "# TUDelft colors palette\n", + "colors = [\"#0C2340\",\"#00B8C8\",\"#0076C2\",\"#6F1D77\",\"#EF60A3\",\"#A50034\",\"#E03C31\",\"#EC6842\",\"#FFB81C\",\"#6CC24A\",\"#009B77\"]" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "2152bd99-12cb-44a2-afee-7b36fb4b4780", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Length of the dataset: 992\n", + "Mean and standard deviation: (38.216, 10.020).\n", + "Mean and standard deviation: (55.941, 18.914).\n" + ] + } + ], + "source": [ + "X1 = univariate_RV_dict(\"Heaviest axle\", \"$AX_{max}$\", \"kN\")\n", + "X2 = univariate_RV_dict(\"Lightest Axle\", \"$AX_{min}$\", \"kN\")\n", + "X1[\"data\"], X2[\"data\"] = np.genfromtxt('./data_axle.csv',\n", + " delimiter=\",\", unpack = True)\n", + "\n", + "print(f'Length of the dataset: {X1[\"data\"].size}')\n", + "print(f'Mean and standard deviation:',\n", + " f'({X1[\"data\"].mean():.3f}, {X1[\"data\"].std():.3f}).')\n", + "print(f'Mean and standard deviation:',\n", + " f'({X2[\"data\"].mean():.3f}, {X2[\"data\"].std():.3f}).')" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "2ccfbc68-6705-4adf-83f8-9ebff6c1015d", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "dist_parameters = st.lognorm.fit(X1[\"data\"], floc = 0)\n", + "dist_object = st.lognorm(*dist_parameters)\n", + "X1[\"LN\"] = univariate_model_dict(\"Lognormal\",\n", + " dist_parameters, dist_object)\n", + "\n", + "dist_parameters = st.gumbel_r.fit(X1[\"data\"])\n", + "dist_object = st.gumbel_r(*dist_parameters)\n", + "X1[\"Gum\"] = univariate_model_dict(\"Gumbel (right)\",\n", + " dist_parameters, dist_object)\n", + "\n", + "dist_parameters = st.lognorm.fit(X2[\"data\"], floc = 0)\n", + "dist_object = st.lognorm(*dist_parameters)\n", + "X2[\"LN\"] = univariate_model_dict(\"Lognormal\",\n", + " dist_parameters, dist_object)\n", + "\n", + "dist_parameters = st.gumbel_r.fit(X2[\"data\"])\n", + "dist_object = st.gumbel_r(*dist_parameters)\n", + "X2[\"Gum\"] = univariate_model_dict(\"Gumbel (right)\",\n", + " dist_parameters, dist_object)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "8f6a77dd-71c1-49e0-9e30-28269efc6d98", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 600x600 with 1 Axes>" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# -----------------------------------------------------------------\n", + "plot_title = \"\"\n", + "font = \"Arial\"\n", + "x_label = \"Random Variable $X_1$\"\n", + "y_label = \"Random Variable $X_2$\"\n", + "legend = False\n", + "grid = False\n", + "save_svg = True\n", + "remove_ticks = False\n", + "remove_ticks_labels = True\n", + "file_name = \"../book/figures/cover_bi\"\n", + "# -----------------------------------------------------------------\n", + "\n", + "M2 = bivariate_model_dict(\"Model 2\", \"Gum\", X1, \"Gum\", X2, 0.54)\n", + "\n", + "M = M2\n", + "\n", + "rvs_temp = M[\"X1X2\"].rvs(1000).T\n", + "\n", + "import matplotlib.cm as cm\n", + "def plot_contour(bivar, xy_lim, data=None,\n", + " design_case=None, design_region=None,\n", + " nb_points=100):\n", + " \n", + " f = plt.figure(figsize=(6,6))\n", + " ax = f.add_subplot() # axes_class=AxesZero)\n", + " plt.setp(ax.spines.values(), linewidth=2)\n", + "\n", + " xlim = [xy_lim[0], xy_lim[1]]\n", + " ylim = [xy_lim[2], xy_lim[3]]\n", + "\n", + " x = np.linspace(xlim[0], xlim[1], nb_points)\n", + " y = np.linspace(ylim[0], ylim[1], nb_points)\n", + " X,Y = np.meshgrid(x,y)\n", + " pdf = np.zeros(X.shape)\n", + " for i in range(X.shape[0]):\n", + " for j in range(X.shape[1]):\n", + " # if X[i,j]>0 and Y[i,j]>0:\n", + " pdf[i,j] = bivar.pdf([X[i,j], Y[i,j]])\n", + " \n", + " ax.contour(X, Y, pdf, levels=8, cmap=cm.winter)\n", + " \n", + " if isinstance(data, np.ndarray):\n", + " ax.scatter(data[0,:], data[1,:], s=10.0,\n", + " facecolors='none', edgecolors='dimgray',\n", + " label='Data')\n", + " \n", + " if isinstance(design_region, np.ndarray):\n", + " ax.plot(design_region[0,:], design_region[1,:],\n", + " label='Design Boundary', color='k')\n", + " ax.fill_between(design_region[0,:], design_region[1,:],\n", + " ylim[1], label='Design Region', color='grey')\n", + " \n", + " if design_case:\n", + " ax.plot(design_case[0], design_case[1], 'ro',\n", + " label='Design Case')\n", + " \n", + " ax.set_aspect(\"equal\")\n", + " ax.set_xlim(xlim)\n", + " ax.set_ylim(ylim)\n", + " # ax.set_xlabel(r\"$X_1$\", fontsize=14)\n", + " # ax.set_ylabel(r\"$X_2$\", fontsize=14)\n", + " if isinstance(design_region, np.ndarray) or design_case:\n", + " ax.legend()\n", + " return f, ax \n", + "\n", + "fig, ax = plot_contour(M[\"X1X2\"], [0, 150, 0, 150],\n", + " data=rvs_temp, nb_points=100)\n", + "\n", + "ax.set_xlabel(x_label, fontfamily=font)\n", + "ax.set_ylabel(y_label, fontfamily=font)\n", + "\n", + "fig.patch.set_alpha(0.)\n", + "ax.patch.set_alpha(0.)\n", + "\n", + "if grid: ax.grid()\n", + "if legend: ax.legend(prop={\"family\":font})\n", + "if remove_ticks: ax.set_xticks([]); ax.set_yticks([])\n", + "if remove_ticks_labels: ax.set_xticklabels([]); ax.set_yticklabels([])\n", + "if save_svg: plt.savefig(file_name + '.svg', bbox_inches=0, transparent=True)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 600x600 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# -----------------------------------------------------------------\n", + "plot_title = \"\"\n", + "font = \"Arial\"\n", + "x_label = \"Consequences\"\n", + "y_label = \"Probability\"\n", + "legend = False\n", + "grid = False\n", + "save_svg = True\n", + "remove_ticks = True\n", + "remove_ticks_labels = True\n", + "file_name = \"../book/figures/cover_fn\"\n", + "# -----------------------------------------------------------------\n", + "\n", + "fig2 = plt.figure(figsize=(6,6))\n", + "ax2 = fig2.add_subplot() # axes_class=AxesZero)\n", + "ax2.set_title(plot_title, fontfamily=font)\n", + "\n", + "\n", + "plt.setp(ax2.spines.values(), linewidth=2)\n", + "\n", + "right = 500\n", + "top = .5e-5\n", + "\n", + "u = np.array([1, 2, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 120, 150, 180, 200, 220, 250, 275, 300, 350, 400, 450, 475])\n", + "v = 1e-8 + top*(np.log(right) - np.log(u))**3/np.log(right)\n", + "\n", + "\n", + "C = 10**-3\n", + "alpha = 1\n", + "\n", + "limit_line_N = np.array([1, 1000])\n", + "limit_line_P = C/limit_line_N**alpha\n", + "\n", + "# Visualize\n", + "\n", + "# plotting\n", + "# ax2.plot(limit_line_N, limit_line_P, '--', label='Limit Line', color=colors[0], linewidth=4)\n", + "ax2.plot(u, v, label='Risk Curve', color=colors[1], linewidth=4)\n", + "ax2.plot(limit_line_N, limit_line_P, '--', label='Limit Line', color=colors[0], linewidth=4)\n", + "\n", + "ax2.set_xscale('log')\n", + "ax2.set_yscale('log')\n", + "\n", + "ax2.set_xlim(1, 1000)\n", + "ax2.set_ylim(10**(-7),.001)\n", + "# ax2.set_yticks([10**(-7),10**(-5),10**(-3),10**(-1)])\n", + "\n", + "ax2.tick_params(axis='x', labelsize=13, width=2, length=8)\n", + "ax2.tick_params(axis='y', labelsize=13, width=2, length=8)\n", + "\n", + "ax2.set_xlabel(x_label, fontfamily=font)\n", + "ax2.set_ylabel(y_label, fontfamily=font)\n", + "\n", + "fig2.patch.set_alpha(0.)\n", + "ax2.patch.set_alpha(0.)\n", + "\n", + "if grid: ax2.grid()\n", + "if legend: ax2.legend(prop={\"family\":font})\n", + "if remove_ticks: ax2.set_xticks([]); ax2.set_yticks([])\n", + "if remove_ticks_labels: ax2.set_xticklabels([]); ax2.set_yticklabels([])\n", + "if save_svg: plt.savefig(file_name + '.svg', bbox_inches=0, transparent=True)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "2ea36977", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "<Figure size 600x600 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# combine ax and ax2 in one figure and overlay them offset to each other\n", + "fig3 = plt.figure(figsize=(6,6))\n", + "ax_bi = fig3.add_subplot() # axes_class=AxesZero)\n", + "\n", + "# add \n" + ] + } + ], + "metadata": { + "colab": { + "collapsed_sections": [], + "provenance": [] + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.7" + }, + "widgets": { + "application/vnd.jupyter.widget-state+json": { + "state": {}, + "version_major": 2, + "version_minor": 0 + } + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git 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mode 100644 index 0000000..16023fc --- /dev/null +++ b/figures/economics.ipynb @@ -0,0 +1,200 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 2, + "id": "65cbe2ec-de72-44d4-8af9-a969b06134a9", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from matplotlib import rcParams\n", + "rcParams.update({'font.size': 16})\n", + "# TUDelft colors palette\n", + "colors = [\"#0C2340\",\"#00B8C8\",\"#0076C2\",\"#6F1D77\",\"#EF60A3\",\"#A50034\",\"#E03C31\",\"#EC6842\",\"#FFB81C\",\"#6CC24A\",\"#009B77\"]" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "id": "fc2eb45c-9f4e-4fbd-91c3-dc0ff10b4c46", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 800x600 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# -----------------------------------------------------------------\n", + "plot_title = \"\"\n", + "font = \"Arial\"\n", + "x_label = \"Year\"\n", + "y_label = \"Normalized Present Value [$-$]\"\n", + "legend = True\n", + "grid = True\n", + "save_svg = True\n", + "remove_ticks = False\n", + "remove_ticks_labels = False\n", + "file_name = \"../book/figures/present_value\"\n", + "# -----------------------------------------------------------------\n", + "\n", + "fig = plt.figure(figsize=(8,6))\n", + "ax = fig.add_subplot() # axes_class=AxesZero)\n", + "ax.set_title(plot_title, fontfamily=font)\n", + "ax.set_xlabel(x_label, fontfamily=font)\n", + "ax.set_ylabel(y_label, fontfamily=font)\n", + "\n", + "plt.setp(ax.spines.values(), linewidth=2)\n", + "# ax.spines[\"left\"].set_position((\"data\", 0))\n", + "# ax.spines[\"bottom\"].set_position((\"data\", 0))\n", + "# ax.spines[\"top\"].set_position((\"data\", 1))\n", + "# ax.spines[\"right\"].set_position((\"data\", 100))\n", + "\n", + "# not a permanent solution (removed the part below 0)\n", + "# ---> find a better way to auto set upper bound\n", + "# ax.spines.bottom.set_bounds(0, 100)\n", + "# ax.spines.left.set_bounds(0, 1.0)\n", + "# ax.spines.top.set_bounds(0, 100)\n", + "# ax.spines.right.set_bounds(0, 1.0)\n", + "\n", + "t = np.linspace(0,101)\n", + "y_2 = 1 / (1 + 0.02)**t\n", + "y_4 = 1 / (1 + 0.04)**t\n", + "\n", + "# plotting\n", + "ax.plot(t, y_2, label='2%', color=colors[0], linewidth=4)\n", + "ax.plot(t, y_4, label='4%', color=colors[1], linewidth=4)\n", + "# ax.plot(1, 0, \">k\", transform=ax.get_yaxis_transform(), clip_on=False)\n", + "# ax.plot(0, 1, \"^k\", transform=ax.get_xaxis_transform(), clip_on=False)\n", + "\n", + "\n", + "\n", + "ax.tick_params(axis='x', labelsize=13, width=2, length=8)\n", + "ax.tick_params(axis='y', labelsize=13, width=2, length=8)\n", + "\n", + "if grid: ax.grid()\n", + "if legend: ax.legend(prop={\"family\":font})\n", + "if remove_ticks: ax.set_xticks([]); ax.set_yticks([])\n", + "if remove_ticks_labels: ax.set_xticklabels([]); ax.set_yticklabels([])\n", + "if save_svg: plt.savefig(file_name + '.svg')" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "id": "a19d456c-b5d3-43d6-8b51-1441f902985d", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 800x600 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# -----------------------------------------------------------------\n", + "plot_title = \"\"\n", + "font = \"Arial\"\n", + "x_label = \"Safety, $-\\ln p_f$ [$-$]\"\n", + "y_label = \"Present Value [€]\"\n", + "legend = True\n", + "grid = False\n", + "save_svg = True\n", + "remove_ticks = True\n", + "remove_ticks_labels = True\n", + "file_name = \"../book/figures/economic_opt\"\n", + "# -----------------------------------------------------------------\n", + "\n", + "fig = plt.figure(figsize=(8,6))\n", + "ax = fig.add_subplot() # axes_class=AxesZero)\n", + "ax.set_title(plot_title, fontfamily=font)\n", + "ax.set_xlabel(x_label, fontfamily=font)\n", + "ax.set_ylabel(y_label, fontfamily=font)\n", + "\n", + "plt.setp(ax.spines.values(), linewidth=2)\n", + "# ax.spines[\"left\"].set_position((\"data\", 0))\n", + "# ax.spines[\"bottom\"].set_position((\"data\", 0))\n", + "# ax.spines[\"top\"].set_position((\"data\", 1))\n", + "# ax.spines[\"right\"].set_position((\"data\", 100))\n", + "\n", + "# not a permanent solution (removed the part below 0)\n", + "# ---> find a better way to auto set upper bound\n", + "# ax.spines.bottom.set_bounds(0, 100)\n", + "# ax.spines.left.set_bounds(0, 1.0)\n", + "# ax.spines.top.set_bounds(0, 100)\n", + "# ax.spines.right.set_bounds(0, 1.0)\n", + "\n", + "t = np.linspace(0,101)\n", + "risk = 1 / (1 + 0.08)**t\n", + "inv = 0 + 0.005*t\n", + "tot = risk + inv\n", + "scale = 0.9\n", + "\n", + "# plotting\n", + "ax.plot(t, scale*risk, '--', label='Risk', color=colors[2], linewidth=4)\n", + "ax.plot(t, 1.05*inv, '-.', label='Investment', color=colors[1], linewidth=4)\n", + "ax.plot(t, tot+.05, label='Total', color=colors[0], linewidth=4)\n", + "# ax.plot(1, 0, \">k\", transform=ax.get_yaxis_transform(), clip_on=False)\n", + "# ax.plot(0, 1, \"^k\", transform=ax.get_xaxis_transform(), clip_on=False)\n", + "\n", + "\n", + "\n", + "ax.tick_params(axis='x', labelsize=13, width=2, length=8)\n", + "ax.tick_params(axis='y', labelsize=13, width=2, length=8)\n", + "\n", + "if grid: ax.grid()\n", + "if legend: ax.legend(prop={\"family\":font})\n", + "if remove_ticks: ax.set_xticks([]); ax.set_yticks([])\n", + "if remove_ticks_labels: ax.set_xticklabels([]); ax.set_yticklabels([])\n", + "if save_svg: plt.savefig(file_name + '.svg')" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.7" + }, + "widgets": { + "application/vnd.jupyter.widget-state+json": { + "state": {}, + "version_major": 2, + "version_minor": 0 + } + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/figures/figures-template.ipynb b/figures/figures-template.ipynb new file mode 100644 index 0000000..e05b9ac --- /dev/null +++ b/figures/figures-template.ipynb @@ -0,0 +1,266 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 3, + "id": "65cbe2ec-de72-44d4-8af9-a969b06134a9", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from matplotlib import rcParams\n", + "rcParams.update({'font.size': 16})\n", + "# TUDelft colors palette\n", + "colors = [\"#0C2340\",\"#00B8C8\",\"#0076C2\",\"#6F1D77\",\"#EF60A3\",\"#A50034\",\"#E03C31\",\"#EC6842\",\"#FFB81C\",\"#6CC24A\",\"#009B77\"]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## **Template #1**" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 800x600 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# -----------------------------------------------------------------\n", + "plot_title = \"this is the title\"\n", + "font = \"Arial\"\n", + "x_label = \"xlabel [$x-units$]\"\n", + "y_label = \"ylabel [$y-units$]\"\n", + "legend = False\n", + "grid = False\n", + "save_svg = True\n", + "remove_ticks = True\n", + "remove_ticks_labels = True\n", + "file_name = \"template_blank\"\n", + "# -----------------------------------------------------------------\n", + "\n", + "fig = plt.figure(figsize=(8,6))\n", + "ax = fig.add_subplot() # axes_class=AxesZero)\n", + "ax.set_title(plot_title, fontfamily=font)\n", + "\n", + "ax.set_xlabel(x_label, fontfamily=font)\n", + "ax.set_ylabel(y_label, fontfamily=font)\n", + "\n", + "plt.setp(ax.spines.values(), linewidth=2)\n", + "ax.spines[\"left\"].set_position((\"data\", 0))\n", + "ax.spines[\"bottom\"].set_position((\"data\", 0))\n", + "ax.spines[\"top\"].set_visible(False)\n", + "ax.spines[\"right\"].set_visible(False)\n", + "\n", + "ax.tick_params(axis='x', labelsize=13, width=2, length=8)\n", + "ax.tick_params(axis='y', labelsize=13, width=2, length=8)\n", + "\n", + "if grid: ax.grid()\n", + "if legend: ax.legend(prop={\"family\":font})\n", + "if remove_ticks: ax.set_xticks([]); ax.set_yticks([])\n", + "if remove_ticks_labels: ax.set_xticklabels([]); ax.set_yticklabels([])\n", + "if save_svg: plt.savefig(file_name + '.svg')\n" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "fc2eb45c-9f4e-4fbd-91c3-dc0ff10b4c46", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 800x600 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# -----------------------------------------------------------------\n", + "plot_title = \"\"\n", + "font = \"Arial\"\n", + "x_label = \"Year\"\n", + "y_label = \"Normalized Present Value [$-$]\"\n", + "legend = True\n", + "grid = False\n", + "save_svg = True\n", + "remove_ticks = False\n", + "remove_ticks_labels = False\n", + "file_name = \"template_exp_decay\"\n", + "# -----------------------------------------------------------------\n", + "\n", + "fig = plt.figure(figsize=(8,6))\n", + "ax = fig.add_subplot() # axes_class=AxesZero)\n", + "ax.set_title(plot_title, fontfamily=font)\n", + "ax.set_xlabel(x_label, fontfamily=font)\n", + "ax.set_ylabel(y_label, fontfamily=font)\n", + "\n", + "plt.setp(ax.spines.values(), linewidth=2)\n", + "ax.spines[\"left\"].set_position((\"data\", 0))\n", + "ax.spines[\"bottom\"].set_position((\"data\", 0))\n", + "ax.spines[\"top\"].set_visible(False)\n", + "ax.spines[\"right\"].set_visible(False)\n", + "\n", + "t = np.linspace(0,101)\n", + "y_2 = 1 / (1 + 0.02)**t\n", + "y_4 = 1 / (1 + 0.04)**t\n", + "\n", + "# plotting\n", + "ax.plot(t, y_2, label='2%', color=colors[0], linewidth=4)\n", + "ax.plot(t, y_4, label='4%', color=colors[1], linewidth=4)\n", + "ax.plot(1, 0, \">k\", transform=ax.get_yaxis_transform(), clip_on=False)\n", + "ax.plot(0, 1, \"^k\", transform=ax.get_xaxis_transform(), clip_on=False)\n", + "\n", + "# not a permanent solution (removed the part below 0)\n", + "# ---> find a better way to auto set upper bound\n", + "ax.spines.bottom.set_bounds(0, 105)\n", + "ax.spines.left.set_bounds(0, 1.05)\n", + "\n", + "ax.tick_params(axis='x', labelsize=13, width=2, length=8)\n", + "ax.tick_params(axis='y', labelsize=13, width=2, length=8)\n", + "\n", + "if grid: ax.grid()\n", + "if legend: ax.legend(prop={\"family\":font})\n", + "if remove_ticks: ax.set_xticks([]); ax.set_yticks([])\n", + "if remove_ticks_labels: ax.set_xticklabels([]); ax.set_yticklabels([])\n", + "if save_svg: plt.savefig(file_name + '.svg')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## **Template #3**" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "a19d456c-b5d3-43d6-8b51-1441f902985d", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 800x600 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# -----------------------------------------------------------------\n", + "plot_title = \"Cumulative distribution function, $F_{N}(n) = P(N \\leq n)$\"\n", + "font = \"Arial\"\n", + "x_label = \"Fatalities [$-$]\"\n", + "y_label = \"Probability [$-$]\"\n", + "legend = False\n", + "grid = False\n", + "save_svg = True\n", + "remove_ticks = False\n", + "remove_ticks_labels = False\n", + "file_name = \"template_cdf\"\n", + "# -----------------------------------------------------------------\n", + "\n", + "fig = plt.figure(figsize=(8,6))\n", + "ax = fig.add_subplot() # axes_class=AxesZero)\n", + "plt.setp(ax.spines.values(), linewidth=2.0)\n", + "\n", + "ax.set_title(plot_title, fontfamily=font, x=0.55, y=1.0)\n", + "ax.set_xlabel(x_label, fontfamily=font)\n", + "ax.set_ylabel(y_label, fontfamily=font)\n", + "\n", + "# data\n", + "N_fatalities = ['0', '10', '100', '']\n", + "N_fatalities_loc = [0.03, 0.33, 0.76, 0.95]\n", + "pdf = ['0', '0.989', '0.999', '1']\n", + "pdf_loc = [0.03, 0.66, 0.86, 0.99]\n", + "\n", + "# plotting\n", + "ax.step(N_fatalities_loc, pdf_loc, color=colors[0], linewidth=4)\n", + "\n", + "# ticks\n", + "ax.set_xticks(N_fatalities_loc)\n", + "ax.set_xticklabels(N_fatalities)\n", + "ax.set_yticks(pdf_loc)\n", + "ax.set_yticklabels(pdf)\n", + "ax.tick_params(axis='x', labelsize=13, width=2, length=8)\n", + "ax.tick_params(axis='y', labelsize=13, width=2, length=8)\n", + "\n", + "# add text\n", + "ax.text(0.8, 0.9, r'} $10^{-3}$', fontsize=16, fontfamily=font)\n", + "ax.text(0.37, 0.725, r'} $10^{-2}$', fontsize=16, fontfamily=font)\n", + "\n", + "current_values = plt.gca().get_yticks()\n", + "plt.gca().set_yticklabels(['{:,.3f}'.format(x) for x in current_values])\n", + "\n", + "if grid: ax.grid()\n", + "if legend: ax.legend(prop={\"family\":font})\n", + "if remove_ticks: ax.set_xticks([]); ax.set_yticks([])\n", + "if remove_ticks_labels: ax.set_xticklabels([]); ax.set_yticklabels([])\n", + "if save_svg: plt.savefig(file_name + '.svg')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "629e2cf8", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.7" + }, + "widgets": { + "application/vnd.jupyter.widget-state+json": { + "state": {}, + "version_major": 2, + "version_minor": 0 + } + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/figures/helper.py b/figures/helper.py new file mode 100644 index 0000000..b9714c0 --- /dev/null +++ b/figures/helper.py @@ -0,0 +1,109 @@ +import numpy as np +import matplotlib.pyplot as plt +import matplotlib.cm as cm +import pyvinecopulib as cop + +class Bivariate: + """Bivariate dependent distribution, design to function in the + same way as an instance of the scipy.stats.rv_continuous class, + specifically, with methods: cdf, pdf, rvs. + """ + + def __init__(self, X1, X2, rho): + """Constructor to initialize Bivariate object. + + Arguments: + --- + X1: scipy.stats.rv_continuous object. Marginal distribution + X2: scipy.stats.rv_continuous object. Marginal distribution + rho: float. Pearson correlation coefficient. + """ + self.X1 = X1 + self.X2 = X2 + self.rho = rho + self.copula_uv = cop.Bicop(family=cop.BicopFamily.gaussian, parameters = [rho]) + + def cdf(self, x): + """Compute cdf with array or list as argument: [x1, x2].""" + x1 = x[0] + x2 = x[1] + u = self.X1.cdf(x1) + v = self.X2.cdf(x2) + return self.copula_uv.cdf(np.array([[u, v]]))[0] + + def pdf(self, x): + """Compute pdf with array or list as argument: [x1, x2].""" + x1 = x[0] + x2 = x[1] + u = self.X1.cdf(x1) + v = self.X2.cdf(x2) + return self.copula_uv.pdf(np.array([[u, v]]))[0]*self.X1.pdf(x1)*self.X2.pdf(x2) + + def rvs(self, size=1): + """Create random sample with keyword argument size.""" + sample = self.copula_uv.simulate(size) + sample_X1 = self.X1.ppf(sample[:,0]) + sample_X2 = self.X2.ppf(sample[:,1]) + return np.vstack([sample_X1.T, sample_X2.T]).T + +def plot_contour(bivar, xy_lim, data=None, + design_case=None, design_region=None, + nb_points=100): + """Contour plot of PDF in the bivariate plane (X,Y). + + bivar: bivariate distribution, defined by + scipy.stats.multivariate_normal. + xy_lim: list. 1x4 list of xlim and ylim (in order) for plot limits. + + Optional arguments: + + data: array. A 2xN array of points. + design_case: list. Typically a 1x2 list defining a key + calculation point; plots as a red dot(s) + design_region: array. A 2xN array of points that define the + boundary of a region that will be shaded in gray between + the boundary and the max y-axis value (ylim[1]). + nb_points: int. Size of the grid (default: 200). + + returns: matplotlib.pyplot Figure and Axis objects. + """ + + f, ax = plt.subplots(1) + + xlim = [xy_lim[0], xy_lim[1]] + ylim = [xy_lim[2], xy_lim[3]] + + x = np.linspace(xlim[0], xlim[1], nb_points) + y = np.linspace(ylim[0], ylim[1], nb_points) + X,Y = np.meshgrid(x,y) + pdf = np.zeros(X.shape) + for i in range(X.shape[0]): + for j in range(X.shape[1]): + # if X[i,j]>0 and Y[i,j]>0: + pdf[i,j] = bivar.pdf([X[i,j], Y[i,j]]) + + ax.contour(X, Y, pdf, levels=8, cmap=cm.Blues) + + if isinstance(data, np.ndarray): + ax.scatter(data[0,:], data[1,:], s=10.0, + facecolors='none', edgecolors='darkgray', + label='Data') + + if isinstance(design_region, np.ndarray): + ax.plot(design_region[0,:], design_region[1,:], + label='Design Boundary', color='k') + ax.fill_between(design_region[0,:], design_region[1,:], + ylim[1], label='Design Region', color='grey') + + if design_case: + ax.plot(design_case[0], design_case[1], 'ro', + label='Design Case') + + ax.set_aspect("equal") + ax.set_xlim(xlim) + ax.set_ylim(ylim) + ax.set_xlabel(r"$X_1$", fontsize=14) + ax.set_ylabel(r"$X_2$", fontsize=14) + if isinstance(design_region, np.ndarray) or design_case: + ax.legend() + return f, ax \ No newline at end of file diff --git a/figures/risk_curve.ipynb b/figures/risk_curve.ipynb new file mode 100644 index 0000000..821ad75 --- /dev/null +++ b/figures/risk_curve.ipynb @@ -0,0 +1,411 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 2, + "id": "65cbe2ec-de72-44d4-8af9-a969b06134a9", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from matplotlib import rcParams\n", + "from scipy.interpolate import make_interp_spline\n", + "rcParams.update({'font.size': 16})\n", + "# TUDelft colors palette\n", + "colors = [\"#0C2340\",\"#00B8C8\",\"#0076C2\",\"#6F1D77\",\"#EF60A3\",\"#A50034\",\"#E03C31\",\"#EC6842\",\"#FFB81C\",\"#6CC24A\",\"#009B77\"]" + ] + }, + { + "cell_type": "code", + "execution_count": 191, + "id": "ba992138", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0. 0.33333333 0.56632333 0.66666667 0.89965667 1. ]\n", + "[1.00100000e-04 6.67666667e-05 4.34676665e-05 3.34333333e-05\n", + " 1.01343332e-05 1.00000000e-07]\n" + ] + } + ], + "source": [ + "print(np.log(x)/np.log(1000))\n", + "\n", + "print(y)" + ] + }, + { + "cell_type": "code", + "execution_count": 285, + "id": "1c820b9d", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(1e-07, 0.001)" + ] + }, + "execution_count": 285, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "right = 500\n", + "top = .5e-5\n", + "\n", + "u = np.array([1, 2, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 120, 150, 180, 200, 220, 250, 275, 300, 350, 400, 450, 475])\n", + "v = 1e-8 + top*(np.log(right) - np.log(u))**3/np.log(right)\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.loglog(u, v, color=colors[0], label=\"Ellipse\")\n", + "ax.set_xlim(1, 1000)\n", + "ax.set_ylim(1e-7, 1e-3)" + ] + }, + { + "cell_type": "code", + "execution_count": 340, + "id": "f7c03e2f", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 1.00e-04 6.00e-05 3.00e-05 1.00e-05 3.98e-06 1.98e-06 9.80e-07\n", + " 6.00e-08 -8.50e-07]\n" + ] + } + ], + "source": [ + "right = 500\n", + "top = .5e-5\n", + "\n", + "u = np.array([1, 2, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 120, 150, 180, 200, 220, 250, 275, 300, 350, 400, 450, 475])\n", + "v = 1e-8 + top*(np.log(right) - np.log(u))**3/np.log(right)\n", + "\n", + "# fig, ax = plt.subplots()\n", + "# ax.loglog(u, v, color=colors[0], label=\"Ellipse\")\n", + "# ax.set_xlim(1, 1000)\n", + "# ax.set_ylim(1e-7, 1e-3)\n", + "\n", + "C = 10**-3\n", + "alpha = 2\n", + "\n", + "limit_line_N = np.array([1, 1000])\n", + "limit_line_P = C/limit_line_N**alpha\n", + "\n", + "N = np.array([1, 7, 20, 40, 60, 100, 160, 200, 300])\n", + "N_pmf = np.array([0.9999,\n", + " 0.00004,\n", + " 0.00003,\n", + " 0.00002,\n", + " 0.00000602,\n", + " 0.000002,\n", + " 0.000001,\n", + " 0.00000092,\n", + " 0.00000091])\n", + "N_cdf = np.cumsum(N_pmf)\n", + "N_exc = 1 - N_cdf\n", + "print(N_exc)" + ] + }, + { + "cell_type": "code", + "execution_count": 341, + "id": "2c5ef408", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 800x600 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# -----------------------------------------------------------------\n", + "plot_title = \"\"\n", + "font = \"Arial\"\n", + "x_label = \"Fatalities, N [$-$]\"\n", + "y_label = \"Probability of Exceedance, $1-F_N(n)$ [$-$]\"\n", + "legend = True\n", + "grid = True\n", + "save_svg = True\n", + "remove_ticks = False\n", + "remove_ticks_labels = False\n", + "file_name = \"../book/figures/fn_simple01\"\n", + "# -----------------------------------------------------------------\n", + "\n", + "fig = plt.figure(figsize=(8,6))\n", + "ax = fig.add_subplot() # axes_class=AxesZero)\n", + "ax.set_title(plot_title, fontfamily=font)\n", + "ax.set_xlabel(x_label, fontfamily=font)\n", + "ax.set_ylabel(y_label, fontfamily=font)\n", + "\n", + "plt.setp(ax.spines.values(), linewidth=2)\n", + "\n", + "# Visualize\n", + "\n", + "# plotting\n", + "# ax.plot(limit_line_N, limit_line_P, '--', label='Limit Line', color=colors[0], linewidth=4)\n", + "ax.plot(u, v, label='Risk Curve', color=colors[1], linewidth=4)\n", + "\n", + "# ax.plot(1, 0, \">k\", transform=ax.get_yaxis_transform(), clip_on=False)\n", + "# ax.plot(0, 1, \"^k\", transform=ax.get_xaxis_transform(), clip_on=False)\n", + "\n", + "ax.set_xscale('log')\n", + "ax.set_yscale('log')\n", + "\n", + "ax.set_xlim(1, 1000)\n", + "ax.set_ylim(10**(-7),.001)\n", + "# ax.set_yticks([10**(-7),10**(-5),10**(-3),10**(-1)])\n", + "\n", + "ax.tick_params(axis='x', labelsize=13, width=2, length=8)\n", + "ax.tick_params(axis='y', labelsize=13, width=2, length=8)\n", + "\n", + "if grid: ax.grid()\n", + "if legend: ax.legend(prop={\"family\":font})\n", + "if remove_ticks: ax.set_xticks([]); ax.set_yticks([])\n", + "if remove_ticks_labels: ax.set_xticklabels([]); ax.set_yticklabels([])\n", + "if save_svg: plt.savefig(file_name + '.svg')" + ] + }, + { + "cell_type": "code", + "execution_count": 343, + "id": "fc2eb45c-9f4e-4fbd-91c3-dc0ff10b4c46", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 800x600 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# -----------------------------------------------------------------\n", + "plot_title = \"\"\n", + "font = \"Arial\"\n", + "x_label = \"Fatalities, N [$-$]\"\n", + "y_label = \"Probability of Exceedance, $1-F_N(n)$ [$-$]\"\n", + "legend = True\n", + "grid = True\n", + "save_svg = True\n", + "remove_ticks = False\n", + "remove_ticks_labels = False\n", + "file_name = \"../book/figures/fn_limit01\"\n", + "# -----------------------------------------------------------------\n", + "\n", + "fig = plt.figure(figsize=(8,6))\n", + "ax = fig.add_subplot() # axes_class=AxesZero)\n", + "ax.set_title(plot_title, fontfamily=font)\n", + "ax.set_xlabel(x_label, fontfamily=font)\n", + "ax.set_ylabel(y_label, fontfamily=font)\n", + "\n", + "plt.setp(ax.spines.values(), linewidth=2)\n", + "# ax.spines[\"left\"].set_position((\"data\", 0))\n", + "# ax.spines[\"bottom\"].set_position((\"data\", 0))\n", + "# ax.spines[\"top\"].set_position((\"data\", 1))\n", + "# ax.spines[\"right\"].set_position((\"data\", 100))\n", + "\n", + "# not a permanent solution (removed the part below 0)\n", + "# ---> find a better way to auto set upper bound\n", + "# ax.spines.bottom.set_bounds(0, 100)\n", + "# ax.spines.left.set_bounds(0, 1.0)\n", + "# ax.spines.top.set_bounds(0, 100)\n", + "# ax.spines.right.set_bounds(0, 1.0)\n", + "\n", + "# Visualize\n", + "\n", + "# plotting\n", + "ax.step(N, N_exc, where='post', label='Risk Curve', color=colors[1], linewidth=4)\n", + "ax.plot(limit_line_N, limit_line_P, '--', label='Limit Line', color=colors[0], linewidth=4)\n", + "# ax.plot(u, v, label='Risk Curve 2', color=colors[2], linewidth=4)\n", + "\n", + "# ax.plot(1, 0, \">k\", transform=ax.get_yaxis_transform(), clip_on=False)\n", + "# ax.plot(0, 1, \"^k\", transform=ax.get_xaxis_transform(), clip_on=False)\n", + "\n", + "ax.set_xscale('log')\n", + "ax.set_yscale('log')\n", + "\n", + "ax.set_xlim(1, 1000)\n", + "ax.set_ylim(10**(-9),.001)\n", + "# ax.set_yticks([10**(-7),10**(-5),10**(-3),10**(-1)])\n", + "\n", + "ax.tick_params(axis='x', labelsize=13, width=2, length=8)\n", + "ax.tick_params(axis='y', labelsize=13, width=2, length=8)\n", + "\n", + "if grid: ax.grid()\n", + "if legend: ax.legend(prop={\"family\":font})\n", + "if remove_ticks: ax.set_xticks([]); ax.set_yticks([])\n", + "if remove_ticks_labels: ax.set_xticklabels([]); ax.set_yticklabels([])\n", + "if save_svg: plt.savefig(file_name + '.svg')" + ] + }, + { + "cell_type": "code", + "execution_count": 350, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([5.e-04, 1.e-06])" + ] + }, + "execution_count": 350, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "limit_line_P" + ] + }, + { + "cell_type": "code", + "execution_count": 368, + "id": "59293d62", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 800x600 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# -----------------------------------------------------------------\n", + "plot_title = \"\"\n", + "font = \"Arial\"\n", + "x_label = \"Fatalities, N [$-$]\"\n", + "y_label = \"Probability of Exceedance, $1-F_N(n)$ [$-$]\"\n", + "legend = True\n", + "grid = True\n", + "save_svg = True\n", + "remove_ticks = True\n", + "remove_ticks_labels = True\n", + "file_name = \"../book/figures/fn_limit00\"\n", + "# -----------------------------------------------------------------\n", + "\n", + "fig = plt.figure(figsize=(8,6))\n", + "ax = fig.add_subplot() # axes_class=AxesZero)\n", + "ax.set_title(plot_title, fontfamily=font)\n", + "ax.set_xlabel(x_label, fontfamily=font)\n", + "ax.set_ylabel(y_label, fontfamily=font)\n", + "\n", + "plt.setp(ax.spines.values(), linewidth=2)\n", + "# ax.spines[\"left\"].set_position((\"data\", 0))\n", + "# ax.spines[\"bottom\"].set_position((\"data\", 0))\n", + "# ax.spines[\"top\"].set_position((\"data\", 1))\n", + "# ax.spines[\"right\"].set_position((\"data\", 100))\n", + "\n", + "# not a permanent solution (removed the part below 0)\n", + "# ---> find a better way to auto set upper bound\n", + "# ax.spines.bottom.set_bounds(0, 100)\n", + "# ax.spines.left.set_bounds(0, 1.0)\n", + "# ax.spines.top.set_bounds(0, 100)\n", + "# ax.spines.right.set_bounds(0, 1.0)\n", + "\n", + "C = 0.003302\n", + "alpha = 1.173\n", + "\n", + "limit_line_N = np.array([1, 10000])\n", + "limit_line_P = C/limit_line_N**alpha\n", + "\n", + "limit_line_N_trim = [1, 5, 1000, 1000]\n", + "limit_line_P_trim = [5e-4, 5e-4, 1e-6, 1e-7]\n", + "\n", + "\n", + "\n", + "# Visualize\n", + "\n", + "# plotting\n", + "ax.step(N, N_exc, where='post', label='Risk Curve', color=colors[1], linewidth=4)\n", + "ax.plot(limit_line_N, limit_line_P, ':', label='Limit Line', color=colors[0], linewidth=4)\n", + "ax.plot(limit_line_N_trim, limit_line_P_trim, '-', label='Limit Line with Cutoffs', color=colors[0], linewidth=4)\n", + "# ax.plot(u, v, label='Risk Curve 2', color=colors[2], linewidth=4)\n", + "\n", + "# ax.plot(1, 0, \">k\", transform=ax.get_yaxis_transform(), clip_on=False)\n", + "# ax.plot(0, 1, \"^k\", transform=ax.get_xaxis_transform(), clip_on=False)\n", + "\n", + "\n", + "\n", + "ax.set_xscale('log')\n", + "ax.set_yscale('log')\n", + "\n", + "ax.set_xlim(1, 10000)\n", + "ax.set_ylim(10**(-7),.01)\n", + "\n", + "if grid: ax.grid()\n", + "if legend: ax.legend(prop={\"family\":font})\n", + "if remove_ticks: ax.set_xticks([]); ax.set_yticks([])\n", + "if remove_ticks_labels: ax.set_xticklabels([]); ax.set_yticklabels([])\n", + "if save_svg: plt.savefig(file_name + '.svg')" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.7" + }, + "widgets": { + "application/vnd.jupyter.widget-state+json": { + "state": {}, + "version_major": 2, + "version_minor": 0 + } + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/figures/risk_types.ipynb b/figures/risk_types.ipynb new file mode 100644 index 0000000..a662a11 --- /dev/null +++ b/figures/risk_types.ipynb @@ -0,0 +1,167 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "id": "65cbe2ec-de72-44d4-8af9-a969b06134a9", + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from matplotlib import rcParams\n", + "rcParams.update({'font.size': 16})\n", + "# TUDelft colors palette\n", + "colors = [\"#0C2340\",\"#00B8C8\",\"#0076C2\",\"#6F1D77\",\"#EF60A3\",\"#A50034\",\"#E03C31\",\"#EC6842\",\"#FFB81C\",\"#6CC24A\",\"#009B77\"]" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "fc2eb45c-9f4e-4fbd-91c3-dc0ff10b4c46", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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ZsGED9evXZ//+/Rm/q/eddBcReerLrm34/de5FLGzVbs/NTWNkd8tYMSk+SQnp+g5OyGEEHltxYoV/PDDD1hZWZGSksKxY8eYPHkyTZo0oXDhwrRv357Lly9nOub+/fts374dW1tb1q1bl6loK126dMad71mzZmVqR6lUMn78+IwCG/7pfz1v3jxKlSrFo0ePNOa5atUqYmNjGTx4cKYCG/4p+Fu3bk1oaCjbt29/63N2dXWlXbt2WQp6W1tbunXrBkBY2Lt+0/F/GjdunGUKPwsLCypVqsTs2bNxdXVl165d1K5d+43niYqKysj7398MlCpVip9//pl169ZhbW2t9lh/f39WrlxJ3bp1OXDgQIEpsEGKbJEPNKhTlaAdy6lc3kNjzOoNu2nb52sexz7XX2JCCCHynJGRERMmTCAqKorNmzfTt29fSpcuDfxz13X79u3UqlWL5cuXZxxz/PhxALy9vbGxsclyTi8vL5ycnHj48CF3794F/ulnDdCmTZss8TVq1ODOnTuZivL/OnbsGPBP4apO8+bNM7XzJgEBAezYseP/d/n5R0xMDIcPH+bkyZPAP1Ptaatp06Z0796d7t274+Pjk/GzcnNzY9++fYSGhtKiRYu3nsfT0xP450NL586d2bBhA48fPwagXbt29OjRA3t7+yzHff/998yfPx9DQ0O2bdumsRB/X0mRLfKFki5O/LF5CW2aNdQYc/LsFRq3H8TfN+7qMTMhhBD5gZWVFZ06dWLVqlXcvn2bhw8fsnLlSipVqkRaWhp+fn78/fffwD+DBuH/Bu6pk951If0ubPp/33XGkAcPHgDg6+urdpEXPz8/AMLDw7N1vuDgYAYPHkzNmjWxsbHB0dERb29vtm3bBuhmlcjx48ezfv161q9fz/bt23nw4AFNmjTh3r17TJo0KctAUk3q1q3L/PnzMTY2ZsuWLXTv3h1HR0dq167NzJkzefZM/crO69evx8jIiLS0NGbPnq3188lvpE92HgsICCAgIOCDmMLvbawszVm3eDIzl6xj+qI1amPuP3z0z8I1s7+lbTNP/SYohBB6UrGs+r6r2ZN/Bj5qKyQkhKioKDw9PTE2Ns60z9nZma+++oqePXvSuHFjTp8+zYYNG5g+fXq2CtC0tH/GAqUPZHzX1Qv/e77PP/8cW1v1XSABKlas+NZzzZ49m2+++QaAChUq0Lp1aypUqEDt2rW5e/duRsGua7a2tmzfvp1q1apx/vx5OnfuzL59+944u0u6ESNG0K1bN3bs2MH+/fsJCgri/PnznD9/nvnz53Py5MmMbyDSVatWjVWrVuHp6cmiRYvo2rUrderUyZXnlhdyXGSnfyWgCwqFgqCgIJ2d733k5+eHn58fLi4uRERE5HU6ec7AwIBvh/WmYlk3+n/9IwmvE7PEvEpIpIffd4wf3odv/HrKwjVCiAJHm1k5lEolL168wMbG5r1/f/Tx8eHWrVucOXNGY/FlamqaMVPH06dPAShevDgA9+7d03ju9D7N6VPoFitWjHv37vHw4UPKli2bJX7FihUUL16c1q1bqz1fsWLFuHXrFsOHD6dp06bZfo7q8ho7diy2trbs2bMnyzSB8+fPf+dzZ4etrS1r166lUaNGHDhwgOXLlzNo0KBsHevg4MCAAQMYMGAASqWSP//8E39/f86fP8+PP/7IqlWrMsWvX7+eSpUqMWnSJMaOHctXX33FhQsXsnygel/l+NV38uRJnT6EUKdtcy8Ob1mMa3HN84dPW7iG3sOm8CpBFq4RQoiCqH79+gAsXrz4jXHp80anTzXXsGFDFAoFhw4d4sWLF1nijx07xuPHj3F3d8/oHpI+2DF92rp/u3HjBgMHDsxYnEUdLy8vjccDfPPNN1SvXj3TEurq7hCfOXMGpVJJ48aN1c7DfejQISB3V4v09PTMWPzn22+/feu37f7+/hQrViyjLzz8c9OsYcOGTJgwAVDfTSb9WwR/f38qV65McHAwM2fO1NXTyHPv9BHX29ubY8eOafXQ5lOe+DBUqVCaoB3LqF/7I40xOw8E4d15KA8iNI/4FkII8X4aM2YM5ubmrF+/noEDB2bcqU6nVCpZuXIly5cvx8HBgd69ewP/9Ldu27YtL168oGfPnsTHx2ccExoamjFd3pAhQzK2+/n5oVAomDJlCpcuXcrYHh8fn9E9o0ePHhpz7d+/P5aWlixevJhNmzZl2vf777+zYMECrly5kmmmjvTpB+Pi4jK2FS1aFIC//vorYzEegJSUFCZOnMiBAwcASEzM+k2vLs2YMQMHBwfi4uIYNWrUG2NLlCjBo0ePGDduXKYPNampqWzevBngjd1AjI2NWb58OQqFgqlTp3Ljxg3dPIm8psohhUKh6tmzZ04Py6JHjx4qAwMDrc9TUDg7O6sAlbOzs97aTE5OVu3cuVOVnJystzbfRVJSsmro+Dkqq1KNND7cardTnTx7Ja9TFfnU+3Ktiw/L69evVSEhIarXr1/r9LxpaWmqZ8+eqdLS0nR63ryyf/9+VaFChVSAytjYWFW/fn1Vx44dVa1atVI5OjqqAJWjo6Pq3LlzmY6Ljo5WVaxYUQWo7O3tVT4+PqpmzZqpTE1NVYCqW7duWX5GU6dOVQEqIyMjVZMmTVRt27ZVOTg4qACVt7d3RvyxY8dUgOqTTz7JdPy2bdtUJiYmKkBVoUIFlY+Pj6pWrVoqQAWoFixYkCl+7ty5KkBla2ur8vX1Ve3cuVOVmpqqql69esb2zz//XNW6deuMPCpVqqQCVPXq1cs4zy+//KICVN27d8/Wz7RkyZIqQHXs2LE3xv36668ZuR89ejRje/q2lJQUlUr1z7X88ccfqwCVnZ2dqkWLFqp27dqpSpQooQJU5cuXVz19+jRL+7dv387UXr9+/VSAqkGDBiqlUpmt56KL6z0nr8Wc1Gs5vpPdu3dvnfTL9vT0pFevXlqfRxR8JibGLPzBn3mTh2NoqP6SffL0Oa17jeKXTXv0nJ0QQojc1Lx5c27fvs2UKVP4+OOPuXv3Lrt27eLPP//E1dWVKVOmcOPGDWrVqpXpOAcHB/766y8mT56Mg4MD+/fv59y5c9SvX5/Nmzfz22+/ZemzPn78ePbt20fjxo25ePEi+/btw87Ojh9++IHff//9rX3cfX19OX/+PD169CAuLo49e/bw6NEjPv/8c44dO8bw4cMzxQ8aNCijFtq/fz/nz5/H0NCQI0eOMHLkSIoWLcqhQ4c4fvw4Hh4eLF++nEuXLlGoUCHOnj2b65MmpA8qBRg8eDDJyclq48zMzDh48CBjx47F0dGRY8eOcfDgQaysrBg/fjxnzpzBzs7ure3NnDkTBwcHTp48mWlKxveVQqXSwRwwQmvpAx+dnZ15+PChXtpMSUlh3759tGzZ8r0ZZBB0+iI9h37Ps+dZ+9ilG9DThxnjBmNsLJPniH+8j9e6KPgSExMJCwvD3d1d46qF76IgDXwU4m10cb3n5LWYk3pNXn3iveJVrwZB25e9cWqoFet24PPlN8Q+i9MYI4QQQgiRm3ReZJ86dSpj5KsQucG9RHEOb1lCy0/ra4wJOn2Jxr6DuX5L+2VnhRBCCCFySudFdt++fWnZsqWuTytEJtZWFmxc9gPf+PXUGBMWHkmTjn7sO3JKj5kJIYQQQuRSdxHp5p19AQEBVKxYUVZ8fAcGBgZMHPklaxZOxNzMVG1M/KvXdBk4gdlL18t1KYQQQgi9kT7ZeczPz4+QkJCMFadEzrVv1YRDmxbh7FRU7X6VSsWUeav5YsQPaleQFEIIIYTQNSmyRYFQrXJZju9czsc1KmmM2bb3GM26DONhZIzGGCGEEEIIXZAiWxQYDvaF2btuHj07tNAYc/nabbx8B/LXxb/1mJkQQgghPjRSZIsCxdTUhIAZXzNr4hCN82XGPHlGq+7+rNu6X8/ZCSGEEOJDIUW2KHAUCgWDerdnx88zKWRjpTYmOSWFwWNnMXZaAKmpaXrOUAghhBAFnRTZosBq0qAWx7Yvo1ypkhpjAn7ZSvu+Y3kW91KPmQkhhBCioJMiWxRopd1cOLJ1Cc0a19UYc/TP8zT2HcSNO/f1mJkQQgghCjIpskWBZ2ttxeblUxnZv6vGmLv3I/i0gx8HA//SY2ZCCCGEKKikyBYfBENDQ6Z8059Vc8dhZmqiNuZF/Cs69hvH/J82ysI1QgghhNCKFNnig9K5rTcHNi6kmKO92v0qlYpJs36i36jpvE5M0nN2QgghhCgopMgWH5yaH5Xn+I7l1KpaQWPM5t2HadFtBJGPHusxMyGEEP8WGBiIQqHI9iMwMDCvU86X3NzcUCgU3LlzR6fnXbNmzRt/H6ampri4uNC6dWuCgoKyHD958mQUCgUTJkx45/YNDQ3p37+/tk8lVxjp+oStW7cmKipK16cVQqecHIqwf8MChk2Yy8Ydh9TGXLh6Ay/fQWxYOoXa1SrqOUMhhBDpLC0tadeu3VvjHB0dcz8ZkYWDgwPe3t5Ztj9+/JirV6+yZ88e9uzZw/r16+nevXseZJg3dF5kz5o1S9enLNACAgIICAggOjo6r1P54JiZmrBi1liqlC/FhJkrUCqVWWIexcTSotsIFk8bTVefz/IgSyGEEPb29qxfvz6v03hvHTlyhJSUFEqW1DylrTYqVKig8feTnJzMmDFjWLBgAcOGDaNdu3ZYWloCMGTIELp06YK9vfounO876S6Sx/z8/AgJCZFP33lEoVAwtG8ntq6cga21pdqYpOQU+n89gwkzl5OWJgvXCCGEeL+UKlWK8uXLY2xsrPe2TUxMmDt3Lo6Ojjx9+pRTp05l7LO3t6d8+fJSZKerUaMGEydO1LrhCRMmULNmTa3PI4QueHvV4ei2pZR2d9UYs3DlZjr1H8/zF/F6zEwIIcS7UqlU/PzzzzRo0AA7OzsKFy5M/fr12bhR/SxSGzZswNPTExsbG8zNzalSpQrTpk0jISEhU9y9e/dQKBS0a9eOqKgovvzyS4oVK4aZmRmVKlVi7ty5am/KvH79mmnTplGlShXMzc2xsbGhYcOG/Pbbb1li0/s7L1myhFOnTvHZZ59hY2ODnZ0dbdu25e7duwDs2rWLjz/+GAsLC9zd3RkxYgSvXr3KdC5NfbJfvHjBlClTqFy5MpaWljg7O9O6dWv++ku309kaGBjg6vrP39fY2NiM7Zr6ZO/fv5/mzZvj7OyMqakpJUqUoHfv3ly/fj1b7R0/fhwLCwuMjY3Zvn277p5IDuW4u8jly5epXLmy1g3fv3+fy5cva30eIXSlrEcJjm1byhfDp3D4xDm1MYeCztCkw2A2r5hGmTcU5EIIoY1+f4fyd/zrdzxaRVpaGoaGhoBCl2nlSGUrc1ZW9siz9tPS0mjfvj27du3C0tISLy8vAI4dO0a3bt24ePEis2fPBv4pxnv16sX69esxNTXF09MTKysrjh8/zoQJE/jf//7HkSNHKFKkSKY2oqKiqF27Nq9evaJevXokJiYSFBTE6NGjuXfvHosXL86IjY2NpXHjxgQHB1OkSBGaN29OQkICQUFBnDx5kkOHDmUU1v+2b98+RowYQalSpWjatCnnzp1j9+7dXLx4EX9/f/z9/alduzafffYZR44cYeHChTx48OCtxWVERASffvopN2/exMnJiebNmxMTE8OePXvYt28fO3fupHXr1rr4VfDw4UOCg4MB3lpDrlu3jt69e2NsbEzDhg0pVKgQ165d49dff2X79u2cPn36jec4d+4cn3/+OSkpKWzcuBFfX1+dPId38U59sq9cucKkSZO0avjKlStaHS9EbihkY8XWVTOYOOsnFq/eojbmdmg4jX0HsWbhJJp61tFzhkKID8Hf8a/5K06+NdPGokWL2LVrF1WqVOHAgQMUL14cgNDQUOrXr8+cOXPo2rUrNWrUYMmSJaxfv57SpUtz8OBBPDz++XDw8uVLunbtyt69e+nfvz/btm3L1MbZs2dp1KgR//vf/zK6PPz++++0adOG5cuX88MPP1CoUCEA+vfvT3BwMG3atOG3337DysoKgDt37tCsWTN+/fVXatWqxdChQzO1sX//fkaPHs2sWbNQKBS8ePGCypUrEx4ejr+/P+vWraNHjx4AXLt2japVq7Jz504eP35M0aJFNf58Bg8ezM2bN+nWrRs///wzpqamAOzevRsfHx+++OILoqKi3rmLSVpaGs+ePePUqVOMHTuWpKQk2rVr99Yie/LkyRgaGnLp0iUqVvxn0gGVSsXIkSNZuHAhc+bMYc2aNWqPDQ4OzvjwsmHDBjp06PBOuevKOxXZwcHBGZ9I3oVCoUClUmX5tCZEfmBoaMj0bwdRubwHQ8fNJTklJUtM3MtXtP/qW6aOGcCQLzvKtSyEELno/v37b32fbdu2LTt37sz497JlywBYtWpVRoEN4OHhwfjx4/npp5+4ceMGNWrUYP78+Rmx6QU2gLW1Nb/99hslS5Zk+/bt3Llzh9KlS2dqd+HChZn6FLdu3Rp3d3fCwsK4efMmH3/8Mffv32f79u3Y2tqybt26jAIboHTp0vz88880atSIWbNmZSmyCxcuzLRp0zKev42NDZ9//jnLli2jfv36GQU2QKVKlShXrhwhISHcvXtXY5EdERHB7t27KVKkCKtWrcoosAHatGlDly5duHPnDrdu3aJSpUpv/LkDBAUFvfH3o1Ao6NWrFwEBAW89V3ph/+/fmUKhYNy4cZQuXZqPPvpI7XG3b9/G29ubuLg41q9fT6dOnd7aVm7LcZH93Xff5UYeQuQ73XyaUdrNlW6DJxL9+GmW/UqlknEzlvH3zVAW/uCvcSVJIYQQ2snOFH61atXK+P+IiAhu376No6Mjdepk/cZx6NChGcVseHg4YWFhFC1aNKNLyb/Z2trSokULNm3aRFBQUKYi28LCgipVqmQ5pnjx4oSFhWX0jT5+/DgA3t7e2NjYZIn38vLCycmJhw8fcvfuXUqVKpWxr0aNGpiYZP77kl48V61aNcu50u+cJyYmZtmXLn0+8aZNm2Jubp5lv7o+4m/y7yn8lEolt27d4sKFCwAMHz6c0aNH4+Likq1zeXp6cvDgQWrWrEmvXr1o0aIFtWrVwsHBgSFDhqg9JjIyEm9vb6Kjoxk0aBBdunTJUf65RYpsId6gTvWKHN+xnK6DJnIx+KbamA3bD3I7NJwNS6fg5FBEbYwQQoh3l9Mp/NLX6yhRosRbYyMjIwHeOL2du7t7pvOmK1SokNo7uEZG/5RX6VPDprfh5ub2xjYePXpEVFRUpiK7cOHCWWLT23zTvjfJyc8nO9RN4bd9+3a6dOlCQEAANWvWpGfPntk616pVq2jXrh0XLlxg8uTJTJ48mcKFC9OyZUu+/PJLGjdunOWYP//8E4VCgYGBAevXr+fbb7/NGGiZl3Q+T7YQBU1xp6Ic2LiQIeNms2X3EbUx5y6H4OUzkI3Lp1KjSjk9ZyiEKGgqW2W9u5h9+WfgY15JTU3Ndqy6WUb+K32mkH93q4DsFbTatpEb0+7l5Ofzrnx9fZkzZw7Dhw/nyy+/xN3dnQYNGrz1OBcXF86dO8fx48fZvXs3hw8fJjg4mPXr17N+/XpGjRrFnDlzMh2jUChYsWIFly5dYtmyZQwePJjff/89t55atkmRLUQ2mJuZsmrueCqVK8XkOSvVvmFGRj+hWZdhLP3xGzq2/jQPshRCFBTazMqhVCp58eIFNjY2GBh8mMthFCtWDPhnVgt1oqOj2bVrF1WrVs3o+3vv3j2N5wsNDQXefUXJ7LQRFhamVRs58bafz/nz5wkJCeGTTz7JdFc9p4YOHcrvv//O4cOH6dWrF3///TcWFhZvPU6hUODl5ZXRfScmJoZffvmFcePGMW/ePIYNG5bpLnybNm3o27cvL1++ZMeOHezZs4dNmzblebeRD/PVJ8Q7UCgU+A/oyuYV07C2VP8mkZiUzJcjpzJ5zkq1K0gKIYTIfSVLlsTZ2ZmoqCi10wXv2LGDAQMGsHHjRkqUKEHJkiV58uQJQUFBWWLj4uI4dOgQgNo+29nRsGFDFAoFhw4d4sWLF1n2Hzt2jMePH+Pu7q6zLhxv8sknnwD/rASZlJSUZf+cOXPo3bu3VpNcwP/dYTY3NycsLIwpU6a8MT4kJISPPvqIFi1aZNru4ODAmDFj+Oijj1CpVERERGTan95n3dbWNmMQ6/Dhw3n6NOt4Kn2SIluIHGrRpB5HtwZQqqSzxpi5yzfQZeBEXrx8pTFGCCFE7kkfJNevXz+ePHmSsT00NJTvv/8eAwMDunXrBsDIkSMB+OqrrzLuWgPEx8fTo0cPXrx4QevWrd95WXJ3d3fatm3Lixcv6NmzJ/Hx/zc9Y2hoKF999VWmnHNb6dKladasGTExMQwdOjRT95E9e/bwv//9DwcHBz777DOt2/Lw8MhYbGbevHmEhIRojC1btiyRkZEcPHiQrVu3Ztp34cIFrl+/jqWlZcbUfup06dKFzz77jJiYmIzfa16R7iJCvIPyZdw4um0pfYZP4difF9TG7D96ik87+rFp+TRKuWkuyIUQQrzZkydPMk1Vp4mnpyf9+/cHYPTo0Rw/fpz9+/dTqlQpGjVqRGJiIidOnOD169dMmTIlY+aRoUOHcurUKbZs2ULFihXx8vLC0tKSEydO8OTJEz766CNWrVql1XNYsWIFt27dYvfu3bi7u9OwYUMSEhIIDAwkKSmJbt26MWLECK3ayIlVq1bh6enJypUrOXjwIHXq1CEiIoLTp09jZGTEpk2bstW1IztGjx7NunXruHHjBoMHD86Y3eS/jIyM+Omnn+jQoQMdO3akRo0aeHh48PjxY06ePElaWhoLFizA1tb2je0tXbqUypUr8+uvv9KjR4+MmU/0TYpsId5R4UI2bF89k/E/LmPpmm1qY27cuU/j9oP4dfF3NKpfU88ZCiFEwfDq1atsTStnZGSUUWQbGRmxe/duli9fzpo1azh8+DAqlYqqVasybNgwunbtmnGcgYEBmzZtokWLFqxatYpTp06hUqkoU6YM33zzDUOHDsXMzEyr5+Dg4MBff/3FvHnz2LJlC/v378fCwoL69eszcOBAvc/r7OLiwvnz5/nxxx/ZsWMHu3fvxsLCgtatWzNx4kRq166ts7ZMTExYtmwZjRs3JigoiHXr1mmcbcTX15eDBw8yf/58zp07x9WrV7Gzs6NFixaMHDmSJk2avLW9UqVKMWHCBCZMmMCAAQOy3Rdc1xSq7Ax5FbnOxcWFiIgInJ2dNQ5E0LWUlBT27dtHy5Ytc2X08odk7Za9jPxuASkp6kdsGxoa8ON4Pwb09JGFa/KAXOsiP0pMTCQsLAx3d3etC7h/k4GP4kOii+s9J6/FnNRr8urLgaSkJPr164eHhwfW1taULVuWxYsX53VaIh/o3akVe9fPo2gRO7X709KUfD1lMUPHzyU5OesKkkIIIYQoWHTSXSQ6OpojR45w8eJFoqOjefbsGXZ2djg6OlKzZk2aNGmilylpcltqaipOTk4cOnQIDw8Prl69SrNmzXB0dMwXy3eKvFWvZhWCdiyj68CJXAm5rTZm7Za93Lx7nw1Lp2gsyIUQQgjx/nvnIjslJYXNmzcTEBDA2bNnAfWTrad/Nf7xxx/j5+dHp06d3tuvay0tLfnhhx8y/l2tWjXatGnDyZMnpcgWALgWd+TQ5kUMGjOT7fsC1cb8deFvPNsNZPOKaXxUsbTaGCGEEEK8396pu8i6detwd3end+/enDlzBnt7e1q3bs23337LnDlz+Omnn5g9ezZjx46lVatWFC5cmL/++otevXrh4eGRo6VR/2vGjBl07NgRDw8PFArFG5coVSqVzJ8/n/Lly2NmZoarqyujRo3i1SvdTKuWkpLCiRMn+Oijj3RyPlEwWJibsWbhJCb599UY8zAqhqadhrBDQyEuhBBCiPdbju9k16tXj7Nnz2Jvb8+wYcPo06cPVatWfetxly9f5pdffmHjxo307t2bpUuXcurUqRwnPG7cOAoXLkyNGjV4/vz5G2NHjhzJokWL8PHxYdSoUVy/fp1FixZx6dIlDh8+nKmDfJcuXdi8ebPGcx07doxGjRpl2jZkyBCsra3p1atXjp+HKNgUCgVfD+5BhTJu9Bs9nfhXr7PEvE5Motew7xlzK5Rxw/rIACUhhBCiAMlxkX379m1mzZrFkCFDMDU1zfZx1apVY+HChcyaNYtFixYxc+bMnDYNwN27d/Hw+Ge52cqVK2ea0P3frl27xuLFi/H19WXbtv+bXs3d3Z1hw4axadOmjEnoAVauXMmSJUs0tvvfORn9/f05ffo0R48ezVhpSIj/+ty7AYe3LKHLwAncC49SGzNzyTqu3Qxj5ZxxWFma6zlDIYQQQuSGHN86Cw0NZdSoUTkqsP/N1NSUr7/+OtOKSjmRXmC/zcaNG1GpVFkmdu/Xrx8WFhZZuqxYW1tjb2+v8fHvfuQjRozgjz/+4MiRI9jb27/T8xAfjkrlPDi2bRmedatrjNnzx0madhqisRAXQgghxPslx3eybWxsdNKwrs6jyblz5zAwMMhYzSmdmZkZ1apV49y5c+903mHDhnH06FGOHTtG0aJF3xo/b9485s2b99a4qKj/K65SUvQzxVt6O/pq70Nma23B/36axvgfl7Nqw261MdduhuLlM5A1CyfSoM7bu2CJ7JNrXeRHKSkpqFQqlEolSqVSZ+dNn4Qg/dxCFGS6uN6VSiUqlYqUlBQMDQ11lluBXfExMjISe3t7tXfcnZ2dOXXqFMnJyTnq6nH//n0WL16Mqakp7u7uGdsbNmzI/v371R7z4sULIiIist1GYmIi+/bty3a8Lvzxxx96be9D1qimB2nJTfh1eyBpat4Mnj5/gc8XY+jp40XT+lJo65pc6yI/MTIywsnJifj4eJKTk3V+/pcvX+r8nELkV9pc78nJybx+/Zrjx4+Tmqp+Ubl0iYmJ2T6vTorsmzdvsmPHDh49eoSLiwvVqlWjZs2a2Nnl3TzACQkJGru0pK/mk5CQkKMiu2TJkmqnKXwTGxsbnJ2d3xoXFRWFUqnEzMyMli1b5qiNd5WSksIff/yBt7f3ezut4vuoZcuWtG/Tkt7DfyD2WVyW/WlKJWu2HUNhZMmMcYMwMZHfjbbkWhf5UWJiIuHh4VhZWel0xUeVSsXLly+xtraWFWZFgaeL6z0xMRFzc3M8PT3f+lrMyWtV6yL76NGjfP755yQlJaFSqTI9QTc3N2rWrEmtWrWoWbMmNWvWpFChQto2mS0WFhbExMSo3Zf+KUQf69j7+/vj7+//1rj0ZToBvRcBxsbGUnjomVf9mgTtWE6XgeP5+4b68Qm/bN7D7bBwfl08maJFCuk3wQJKrnWRn6SlpaFQKDAwMNDp7ELpX5mnn1uIgkwX17uBgQEKhULnfyO0LrInTJhAYmIi3t7etGjRgujoaC5fvsyFCxcICwsjLCwsY3YPhULx1tvwulK8eHFCQkJISkrKckc7IiICe3t7mRVE5KmSLk78sXkJA76Zwe6DJ9TGnDx7hcbtB7Fp+VQqly+l5wyFEEII8a60/oj7999/U7ZsWQ4cOMCIESOYMWMG+/fvJyYmhnv37rF161bGjBlDkyZN9HYXG6B27doolcqM1SjTJSYmcvnyZWrVqqW3XN4kICCAihUrEh0dndepiDxgZWnOusWTGTesj8aY+w8f0bTTEHYfUl+ICyGEECL/0brINjMzo0aNGmr7wZQoUQJfX1+mT5/OH3/8wZMnT7RtLts6d+6MQqFgwYIFmbavXLmShIQEunfvrrdc3sTPz4+QkBAcHR3zOhWRRwwMDPh2WG/WL5mMhbn6vl6vEhLpPngSPy5eK7MFCCGEEO8BrYvsjz/+mMePH+sil2xZt24dU6dOZerUqTx+/Ji4uLiMf69bty4jrkqVKvj5+bF9+3Z8fX1ZtWoVo0aNwt/fHy8vr0wL0QiRH7Rt7sXhLYtxLa75A9e0hWvoPWwKrxKyriAphBAFkZubGwqFgsDAwFxro0ePHigUCtasWZOxbfLkySgUCiZMmPBO51yzZg0KhYIePXpkK/7OnTsoFArc3Nzeqb13ldM8038f6h6GhobY2tpSrVo1Jk6cqHbGj/TYd+0+nN7+nTt33ul4fdK6T/bAgQPp0KEDDx8+xMXFRRc5vdHq1asJCgrKtG3ixIkAeHl50bNnz4ztCxYswM3NjZ9++om9e/dib2/P0KFDmTJligwGEflSlQqlCdqxjB5DJnPq3FW1MTsPBHH3/kM2LZ9KCWcnPWcohBBCQNOmTbN8C5+UlMT9+/e5cOECV65cYc+ePZw8eRJLS8s8yjJvaV1kN27cmM6dO9OhQwf27NmT6ysg5uSTrKGhIaNGjWLUqFG5l5CWAgICCAgIkD7ZIkPRInb8vnYOo6cs4pdNe9TGBF+/i5fPINYHfM8ntT/Sc4ZCCFHwDRkyhC5durxzXePj40PdunWxtbXVcWb5w/jx42nUqJHafcHBwXh7e3P58mUWL17M2LFjM/Zdv34d+Gee+IJO69u5tra2nDp1inPnzlG9enXmzJnDvXv3dJDah0H6ZAt1TEyMWfiDP/MmD8fQUP3L9MnT57TuNUpjIS6EEOLd2dvbU758+Xcusm1tbSlfvjzFihXTcWb5X5UqVTJ6Gfz++++Z9pUvX57y5cvnRVp6p5OBj3fu3EGlUhEREcGYMWMoVaoUxYoVo02bNkyZMoX9+/frddCjEAWBQqGgX4927FozG7tCNmpjUlJSGTZhLqO/X0RKin6mxxRCiLwWGBiIQqFgxIgR3Lx5k44dO2Jvb4+5uTk1a9bkl19+UXvc7du36dmzJ8WLF8fS0hIvLy9OnFA/c9N/+2SPGTPmjX20d+zYgUKhoH379oDmvs4qlYoVK1ZQo0YNLC0tcXFxYezYsbx+nXWszb1791AoFBq74zZq1AiFQsHhw4czbY+MjGT06NFUqVIFa2trTE1NKVGiBL179+bmzZtqz6Vr6X3LY2NjM21X1yf7+fPnGflaWlpia2tL/fr1CQgIyFbf7dTUVHx8fFAoFHh5efHq1SudPpd3pfW9+hcvXnDr1i0uXrzIxYsXuXDhApcvXyY6Opo9e/awd+/ejNgSJUoQFhambZNCfFC86tUgaPsyugycQMgt9a+fFet2cOPOPdYu+o4idgXzq0khPiT9tt7m7+h3LBRUkJaWiqGhEeThgo+VHS1Z2aFMrrZx7do16tSpg5mZGfXr1+fJkyecPn2aL7/8kqdPn2bqLnrhwgW8vb159uwZH330EZ988gnnz5/n008/zdZgw549ezJr1iw2b97M1KlTs+zfsGFDRtyb9O7dm3Xr1mFlZUXTpk1JSEhg7ty5We74vqubN2/SsGFDHj9+TMWKFfnss8+Ij4/n7Nmz/Prrr+zatYvg4GBcXV110p4m+/btA6By5cpvjHv9+jWenp4EBwdTqlQpmjVrRkJCAkFBQZw+fZpz585lGpD6X0qlkkGDBrF7924aNGjA3r17800fcK2LbIVCQbly5ShXrhxdu3bN2B4aGsqFCxcyFd8PHjzQtrkCR/pki+xwL1Gcw1uW8NWoaew7ckptTNDpSzT2HczmFVOpUNZdzxkKIXTp7+hX/PUg68wMIrPDhw/TuXNnVq9enVFYLV68mGHDhjFr1iz8/f1RKBQolUr69u3Ls2fP+PHHHxkzZgwAKSkpDBgwQOOd73+rXLky1atX59KlS5w/fz7TehsvX75k7969FC5cmJYtW2o8x7Zt21i3bh2lSpUiMDAw4w71hQsXaNq0qTY/igxff/01jx8/ZtasWXz99dcZ2+Pi4vjss88yiu3x48frpL1/e/36NWFhYaxZs4alS5dibGyc8bPWZOvWrQQHB9O9e3fWrVuXMSX03bt3qV27NmvXruW7777D3V3937VBgwaxdetW6tevz/79+7GystL583pXuTbFhoeHBx07dmTGjBkcPHiQJ0+eyF1sNaRPtsguaysLNi77ga8Ha55mKSw8kiYd/TQW4kIIUZAYGRmxdOnSTHcuBwwYgKmpKTExMcTExABw6tQprly5QvXq1TMVfcbGxixduhQHB4dstderVy8ANm7cmGn7jh07eP36NZ07d37jatLLli0DYN68eZm6gNSsWTOjD7O2XF1dadeuHf7+/pm229raZkxfrIt6rHHjxlmm8LOwsKBSpUrMnj0bV1dXdu3aRe3atd94nqioqIy8/73mSqlSpfj5559Zt24d1tbWao/19/dn1apV1K5dm3379uWrAhtyschWp0SJEvpsTogCx8DAgEn+fVmzcCLmZqZqY+JfvabLwAnMXroelUql5wyFEEJ/ypQpQ+HChTNtMzExyRismN43N33q3xYtWmQ5h5mZGc2aNctWe127dsXIyIgtW7Zken9NL7rf1FVEqVRy4sQJDA0N8fb2zrK/Xbt22crhbQICAtixYweGhoYZ22JiYjh8+DAnT54E/plqT1tNmzale/fudO/eHR8fH2xs/hk75Obmxr59+wgNDVX78/4vT09PAGbNmkXnzp3ZsGFDxvor7dq1o0ePHmoHn37//ffMnz8fQ0ND1q5dq7EQz0s5LrKHDx+epRN7Tj1+/Jhhw4ZpdQ4hPmTtWzXh0KZFODsVVbtfpVIxZd5qvhjxAwmvE/WcnRBC6IednZ3a7enTw6WvkBsZGQmAs7Oz2nhNXRH+y9HRkc8++4yHDx9mDJh8/Pgxhw8fpnTp0tSrV0/jsbGxsSQnJ1O4cGHMzc2z7NflIjTBwcEMHjyYmjVrYmNjg6OjI97e3mzbtg1AJzdgxo8fz/r161m/fj3bt2/nwYMHNGnShHv37jFp0iQSEhKydZ66desyf/58jI2N2bJlC927d8fR0ZHatWszc+ZMnj17pva49evXY2RkRFpaGosXL9b6+eSGHPfJDggI4JdffsHPz48vv/ySMmWyP6jh5s2brFq1ihUrVvD69WsWLVqU0+aFEP9ftcplOb5zOd0GT+LMxWtqY7btPcbdew/ZuGwqLsWz93WoECLvVXbUYuBWPhr4mNv+3b1Am7iczNncq1cv9u3bx6ZNm/D09OR///sfqampb10x8W05GBgYZLr7nB1paWlZts2ePZtvvvkGgAoVKtC6dWsqVKhA7dq1uXv3Ln5+fjlqI7tsbW3Zvn071apV4/z583Tu3Jl9+/Zl63c0YsQIunXrxo4dO9i/fz9BQUGcP3+e8+fPM3/+fE6ePEnp0qUzHVOtWjVWrVqFp6cnK1asoFevXtStWzdXntu7ynGRfe7cOYYOHcrMmTOZNWsW9erV49NPP6VevXpUqFCBIkWKYGVlRXx8PLGxsYSEhHD69Gn++OMPzp49i0ql4pNPPsm3nzr0TQY+Cm042Bdm77p5jPxuAeu27lcbc/nabbx8B/Lb0inUrfHmUd5CiPxBm1k5lEolL168wMbGRlY3/v/S72Dfv39f7f70O93Z0bZtW2xsbNi2bRtLlixh06ZNAG8tsosUKYKZmRmxsbHEx8dn6T8cHR2dpWhO//2pK6bhn6nv/i0sLIyxY8dia2vLnj17aNCgQab98+fPf+vz04atrS1r166lUaNGHDhwgOXLlzNo0KBsHevg4MCAAQMYMGAASqWSP//8E39/f86fP8+PP/7IqlWrMsWvX7+eSpUqMXHiRL799lv69+/PhQsXMDY2zo2n9k5y/OqrXr06J0+eZMuWLdStW5dTp04xdepUWrVqhYeHB7a2thlr13t4ePD5558zdepUzpw5Q7169fjf//7HiRMnqFatWi48nfePDHwU2jI1NSFgxtfMmjhE4x/UmCfPaNXdX2MhLoQQBVn6zB27du3KUrCmpaVx8ODBbJ/LzMyMjh07EhMTw44dOzh58iT169enVKlSbzxOoVDQpEkTlEolu3btyrL/31Mep0svxJ89e0ZKSkqmfc+fP+fGjRuZtp05cwalUknjxo2zFNgAhw4dAv6vG01u8PT0pH///gB8++23b72J6O/vT7FixTh+/HjGNgMDAxo2bJgxJ3l4eHiW40xN/xmXNHLkSCpUqEBwcDAzZ87U1dPQiXf+iNuhQwf+/PNPLl68yMSJE/nkk0+wsLBApVJlPCwsLGjQoAGTJk3i4sWLnDx5MmOSdiGE7igUCgb1bs+On2dSyEb96OrklBQGj53F2GkBpKaqvysihBAFUe3atWnQoAE3b97k66+/zigylUolo0ePzvFsG+mzjIwYMQKVSvXWubHTjRgxAoDRo0dnLC8OcOPGDcaNG5clvnDhwri4uJCUlMTy5cszticmJjJgwIAsC7UULfrPOJ2//vorY2YV+GeqwokTJ3LgwIGM43PTjBkzcHBwIC4uLtNc5eqUKFGCR48eMW7cOF68eJGxPTU1lc2bNwNQp04djccbGxszb948FAoFU6dOzfLBIy9p/T1StWrVmDx5MsePH+fly5fEx8cTERHBq1evePnyJUFBQUyePFnuXAuhB00a1OLY9mWUK1VSY0zAL1tp33csz+JkDl4hxIfjl19+wcXFhfnz51OhQgU6depEhQoVWLhwIR9//HGOztWwYUPc3Nx4+PAhJiYmdOrUKVvHeXt7M3bsWB49ekT16tVp2bIlLVu2pFq1anh4eKg9Jr1/9bBhw/jkk0/w9fWlZMmSHDp0iDZt2mSKbdSoEdWrV+fRo0eULVuW1q1b06ZNG1xcXJg6dSqVKlUC4NGjRzl6vjllZ2fHnDlzAPjtt984duyYxtiBAwfy8ccf8+eff+Lm5kbLli3x8fGhVKlSbNy4kfLly2eZjvC/6tatS9++fUlKSqJfv375ZmYtnXfWsrCwoFixYmpHzgohcl9pNxeObF1Cs8aaB4Ac/fM8jX0HceOO+v6JQghR0JQuXZqzZ88yaNAgEhIS+P3337G2tmbXrl00b948R+f693LprVq1yjKN4JvMmDGDLVu2UKNGDU6cOMH58+fp3bs3+/er7843dOhQfv31V2rVqsXFixc5fvw4jRo14sKFC1SoUCFTrKGhIUeOHGHkyJEULVqUQ4cOcfz4cTw8PFi+fDmXLl2iUKFCnD17NtfHgvXs2ZPGjRsDMHjwYJKTk9XGmZmZcfDgQcaOHYujoyPHjh3j4MGDWFlZMX78eM6cOaNxFpl/+/HHH3FwcODkyZOZ7vrnJYUqv5T7HzgXFxciIiJwdnbm4cOHemkzJSWFffv20bJly3w1UEDoRlpaGt/PXc38nzZqjLGxsuTnBRNo1ih/jcjWNbnWRX6UmJhIWFgY7u7umJmZ6ey8MvBRfEh0cb3n5LWYk3pNp6++p0+f6vJ0QggtGBoaMuWb/qyaOw4zU/UrkL2If0XHfuNYsHJTvvl6TQghhCgIdFpk29vb4+rqSqtWrRg3bhybN2/m+vXruTqK9X0XEBBAxYoVZQo/kWs6t/XmwMaFFHPMumIW/LMowcSZK+g/egavE7VfBUwIIYQQOi6yly5dSuvWrXn+/DlLliyha9euVK5cGSsrK2rXrk3fvn1ZtGgRQUFBGlfw+dDIFH5CH2p+VJ7jO5ZTq2oFjTGbdv1Bi24jiHz0WI+ZCSGEEAVTjhejeZOBAwdm+vfdu3e5cuUKly9f5urVqxw9epQ1a9YA/wwa+O/UM0KI3OPkUIT9GxYwbMJcNu44pDbmwtUbePkOYuOyH95YkAshhBDizXJ1RESpUqXw9fVlypQpbN++nV9++YXevXtjaGgo/T+FyANmpiasmDWW6d8O0jhA5FFMLM27DtdYiAshhBDi7XK1yH758iX/+9//6NmzJw4ODnz66aecPn2aESNGEBgYmJtNCyE0UCgUDO3bia0rZ2Brbak2Jik5hf5fz2DCzOUal/MVQgghhGY67S4C8ODBA3bv3s3u3bs5fvw4SqWSBg0aMH78eFq3bk3p0qV13aQQ4h14e9Xh6LaldB4wgTthWZesBVi4cjPXb93j5wUTsLVWv5KkEEIIIbLS6Z3satWq4e7uzuTJk3FwcGDt2rU8fvyYo0ePMnLkSCmwhchnynqU4Ni2pTRtWFtjzKGgMzRuP5jbGgpxIYR2pPukEHkrt16DOi2yr169iqmpKc2aNaNGjRoUKVJE4wo/4h8yhZ/Ia4VsrNi6agZD+2peFvh2aDiNfQdx+PhZPWYmRMFmaGgI/LNYkhAi76S/BtNfk7qi0yJ7xowZ+Pj4cOXKFcaMGcNnn32Gk5MTxYsXp0WLFowZM4YNGzZw7do16ef5/8kUfiI/MDQ0ZPq3g1gxeywmGlZEjHv5ivZffcuSn/8nd96E0AFjY2NMTU2Ji4uT15QQeUSlUhEXF4epqanOVwTWaZ/sMWPGZPx/UlIS165d48qVKxmPVatWZcyPbWZmRkJCgi6bF0JoqZtPM0q7udJt8ESiH2ddwVWpVPLt9KX8fTOUhVNGYqphJUkhRPbY29sTERHBw4cPsbW1xdjYGIVCodU5lUolycnJJCYmyrLqosB71+tdpVKRkpJCXFwc8fHxODs76zy3HBfZdnZ2jBkzhrFjx74xztTUlBo1alCjRo1M28PDwzPmzRZC5D91qlfk+I7ldB00kYvBN9XG/LbtALfuPmDD0ik4ORTRc4ZCFBw2NjYAPHnyhIiICJ2cU6VS8fr1a8zNzbUu2IXI77S93k1NTXF2ds54LepSjovsuLg4bt26pXafSqV66xN0dXXF1dWV1q1b57RpIYSeFHcqyoGNCxkybjZbdh9RG3PucghePgPZuHwqNaqU03OGQhQcNjY22NjYkJKSopOulCkpKRw/fhxPT0+df/0tRH6jzfVuaGiYq68RnXYXsbW1ZezYsYwbN06XpxVC5AFzM1NWzR1PpXKlmDxnpdo+o5HRT2jWZRhLf/yGjq0/zYMshSg4jI2NdfIH39DQkNTUVMzMzKTIFgVefr7eddpZKz4+njt37ujylEKIPKRQKPAf0JXNK6ZhbWmhNiYxKZkvR05l8pyVKJVKPWcohBBC5E8yIkII8VYtmtTj6NYAPEoU1xgzd/kGugycyIuXr/SYmRBCCJE/SZEthMiW8mXcOLZ9GY0/qakxZv/RU3za0Y+793QzgEsIIYR4X0mRLYTItsKFbNi+eiaD+7TXGHPjzn0atx9E4KkLesxMCCGEyF/eqcg+f/48AQEBBAUFERsbq+ucPiiy4qN43xgZGTJzwhCWTB+NsbH6sdPP4l7S7otvWP7rdllkQwghxAfpnYrsv//+m2HDhtGkSRMcHBwoVqwY3t7eADx69IjIyEidJlmQyYqP4n3Vu1Mr9q6fR9Eidmr3p6Up+XrKYoaOn0tysiwbLYQQ4sOS4yJ7y5YtjBkzhk8//RQ7OztUKhXR0dEcOfLPXLoHDx7E1dWV4sWL06ZNG3744Qf279/PkydPdJ68ECJv1atZhaAdy6hasYzGmLVb9tKqpz+PY5/pMTMhhBAib+V4nuwOHTrQoUOHjH/fv3+fCxcuZDwuXrzIkydPePToEXv27GHv3r0ZsSVKlCAsLEw3mQsh8gXX4o4c2ryIQWNmsn1foNqYvy78jWe7gWxeMY2PKpbWb4JCCCFEHtB6MZqSJUtSsmRJfH19M7aFh4dnKrovXLhATEwMDx480LY5IUQ+ZGFuxpqFk6hcvhRT5q1WG/MwKgbvzkNZPnMMPi0b6TdBIYQQQs90uuJjuvSl09u1a5exLSIiggsXZLYBIQoqhULB14N7UKGMG/1GTyf+1essMQmvE+k17HvG3Apl3LA+GBjIBEdCCCEKJr39hXN2dqZNmzb6ak4IkUc+927A4S1LcHMtpjFm5pJ1dPf7Tm0hLoQQQhQEchtJCKFzlcp5cGzbMjzrVtcYs+ePkzTtNIR74VF6zEwIIYTQDymyhRC5wr6wLTt/mUX/Hu00xly7GYqX70BO/HVZb3kJIYQQ+iBFthAi1xgbGzF38nAW/jASIyNDtTFPn72gTZ/RrPptl56zE0IIIXKPFNlCiFz3Zdc2/P7rXIrY2ardn5qaxsjvFjBi0nxSUlL1nJ0QQgihe1JkCyH0okGdqgTtWE7l8h4aY1Zv2E2b3qN5HPtcf4kJIYQQuUDnRfapU6c4dOiQrk8rhCgASro48cfmJbRp1lBjzMmzV2jcfhB/37irx8yEEEII3dJ5kd23b19atmyp69MWWAEBAVSsWJHo6Oi8TkUIvbCyNGfd4smMG9ZHY8z9h49o2mkIuw+d0F9iQgghhA7lSncRlUqVG6ctkPz8/AgJCcHR0TGvUxFCbwwMDPh2WG/WL5mMhbmZ2phXCYl0HzyJHxevRalU6jlDIYQQQjvSJ1sIkWfaNvfi8JbFuBbX/CFz2sI19B42hVcJsnCNEEKI94cU2UKIPFWlQmmCdiyjfu2PNMbsPBCEd+ehPIh4pMfMhBBCiHcnRbYQIs8VLWLH72vn8EWXzzXGBF+/i5fPIP48d1WPmQkhhBDvRopsIUS+YGJizMIf/Jk3eTiGhurfmp48fU7rXqP4ZdMePWcnhBBC5IwU2UKIfEOhUNCvRzt2rZmNXSEbtTEpKakMmzCX0d8vkoVrhBBC5FtSZAsh8h2vejUI2r6MCmXcNMasWLcDny+/IfZZnP4SE0IIIbJJimwhRL7kXqI4R/4XQMtP62uMCTp9ica+g7l+K0yPmQkhhBBvJ0W2ECLfsrayYOOyH/h6cA+NMWHhkTTp6Me+I6f0mJkQQgjxZlJkCyHyNQMDAyb592XNwomYm5mqjYl/9ZouAycwZ9lvshiWEEKIfEGKbCHEe6F9qyYc2rQIZ6eiaverVCq+n7uKL0dOJeF1op6zE0IIITKTIlsI8d6oVrksx3cu5+MalTTGbN1zlGZdhvEwMkaPmQkhhBCZ6bzIbt26Nd26ddP1aYUQAgAH+8LsXTePnh1aaIy5fO02Xr4DOXPxmh4zE0IIIf6PzovsWbNmsW7dOl2fVgghMpiamhAw42tmTRyCgYH6t7GYJ89o2X0k67bu13N2QgghhHQXybHBgwfj6uqKjY0Nzs7OjBgxguTk5LxOS4gPjkKhYFDv9uz4eSaFbKzUxiSnpDB47CzG/7ictDSlnjMUQgjxIZMiO4eGDBnCjRs3ePHiBVeuXOHKlStMnz49r9MS4oPVpEEtjm1fRrlSJTXGLFu7nTmrdvI87qUeMxNCCPEhkyI7hypWrIilpSXwz2wGBgYG3L59O4+zEuLDVtrNhSNbl9CscV2NMcG3HuDdeRg37tzXY2ZCCCE+VO9dkT1jxgw6duyIh4cHCoUCNzc3jbFKpZL58+dTvnx5zMzMcHV1ZdSoUbx69UqrHH788UesrKxwcHDgypUrjBgxQqvzCSG0Z2ttxeblUxnZv6vGmLv3I/i0gx8HA//SY2ZCCCE+RO9dkT1u3DiOHj1KqVKlsLOze2PsyJEj8ff3p2LFiixevJiOHTuyaNEiWrdujVKZuX9mly5dUCgUGh+BgYEZsWPHjiU+Pp6QkBAGDhxIsWLFcuOpCiFyyNDQkCnf9GfV3HGYmZqojXkR/4qO/caxYOUmWbhGCCFErjHK6wRy6u7du3h4eABQuXJl4uPj1cZdu3aNxYsX4+vry7Zt2zK2u7u7M2zYMDZt2pRpqsGVK1eyZMkSje3a2tpm2VahQgWqVq1Kz549OXbs2Ls+JSGEjnVu601pd1e6DppIVPSTLPtVKhUTZ67g2o1QFk0bpXElSSGEEOJdvXd3stML7LfZuHEjKpUqS1eOfv36YWFhwfr16zNtt7a2xt7eXuPD2NhYbTspKSncunXrnZ6LECL31PyoPMd3LKdW1QoaYzbt+oMW3UYQ+eixHjMTQgjxIdDbnezo6GiSkpIoUaKEXto7d+4cBgYG1KlTJ9N2MzMzqlWrxrlz53J8zri4OHbs2EG7du2wtbUlODiYqVOn0qxZM43HzJs3j3nz5r313FFRURn/n5KSkuPc3kV6O/pqTwh9K2Jnw+61sxkxcT5bfj+iNubC1Rt4+Qxk3ZLJ1PyovJ4zFEL35L1dfEjy8/WutyK7Xbt2nDt3jtTUVL20FxkZib29PaamWb8GdnZ25tSpUyQnJ2Nior7fpjoKhYL169fj7+9PcnIyDg4O+Pr68v3332s85sWLF0RERGS7jcTERPbt25fteF34448/9NqeEPrW2qsyRooUNv5+Qm0/7EePn9Ky+0j6dmxKg1qa73wL8T6R93bxIdHX9Z6YmJjtWL32ydbnIKOEhAS1BTb8czc7PSYnRbaNjQ2HDx/OUR7pi9a8TVRUFEqlEjMzM1q2bJmjNt5VSkoKf/zxB97e3hq7wwhREKSkpKBQKGjd/FMGjJnFi5dZZxhKSU1j+caDGJvbMMn/SwwNDfMgUyG0J+/t4kOi7+s9vYbMjvdu4GN2WVhYEBMTo3Zf+qcQCwuLXM/D398ff3//t8a5uLhk3PHW95uisbGxvBGLD0KzxvU4tm0pnQdM4E5YuNqYxT//j5t3H/DzggnYWqtfSVKI94G8t4sPSX683nNcZL/r6oY56TKhC8WLFyckJISkpKQsd7QjIiKwt7fP0V3sgiQ2OYVhN+7zpVNhZAIz8aEp61GCY9uW8sXwKRw+oX5sxqGgMzRuP5jNK6ZRxt1VzxkKIYQoCHJcZE+YMAGFQpHjhlQq1Tsd965q167NoUOHOHv2LA0bNszYnpiYyOXLl/H09NRbLm8SEBBAQEAA0dHRemtzTeQTNkTFsiEqFleTItwLj6GPqyOFjAvsFxtCZFLIxoqtq2YwcdZPLF69RW3M7dBwGvsOYs3CSTT1rKM2RgghhNAkx1WVoaEhSqWSHj16YGCQ/RkA9+7dS2xsbE6be2edO3dm+vTpLFiwIFORvXLlShISEujevbvecnkTPz8//Pz8MnUXyU1KlYrl4f9X0IcbGDPy9kPGh0bS1akIg1wdqWlrmet5CJHXDA0Nmf7tICqVc2fY+HkkqxmZHvfyFe2/+pZpYwfi90UHvd4oEEII8X7LcZFdoUIFrl27xvjx4ylbtmy2j6tXr55Oiux169Zx//59AB4/fkxycjJTp04FoGTJkvTs2ROAKlWq4Ofnx5IlS/D19aVly5Zcv36dRYsW4eXllWkhmg/JkdgX3ElIyrI9IU3J6ojHrI54TG0bSwaVcKSzU2EsZPCXKOC6+zanjHsJug2eSPTjp1n2K5VKvp2+lL9vhrJwykhMNawkKYQQQvxbjovsmjVrcu3aNS5evJijIltXVq9eTVBQUKZtEydOBMDLyyujyAZYsGABbm5u/PTTT+zduxd7e3uGDh3KlClTcnQXviBZFv72binnXrzi3N+h+N+4Tx/nogx0daCcpbkeshMib9SpXpHjO5bTddBELgbfVBvz27YD3A4NZ8PSKTgWLaznDIUQQrxvclxp1qxZE5VKxaVLl3J0nK6m7wsMDESlUql9BAYGZoo1NDRk1KhR3Lx5k6SkJCIiIpg3bx5WVvlnxoCAgAAqVqyolz7ZKpWKilbm2Gez7/Xz1DQW3H9E+ZNX+fTcdbY+iiVFqczlLIXIG8WdinJg40I6tflUY8zZS9fwbDdAYyEuhBBCpMtxkf3ZZ58xfPhwypUrl6Pjli1bxtGjR3PaXIHn5+dHSEgIjo6Oud6WQqFgahlXHjaqzm9VStHANvsfNo4+fUHHK3coefwyk24/JPx11i4nQrzvzM1MWTV3PN9/3V9j/+vI6Cc06zKMrXvk/UwIIYRmOS6yy5Yty/z58/nyyy9zdFz16tXx8vLKaXMiF5gaGNCtuD1Ha5ZlYdITBjrbY22YvUshKimFH0IjcDt+mbYXb3Lg8XOUelxkSIjcplAo8B/Qlc0rpmFtqX4u/cSkZL4Y8QOT56xEKd/uCCGEUOPD7JgsMpRUpbKoXAkiG9VgRUV3qllnb4EeJbD78XNaXLxJmRNXmBUWyZPkrLMzCPG+atGkHke3BuBRorjGmLnLN9Bl4ES1K0gKIYT4sEmRncf02Sf7TayMDOnv6sDFepU5/XFFehW3x9Qge9OVhb5OYsytcJwDL9Hj6h3+fPZSZ33whchL5cu4cWz7Mhp/UlNjzP6jp/i0ox+h9/W74JYQQoj8TYrsPKbPPtnZoVAoqFvImrVVShHhVZ055UpQ2sL07QcCySoVv0XF0uBsCFVPBbPsQTQvU9NyOWMhclfhQjZsXz2TwX3aa4y5cec+jXwHEXjqgh4zE0IIkZ9JkS00KmJizCi3YtxsUJVDNcvj42CHYTbX4giOf83g6/coHniRQSFhXH2ZkLvJCpGLjIwMmTlhCEumj8ZYw+w8z+Je0u6Lb1j+63b5JkcIIYQU2eLtDBQKvO1t2V69LPc9q/NdKWeKmxpn69j4NCXLw2OoeiqYT85cY33kExLTZKCYeD/17tSKvevnUbSIndr9aWlKvp6ymKHj55IsYxSEEOKDJkW2yBFnMxMml3bhnmc1tlcrg3cRm2wfe+p5PD2D7+ISdImvbz7gbkJiLmYqRO6oV7MKQTuWUbViGY0xa7fs5fNeo3gc+0yPmQkhhMhPpMjOY/ll4GNOGRsY4ONYmEO1KnCrQVVGuTlROJuL3MSmpDLnXhSlT1yh2fkb7Ix+SqpSvl4X7w/X4o4c2rwI35aNNMacPh+MZ7uBXA25o7/EhBBC5BtSZOex/Dbw8V2UsTRjTrmSPPSqztrKHtTNwSI3h2Lj8Ll8G/cTl5ly5yGRicm5mKkQumNhbsaahZOY5N9XY8zDqBi8Ow9lx75A/SUmhBAiX9BLkf369WuOHz/O8ePHuXjxIq9eyZyyBZG5oQG9nItyum4lLtWrTH8XByyzucjNw8RkvrsbQYnjl+hw+RZHYuNk8JjI9xQKBV8P7sHGZT9gZWmuNibhdSK9hn3P1AU/y8I1QgjxAdFLkf3gwQMaN26c8XB0dGTlypX6aFrkkWo2lqyo5E5ko+oEVHCjspX6AuS/0lSwLfoZTc/foPzJq8y7F8XT5NRczlYI7Xzu3YDDW5bg5lpMY8zMJevo7vcd8a9e6zEzIYQQeUVv3UXS70rGxcVx4MABZs+eTUKCTOtW0NkYGTG4hCNX61fhRJ2KdCtWBBNF9uYBvJWQyKibD3AOukif4LuceR4vd7dFvlWpnAfHti3Ds251jTF7/jhJ005DuBcepcfMhBBC5AW9FNnlypVDqVSSlvbPwiQNGjTg+vXrWFhkbwlv8f5TKBQ0sLPmt49KE+5VnR/LuOJunr1FbhKVKtZGPqHumWvUPP03K8NjeCWL3Ih8yL6wLTt/mUX/Hu00xly7GYqX70BO/HVZb3kJIYTQvzwb+GhoaJhXTYs85mBqzBiP4txpWJV9NcrRumihbF+Il14m0D8kjOJBlxh6/R4h8fJtiMhfjI2NmDt5OAt/GImRkfr3uafPXtCmz2hW/bZLz9kJIYTQF5ldJI+9r1P46YKBQkGLooXYXaMcYZ7VGO9RHEeT7C1y8yI1jSUPoqn0ZzBeZ0PYFBVLsgwqE/nIl13b8PuvcyliZ6t2f2pqGiO/W8CISfNJSZFxB0IIUdDotMiOiopiy5YtzJ07l127/rlDc/78eVJSZOUzTQrCFH66UMLclKllXHngVY3NVUvTuHD2F7k5/uwlXa/ewTXoEuNuhXPvdVIuZipE9jWoU5WgHcupXN5DY8zqDbtp03s0j2Of6y8xIYQQuU4nRXZcXBy9evWiZMmSdO3alW+++YZt27YBMHz4cNzd3Tlz5owumhIFnImBAZ2cinC0dgWuf/IRw0s4YavhK/f/iklOZUZYJB7HL9Pqwk32xDwjTQZKijxW0sWJPzYvoU2zhhpjTp69QuP2g/j7xl09ZiaEECI3aV1kJyQk0KRJE9avX0+RIkXo0KFDphkgTExMiIyMxNvbm9DQUG2bEx+Q8lbmLKhQkshG1VldyZ1aNpbZOk4F7HvynNaXblHq+GWmh0YQnSTfpoi8Y2VpzrrFk/l2aG+NMfcfPqJppyHsPnRCj5kJIYTILVoX2bNnz+bSpUv06dOHsLAwNm/enGn/sWPH+Pbbb4mPj2fmzJnaNic+QBaGhnzp4sC5epU5V7cSXzoXxdwge5fu/cRkxt9+iGvQJbpcuU3Q0xcyDaDIEwYGBowb3of1SyZjYW6mNuZVQiLdB09i5pJf5ToVQoj3nNZF9ubNm3F2dmbFihWYman/wzF16lQ8PDwIDAzUtjnxgatla8Xqyh5ENKrOgvIlKW+p/pr7rxSVis2PntLo3HUq/xnM4vuPiJPBZiIPtG3uxeEti3EtrnkcxtQFv9Br6Pe8SpCFa4QQ4n2ldZEdFhZG3bp1MTbWPCuEQqGgatWqhIeHa9ucEADYGRsxvKQTIZ98xNFa5enoWBijbC5yE/LqNcNu3Kd40CX6/R3KxRevcjlbITKrUqE0QTuWUb/2Rxpjdh4IwrvzUB5EPNJjZkIIIXRF6yLb0tKSR4/e/kcgMjJSFp9R40Oewk8XFAoFjYvYsqVaGcK9qjG1tAslzEyydWxCmpJVEY+pefpv6pz+m18iHpOQJovcCP0oWsSO39fO4Ysun2uMCb5+Fy+fQZw6H6zHzIQQQuiC1kV2nTp1OHfuHNeuXdMYc/nyZS5cuECdOnW0ba7AkSn8dMfJ1ITxpZwJ9azG7uplaWFvS/bubcO5F6/48u9QnAMvMfLGfW6+kq/pRe4zMTFm4Q/+zJs8HEND9W/HT54+5/Oe/vyyaY+esxNCCKENrYtsf39/kpOTadWqFbt27SIuLi5jX0pKCnv27KFdu3akpaXh5+enbXNCvJWhQkFrBzv21SzPnYZVGeNeDHtjo2wd+zw1jQX3H1H+5FU+PXedrY9iSZFFbkQuUigU9OvRjl1rZmNXSP388CkpqQybMJfR3y+ShWuEEOI9oXWR3bRpU6ZPn054eDi+vr4ULlwYhULB1q1bsbCwoG3btjx48IDRo0fTqlUrXeQsRLZ5WJjxY9kSPGxUnd+qlKJBIetsH3v06Qs6XrlDyeOXmXT7IeGyyI3IRV71ahC0fRkVyrhpjFmxbgc+X35D7LM4jTFCCCHyB50sRjN27FgOHz7MZ599hrm5OSqVisTERAwMDGjYsCE7duyQ6ftEnjI1MKBbcXtOfFyRq/WrMNjVAWsNX8//V1RSCj+ERuB2/DLtLt3i4JPnKGV6NZEL3EsU58j/Amj5aX2NMUGnL9HYdzDXb4XpMTMhhBA5pbNl1Rs3bsz+/ft58eIF0dHRREZGEh8fT2BgIG3bttVVM0JorYq1BQEV3YlsVIMVFd2pZp29AblKYFfMM5pfuEmZE1eYFRbJk2RZ5EbolrWVBRuX/cDXg3tojAkLj6RJRz/2HTmlx8yEEELkhM6K7J07d7Jw4UIMDAwoWrQoTk5OnDx5El9fX3bs2KGrZoTQGSsjQ/q7OnCxXmVOf1yRXsXtMTXI3lDJ0NdJjLkVjnPgJXpcvcOfz17K4iFCZwwMDJjk35c1CydibmaqNib+1Wu6DJzAnGW/ybUnhBD5kNZFdmpqKl27dqV9+/b89NNPmfZdv36dnTt30qFDB/r3769tU0LkCoVCQd1C1qytUooIr+rMKVeC0hbqC5v/Slap+C0qlgZnQ6h6KphlD6J5mSrTAArdaN+qCYc2LcLZqaja/SqViu/nruLLkVNJeJ2o5+yEEEK8idZF9sqVK9m8eTPlypVj+vTpmfb17duXffv2UaFCBVavXs3y5cu1bU6IXFXExJhRbsW42aAqh2qWx8fBDsNszgMYHP+awdfvUTzwIoNCwrj6MiF3kxUfhGqVy3J853I+rlFJY8zWPUdp1mUYDyNj9JiZEEKIN9G6yF69ejV2dnacPHkyS99rU1NTmjdvzrFjx7Cxsclyp1uI/MpAocDb3pbt1cty37M635Vyprip5lVN/y0+Tcny8BiqngrmkzPXWB/5hMQ0mQZQvDsH+8LsXTePnh1aaIy5fO02Xr4DOXNR85oFQggh9EfrIvv27dt4enpSuHBhjTFFixalQYMG3LhxQ9vmChxZ8TH/czYzYXJpF+55VmN7tTJ4F1E/l7E6p57H0zP4Li5Bl/j65gPuJshX+uLdmJqaEDDja2ZNHIKBgfq37pgnz2jZfSTrtu7Xc3ZCCCH+S+si29TUlFevXr01Li0tDWPj7N0J/JDIio/vD2MDA3wcC3OoVgVuNajKKDcnCmdzkZvYlFTm3Iui9IkrNDt/g53RT0lVymA1kTMKhYJBvduz4+eZFLKxUhuTnJLC4LGzGDstgFQZHyCEEHlG6yK7atWqnDhxgtu3b2uMuX//PoGBgVStWlXb5oTIF8pYmjGnXEkeelVnbWUP6tqqL3jUORQbh8/l27ifuMyUOw+JTEzOxUxFQdSkQS2ObV9GuVIlNcYE/LKVDl+N5VncSz1mJoQQIp3WRfbgwYNJSkqiadOmbNu2jcTE//s6PCkpid27d/Ppp5+SlJTEoEGDtG1OiHzF3NCAXs5FOV23EpfqVaa/iwOW2Vzk5mFiMt/djaDE8Ut0uHyLI7FxMhWbyLbSbi4c2bqEZo3raow5cvI8jdsP5sad+3rMTAghBOigyPbx8cHPz4/w8HA6deqEtbU1Tk5OODk5YW1tjY+PD6GhoXz11Vd07dpVFzkLkS9Vs7FkRSV3IhtVZ0mFklSyMs/WcWkq2Bb9jKbnb1D+5FXm34viaXJqLmcrCgJbays2L5/KyP6a31vv3nvIpx38OBj4lx4zE0IIoZPFaBYvXsy2bdto0qQJhoaGxMTEEBMTg0KhoH79+mzcuJEVK1booikh8j0bIyP8SjgRXL8Kx+tUoFuxIpgosjcP4K2ERPxvPsA56CJfBN/lzPN4ubst3sjQ0JAp3/Rn1dxxmJqoH/fyIv4VHfuNY8HKTXI9CSGEnmRv1FY2+Pj44OPjA0BsbCypqakUKVIEIyOdNSHEe0WhUNDQzoaGdjbML5fCLxGPWfEwhrDXSW89NlGpYk3kE9ZEPqG6tQWDXB3pVqwIlkaGeshcvI86t/WmtLsrXQdNJCr6SZb9KpWKiTNXcO1GKIunj8bM1CQPshRCiA+HzpZV/7ciRYrg6OgoBbYQ/5+DqTFjPIpzp2FV9tUoR+uihbL94rv0MoH+IWEUD7rE0Ov3CImXRW6EejU/Ks/xHcupVbWCxphNu/6gRbfhagtxIYQQuqOTIvvs2bN07tyZSpUq4ebmRokSJdQ+SpbUPBJeiA+BgUJBi6KF2F2jHGGe1RjvURxHDV/x/9eL1DSWPIim0p/BeJ0NYVNULMlKWeRGZObkUIT9GxbQtZ23xpjzV27g6TOQ81eu6zEzIYT4sGh9q/nUqVM0adKElJSUt/b1U2SzX6oQH4IS5qZMLePKpFLO7Ix5xrIH0QQ+y950a8efveT4s5c4mBjR19mB/q4OuJmb5nLG4n1hZmrCitnfUrl8aSbOWoFSzYexRzGxNO86nCXTv6bLGwpyIYQQ70brInvKlCkkJyfTsWNHhgwZQvHixaWbiBA5YGJgQCenInRyKsL1+NcsD49mbeQT4rKxkEhMciozwiL5MSySlkULMcjVgeb2hTCUD7QfPIVCwbCvOlGhjBtfjJhC3Musi4YlJafQb/R0/r55l+9H98PQUPr8CyGErmhdDZ8+fZqyZcuyefNmXeQjxAetgpU5Cyu4MaOsK5uiYlkWHsP5F29fUVUF7H38nL2Pn1PSzIT+rg70dXbA0VRWWf3QeXvV4ei2pXQeMIE7YeFqYxau3Mz1W/f4ecEEbK2zv7CSEEIIzbTuk61SqahcubIuchFC/H8WhoZ86eLAuXqVOVe3El86F8XcIHsv1/uJyYy//RDXoEt0uXKboKcvZNq2D1xZjxIc27aUpg1ra4w5FHSGxu0Hc1tDIS6EECJntC6yq1evzrVr13SRywcpICCAihUrEh0dndepiHyqlq0Vqyt7ENGoOgvKl6S8pVm2jktRqdj86CmNzl2n8p/BLL7/iLgUWeTmQ1XIxoqtq2YwtG8njTG3Q8Np0n4wR06c02NmQghRMGldZI8dO5abN2+ycOFCXeTzwfHz8yMkJARHR8e8TkXkc3bGRgwv6UTIJx9xtFZ5OjoWxiibfa9DXr1m2I37FA+6RL+/Q7mYjS4oouAxNDRk+reDWD5rDCbG6rsSPX8Rj2/fsSz5+X/yDYgQQmhB6z7ZKSkp+Pj44O/vz7p166hbty52dnZqZxJRKBR8//332jYpxAdNoVDQuIgtjYvY8igpmdUP/1nkJjwx+a3HJqQpWRXxmFURj6ltY8mgEo50diqMhQx4+6B0921OGfcSdBs8kejHT7PsVyqVfDt9KX/fDGXhlJGYysI1QgiRY1oX2e3atUOhUKBSqbh48SIXL17MEpO+X4psIXTLydSE8aWcGetRnH2Pn7MsPJoDT+LIzv3Hcy9ece7vUPxv3KePc1EGujpQztI813MW+UOd6hU5vmM5XQdN5GLwTbUxv207wO3QcDYsnYJj0cJ6zlAIId5vWhfZkyZNkvmvhchjhgoFrR3saO1gR2hCIj89jGH1w8c8yUYf7OepaSy4/4gF9x/RpLANg1wdaOtgh3E2B1qK91dxp6Ic2LiQIeNms2X3EbUxZy9dw7PdADYun0qNKuX0nKEQQry/tC6yJ0+erIM0hBC64mFhxo9lS/B9aRe2PXrKsvAYTj7P3iI3R5++4OjTFxQzNeYrZwf6uRTFVRa5KdDMzUxZNXc8lcqVYvKclWr7YUdGP6FZl2EsmzmGDp83yYMshRDi/aPXW1WXLl3SZ3NCfNBMDQzoVtyeEx9X5Gr9Kgx2dcDaMHsv+aikFH4IjcDt+GXaXbrFwSfPUcoguAJLoVDgP6Arm1dMw9rSQm1MYlIyX4z4gclzVqpdQVIIIURmOlma8eLFi6xYsYKwsDCSkpIy3QlRKpUkJiYSHR1NVFQUqakyhZgQ+lbF2oKAiu7MLFuC36KesCw8hisvE956nBLYFfOMXTHP8DA3ZaCrA184F8XeRBa5KYhaNKnH0a0BdB4wntAHkWpj5i7fQMite6yaOw4ba0s9ZyiEEO8PrYvs8+fP07BhQ5KTkzOK6/SBjunS/12lShVtmxNCaMHKyJABro70d3HgTFw8y8Jj2PwoliTl2+9Sh75O4ptb4Uy4/ZCOToUZ5OpI/UJWMiajgClfxo1j25fRZ/gUjv15QW3M/qOn+LSjH5tXTMOjpLOeMxRCiPeD1t1FZs6cSVJSEm3atGHnzp0MHDgQhULBrl272L59OwMGDEChUFCpUiXOnZMFDoTIDxQKBXULWbO2SikivKozp1wJSltkr+91skrFb1GxNDgbQtVTwSx7EM3L1LRczljoU+FCNmxfPZPBfdprjLlx5z6NfAcReEp9IS6EEB86rYvsP//8EycnJzZv3kybNm3o2rUrSqUShUJBu3btWLZsGUuWLCEkJIRFixbpImchhA4VMTFmlFsxbjaoyqGa5fFxsMMwmzeng+NfM/j6PYoHXmRQSBhXs9EFRbwfjIwMmTlhCEumj8bYWP2Xns/iXtLui29Y/ut2WbhGCCH+Q+siOzY2lpo1a2Ji8s9iBeldQs6fP58RM3DgQFxdXdm0aZO2zQkhcomBQoG3vS3bq5flvmd1vivlTHHT7PW9jk9Tsjw8hqqngvnkzDXWRz4hMU0GxxUEvTu1Yu/6eRQtYqd2f1qakq+nLGbo+LkkJ6foOTshhMi/tC6yzc3NMwpsgEKFCmFnZ8eNGzcyxdWoUYPbt29r25wQQg+czUyYXNqFe57V2F6tDN5FbLJ97Knn8fQMvotL0CW+vvmAuwmJuZip0Id6NasQtGMZVSuW0RizdstePu81isexz/SYmRBC5F9aF9llypThypUrmbaVLVuWCxcy99NLTEyUmUWEeM8YGxjg41iYQ7UqcKtBVUa5OVFYQ9eB/4pNSWXOvShKn7hCs/M32Bn9lNRsDLAU+ZNrcUcObV6Eb8tGGmNOnw/Gy2cQV0Pu6C8xIYTIp7Quslu1akVYWBgjRowgLi4OgE8++YTQ0FB+//13AG7dukVgYCDu7u7aNieEyCNlLM2YU64kD72qs7ayB3VtrbJ97KHYOHwu38b9xGWm3HlIZGJyLmYqcouFuRlrFk5ikn9fjTHhkdF4dx7Kjn2B+ktMCCHyIa2L7BEjRuDu7s7ixYvp1q0bAH5+fhgaGtK+fXtq1qxJjRo1SEpKomvXrlonnF+8fv2a0qVLY2WV/UJDiILA3NCAXs5FOV23EpfqVaa/iwOW2Vzk5mFiMt/djaDE8Ut0uHyLI7FxMmDuPaNQKPh6cA82LPsBK0tztTEJrxPpNex7pi34RRauEUJ8sLQusgsVKsTp06fx8/OjTp06ALi7u7N27VrMzMy4dOkSCQkJtG7dmtGjR2udcH4xadIkSpYsmddpCJGnqtlYsqKSOxFe1VlSoSSVrNQXXf+VpoJt0c9oev4G5U9eZf69KJ4mS3ey90lr7wYc3rIEN9diGmN+XPIrPYZMJv7Vaz1mJoQQ+YNOllUvWrQoixYt4rvvvsvY1rVrV6Kiojh9+jR37txh586dmJpmbx7e/O7ChQscOHCAMWPG5HUqQuQLtsZG+JVwIrh+FY7XqUC3YkUwyeYiNbcSEvG/+QDnoIt8EXyXM8/j5e72e6JSOQ+ObVtGw4+raYz5/dAJmnYawr3wKP0lJoQQ+YBOimxNLC0t+fjjj/Hw8NDZOWfMmEHHjh3x8PBAoVDg5uamMVapVDJ//nzKly+PmZkZrq6ujBo1ilevXr1z+6mpqfTr14+AgIBMs6oIIf7pStDQzobfPipNuFd1fizjirt59j5cJypVrIl8Qt0z16h5+m9WhsfwSha5yffsC9uya81s+nVvqzHm2s1QvHwHcuKvy/pLTAgh8liuFtm5Ydy4cRw9epRSpUphZ6d+3tZ0I0eOxN/fn4oVK7J48WI6duzIokWLaN26dZZ+gl26dEGhUGh8BAYGAjB79myqV6+Op6dnbj1FIQoEB1NjxngU507DquyrUY7WRQtl+w3n0ssE+oeEUTzoEkOv3yMkXha5yc+MjY2Y9/0IFv4wEiMjQ7UxT5+9oE2f0az6bZeesxNCiLyhUOXwe9kmTZq8e2MKBUeOHHnn4wFCQ0Mz7oxXrlyZ+Ph47t27lyXu2rVrVKlSBR8fH7Zt25axffHixQwbNozffvstY6AmwMuXL0lKStLYrq2tLffv3+fTTz/l0qVLFC5cmMDAQD7//HPi4+O1ek4ALi4uREREYFLIgRpTD2p9vuxQqVQ8f/acQnaFUGTzq30htJGkVBKTnEpMUgopOewSYm1kiJOJMYWNjcjp5SrXuv68jE/gdlg4qW/4FsLB3o6SLk7yu8glcr2LD4m+r/eLE5qR/DwGZ2dnHj58+MbY7E14+y/pd3T/S6FQaOxHmb5PF08+u11PNm7ciEqlYsSIEZm29+vXj7Fjx7J+/fpMRba1tTXW1tZvPOfJkyeJjo6mbNmyAKSkpPDq1Svs7e3Zvn27Tu5uJ6eq+OvBS63Pk31GoIMPCULktpek8hJtBkfKta43tsXfuPuRCh6Fy+8id8n1Lj4kerzeU7N/gyjHRfYff/yR6d9paWn4+/tz+/ZtBg4cSLt27XB3d8fIyIjIyEj27NnDvHnzqFatGr/88ktOm3tn586dw8DAIGPGk3RmZmZUq1aNc+fO5ficnTp1omnTphn/Pn36NH369OHy5csULVpU7THz5s1j3rx5bz13VJQMChJCCCGEKChyXGR/+umnmf49a9Ysbty4wd69e2nWrFmmfS4uLtSpU4fPPvuMxo0bs2bNGqZNm6ZdxtkUGRmJvb292hlNnJ2dOXXqFMnJyTkavGhhYYGFhUXGv4sWLYpCocDFxUXjMS9evCAiIiJnyQshhBBCiPdajovs//rpp59o0KBBlgL73xo0aECjRo1Yt26d3orshIQEjVMGmpmZZcRoM0NIo0aN3tof28bGBmdn57eeKyoqShZtEEIIIYQoILQusqOioqhevfpb46ysrHj69Km2zWWbhYUFMTExavclJiZmxOQ2f39//P393xqXMfDRSEGNEm/uG64rMjhG5HepKhWPk1OJTk4hMS1nH0LNDQ1wNDGmqIkRBiDXeh5LeJ3I7dBwkpJTNMYULmSDR8niGBi8dxNf5Svy3i4+JHof+GikIDmbsVoX2W5ubgQFBfHy5UuNAwejoqI4cuQI5cqV07a5bCtevDghISEkJSVluaMdERGBvb19vpznuqilMaf9qumlrZSUFPbt20fLlg0wNjbWS5tCvAuVSkXg0xcsC49hR8wzUrMxM8lr4B5KYgxT6eJgR6V7kQxtIdd6XnocW44eQyZz6txVtfsTAcMKpdi0fColnJ30m1wBIu/t4kOi7+vdZYYxEc+zF6v17YJevXrx5MkTmjdvzrVr17LsP336NN7e3rx69YqBAwdq21y21a5dG6VSydmzZzNtT0xM5PLly9SqVUtvubxJQEAAFStWJDo6Oq9TESLfUigUNC5iy5ZqZXjgVY0fSrvgapa9D8kJaUp+jopllKk9n5y/wZqIxySkySI3eaFoETt+XzuHL7p8rjEm+PpdvHwGcep8sB4zE0II3dO6yPb396dx48acPn2ajz76CFdXV+rWrUvdunUpVqwYDRo0ICQkhK5du9KvXz9d5JwtnTt3RqFQsGDBgkzbV65cSUJCAt27d9dbLm/i5+dHSEgIjo6OeZ2KEO+FYqYmTCjlTJhnNXZXL0sLe1uy+wXhuRcJfPF3KM6Blxh54z43X73O1VxFViYmxiz8wZ95k4djaKj+T9CTp8/5vKc/v2zao+fshBBCd7TuLmJsbMzBgwdZuHAhy5cv5+7du5lm06hYsSIjR46kb9++2jYFwLp167h//z4Ajx8/Jjk5malTpwJQsmRJevbsCUCVKlXw8/NjyZIl+Pr60rJlS65fv86iRYvw8vLKNEe2EOL9Y6hQ0NrBjtYOdoQmJPLTwxhWP3zMk5S3z6X9PDWNBfcfseD+I5oUtmGQqwNtHewwlr7AeqFQKOjXox1lS5Wg59Dvefb8RZaYlJRUhk2Yy7WbocwYNxhjY63/XAkhhF7leMXHt4mMjCQyMhKFQoGzszNOTrrtV9eoUSOCgoLU7vPy8sq0WE5aWhoLFizgp59+4t69e9jb29O5c2emTJmClZWVTvPSVvrAx+ysIKQr/9ePqaX02xMFQpJSybZHT1kWHsPJ5zlb1KmYqTFfOTvQz6UorubqZyYSuhf2IJLOA8Zz/fY9jTFe9aqzdtF3FLGz1V9i7zF5bxcfEn1f7zmp13R62yYqKoqTJ08SFBTEw4cPcXJy4vz586SkaB5NnlOBgYGoVCq1j/+uRmloaMioUaO4efMmSUlJREREMG/evHxVYEufbCF0x9TAgG7F7TnxcUWu1q/CYFcHrDV0SfivqKQUfgiNwO34ZdpdusXBJ89R6vYehFDDvURxjvwvgJaf1tcYE3T6Eo19B3P9VpgeMxNCCO3opMiOi4ujV69elCxZkq5du/LNN9+wbds2AIYPH467uztnzpzRRVMFjvTJFiJ3VLG2IKCiO5GNahBQzhU3ZfY+7CuBXTHPaH7hJmVOXGF2WCRP3jDtnNCetZUFG5f9wNeDe2iMCQuPpElHP/YdOaXHzIQQ4t1pXWQnJCTQpEkT1q9fT5EiRejQoQP/7oFiYmJCZGQk3t7ehIaGatucEELkiJWRIf2cizI/OZYTNcvRq7g9pgbZGyoZ+jqJb26F4xx4iR5X7/Dns5fouIed+P8MDAyY5N+XNQsnYm6mvrtO/KvXdBk4gTnLfpPfgxAi39O6yJ49ezaXLl2iT58+hIWFsXnz5kz7jx07xrfffkt8fDwzZ87UtjkhhHgnCuBjW0vWVilFhFd15pQrQWmL7PW9Tlap+C0qlgZnQ6h6KphlD6J5mSrTAOaG9q2acGjTIpydiqrdr1Kp+H7uKr4cOZWE14l6zk4IIbJP6yJ78+bNODs7s2LFiozlyv9r6tSpeHh4ZOkzLaRPthB5oYiJMaPcinGzQVUO1SyPj4MdhtmcBzA4/jWDr9+jeOBFBoWEcfVlQu4m+wGqVrksx3cu5+MalTTGbN1zlOZdhxMR9ViPmQkhRPZpXWSHhYVRt27dN47oVCgUVK1alfDwcG2bK3CkT7YQecdAocDb3pbt1cty37M635Vyprhp9kanx6cpWR4eQ9VTwXxy5hrrI5/keOl3oZmDfWH2rptHjw7NNcZc+vsWnj4DOHMx60JoQgiR17Qusi0tLXn06NFb4yIjI7GwsNC2OSGEyBXOZiZMLu3CPc9qbKtWhqZFbLJ97Knn8fQMvotL0CW+ufmAuwnSjUEXTE1NWDrjG2ZO8MNAwxzmMU+e0bL7SNZvO6Dn7IQQ4s20LrLr1KnDuXPn1C6pnu7y5ctcuHCBOnXqaNucEELkKmMDA3wdC/NHrQrcalCVUW5OFM7mQiixKanMvhdF6RNXaH7+Bjujn5KqlAF62lAoFAzu04EdP8+kkI366VeTU1IYNGYmY6cFkCp95YUQ+YROllVPTk6mVatW7Nq1i7i4uIx9KSkp7Nmzh3bt2pGWloafn5+2zQkhhN6UsTRjTrmSPPSqztrKHtS1zf4c+wdj4/C5fBv3E5eZcuchkYnJuZhpwdekQS2ObV9G2VIlNMYE/LKVDl+N5VlczhYiEkKI3KB1kd20aVOmT59OeHg4vr6+FC5cGIVCwdatW7GwsKBt27Y8ePCA0aNH06pVK13kXKDIwEch8j9zQwN6ORfldN1KXKpXmf4uDlhmc5Gbh4nJfHc3ghLHL9Hh8i2OxMbJ9HPvqLSbC0e3BtCscV2NMUdOnqdx+8HcvPtAj5kJIURWOlmMZuzYsRw+fJjPPvsMc3NzVCoViYmJGBgY0LBhQ3bs2CHT92kgAx+FeL9Us7FkRSV3Iryqs6RCSSpZmWfruDQVbIt+RtPzNyh/8irz70XxNDk1l7MteGytrdi8fCoj+3fVGHP33kOatB/MwcC/9JiZEEJkprNl1Rs3bsz+/ft58eIF0dHRREZGEh8fT2BgIG3bttVVM0IIkS/YGhvhV8KJ4PpVOF6nAl2dimCsyN48gLcSEvG/+QDnoIt8EXyXs8/j5e52DhgaGjLlm/6smjsOUxP1s8G8iH9Fx37jWLByk/xshRB5QmdFdsYJDQwoWrQoTk5Ob5zWTwghCgKFQkFDOxs2VC3NQ6/qzCjjipt59ha5SVSqWBP5hI/PXKPWX3+z6mEMr2TgXrZ1buvNwU2LKOZor3a/SqVi4swV9B89g8Qk6RMvhNAvnRbZUVFRbNmyhblz57Jr1y4Azp8/T0pKii6bEUKIfMnB1JixHsW527Aq+2qUo3XRQtl+k734IoF+18IoHnSJodfvERIvi9xkR82PynN8x3JqVa2gMWbTrj9o0W04UdFP9JiZEOJDp5MiOy4ujl69elGyZEm6du3KN998w7Zt2wAYPnw47u7unDlzRhdNCSFEvmegUNCiaCF21yhHmGc1xnsUx1FDt4b/epGaxpIH0VT6MxivsyFsioolWSmL3LyJk0MR9m9YQNd23hpjzl+5gafPQM5fua7HzIQQHzKti+yEhASaNGnC+vXrKVKkCB06dMjU/83ExITIyEi8vb0JDQ3VtjkhhHivlDA3ZWoZVx54VWNz1dI0srPO9rHHn72k69U7uAZdYtytcO69TsrFTN9vZqYmrJj9LdPGDtK4cM2jmFiadx3Opp1/6Dk7IcSHSOsie/bs2Vy6dIk+ffoQFhbG5s2bM+0/duwY3377LfHx8TLDiBoyhZ8QHwYTAwM6ORXhWJ2KhHzyEcNKOGJrZJitY2OSU5kRFonH8ct8fvEmex8/I00G82WhUCgY9lUntq6cga21pdqYpOQU+o2ezoSZy0lLk/7vQojco3WRvXnzZpydnVmxYgVmZmZqY6ZOnYqHhweBgYHaNlfgyBR+Qnx4KliZs7CCG5GNqrO6kju1bNQXhP+lAvY+fs7nF29R6vhlpodGEJ0kY17+y9urDke3LaW0u6vGmIUrN9Op/3jiXsbrMTMhxIdE6yI7LCyMunXrvnEmEYVCQdWqVQkPD9e2OSGEKDAsDA350sWBc/Uqc65uJb50Loq5hq4O/3U/MZnxtx/iGnSJLlduE/T0hUxV9y9lPUpwbNtSmjasrTHmUNAZGrcfzO0w+dskhNA9rYtsS0tLHj169Na4yMhILCwstG1OCCEKpFq2Vqyu7EFEo+osKF+Scpbqvxn8rxSVis2PntLo3HUq/xnM4vuPiEuRRW4ACtlYsXXVDIb27aQx5nZoOE3aD+bIiXN6zEwI8SHQusiuU6cO586d49q1axpjLl++zIULF6hTp462zQkhRIFmZ2zE8JJOXP/kI47WKk9Hx8IYZXORm5BXrxl24z7Fgy7R7+9QLr54lcvZ5n+GhoZM/3YQy2eNwUTDN67PX8Tj23csS37+n3wbIITQGa2LbH9/f5KTk2nVqhW7du0iLi4uY19KSgp79uyhXbt2pKWl4efnp21zQgjxQVAoFDQuYsuWamV44FWNH0q74Gpmkq1jE9KUrIp4TM3Tf/PxX3+zJuIxCR/4IL/uvs3Zv2EBjkULq92vVCr5dvpSBo2dRZIsXCOE0AGti+ymTZsyffp0wsPD8fX1pXDhwigUCrZu3YqFhQVt27blwYMHjB49mlatWukiZyGE+KAUMzVhQilnwjyrsat6WZrb25K9e9twNu4VX/wdinPgJUbeuM/NV69zNdf8rE71ihzfsZwaVcppjPlt2wFa9vAn+vFTPWYmhCiIdLIYzdixYzl8+DCfffYZ5ubmqFQqEhMTMTAwoGHDhuzYsUOm79NApvATQmSXoUJBGwc79tcsz52GVRnjXgx7Y6NsHfs8NY0F9x9R/uRVPj13na2PYkn5ABe5Ke5UlAMbF9KpzacaY85euoaXz0Au/X1Tj5kJIQoanS2r3rhxY/bv38+LFy+Ijo4mMjKS+Ph4AgMDadu2ra6aKXBkCj8hxLvwsDDjx7IleNioOr9VKUWDQtlf5Obo0xd0vHKHkscvM+n2Q8I/sEVuzM1MWTV3PN9/3R+Fhv7uEY8e81nnYWzdc1TP2QkhCgqdFdk7d+5k4cKFGBgYULRoUZycnDh58iS+vr7s2LFDV80IIYT4F1MDA7oVt+fExxW5Wr8Kg10dsDbM3lt7VFIKP4RG4Hb8Mu0u3eLgk+coP5CBfwqFAv8BXdm8YhrWlupnvkpMSuaLET/w/dxVKD/Au/5CCO1oXWSnpqbStWtX2rdvz08//ZRp3/Xr19m5cycdOnSgf//+2jYlhBDiDapYWxBQ0Z2IRjVYXtGNqtbZmzZVCeyKeUbzCzcpe+IKs8MieZL8YSxy06JJPY5uDcCjRHGNMXOW/UaXgRN58VJmaxFCZJ/WRfbKlSvZvHkz5cqVY/r06Zn29e3bl3379lGhQgVWr17N8uXLtW1OCCHEW1gbGTLA1ZFL9Spz+uOK9Cpuj6lB9oZK3n2dxDe3wnEOvESPq3f489nLAj+tXfkybhzbvoxG9WtojNl/9BSfdvQj9H6EHjMTQrzPtC6yV69ejZ2dHSdPnszS99rU1JTmzZtz7NgxbGxsstzpFkIIkXsUCgV1C1mztkopIryqM6dcCUpbmGbr2GSVit+iYmlwNoSqp4JZ9iCal6kFdxrAwoVs2PHzLAb19tUYc+POfRr5DiLw1AU9ZiaEeF9pXWTfvn0bT09PChdWP/coQNGiRWnQoAE3btzQtjkhhBDvoIiJMaPcinGzQVUO1SyPj4MdhtmcBzA4/jWDr9+jeOBFBoWEcfVlQu4mm0eMjAyZNXEoS6aPxljDrC3P4l7S7otvWP7r9gJ/h18IoR2ti2xTU1NevXp7P7W0tDSMNay2JYQQQj8MFAq87W3ZXr0s9z2r810pZ4qbZu+9OT5NyfLwGKqeCuaTM9dYH/mExLSCNyCwd6dW7F0/j6JF7NTuT0tT8vWUxQwdP5fkD6TvuhAi57QusqtWrcqJEye4ffu2xpj79+8TGBhI1apVtW1OCCGEjjibmTC5tAv3PKuxrVoZmhaxyfaxp57H0zP4Li5Bl/jm5gPuJiTmYqb6V69mFYJ2LKNqxTIaY9Zu2cvnvUbxOPaZHjMTQrwvtC6yBw8eTFJSEk2bNmXbtm0kJv7fG21SUhK7d+/m008/JSkpiUGDBmnbnBBCCB0zNjDA17Ewf9SqwK0GVRnl5kThbC5yE5uSyux7UZQ+cYXm52+wM/opqcqC0Y3CtbgjhzYvwrdlI40xp88H4+UziKshd/SXmBDivaB1ke3j44Ofnx/h4eF06tQJa2trnJyccHJywtraGh8fH0JDQ/nqq6/o2rWrLnIuUGTFRyFEflLG0ow55Ury0Ks6ayt7UNfWKtvHHoyNw+fybdxPXGbKnYdEJibnYqb6YWFuxpqFk5jk31djTHhkNN6dh7JjX6D+EhNC5Hs6WYxm8eLFbNu2jSZNmmBoaEhMTAwxMTEoFArq16/Pxo0bWbFihS6aKnBkxUchRH5kbmhAL+einK5biYv1KtPfxQHLbC5y8zAxme/uRlDy+GU6XL7Fkdi493qQoEKh4OvBPdiw7AesLM3VxiS8TqTXsO+ZtuAXWbhGCAHocMVHHx8f/vjjDxITE3n8+DFRUVG8evWKEydO0LlzZ101I4QQQs+q21iyopI7EV7VWVKhJJWs1Bea/5WqUrEt+hlNz9+g/MmrzL8XxdPk1FzONve09m7A4S1LcHMtpjHmxyW/0mPIZOJfvdZjZkKI/EjrInvPnj1ZthUpUgRHR0eMjP6vT9/Lly/54osvtG1OCCFEHrE1NsKvhBPB9atwvE4FujoVwViRvXkAbyUk4n/zAc5BF/ki+C5nn8e/l3e3K5Xz4Ni2ZTT8uJrGmN8PnaBppyHcC4/SX2JCiHxH6yK7bdu2DB48mNevNX9qP3z4MJUrV+bXX3/VtjkhhBB5TKFQ0NDOhg1VS/PQqzozyrjiZp69RW4SlSrWRD7h4zPXqPXX36x6GMOr92yRG/vCtuxaM5t+3dtqjLl2MxQv34Gc+Ouy/hITQuQrWhfZhQsXZsWKFdSoUYOLFy9m2peQkMDgwYNp1qwZ4eHheHp6atuc+H/t3XdUVNf3NvDnDh2kKUXpxQYWbNFYscRETWLU2FvsjdjQaOwNNdHYQII1GrvGmkT9WqKARhMbFkRB6U2aWACpM+8feeUXwozOMIX2fNZirXDvvvds9AQ3l3PPJiKqQKz0dPCtiw0iO3rgTIsG+NzSTO5/WO68ysH4h9GwCQrB1EcxCMuqPE1udHS0sX7ZDGxaMRPa2lpSY55nvkLvUbOxY/8pDWdHRBWB0kX2w4cP0atXL4SHh6Nt27ZYvXo1JBIJrly5gqZNm2LLli0wNTXF9u3bcfnyZVXkTEREFYxIENDT0gy/tmiAqE7NsMDFBta68jW5eVVYhM1xKWj05wN43gjDoeQM5FeSlwfHDOmN3/asQy1zU6nnCwuLMHPJRsxYvAEFBZV3PToRKU7pItvKygq//fYbtm/fDn19fSxcuBDu7u7o0qULoqKiMGDAADx69Ahjx8re/oiIiKoORwM9+NSzR5xnMxz2qIvO5sZyXxuc+RpD7j+FfVAI5kfEI+ZNnhozVY0OrT0QdGILGjd0kRmz88Cv6P3VbKQ/f6nBzIioPKlsd5GxY8fi1KlTEIlECA8Ph0QiweDBg3H48GFuT0dEVA3pikQYWLsWLrd2R1j7ppjmYA1TGUsr/is1vxCro5PgEnwXn90Jx+m0TBRV4BclHe1q48Lhzej9SUeZMVdv3EPnfpMQ+jhSg5kRUXlRSZFdWFiIlStX4tNPP0VRUREaN24MPT09HD58GJ07d35ny3UiIqr63GoYYJObExI9m2NHI2e0NDGS6zoJgNNpL/DZnQi4Bt/F6qhEpOQVqDfZMqphZIC9fksxb+pXMmNiE57ho4Ff49fzVzSYGRGVB6WL7D///BPNmjXD4sWLUVRUBB8fH9y9exd37txBq1atEBwcDA8PD6xatQpFRZXrDXIiIlItI20tjLWzwq22jXHzw0YYY2sJA5F8/xTF5uZj/pME2AeFYPC9Jwh6/qrCbQMoEokwf/oo7Nu8FIYG+lJjsnNyMWzKYny/eU+Fy5+IVEfpIrtTp04ICwuDh4cHbt68ifnz50MkEqFhw4a4fv06fHx8IBaLsWjRIrRs2VIVORMRURXQyrQGdjZ2QWLn5tjY0BENjKQXpf9VIJHg8LPn6HzzERr/+QB+sc/wsoK9VPhFD09cPOIHexvZyyV9Nu7CV9OWITuHjWuIqiKli2wtLS0sWbIEN27cQJMmTUreXCTC/PnzcfPmTXh4eODBgwfKDkdERFWMuY42pjvWxqP2TXGpVUMMsK4JbTmb3IRlv8G0x7GwCQrB+NAo3HmVreZs5dfErS6CTgSg3QdNZcacOBuEjwdNQ1ziMw1mRkSaoHSR/ffff2PJkiUlujv+V5MmTXDjxg0sWrRI2eGqHH9/f7i7uyMlJaW8UyEiKleCIKBLLVMcaVYPcZ7NsKKuHez1deW6NqdIjB2JaWh5PRRt/grF7sQ0vCkq/20ALWuZ47eff8DowZ/JjLn/6Ck8+07GtVt8EEVUlShdZDdv3lyuOG1tbSxdulTZ4aocLy8vhIWFcQcWIqJ/qaOni4Wutojq2AynmtdHDwtTyPdsG7jxMhujQ6NgG3gH3o9jEZFdvssxdHV1sGmFN9YvnQ4tLen/7KY/f4HPRnhj9+HTGs6OiNRF4SI7ODgY4eHhCg+0fft27pVNREQK0RYJ6G1ljrMtG+JpRw/Mda4DCx3Zvzn9t8zCImyIfYYGV++j281HOPosAwXl1ORGEASMH94Hp3avhbmZidSYgoJCTF3wA75Z7svGNURVgMJFdufOnbFq1Sqp5/r16wdfX1+p54KDg7F7925FhyMiIgIAuBjq47v6Dkjo3Bz7m7iig5n8TW4uPX+FAfeewjH4LhY/SUBCbvk0ufFs2wJBxwPgVs9JZsyWPSfQd8wcZGSycQ1RZVam5SKythw6efIkbt26pVRCRERE76InEmGojQWutHHH/XZNMMXeCsYylmH8V3JeAVZEJcIx6C76hETgXPoLiDW8jZ6zgw3++MUfvbq1kxkTdD0EXb+cgkcR0RrMjIhUSWUdH4mIiDStibEh/N2dkdi5Bba4O8HD2FCu68QATqVmosftcNS/cg9ro5OQnq+5JjfGNQxxMGAFvpkyXGZMVFwSug7wwpk/rmksLyJSHRbZRERU6Rlra2GivTVC2jbGtTbuGGFjAT2RfK9KRr7Jw5yIeNgFhWDE/ae4lvlaI01iRCIRFnuPxe5Ni2Cgryc1Jiv7DQZPWogfAvazcQ1RJcMim4iIqgxBENDWzBh7mrgi0bM5fmjggLqG0gvY/8oTS7AvOQPtb4Sh2bVQBMSl4HWh+jsVf/lpV5w/5Avb2pZSz0skEixbtwNjZvog502u2vMhItVgkU1ERFVSLV0dzHKqg/AOHjjfsiH6WplDS859AO9n5WDKoxjYBN7B5LBo3H+do9ZcmzWuj+CTW9CmRSOZMUd/v4QeQ6YjMTlNrbkQkWqwyCYioipNJAjobmGK483rI7ZTcyxxtYWNno5c12YVibElPhUe1x6g/d8PsS8pHblqanJjZVETp/eux/D+PWTGhIRGoFPfifj7zkO15EBEqsMim4iIqg1bfV0srWuHmE7NcKxZPXxUS/qe1dJce5GFEQ8iYRcUgjnhcYjMUf3SDT09Xfy4eg6+X+gFkUj6P9Gp6ZnoNWwm9h37n8rHJyLVYZFNRETVjo5IhH7WNXGhlRsiOnjA27E2zLW15Lo2o6AQa2OSUffKPfS49RinUp+jUKy6lxIFQcCUUf1x4qfvYWZSQ2pMfkEBJs/9Ht+u9EehBtaNE5Hi5Gub9R8nT56Ei4tLqeOCIMg8l56eXpahiIiI1KqekT7WNXSETz17HHmWgS3xqfjrZZZc157LeIlzGS9hp6+LCXZWGGtrCRt9XZXk1bVDK1w+HoBBExcgIjJOaoz/rqN4/CQGuzYthrmp/M15iEj9ylRkZ2VlIStL+jegd50TBDnfOCEiItIwAy0RvrK1xFe2lgh5lY0t8anYn5yObDnWYCfk5mPx0wQsj0zEF1ZmmGxvja41TZT+d6+ukx0uHfXHWO+VOHf5L6kxf1y9hS5fTsHhrSvRwNVBqfGISHUULrIvX76sjjyIiIgqjOYmRtjayBlr6ttjX3I6AuJT8TDrzXuvK5RIcCwlE8dSMlHfUB+T7K0wytYS5jpleqYFADA1roHDW3ywbN1ObNh2UGpMZEwCun45BT9tXIiu7VuWeSwiUh2F/6/39PRURx6VxqhRo3DgwAHo6v7frwOPHj2KHj1kvw1ORESVk6mONrwcamOKvTWuvniNgLhUHE15jgI5GsNE5OTCOzwO85/EY3DtWphsb40PTI3K9HRbS0sLy+dMQKMGzvCatxZ5UrpTvsrKxoDx87Fk1li41jZSeAwiUi2++FgGEyZMKF4Wk5WVxQKbiKiKEwQBHc1NcMCjLhI8m2N1PXs4GcjX5CZXLMHupHS0+fshWv0Vih0Jqcgu48uKg77ojnOHfFHH2kLqeYlEgqU/7MCWg+eQm5dfpjGISDVYZBMRESnASk8H37rYILKjB860aIDPLc3k/sf0zqscjH8YDZugEEx9FIOwLMWb3LRs2hDBJ7aglYebzJg/bz/GZyNnITmFmw4QlZdKV2SvXr0aAwYMgIuLCwRBgJOTk8xYsViMDRs2oGHDhtDX14e9vT1mzZqF7OxspXLYv38/atasCTc3N6xcuRKFhYVK3Y+IiCofkSCgp6UZfm3RAFGdmmGBiw2sdeVrcvOqsAib41LQ6M8H8LwRhkPJGcgXy9/kprZVLZw9sBFD+nSXGXPnfjg69Z2EW/ceyX1fIlKdSldkz58/H5cuXYKrqyvMzc3fGTtz5kx4e3vD3d0dfn5+GDBgAHx9ffH5559D/J9vZoMHD4YgCDI/AgMDAQDTpk1DeHg40tPTsXfvXuzevRvLli1T15dLRESVgKOBHnzq2SPOsxkOe9RFZ3P5t9MLznyNIfefwj4oBPMj4hHzJk+u6/T1dLF17Tys/HayzMY1z1Iz0GPIdBw6eUHufIhINQSJRI63NyqQqKio4n24GzdujKysLMTExJSKe/jwIZo0aYK+ffvi2LFjxcf9/Pwwbdo07N+/H0OHDi0+/vr1a+Tlyf7GZmpqCh2d0k8oDhw4gCVLluDJkydKfFWAnZ0dEhMTYWtri4SEBKXuJa+CggKcOXMGvXr1kvq1EVUVnOtUHh5lvcGW+BT8nJSOlwqswRYA9LI0w2R7K/SwMIOWHC9KXgi6gdEzluPla9m/qZ0+fhCWzR4PLS35mu4QVQaa/v6uSL2m8JPsTp06YcmSJcWfx8XF4fnz54pnWUbSGt1Ic/DgQUgkEsyYMaPE8fHjx8PQ0BD79u0rcdzY2BgWFhYyP2T9xYlEIlSyn1OIiEgD3GoYYJObExI9m2NHI2e0NJFvxw8JgNNpL/DZnQi4Bt/F6qhEpOSV3k3k37p7tsalYz+irrO9zJhN2w9j4MQFePlavkY7RKQchbfwu337NmxsbIo/d3Z2xvDhw/Hzzz+rNDFl3bx5EyKRCK1bty5xXF9fH82aNcPNmzfLdN/Dhw+jR48eMDExwYMHD7Bs2TIMGDBAZvz69euxfv369943OTm5+L8LCt79zVRV3o6jqfGIygvnOpUnXQAjrc0x0toct15lY2tiOo6kPMcbOVqxx+bmY/6TBCx5mog+lmaYaGuBjmY1pG4D6GxfBxcObcKYmT64fO2O1PudD/wbXfpNxn7/5ajrbKfsl0ZU7iry93eFi2xdXV3cvHkT8fHxsLGxgUQigVgsLrXGWRZZ68ZULSkpCRYWFtDTK73Fkq2tLa5du4b8/PwS+13L48cff8SkSZNQUFCAOnXqYMSIEZg3b57M+FevXiExMVHu++fm5uLMmTMK5aSsCxe4Vo+qB851qgj6AugOAZe1DPA/LUMkit7/T3GBRIJfUjPxS2om7MUF+KToDboUvYERShfqo/t2gIEOcCZIeqH9JDoBnb+cjKkjeqFJA0dlvxyiCkFT399zc3PljlW4yO7YsSN+//334l09BEHAgQMHcODAgfdeKwiCxnbiyMnJkVpgA/88zX4bo2iRHRQUpFC8iYkJbG1t3xuXnJwMsVgMfX199OrVS6ExyqqgoAAXLlxA9+7duU6VqjTOdaqIBuKffa2DXmRha2IaTqW9QKEcqw/jRTrYIdLBAT0zDLY2x0Q7SzQ3Niw+X1BQAJFIhB4feWL28s3Il/KEL+dNHtbuOIXl34zH5K/6Kd3+nai8aPr7+9saUh4KF9mbN2/GixcvcOPGDeTn50MQBLnXJGty7bKhoSFSU1Olnnv7U4ihoaHU86rk7e0Nb2/v98a9XUgPQONFgI6ODgsPqhY416ki6m5VE92taiI5Lx87E9KwLSEV8bnvbySTIxbjp+QM/JScgdamRphsb41BtWvh7RQf3r8nGjWsi6FTFiElrfS7U2KxGAu/34pHT2OxaflM6Okp9tCJqCKpiN/fFV674eDggODgYOTm5kIsFkMikWD48OHFS0be96EpNjY2SE9Pl7pjSGJiIiwsLBR+ik1ERKQudfR0sdDVFlEdm+FU8/roYWEKeZ8v33iZjdGhUbANvINvniQgUfhnB5HWzd0RdHwLmjeuL/Pa/cf+h17DvaUW4kRUdkovkPb09ISbm+yuU+Xlgw8+gFgsxo0bN0ocz83Nxd27d9GqVatyyqwkf39/uLu7IyUlpbxTISKiCkBbJKC3lTnOtmyIpx09MMepDix05PvFc2ZhETbFp8JLzxI9Qp7g2LPnsLKuhXOHfDGwdzeZ190IeQjPvpMQEhquqi+DqNpTusi+fPly8Yt/UVFR2LVrF1atWoV169Zh3759iI+PVzrJshg0aBAEQcDGjRtLHN++fTtycnIwbNiwcsnrv7y8vBAWFgZra+vyToWIiCoYF0N9fN/AAQmdm2N/E1d0MJO/yc2lzNfof+8JHIPvYnV8Gpau/AbLvpkgc/114rM0fDxoGo7+fklV6RNVawqvyZYmMzMTEyZMwPHjx6We7927N7Zv3w4LCwulx9q7dy9iY2MBAGlpacjPz4ePjw8AwNHRESNGjAAANGnSBF5eXti8eTP69euHXr164dGjR/D19YWnp2eJRjREREQVmZ5IhKE2FhhqY4EHr3OwJT4Fe5PS8bro/cswk/MKsCIqESujEvF565aYE+AE/9k+yMrKKRWbm5eP0TNW4GF4FBbNHKOxHcGIqiKli+w3b96ga9euuHfvHkxNTdGzZ084OzujqKgIUVFROH/+PE6dOoXY2Fj89ddfSq+D3rlzZ6kdPhYtWgTgn6Urb4tsANi4cSOcnJywbds2nD59GhYWFpg6dSqWL1/ObxxERFQpNTE2hL+7M76r74ADyekIiE/FvdelC+b/EgM4lZqJUxDBYd0y1LgQhNdnL0HILn3tDwH78TA8GjvWzYeJsXxNdIioJKWL7A0bNuDevXv47LPPsG/fPpiYmJQ4/+rVKwwbNgxnzpzB5s2b5dpp410CAwPljtXS0sKsWbMwa9YspcZUJ39/f/j7+3NNNhERKcRYWwsT7a0xwc4Kf73MQkB8Ko48y0CeHE1u4gqLgC4dIOrUFqLb96AT/BdE0XElXrQ8e+kaug3wwuGtK+Hi+P6taImoJKUf5x46dAgWFhY4ePBgqQIb+Gef6EOHDqFWrVrYv3+/ssNVOVyTTUREyhAEAW3NjLGniSsSPZvj+7q2qCOWryeFWEsLha1b4M3sKXgzbzoKOraB5F9b+T1+GovO/SYj8NptdaVPVGUpXWQ/ffoUnTp1gpGR7F8nGRkZoWPHjnjy5ImywxEREZEMtXR1MNPBGv756TjTrC76WplDS859AMV2dZA3uC+yVy1A7uA+KLKpDQDIfPkafUbPwZY9xzXa74KoslN6uYiOjg6ysrLeG5ednc2OUkRERBogAvBRTRP0tK6FhNw87EhIw/aEVCTlle7+WIq+Hgo7fojCjh9CFBkDnSt/QRISim+W+yH0cRTWL50OXd2K1fSDqCJS+km2h4cHgoODi3f8kCY6OhpBQUHw8PBQdrgqh/tkExGROtnp62FpXTvEdGqGY83q4aNapZd2yiJ2dULeqMHIXjkPeX16Ytel6/hs5CykZWSqMWOiqkHpInvSpEnIzc3FJ598gqtXr5Y6f+XKFfTo0QP5+fkYN26cssNVOVyTTUREmqAjEqGfdU1caOWGiA4e8HasDXNtLfkurmGEgu6eyFk2B5fatEKLuWtx5yGXgBK9i9LLRYYOHYqzZ89i//798PT0hKWlJRwdHQEAMTExSE9Ph0QiwaBBgzBy5EilEyYiIiLl1DPSx7qGjvCpZ48jzzKwJT4Vf718/9JPAChyb4AE9wb4IDQaA+NSsK5La9joK7c9L1FVpJLNovfu3YtNmzbB0dERqampuHnzJm7evIm0tDQ4ODhg48aNOHDggCqGIiIiIhUx0BLhK1tLXP+wEe60bYwJdlYw0pKvNBCbmeKQSAf2gXfwZUgE/sh4yRcjif5FJR0fAWDq1KmYOnUqEhISkJSUBIlEAhsbG9jb26tqCCIiIlKT5iZG2NrIGWvq22Pf/29y8zDrzXuvEwsCjqdm4nhqJuob6mOSvRVG2VrCXEdlJQZRpaTytod2dnZo3bo12rRpwwJbDnzxkYiIKhJTHW14OdTGg3ZNENzaDUNq14KOnJuDReTkwjs8DjaBdzD6QSRuvMji022qtthbvJzxxUciIqqIBEFAR3MTHPCoiwTPFvBxsYVJbq5c1+aKJdidlI42fz9Eq79CsSMhFdmFRWrOmKhiYZFNRERE72Slp4MF9ezwvHcnTH+dCe3Qx4BYLNe1d17lYPzDaNgGhWDaoxiEZeWoOVuiioFFNhEREclFSxCwsX8PXO7YDLbrA6Bz9hKEV6/luvZlYRH84lLQ6M8H8LwRhkPJGciXs1AnqoxYZBMREZFCOrT2wJ+71qDl06cwXPgd9Hbuh1ZEpNzXB2e+xpD7T2EfFIL5EfGIeZOnxmyJygeLbCIiIlKYo11tXDi8GV981A46dx7AYNN2GC5fB53LfwI579+VBABS8wuxOjoJLsF38dmdcJxOy0QRX5SkKoJFNhEREZVJDSMD7PVbinlTvwIAiFLSoHf0NxgtWAW9fUchik2Q6z4SAKfTXuCzOxFwDb6L1VGJSM0rUGPmROqndJHdrVs3HDhwALlyvnFMJXELPyIiqsxEIhHmTx+FvX5LYWigDwAQ8gugc/0WDNdshsH3m6F9/RaQny/X/WJz8zH/SQLsgkIw5N5TBD9/xW0AqVJSusi+fPkyRowYgdq1a2PSpEn466+/VJFXtcEt/IiIqCro09MTFw77wd6m5L9nWnEJ0N93FEbzV0P3l99gkiVf+/YCiQSHnmXA8+YjNP7zAfxin+FlQaE6UidSC6WL7OvXr2PChAnQ0tLCtm3b0L59e7i7u2Pt2rV49uyZKnIkIiKiSqCpe10EnQhAuw+aljonvHkD3cA/UTTXB41OnManJobQFuTrchOW/QbTHsfCJigE40OjcOdVtqpTJ1I5pYvsNm3aICAgAMnJyTh8+DB69uyJp0+fYu7cuXBwcMDnn3+O48ePo6CAa6uIiIiqOsta5vjt5x8watCnUs8LAGIvXsHD6YtxzEwfK+rawV5fV6575xSJsSMxDS2vh6LNX6HYnZiGN0XcBpAqJpW9+Kirq4sBAwbg999/R0JCAtavX4/WrVvj7NmzGDBgAGxsbDBjxgyEhoaqakgiIiKqgHR1deDrMwvrlkyDlpb0UiP9+QuM+moW7G7dRVTHZjjVvD56WJhCzg7uuPEyG6NDo2AbeAfej2MRkS3fjiZEmqKW3UWsrKwwY8YMbNu2DVOmTIEgCMjIyICvry88PDzQrVs33Lp1Sx1DExERUQUgCAImjOiLU7vXwtzMRGpMQUEhpi74AfN8/NDT3BhnWzbE044emONUBxY62nKNk1lYhA2xz9Dg6n18dPMRjj17jgI2uaEKQOVFdnx8PFatWgV3d3c0adIE/v7+qFGjBiZMmIA9e/bgs88+Q1BQENq1a4eTJ0+qengiIiKqQDzbtkDQ8QC41XOSGbNlzwn0HTMHGZkv4WKoj+8bOCChc3Psb+KKDmbGco/1x/NX6H/vCRyD72LxkwQk5LLJDZUflRTZ2dnZ2L17N7p27QpnZ2csWrQIjx8/RseOHbF7924kJydjy5YtGD58OE6dOoUDBw6gsLAQ8+bNU8XwlRq38CMioqrO2cEGf/zij17d2smMCboegq5fTsGjiGgAgJ5IhKE2FrjSxh332zXBFHsrGMtYevJfyXkFWBGVCMegu+gTEoFz6S8g5jaApGFKF9nDhw+HtbU1xo4di8DAQNSuXRvffvstnjx5gsDAQIwYMQIGBgYlrhk4cCD09fURGxur7PCVHrfwIyKi6sC4hiEOBqzAN1OGy4yJiktCtwFf48wf10ocb2JsCH93ZyR2boEt7k7wMDaUa0wxgFOpmehxOxz1r9zD2ugkpOdzIwbSDKWL7AMHDqCgoAB9+vTB77//jri4OKxcuRKurq4yr8nNzUWLFi0wefJkZYcnIiKiSkIkEmGx91js3rQIBvp6UmNeZ+dg8KSF+CFgf6kmNMbaWphob42Qto1xrY07RthYQE8k36uSkW/yMCciHnZBIRhx/ymuZb5mkxtSK/neKniHH374ASNHjoSFhYXc1+jr6+Pq1avKDk1ERESV0JefdoWrox0GT1qIxGdppc5LJBIsW7cDD8Oj4L/6m+JOkm8JgoC2ZsZoa2aMDQ0csCsxHVviUxD55v1rsPPEEuxLzsC+5Aw0rWGIyQ5WGFbHAsbaWir7+ogAFTzJ/v3337Fjx473xnl7e6NBgwbKDkdERERVQLPG9RF8cgvatGgkM+bo75fQY8h0JCaXLsTfqqWrg9nOdRDR0QPnWjZAXytzaMm5D+D9rBxMDouBTeAdTAmLxv3XOYp+GUQyKV1kBwYGIiws7L1x9+/f5xpsIiIiKmZlUROn967H8P49ZMaEhEagU9+J+PvOw3feSyQI+NjCDMeb10dMp2ZY4moLGz0dufLIKhIjID4VHtceoP3fD7EvKR25bHJDSlJ4uciQIUOQmJhY4tj58+fRqVMnmde8fPkSoaGhcHZ2VjxDIiIiqrL09HTx4+o5aNLQFfNWBUAsZY/r1PRM9Bo2E5t8vDH8S9kF+Vt2+npYWtcOC1xs8FvaCwTEp+Bixiu58rn2IgvXXmRhxuNYjLG1xER7K7ga6r//QqL/ULjI7t27N4YNG1b8uSAISE1NRWpq6juv09LSwpIlSxTPkIiIiKo0QRAwZVR/NKzrhK+mLcOLV1mlYvILCjB57vcIfRwJn7mToC3HGmodkQj9rGuin3VNRGS/wdb4VOxKTENmYdF7r80oKMTamGSsjUnGJ7VMMdnBCp9amENbzhcticr0JNvOzg5isRgSiQRdu3ZF9+7dMX/+fKnxgiBAX18fzs7OsLS0VDphIiIiqpq6dmiFy8cDMGjiAkRExkmN8d91FI+fxGDXpsUwN5W/UU19IwOsa+gIn3r2OPIsA1viU/HXy9LFvDTnMl7iXMZL2OnrYoKdFcbaWsJGX1fusal6KtPuIh07diz+76+++grt2rWDp6enypIiIiKi6qmukx0uHfXHWO+VOHf5L6kxf1y9hS5fTsHhrSvRwNVBofsbaInwla0lvrK1RMirbGyJT8X+5HRky7EGOyE3H4ufJmB5ZCK+sDLDZHtrdK1pAkHg020qTekXH3ft2oXx48erIpdqiR0fiYiISjI1roHDW3wwc8IQmTGRMQno+uUUnA/6u8zjNDcxwtZGzkj0bI7Nbo5oVMPg/RcBKJRIcCwlEx/deoyGV+9jQ0wyMgsKy5wHVU0KP8levHgxAGDGjBmoWbNm8efyEAQBy5YtU3TIKs3LywteXl6ws7Mr9UIpERFRdaWlpYXlcyagUQNneM1bizwpnRpfZWWj/7h5WD5nAqaPG1TmJ8qmOtrwcqiNKfbWuPriNQLiUnE05TkK5GhWE5GTC+/wOMx/Eo/BtWthsr01PjA14tNtUrzI9vHxgSAIGD58OGrWrFn8+bu6Jr09zyKbiIiIFDHoi+6o62yPIZMXITklvdR5iUSCRd9vxcPHUfBbNRv6emVfKy0IAjqam6CjuQk25hXgp8Q0bE1IRYwcTW5yxRLsTkrH7qR0tDAxxGR7awypXQtGbHJTbZXpSbYgCMUdHt9+TkRERKQOLZs2RPCJLRgyeRFu3XskNebQqQt4GhOPAz+uQB1r+btQy2Klp4NvXWzwjXMdnEt/iYD4FJxOewF5GrHfeZWD8Q+jMTs8DiNtLDDJ3gruNQyVzokqF4WL7KVLl77zcyIiIiJVq21VC2cPbMS0BT/g4MkLUmNu3XuMTn0n4WDACrTycFPJuFqCgF6WZuhlaYbYN3nYlpCKHQmpSM1//xrsl4VF8ItLgV9cCjqZG2OyvTX6WZtDV6T0K3FUCfBvmYiIiCoFfT1dbF07Dyu/nQyRjEL1WWoGegyZjkMyCnFlOBroYWU9e8R7Nsdhj7robC7/FoLBma8x5P5T2AeFYH5EvFxLUKhyU/hJ9k8//aTUgGPGjFHqeiIiIqq+BEHAtHED0bCeI8bMWIGXr7NLxeTlF2D87FUIDY/EstnjoaWl2nXRuiIRBtauhYG1a+FR1htsiU/Bz0npeClHk5vU/EKsjk7Cd9FJ6GVphsn2VuhhYQYtLr2tchQusseNG6fUGmwW2URERKSsjz3b4NKxHzFo4kI8jY6XGrNp+2E8ehKDnzYshKlxDbXk4VbDAJvcnLCqnj0OPctAQHwqbr8qXfj/lwTA6bQXOJ32Ao76uphob4Wxtlaw0tNRS56keQoX2SNHjuSLjkRERFTu6rs44NJRf4yZsQIXr9yUGnM+8O/ixjX1nO3VlouRthbG2llhrJ0Vbr7MQkB8Kg4lZ+CN+P1NbmJz8zH/SQKWPE3El9Y1MdneCh3NjVlvVXIKF9m7d+9WQxpEREREijM3NcYv21dj8dpt8Nt5RGrMk6h4dP1yCnZvWoxuHT9Qe04fmNbAB6Y1sK6BA35OTMOWhFSEZ+e+97oCiQSHnmXg0LMMuBsZYLK9FUbYWMBUp0wNuqmc8cVHIiIiqtS0tbWwat5kbFkzF7o60pdbvHiVhX5jv8Xmn355Z28PVTLX0cYMpzp41L4pLrVqiAHWNaEt59PpsOw3mPo4FjZBIRgfGoU7cixBoYpFox0fAWD58uWKDklERET0XsP69UA9ZwcMnbIIKWnPS50Xi8WYt+pHhIZHYdPymdBTonGNIgRBQJdapuhSyxTJefnYmZCGbQmpiM/Nf++1OUVi7EhMw47ENLQ2NcJke2sMql0LBlp8TlrRabzjI4tsIiIiUpfWzd0RdHwLhkxeiJDQCKkx+4/9D0+i4nHgx+Wwtqyp0fzq6OlioastvnW2wZn0FwiIT8G59JdyNbm58TIbN15GwftxLEbZWmKSvRXqGxmoPWcqG3Z8LGf+/v7w9/dHSkpKeadCRERUJdjWscS5Q774ev5aHPn1D6kxN0IewrPvJBzcsgLNGzfQcIaAtkhAbytz9LYyR1ROLrbGp+KnxDSkF7y/yU1mYRE2xD7Dhthn6FbTBJPtrdHbygw6bHJToQgSTS1Moneys7NDYmIibG1tkZCQoJExCwoKcObMGfTq1Qs6MtawEVUFnOtUnXC+/x+JRIIN2w5h6Q/bZf7GXV9PFwHfz0X/z7pqOLvS8sRiHHv2HAHxqbj64rVC19bR08E4WytMsLeEnb6emjKseDQ93xWp11T6ump0dDSCgoKQmJgIHR0dODg4oGPHjrC1tVXlMERERETvJQgCvCcOgVs9J4yd6YPX2TmlYnLz8jF6xgo8DI/CopljZHaS1AQ9kQhDbSww1MYCD17nYEt8CvYmpeN10fu3AUzOK8CKqESsjErE51bmmGxvhe61TCHiaoNyo5IiOyYmBlOmTMG5c+dKnROJRBg0aBD8/Pxgbm6uiuGIiIiI5Naza1tcOuqPQRMXICouSWrMDwH78TA8GjvWzYeJsZGGMyytibEh/N2d8V19BxxITkdAfCruvS79Q8J/iQGcSs3EqdRMuBroYaK9FUbbWsJCt3r/VqM8KP3jWnJyMtq3b4///e9/sLS0xNChQzF37lzMnTsXgwYNgomJCQ4cOIAuXbogKytLFTkTERERKaRhPSdcPh6Azu1ayIw5e+kaug3wQlRsogYzezdjbS1MtLdGSNvGuNbGHSNsLKAnku/pdOSbPMyJiIddUAhG3H+Ka5mvNbZ9IamgyF6xYgWSk5Mxbtw4xMbGYu/evVi1ahVWrVqFAwcOIC4uDgMHDsSDBw+wcuVKVeRMREREpLCaZiY48dMaTP6qn8yYx09j0bnfZAReu63BzN5PEAS0NTPGniauSPBsjrX1HeBqIN/a6zyxBPuSM9D+RhiaXQvFlvgUvC4sUnPGpHSR/euvv8LV1RVbtmyBnl7pv2wjIyPs2bMHtra2OHTokLLDEREREZWZtrYW1iyais2rZkNHRifFzJev0Wf0HGzdc6JCPvm10NXBbOc6iOjogXMtG6CvlTm05Fx6fT8rB5PDYmATeAdTwqJxX44lKFQ2ShfZGRkZaNGixTtfFNDV1cWHH36IZ8+eKTscERERkdK+GvgpTu9bD8ta0t8XKyoSY/ZyX0xdsA75+QUazk4+IkHAxxZmON68PmI6NcMSV1vY6Mm39jqrSIyA+FR4XHuA9n8/xL6kdOTK8YIlyU/pItvNzQ2hoaHvjYuMjISrq6uywxERERGpRNuWTRB0IgAe7vVkxvx85DQ+GzkLaRmZGsxMcXb6elha1w4xnZrhWLN6+KiWidzXXnuRhREPImEfFII54XGIzMlVY6bVh9JF9sKFC/Ho0SPMmzcPYrH0n4D8/PwQEhKC2bNnKzscERERkcrY21jj/GFf9OvVWWbM9VsP4Nl3Mu6HPdVcYmWkIxKhn3VNXGjlhvAOTeHtWBvm2lpyXZteUIi1Mcmoe+Ueetx6jFOpz1EornjLZSqLMnV8/K8GDRpgzZo1OH78OAYOHAgnJyfo6+sjKSkJ586dw+XLl9GuXTvo6uqqJGkiIiIiVTE00MfuTYvRuKErlq/fKTUmPikF3QdNxZbv56LvOwryiqS+kQHWNXSETz17HHmWgYD4FPz9Mluua89lvMS5jJew09fFBDsrjLOzRB091nGKULjjo0gkgiAIxS8C/Pu/i2/6r43P/31OEAQUFfFtVmnY8ZFIfTjXqTrhfFfObxeuYsLsVcjKfiMz5tuvR2LetK/KtXFNWYW8ykZAfAr2J2cgR4E12NqCgD7/v8lNl5omJWq98lSlOj4uWbKkzIkRERERVWSfd++Ai0c2Y/CkhYiJT5Ya893mPXgYEY1ta+ehhpGBhjNUTnMTI2xr5IK19R2w7/83uXmYJfsHircKJRIcTXmOoynPUd9QH5PsrTDK1hLmMnZoIRbZRERERCU0auCCy8cCMHLqUlz5+67UmN/OX8FHsYk4tMUHTvZ1NJugCpjqaMPLoTam2Fvj6ovXCIhLxdGU5yiQY4FDRE4uvMPjMP9JPAbXroXJ9tb4wNSowjzdrigq3+85iIiIiNTMoqYpTu1ei/HDvpAZ8zA8Cp79JuHKX3c1l5iKCYKAjuYmOOBRFwmezbG6nj2c5GxykyuWYHdSOtr8/RCt/grFjoRUZLPJTTGNFtkhISGaHE5tTp8+jRYtWsDIyAi1a9fG2rVryzslIiIiUjEdHW2sXzYDm1bMhLaMHTqeZ75C71GzsfPArxrOTvWs9HTwrYsNnnb0wOkWDfCZpRnkfTZ951UOxj+Mhm1QCKY9ikFYFpvcqGQhzZ07d7B161ZER0cjLy+vxMuOYrEYubm5SElJQXJyMgoLC1UxZLk5f/48JkyYgD179sDT0xM5OTmIi4sr77SIiIhITcYM6Y36ro4Y7rUEGZkvS50vLCzCjMUbEPo4EmsWTZXZSbKy0BIE9LI0Qy9LM8S+ycO2hFTsSEhFav77a7iXhUXwi0uBX1wKPM2NMdneGn2tzaFbCV8SVZbSs+DWrVvo2LEj8vPzZe448vbzJk2aKDtcuVu0aBEWLVqEbt26AQBMTEzQuHHjcs6KiIiI1KlDaw8EndiCwZMWIPRxlNSYHQd+xeOnsdi7eRksappqOEP1cDTQw8p69ljiaouTqZkIiEtBYOZrua4NynyNoMzXsNLVxlhbK0ywt5J7KUpVoPSPFd9//z3y8vLQu3dvnDx5EpMmTYIgCDh16hSOHz+OiRMnQhAENGrUCDdv3lQ64dWrV2PAgAFwcXGBIAhwcnKSGSsWi7FhwwY0bNgQ+vr6sLe3x6xZs5CdLd8ekf+VnZ2Nmzdv4tmzZ2jYsCGsra3Ru3dvREdHl/GrISIiosrC0a42LhzejN6fdJQZc/XGPXTuNwmhjyM1mJn66YpEGFi7Fi63dkdY+6aY5mANUzmb3KTmF2J1dBJcgu/iszvhOJ2WiSLFdpCulJQusv/880/Url0bhw8fRu/evTFkyBCIxWIIgoA+ffogICAAmzdvRlhYGHx9fZVOeP78+bh06RJcXV1hbm7+ztiZM2fC29sb7u7u8PPzw4ABA+Dr64vPP/+8VHfKwYMHQxAEmR+BgYHIzMyERCLBsWPH8L///Q/R0dGoXbs2+vXrV2qvcCIiIqp6ahgZYK/fUsyb+pXMmNiEZ/ho4Nf47cJVDWamOW41DLDJzQmJns2xo5EzWpoYyXWdBMDptBf47E4E6l65h9VRiUjNK1BvsuVI6SI7IyMDLVu2LO7m+HZJyK1bt4pjJk2aBHt7exw6dEjZ4RAZGYmMjAxcuHABNjY2MuMePnwIPz8/9OvXD8ePH8f48eOxfv16rF+/HpcvXy6Vy/bt25GWlibzo3379jA2NgYATJ8+HU5OTjA0NMSqVatw9+5dxMfHK/21ERERUcUnEokwf/oo7PVbCkMDfakx2Tm5GDp5Eb7fvKfKPogz0tbCWDsr3GrbGDc+bITRtpYwkHPtdcybPMx/kgC7oBAMufcUwc9fVbk/J6WLbAMDgxLt0s3MzGBubo7Hjx+XiGvRogWePHmi7HBwcXGRK+7gwYOQSCSYMWNGiePjx4+HoaEh9u3bV+K4sbExLCwsZH7o6OjA1NQUjo6O3AeSiIiI0KenJy4c9oO9jbXMGJ+Nu/DVtGXIznl/w5fK7APTGvipsQsSOzfHhgYOaGAk/YeP/yqQSHDoWQY8bz5C4z8fYHPsM7wsqNybZLyl9IuP9erVw71790ocq1+/Pm7fvl3iWG5urkZ3Frl58yZEIhFat25d4ri+vj6aNWtW5vXhkyZNwqZNm/Dxxx/D0tISixYtQsuWLeHg4CA1/u3T8/dJTv6/rlIFBZr51cnbcTQ1HlF54Vyn6oTzXbPc6jni4hFfjJq+Atdvh0qNOXE2CE9jErB/8zLY2VhpOEPNqgHAy9YCU2xqIehFFrYmpuFU2gsUyvGQOiz7DaY+jsXciHgMtjbHRDtLNDc2fOc1FXm+K11kf/rpp1ixYgVmzJiBZcuWwdTUFO3bt8eGDRvw22+/4fPPP0dERAQCAwPlfgqtCklJSbCwsICeXum3WG1tbXHt2jXk5+eXeAovjzlz5iAzMxMtWrSAWCxGhw4dcPz4cZnxr169QmJiotz3z83NxZkzZxTKSVkXLlzQ6HhE5YVznaoTznfNmjiwC/R1gMt/SS+0HzyKRIcvxmP6V5+hgYuthrMrPyMAfAoRLmoZ4Ly2IdKF978smSMW46fkDPyUnIF64nz0KHqDDkVv8K59STQ133Nzc+WOFSRKLoB58eIFWrVqhejoaPTo0QOnT59GdHQ0GjRoAOCfNdrh4eF48+YNli9fjgULFigzXAmNGzdGVlYWYmJiSp1zdXVFQUGB1D2sR44cib179yIzMxNmZmYqy0caRZ5ki8Vi2Nraamy3koKCAly4cAHdu3eHjo6ORsYkKg+c61SdcL6XH4lEgp0HfsO81T+iqEgsNUZHRxtrF03FyAE9NZxd+SsUS3A24yW2Jabj/PNXUKQANdfWwsg6tTDe1gL1Df9vKYqm57uzszMSExNha2uLhISEd8Yq/STbzMwM169fx4oVK1CrVq3iBH7++WdMnDixuMtj7969MXv2bGWHk5uhoSFSU1Olnnv7U4ih4bt/BaEK3t7e8Pb2fm+cnZ1d8RNvTX9T1NHR4TdiqhY416k64XwvH5NHfQn3Bs4YMXUZMl+8KnW+oKAQMxZvwOOnMVg930tmJ8mqSAdAPxtL9LOxRFROLrbGp+KnxDSky7EGO7OwCJviU7EpPhXdappgsr01eluZ4e0Mr4jzXSXtdywtLeHr64slS5YUHxsyZAiSk5Nx/fp1PH36FCdPnpS6dENdbGxskJ6ejry8vFLnEhMTYWFhofBSESIiIqL38WzbAkHHA+BWz0lmzJY9J9B3zBypHSSrAxdDfXzfwAEJnZtjXxNXtDerIfe1fzx/hf73nsAx+C6WRSUhXTXlrMqpNKvo6Gjs3r0bK1euxJo1a/Dbb7/Bzs5Oo2ux3/rggw8gFotx48aNEsdzc3Nx9+5dtGrVSuM5SePv7w93d3ekpKSUdypERESkIs4ONvjjF3/06tZOZkzgtTvo+uUUPIqovk3t9EQiDLOxwNU2jXC/XRNMsbeCsZZ85WlyXgFWxjzDBD1L9L8fiXPpLyCuQNsAqqTIjomJQa9evVC3bl2MHTsWixcvxrx58zBs2DA4OTlh+PDhyMzMVMVQchs0aBAEQcDGjRtLHN++fTtycnIwbNgwjeYji5eXF8LCwmBtLXv7HyIiIqp8jGsY4mDACnwzZbjMmKi4JHQb8DXO/HFNg5lVTE2MDeHv7ozEzi2wxd0JHu/ZWeQtsSDg1/SX6HE7HIPuPVVzlvJTek12cnIy2rdvj+TkZFhZWaF79+6wt7cH8E/xfe7cORw4cAChoaG4evUqatSQ/9cB0uzduxexsbEAgLS0NOTn58PHxwcA4OjoiBEjRgD454VLLy8vbN68Gf369UOvXr3w6NEj+Pr6wtPTE0OHDlUqDyIiIqL3EYlEWOw9Fo0aOGPy3DV4k1t6Gevr7BwMnrQQi73HYtakodW+H4exthYm2ltjgp0V/nqZhYD4VBx5loE88fufUn9qaab+BOWkdJG9YsUKJCcnY9y4cfDz8yu17jo7Oxtjx47FL7/8gpUrV2L16tVKjbdz504EBQWVOLZo0SIAgKenZ3GRDQAbN26Ek5MTtm3bhtOnT8PCwgJTp07F8uXLIZKzIxERERGRsr78tCtcHe0weNJCJD5LK3VeIpFg2bodeBgeBf/V38jsJFmdCIKAtmbGaGtmjPUNHLA7MR1b4lMQ+ab0DyrAPzuQDKpdS8NZyqb0Fn52dnYwMDBAeHi4zMI1Pz8fdevWhZaWlsa2p6ss/P394e/vjydPnqCwsFCuLWFUpaCgAGfOnEGvXr0q3Bu5RKrEuU7VCed7xZaa/hxDpyzG33ceyoxp3rg+Dgb4wLaOpQYzqxzEEgkuZrxEQHwqfk3NxL83SpzpWBvrGzqqdfy3u8HJU68p/Tg3IyMDLVq0eOeTYV1dXXz44Yd49uyZssNVOVyTTUREVH1YWdTE6b3rMbx/D5kxIaER6NR34jsL8epKJAj42MIMJ5rXR6xnMyxwqg1zSREAYKJ9xeqmqXSR7ebmhtBQ6d2N/i0yMhKurq7KDkdERERUqenp6eLH1XPw/UIvmQ8pU9Mz0WvYTOw79j8NZ1d52OnrYYmLDbbnpeFi83poYGRQ3imVoHSRvXDhQjx69Ajz5s2DWCy9u5Gfnx9CQkI02oyGiIiIqKISBAFTRvXHiZ++h5mJ9E0h8gsKMHnu9/h2pT8KC4s0nGHloQ2gk7lxeadRisIvPi5evLjUsQYNGmDNmjU4fvw4Bg4cCCcnJ+jr6yMpKQnnzp3D5cuX0a5dOzZ/keLtmmzuk01ERFT9dO3QCpePB2DQxAWIiIyTGuO/6ygeP4nBrk2LYW5a8YpJkk7hFx9FIhEEQcDby/7938U3/dfWM/8+JwgCior4k5g0iiykVxW+HEPVBec6VSec75XTy9dZGDPTB+cD/5YZ4+pkh8NbV6KBq4MGM6vYND3fFanXFH6S/e/W6URERESkPFPjGjiydSWWrduJDdsOSo2JjElA1y+nYNemRfjYs42GMyRFscgmIiIiqgC0tLSwfM4ENGrgDK95a5GXX1Aq5lVWNvqPm4cVcydi2tiB1b5xTUWmdDOaf4uKikJQUBCSk5Ohp6cHa2treHp6FneAJCIiIqJ3G/RFd9R1tseQyYuQnJJe6rxEIsHC77Yg9FEk/FbNhr4e33mriFRSZGdmZmLChAk4fvy41PO9e/fG9u3bYWFhoYrhqhS++EhERET/1bJpQwQdD8DQKYtw695jqTGHTl3A05h4HPhxBepYs8aqaJTewu/Nmzfo2rUrjh07BhMTEwwaNAjffvstvvnmG3z55ZcwNjbGqVOn8PHHHyM/P18VOVcpbEZDRERE0tSxtsDZA5swpE93mTG37j1Gp76TcOveIw1mRvJQ+kn2hg0bcO/ePXz22WfYt28fTExMSpx/9eoVhg0bhjNnzmDz5s3w9vZWdkgiIiKiakFfTxdb185D44Z1sWjNVqk9SZ6lZqDHkOnYvOobDH5HQU6apfST7EOHDsHCwgIHDx4sVWADgImJCQ4dOoRatWph//79yg5HREREVK0IgoBp4wbil+2rYGpsJDUmL78A42evwsLvt3C75ApC6SL76dOn6NSpE4yMpP+lA4CRkRE6duyIJ0+eKDscERERUbX0sWcbXDr2I+o6y95QYtP2wxg4cQFevs7SYGYkjdJFto6ODrKy3v8XmZ2dzW1miIiIiJRQ38UBl47646OOH8iMOR/4N7r298KT6HgNZkb/pXSR7eHhgeDgYMTGxsqMiY6ORlBQEDw8PJQdjoiIiKhaMzc1xi/bV2Pq2IEyYyIi49D1yyn448pNDWZG/6Z0kT1p0iTk5ubik08+wdWrV0udv3LlCnr06IH8/HyMGzdO2eGqHH9/f7i7u3MLPyIiIpKbtrYWVs2bjC1r5kJXRjvxF6+y0G/st/DfdRQSiUTDGZLSRfbQoUMxbNgwREREwNPTE7Vr10abNm3Qpk0bWFtbo3Pnznjy5AkGDhyIkSNHqiLnKoVb+BEREVFZDevXA2cPbIS1ZU2p58ViMb5d6Y/J365BXh63UtYkpYtsANi7dy82bdoER0dHpKam4ubNm7h58ybS0tLg4OCAjRs34sCBA6oYioiIiIj+pXVzdwQd34LmjevLjNl/7H/oNdwbKWnPNZhZ9aaSIhsApk6diqioKMTFxeGvv/7C9evXERsbi+joaEybNo0vPRIRERGpiW0dS5w75IuBvbvJjLkR8hCefSchJDRcg5lVX0oX2XPnzsXu3buLP7ezs0Pr1q3Rpk0b2NvL3mKGiIiIiFTHQF8PO9YtwLJvJsh8uJn4LA0fD5qGo79f0nB21Y/SRfb27dvh6+urilyIiIiISAmCIMB74hAc3roSxkaGUmNy8/IxesYKLFu3Q2oHSVINpYvsgoICODo6qiIXIiIiIlKBnl3b4tJRf7g42MiM+SFgPwZPWoRXr7M1mFn1oXSRPWTIEJw/fx63b99WRT7VDrfwIyIiInVoWM8Jl48HoHO7FjJjzl66hm4DvBAVm6jBzKoHbWVv0L17dwQHBxdv2+fh4YGaNWtCJCpdvwuCgGXLlik7ZJXi5eUFLy8v2NnZITGRE5yIiIhUp6aZCU78tAbzV/+IgJ+PS415/DQWnftNxh6/JejcrqWGM6y6lC6yBw0aBEEQIJFIcP36dVy/fr1UzNvzLLKJiIiINEtbWwtrFk1FowYumLlkIwoKCkvFZL58jT6j5+D7BV9jwog+3BVOBZQushcvXsy/CCIiIqIK7quBn6K+qwOGTVmCtIzMUueLisSYvdwXDx5HYv3S6dDVld5JkuSjdJG9dOlSFaRBREREROrWtmUTBJ0IwOCJC3H/0VOpMT8fOY2IqDjs918Gy1rmGs6w6ijTi49FRUXYtGkTPD094ebmhh49emDPnj2qzo2IiIiIVMzexhrnD/uib09PmTHXbz2AZ9/JuB8mvRCn91O4yM7Pz0e3bt3g7e2NK1euIDw8HOfPn8fo0aMxcOBAdeRIRERERCpkZGiAn32XYLH3WJkx8Ukp6D5oKk6eDdJgZlWHwkX2jz/+iODgYNjY2GDTpk04ffo0vvvuO5iZmeHYsWPYt2+fOvIkIiIiIhUSBAHfTBmOAwErYGSoLzUm500uRkxdipUbd7FxjYIULrKPHj0KAwMD/Pnnn5g6dSp69uyJOXPm4PLlywCAgwcPqjxJIiIiIlKPz7t3wB+/+MPJvo7MmO8278Hwr5ciK/uNBjOr3BQush8/foxOnTrBwcGhxPGmTZuiZcuWuHfvnsqSIyIiIiL1a9TABZePBaBjm2YyY347fwUfDfwasQnPNJdYJaZwkf369WuYm0t/09TZ2RkZGRlKJ1WdsOMjERERVQQWNU1xavdajB/2hcyYh+FR8Ow7CVf/vqu5xCophYvsgoICaGtL3/lPV1cX+fn5SidVnXh5eSEsLAzW1tblnQoRERFVczo62li/bAY2rZgJbW0tqTEZmS/x+VezsfPArxrOrnIp0xZ+RERERFR1jRnSG7/tWYda5qZSzxcWFmHG4g2YuXiD1A6SxCKbiIiIiKTo0NoDQSe2oHFDF5kxOw78ii9GfYP05y81mFnlwCKbiIiIiKRytKuNC4c3o/cnHWXGXPn7Ljr3m4TQx5EazKziK1Nb9ZMnT8LFpfRPNenp6QAg9Rzwz36MkZH8CyAiIiKqLGoYGWCv31J857cHq/1+lhoTm/AMHw38GtvXLcDn3TtoOMOKqUxFdlZWFrKysmSej4mJkXpcEISyDEdERERE5UgkEmH+9FFwr++MiXO+Q86b3FIx2Tm5GDp5ERbOGI05XiOqfd2ncJH9tukMEREREVUvfXp6wsXRFoMnLUR8kvTth3027sLD8CgEfD8XRoYGGs6w4lC4yPb09FRHHkRERERUCTR1r4ugEwEY/vVSXLt5X2rMibNBiIxJxKGtPrC3qZ7bFPPFRyIiIiJSiGUtc/z28w8YNehTmTH3Hz1Fpz6TcO3WAw1mVnGwyCYiIiIihenq6sDXZxbWLZkGLS3pJWX68xf4bIQ3dh8+reHsyh+LbCIiIiIqE0EQMGFEX5zavRbmZiZSYwoKCjF1wQ/4ZrkvCguLNJxh+WGRTURERERK8WzbAkHHA+BWz0lmzJY9J9B3zBxkZFaPxjUsssuZv78/3N3dkZIi/Q1dIiIiosrA2cEGf/zij17d2smMCbx2B12/nIJHEdEazKx8sMguZ15eXggLC4O1dfV885aIiIiqDuMahjgYsALfTBkuMyYqLgndBnyNM39c02Bmmscim4iIiIhURiQSYbH3WOzetAgG+npSY15n52DwpIVYt+UAJBKJhjPUDBbZRERERKRyX37aFecObYJtbUup5yUSCZb+sB1jvX2kdpCs7FhkExEREZFaNG/cAEEntqBNi0YyY3757RJ6DJmOxOQ0DWamfiyyiYiIiEhtrC1r4vTe9Rjev4fMmJDQCHTqOxF/33mowczUi0U2EREREamVnp4uflw9B98v9IJIJL38TE3PRK9hM7Hv2P80nJ16sMgmIiIiIrUTBAFTRvXH8Z3fwcykhtSY/IICTJ77Pb5d6V/pG9ewyCYiIiIijenW8QNcPh6A+q4OMmP8dx1F/3HfIvPlaw1mplossomIiIhIo+o62eHSUX983LmNzJg/rt5Cly+nIDwyToOZqQ6LbCIiIiLSOFPjGjiydSVmThgiMyYyJgFdv5yC80F/azAz1WCRTURERETlQktLC8vnTMCOdfOhp6sjNeZVVjb6j5uHTTsOV6rGNSyyiYiIiKhcDfqiO84d8kUdawup5yUSCRZ+twUTZq9Gbl6+hrMrGxbZRERERFTuWjZtiKDjAWjl0VBmzKFTF9Bz6HQkp6RrMLOyYZFNRERERBVCHWsLnD2wCUP6dJcZc+veY3TqOwm37j3SYGaKY5GtoBo1apT40NHRQdOmTcs7LSIiIqIqQV9PF1vXzsPKbyfLbFzzLDUDPYZMx5FfL2o4O/mxyFZQVlZWiQ83NzcMHjy4vNMiIiIiqjIEQcC0cQPxy/ZVMDU2khqTl1+ASXPX4OBvV1BUVPEa17DIVsKNGzcQFhaGUaNGlXcqRERERFXOx55tcOnYj6jrbC8z5nTgbQydsgQvX2dpMLP3q3RF9urVqzFgwAC4uLhAEAQ4OTnJjBWLxdiwYQMaNmwIfX192NvbY9asWcjOzlZJLjt37kTPnj1hY2OjkvsRERERUUn1XRxw6ag/Pur4gcyYC8E30LW/F55Ex2sws3erdEX2/PnzcenSJbi6usLc3PydsTNnzoS3tzfc3d3h5+eHAQMGwNfXF59//jnEYnGJ2MGDB0MQBJkfgYGBJeKzs7Nx6NAhjBs3TtVfIhERERH9i7mpMX7ZvhpTxw6UGRMRGYfeI2cjr4Js8add3gkoKjIyEi4uLgCAxo0bIytL+q8GHj58CD8/P/Tr1w/Hjh0rPu7s7Ixp06bh0KFDGDp0aPHx7du3Y/PmzTLHNTU1LfH5L7/8AkNDQ3z66afKfDlEREREJAdtbS2smjcZjRo4Y9qC9cgvKCgVs3bxVOjp6ZZDdqVVuifZbwvs9zl48CAkEglmzJhR4vj48eNhaGiIffv2lThubGwMCwsLmR86OiW7EO3YsQNfffUVtLUr3c8pRERERJXWsH49cPbARlhb1ixxfNHMMfise4dyyqo0QVKZ+lP+x9sn2TExMaXOffLJJ7h48SJycnKgp6dX4lz79u0RERGBtLS0Mo0bHh4ONzc3hIeHo169eu+MXb9+PdavX//eeyYmJgIARCIR6tSpU6a8FCWRSJCXlwc9PT0IgqCRMYnKA+c6VSec71RdFBUV4fmLVygoKIS+vh5qmpmofczk5GSIxWLo6OggP//dy1Kq7GPYpKQkWFhYlCqwAcDW1hbXrl1Dfn4+dHUV/5XCzp070bFjx/cW2ADw6tWr4gJaHmKxWKF4IiIiouruTXY+ErNfa2w8ebYMrLJFtrQn2G/p6+sXx5SlyF6zZo3csSYmJrC1tX1vXFJSEgBAW1sbVlZW74xNSUmBtbX1e+/5vri3P41p8um5psn7Z1WZc1DV/ZW5j6LXKhKvivleHeY6wPmuqftwvlcMVX2+q/LenO+qk5qaiqKiouJa8p0klVijRo0kjo6OUs81btxYYmVlJfXcgAEDJAAkeXl5asxOfdzc3FQSZ2trKwEgsbW1VUVaFZK8f1aVOQdV3V+Z+yh6rSLxqpjv1WGuSySc75q6D+d7xVDV57sq7835Xj4q3YuP8rKxsUF6ejry8vJKnUtMTISFhUWZnmJXBF5eXiqNq8oqwp+BunNQ1f2VuY+i1yoSz/kuv4rwZ8D5rlw857v8KsKfgTpzUOW9Od/LR5V98XHhwoVYuXIlgoOD0bFjx+Ljubm5qFWrFjp16oSzZ89qMNuKx87ODomJibC1tUVCQkJ5p0OkNpzrVJ1wvlN1UpHne5V9kj1o0CAIgoCNGzeWOL59+3bk5ORg2LBh5ZMYEREREVV5le7Fx7179yI2NhYAkJaWhvz8fPj4+AAAHB0dMWLECABAkyZN4OXlhc2bN6Nfv37o1asXHj16BF9fX3h6epZoRENEREREpEqVrsjeuXMngoKCShxbtGgRAMDT07O4yAaAjRs3wsnJCdu2bcPp06dhYWGBqVOnYvny5RCJquxDfCIiIiIqZ5WuyA4MDJQ7VktLC7NmzcKsWbPUlxARERER0X/wcS4RERERkYqxyCYiIiIiUrFKt1yEVMfb2xuvXr2CiYlJeadCpFac61SdcL5TdVKR53ul3iebiIiIiKgi4nIRIiIiIiIVY5FNRERERKRiLLKJiIiIiFSMRTa9U2FhIaZPn46aNWvCzMwMY8eORW5ubnmnRaQ2R44cQYcOHVCjRg04OTmVdzpEapGXl4fx48fDxcUFxsbGqF+/Pvz8/Mo7LSK1mTJlCuzt7WFiYgJbW1vMmDED+fn5ah2TRTa906pVq3D58mU8ePAAT548QVhYGObMmVPeaRGpjbm5Ob7++musXLmyvFMhUpvCwkLUrl0b58+fx8uXL3HkyBH4+PjgyJEj5Z0akVp8/fXXePz4MV69eoV79+7h3r17WLVqlVrH5O4i9E4ODg5Ys2YNBg8eDAA4d+4cBgwYgMzMTGhpaZVzdkTqc/LkScyYMQMxMTHlnQqRRowfPx4GBgbw9fUt71SI1CotLQ2DBw9G7dq1sX//frWNwyfZVcTq1asxYMAAuLi4QBCEd/6aWywWY8OGDWjYsCH09fVhb2+PWbNmITs7u0TcixcvEB8fj2bNmhUfa9GiBV6/fs3Cg8qdOuY8UUWkibleUFCAK1euoGnTpirOnkgx6pzv3333HWrUqAErKyvcu3cPM2bMUM8X8ZaEqgQAkpo1a0o++ugjibm5ucTR0VFm7LRp0yQAJH379pVs27ZNMnPmTIm2trakS5cukqKiouK4uLg4CQBJcnJy8bH8/HwJAElISIgavxqi91PHnP+3EydOvPOeRJqi7rkukUgkEyZMkLRq1UqSl5enhq+ASH6amO9hYWGSBQsWSOLj49XwFfwfFtlVRGRkZPF/N2rUSOakDA0NlQiCIOnXr1+J476+vhIAkv379xcfy8zMlACQPH78uPhYamqqBIDk6dOnqv0CiBSkjjn/byyyqaJQ91yfOXOmpEmTJpK0tDSV5UxUVuqe728dOXJE0rlzZ6XzfRcuF6kiXFxc5Io7ePAgJBJJqV+RjB8/HoaGhti3b1/xMTMzM9jb2+Pu3bvFx0JCQmBsbMxdF6jcqWPOE1VE6pzrM2bMwIULF/DHH3/AwsJCFekSKUVT39sLCgoQERFR1jTlwiK7mrl58yZEIhFat25d4ri+vj6aNWuGmzdvljg+btw4rF69GklJSUhLS8PSpUsxatQovvRIlYaic76oqAi5ubkoKCiARCJBbm4u8vLyNJkyUZkoOtenTZuGixcv4tKlS7C0tNRkqkRKU2S+v3z5Ert378aLFy8gkUhw//59+Pj44JNPPlFrjiyyq5mkpCRYWFhAT0+v1DlbW1ukp6eX2Ddy/vz56NSpExo1aoS6devCzc0N33//vSZTJlKKonN+7969MDAwwMCBAxEXFwcDAwM0aNBAkykTlYkicz02NhZ+fn54+vQpnJ2dUaNGDdSoUQM9e/bUdNpEZaLIfBcEAfv27SveF75Pnz7o1auX2veG11br3anCycnJkTohgX9++nsbo6urCwDQ1taGr68vt3SiSkvROT9q1CiMGjVKU+kRqYwic93R0RES7uBLlZgi893ExAQXL17UZHoA+CS72jE0NJT5q++3nRwNDQ01mRKRWnHOU3XBuU7VSWWY7yyyqxkbGxukp6dLnZiJiYmwsLAofqJHVBVwzlN1wblO1UllmO8ssquZDz74AGKxGDdu3ChxPDc3F3fv3kWrVq3KKTMi9eCcp+qCc52qk8ow31lkVzODBg2CIAjYuHFjiePbt29HTk4Ohg0bVj6JEakJ5zxVF5zrVJ1UhvnOFx+riL179yI2NhYAkJaWhvz8fPj4+AAAHB0dMWLECABAkyZN4OXlhc2bN6Nfv37o1asXHj16BF9fX3h6emLo0KHl9jUQKYJznqoLznWqTqrUfFdrqxvSGE9PTwkAqR+enp4lYgsLCyU//PCDpH79+hJdXV2JjY2NZObMmZLXr1+XT/JEZcA5T9UF5zpVJ1VpvgsSCffwISIiIiJSJa7JJiIiIiJSMRbZREREREQqxiKbiIiIiEjFWGQTEREREakYi2wiIiIiIhVjkU1EREREpGIssomIiIiIVIxFNhERERGRirHIJiIiIiJSMRbZREREREQqxiKbiIiIiEjFWGQTEREREakYi2wiogpMIpFUizGJiKoaFtlERAqKiYmBIAhyfYwaNarM4xw8eBBDhgxROt9Ro0ZBEATs2LGj+NjSpUshCAIWLlz43jFlxVYkgYGBEAQBIpEIwcHB74zt3LkzBEHAxYsX33vft1/7249mzZqpKON/vP27efvRoUMHld6fiMqPdnknQERUmQ0bNuyd59u1a1em+wYHB2Po0KFo3759ma6vLGOqmkQiwZgxY3D//n0YGhqq7L6NGzeGh4cHHB0dVXZP4J/5UVhYiJSUFLmKfiKqPFhkExEpYd++fWq5r1gsVst93/r6668xePBgWFhYvHdMabEVWWRkJObNm4dNmzap7J5ffPEFfHx8VHa/tyZMmIAJEyYgMDCQRTZRFcPlIkRE1ZCFhQUaNmwoV+GsSGx5q127NrS1tbF582ZcvXq1vNMhomqMRTYRkYZkZmZi6dKlaNWqFUxNTaGrq4s6deqgf//+uHnzZnHcqFGj0KVLFwDAn3/+CUEQ0Llz5zLdS5b/rrN+15jvWpN98eJF9OrVC7Vq1YK+vj7c3NywdOlSZGdnl4o9e/YsevToAVtbW+jp6cHBwQFfffUVHj16JNefnzxcXV0xZ84ciMVijB49Gm/evFHZvYmIFMEim4hIA1JTU/HBBx9g2bJleP78Obp27Yru3btDIpHg2LFj6NChA27dugXgn3W6H330EQDA0tISw4YNQ/fu3ct0L3m9b0xpvvvuO3Tv3h0XL15Ew4YN8emnn+LVq1dYtmwZOnTogMzMzOLYvXv34tNPP8Xly5fh5uaGzz//HEZGRtizZw9at26N0NBQhfJ9l8WLF6NRo0Z4+vQp5s+fr7L7EhEpgkU2EZEG+Pj4IDIyEl9//TUiIyNx4sQJnD59GjExMfjiiy+Qn5+PrVu3Avhnne6CBQsAAPXr18e+ffuKP1f0XvJ635j/dfnyZcyfPx92dna4desW/vzzTxw7dgxRUVEYNWoU7t69i6lTpxbHL126FFpaWggJCcHFixdx9OhRhIWFYfr06cjKysIPP/ygUL7voqenh127dkFLSwu+vr74888/VXZvIiJ5scgmIlLCu7bv27hxY3FczZo10aNHDyxfvhyCIBQf19fXx+jRowEA0dHRco2pynuV1Zo1ayCRSLBp0yY0bdq0+Lienh5+/PFHWFtb49ChQ0hMTAQAJCcnQ0dHBzY2NsWxgiBg/vz58PPzw5gxY1Sa3wcffIDZs2dDLBZjzJgxXDZCRBrH3UWIiJTwri383Nzciv976dKlpc5nZmbiwYMHOHfuHAAgLy9PrjFVea+yKCoqKt6L+u067n8zMDBAp06d8Msvv+DKlSsYPHgwOnXqhHPnzqFly5YYOXIkevbsiVatWsHKygpff/21WvJctmwZfv31Vzx69AgLFy7EunXrVHr/OXPm4Ndff1X4uh07dnA/bKJqgEU2EZESFNnCLzo6Gv7+/rh69SoiIiKK1yy/fRqtSKdFVd5LURkZGcjJyQHwz1P1d4mPjwfwT2HZp08f3L59G0uXLsXSpUtRs2ZN9OrVC2PGjJFarCvr7bKR9u3bY+PGjejfvz/atm2rsvsnJSUhPDxc4euysrJUlgMRVVwssomINODgwYMYOXIkCgsL4eLigo8++ggNGzZEq1atIJFI0KdPn3K5V1kUFRUB+KeI7d+//ztj69atCwCws7PDzZs3ERwcjF9//RUXL17EgwcPsG/fPuzbtw+zZs1S6brst9q0aQNvb2+sXbsWo0ePxt27d1V277e5ExFJwyKbiEjNsrKyMHHiREgkEpw4caJUEXzixIlyuVdZ1apVCzo6OigoKMDOnTuhp6cn13WCIMDT0xOenp4A/tklZdeuXZg/fz7Wr1+PadOmwcHBQeX5Ll++HL/++ivCw8OxaNEild+fiEgavvhIRKRmoaGheP36NZo0aSL1KfP58+cBlOy4+O8XGpW9l7xkjflfurq6aNu2LcRicfEa8H+TSCTo0qUL2rVrhxs3biAsLAxNmzZFz549S8RZWVlh7ty5aNq0KSQSSfFLkqqmr6+PXbt2QSQSYf369Xj8+LFaxiEi+jcW2UREamZpaQkACA8PL7GGVyKRYMuWLdi2bRsAIDc3t/icvr4+AODly5dK30tessaUZubMmQD+abkeEhJSfFwsFmPhwoUIDAxEdHQ0PDw8UL9+fSQlJeHcuXM4evRoifvcvn0bjx49gpGREdzd3Uuce/z4MR4/fly8/lsZbdu2xYwZMyAWi5GSkqL0/YiI3odFNhGRmrm6uqJ379548+YNmjVrhp49e6Jv375wcnLC5MmT0bBhQwAoUfw5OztDS0sLoaGh6NatW3FRW5Z7yUvWmNL06dMHs2fPRnx8PFq3bo0PP/wQ/fr1Q7169bBq1SoYGhri2LFj0NPTg7a2dnHxP2DAALRs2RIDBgxA586d0aZNG+Tl5eGHH36AqalpiTHc3Nzg5uaGGzduKPy1SOPj44P69eur5F5ERO/DIpuISAMOHTqE5cuXw9nZGYGBgbh48SJq1aqF7777Drdv30aTJk2QlJSE27dvA/hnKcXOnTvh7OyMK1eu4LfffivzveT1rjGlWbt2LX799Vd069YNEREROHPmDEQiEcaOHYt79+6hXbt2xbH9+vXDuXPn0LNnT8TFxeHkyZMICwtDz5498ccff2DSpEkK5VoWBgYG+OmnnyAS8Z8+IlI/QaLOfZ6IiIiUYGJigkuXLqFVq1blMv7SpUuxbNkyLFiwAD4+PmobJzAwEF26dEH79u1x9epVtY1DRJrDH+eJiKhCunr1KgoLC9GgQYPyToWISGHcwo+IiCqcwsJCjB49GuvXr4exsXF5p4NTp04hJiYGjo6OWLlypcruu23bNgQHB/NlTKIqiEU2ERFVONra2ggJCUGNGjXKOxUA/2ydGBoaCg8PD5UW2deuXcP+/ftVdj8iqji4JpuIiIiISMW4JpuIiIiISMVYZBMRERERqRiLbCIiIiIiFWORTURERESkYiyyiYiIiIhUjEU2EREREZGKscgmIiIiIlIxFtlERERERCrGIpuIiIiISMVYZBMRERERqdj/A86zMlvFqrWsAAAAAElFTkSuQmCC", + "text/plain": [ + "<Figure size 800x600 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# -----------------------------------------------------------------\n", + "plot_title = \"\"\n", + "font = \"Arial\"\n", + "x_label = \"Fatalities, N [$-$]\"\n", + "y_label = \"Probability of Exceedance, $1-F_N(n)$ [$-$]\"\n", + "legend = True\n", + "grid = True\n", + "save_svg = True\n", + "remove_ticks = False\n", + "remove_ticks_labels = False\n", + "file_name = \"../book/figures/risk_types\"\n", + "# -----------------------------------------------------------------\n", + "\n", + "fig = plt.figure(figsize=(8,6))\n", + "ax = fig.add_subplot() # axes_class=AxesZero)\n", + "ax.set_title(plot_title, fontfamily=font)\n", + "ax.set_xlabel(x_label, fontfamily=font)\n", + "ax.set_ylabel(y_label, fontfamily=font)\n", + "\n", + "plt.setp(ax.spines.values(), linewidth=2)\n", + "# ax.spines[\"left\"].set_position((\"data\", 0))\n", + "# ax.spines[\"bottom\"].set_position((\"data\", 0))\n", + "# ax.spines[\"top\"].set_position((\"data\", 1))\n", + "# ax.spines[\"right\"].set_position((\"data\", 100))\n", + "\n", + "# not a permanent solution (removed the part below 0)\n", + "# ---> find a better way to auto set upper bound\n", + "# ax.spines.bottom.set_bounds(0, 100)\n", + "# ax.spines.left.set_bounds(0, 1.0)\n", + "# ax.spines.top.set_bounds(0, 100)\n", + "# ax.spines.right.set_bounds(0, 1.0)\n", + "\n", + "# Given Parameters\n", + "\n", + "N_fatalities = np.linspace(1,1000,1000) # fatalities\n", + "\n", + "P_df = 0.1; beta = 0.1\n", + "\n", + "alpha = 2\n", + "k = 3\n", + "N_A = 100\n", + "\n", + "r= 0.025\n", + "I = 5*10**6\n", + "B = 0.33\n", + "\n", + "# Individual Risk\n", + "\n", + "Pf_ind_risk = (beta*(10**-4))/P_df # per year\n", + "\n", + "# print('Acceptable Failure Probability: ', Pf_ind_risk)\n", + "\n", + "# Societal Risk\n", + "\n", + "C = ((beta*100)/(k*np.sqrt(N_A)))**2 # binomial distribution\n", + "\n", + "Pf_SR = (C/(N_fatalities**alpha))\n", + "\n", + "# Economic Risk\n", + "\n", + "D_damage = (5*10**7)*N_fatalities\n", + "\n", + "Pf_ER = (I*B*r)/(D_damage)\n", + "\n", + "# Visualize\n", + "\n", + "# plotting\n", + "ax.plot(N_fatalities, Pf_SR, label='Societal Risk', color=colors[0], linewidth=4)\n", + "ax.plot(N_fatalities,Pf_ER, label='Economic Risk', color=colors[1], linewidth=4)\n", + "ax.axhline(Pf_ind_risk, label='Individual Risk', color=colors[2], linewidth=4)\n", + "\n", + "# ax.plot(1, 0, \">k\", transform=ax.get_yaxis_transform(), clip_on=False)\n", + "# ax.plot(0, 1, \"^k\", transform=ax.get_xaxis_transform(), clip_on=False)\n", + "\n", + "ax.set_xscale('log')\n", + "ax.set_yscale('log')\n", + "\n", + "ax.set_ylim(10**(-7),.1)\n", + "# ax.set_yticks([10**(-7),10**(-5),10**(-3),10**(-1)])\n", + "\n", + "ax.tick_params(axis='x', labelsize=13, width=2, length=8)\n", + "ax.tick_params(axis='y', labelsize=13, width=2, length=8)\n", + "\n", + "if grid: ax.grid()\n", + "if legend: ax.legend(prop={\"family\":font})\n", + "if remove_ticks: ax.set_xticks([]); ax.set_yticks([])\n", + "if remove_ticks_labels: ax.set_xticklabels([]); ax.set_yticklabels([])\n", + "if save_svg: plt.savefig(file_name + '.svg')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "59293d62", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.7" + }, + "widgets": { + "application/vnd.jupyter.widget-state+json": { + "state": {}, + "version_major": 2, + "version_minor": 0 + } + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/figures/solution.py b/figures/solution.py new file mode 100644 index 0000000..271f531 --- /dev/null +++ b/figures/solution.py @@ -0,0 +1,264 @@ +"""Set of helper functions for Week 8 part of Project 4, 2023. + +Primary purpose is: + 1) define dictionaries to track information about bivariate + and univariate probability models, as well as a few + important characteristics, + 2) print and plot results, + 3) perform simple calculations (e.g., covariance, ecdf etc). + +Organized in order used in solution notebooks. +""" + +import numpy as np +import matplotlib.pyplot as plt +import scipy.stats as st + +from helper import plot_contour +from helper import Bivariate + +def univariate_RV_dict(name, symbol, unit): + """Create a dictionary to track a random variable.""" + d = {"name":name, "symbol":symbol, "unit":unit} + d = create_plot_label(d) + return d + +def create_plot_label(univariate_dict): + """Combine RV name, symbol, unit into key xlabel.""" + univariate_dict["label"] = (univariate_dict["name"] + ", " + + univariate_dict["symbol"] + " [" + + univariate_dict["unit"] + "]") + return univariate_dict + +def univariate_model_dict(dist_type, parameters, + distribution, empirical=False, note=None): + """Create a dictionary to track a distribution model. + + dist_type: string, + parameters: tuple, from scipy.stats rv_continuous + distribution: frozen instance of scipy.stats.rv_continuous + empirical: boolean. Set to True if distribution is a sample + (array). This is just a placeholder to support other functions + that will be used for printing results + (e.g., compare_univar_prob). + note: string (optional) + """ + model = {"type":dist_type} + model["parameters"] = parameters + model["distribution"] = distribution + model["empirical"] = empirical + model["note"] = note + + if empirical: + model["N"] = len(distribution) + model["sample"] = distribution + + return model + +def print_dist_model_summary(RV, model_key): + """Prints info about a model.""" + print(f'Random variable {RV["name"]}, model \"{model_key}\" is:\n' + f' distribution: {RV[model_key]["type"]}\n' + f' parameters: {[f"{i:.3f}" for i in RV[model_key]["parameters"]]}\n' + f' (μ,σ) dist: ' + f'({RV[model_key]["distribution"].mean():.3f}, ' + f'{RV[model_key]["distribution"].std():.3f})\n' + f' (μ,σ) data: ' + f'({RV["data"].mean():.3f}, {RV["data"].std():.3f})\n') + +def calculate_covariance(X1, X2): + """Covariance of X1 and X2 (numpy arrays).""" + mean_x1 = X1.mean() + mean_x2 = X2.mean() + diff_x1 = X1 - mean_x1 + diff_x2 = X2 - mean_x2 + product = diff_x1 * diff_x2 + covariance = product.mean() + return covariance + +def pearson_correlation(X1, X2): + """Pearson correlation of X1 and X2 (numpy arrays).""" + covariance = calculate_covariance(X1, X2) + correl_coeff = covariance/(X1.std()*X2.std()) + return correl_coeff + +def bivariate_model_dict(model_name, + X1_key, X1, X2_key, X2, rho): + """Create dictionary to track the bivariate model. + + model_name: string. Arg is root name, which has + marginal info added; used for plot title. + X1, X2: dict.from univariate_RV_dict() + X1_key, X2_key: string. Name of model of X1, X2 + rho: correlation coefficient + + returns: dictionary + """ + + d = {"X1_key":X1_key, "X1":X1[X1_key], + "X2_key":X2_key, "X2":X2[X2_key], + "rho":rho} + + d["title"] = (model_name + ": " + + r"$X_1 \sim$" + X1_key + ", " + + r"$X_2 \sim$" + X2_key + ", " + + r"$\rho$ = " + f"{rho:.2f}") + + d["xlabel"], d["ylabel"] = X1["label"], X2["label"] + d["X1X2"] = Bivariate(d["X1"]["distribution"], + d["X2"]["distribution"], + d["rho"]) + d["data"] = np.array([X1["data"], X2["data"]]) + d["data_X1"], d["data_X2"] = X1["data"], X2["data"] + + return d + +def compare_bivar_prob(point, model): + """Compare probabilities at a given point (bivariate). + + point: array or list; size = 2. + model: dictionary defining bivariate distribution. + + returns: none, except printed output. + """ + + data_X1 = model["data_X1"] + data_X2 = model["data_X2"] + N = data_X1.size + + left_emp = sum(data_X1 < point[0])/N + bottom_emp = sum(data_X2 < point[1])/N + lower_left_emp = sum((data_X1 < point[0])*(data_X2 < point[1]))/N + + union_emp = 1 - lower_left_emp + intersection_emp = 1 - (left_emp + bottom_emp - lower_left_emp) + + lower_left = model["X1X2"].cdf(point) + union = 1 - lower_left + + left = model["X1"]["distribution"].cdf(point[0]) + bottom = model["X2"]["distribution"].cdf(point[1]) + intersection = 1 - (left + bottom - lower_left) + + print(f'-------------------------------------------------') + print(f' Comparison, Empirical Values in ( )') + print(f'-------------------------------------------------') + print(f'Lower left, P[X1<x1, X2<x2] = {lower_left:.5f}', + f'({lower_left_emp:.5f})') + print(f'Left side, P[X1<x1] = {left:.5f}', + f'({left_emp:.5f})') + print(f'Bottom half, P[X2<x2] = {bottom:.5f}', + f'({bottom_emp:.5f})') + print(f'-------------------------------------------------') + print(f'Case 1: P[X1>x1 or X2>x2] = {union:.5f}', + f'({union_emp:.5f})') + print(f'Case 2: P[X1>x1 and X2>x2] = {intersection:.5f}', + f'({intersection_emp:.5f})') + print(f'-------------------------------------------------') + +def compare_univar_prob(point, model, dist_key): + """Compare probabilities at a given point (univariate). + + point: float + model: dictionary defining univariate distribution + dist_key: specify which distribution model to use + + returns: none, except printed output. + """ + + data = model["data"] + N = data.size + p_data = sum(data < point)/N + if model[dist_key]["empirical"]: + N_model = model[dist_key]["N"] + n_eval = sum(model[dist_key]["sample"]<point) + p_model = n_eval/N_model + else: + X = model[dist_key]["distribution"] + p_model = X.cdf(point) + + print(f'---------------------------------------') + print(f' Results for {model["name"]}, case {dist_key}') + print(f' Comparison, Empirical Values in ( )') + print(f'---------------------------------------') + print(f'P[X<x] = {p_model:.5f} ({p_data:.5f})') + print(f'P[X>x] = {1 - p_model:.5f} ({1 - p_data:.5f})') + print(f'There are {N} points in the data set.') + if model[dist_key]["empirical"]: + print(f'This distribution is from MCS:') + print(f' number of smaples = {N_model}') + print(f'---------------------------------------') + +def ecdf(var): + """Empirical cdf from list or array. Returns [F(x), x].""" + x = np.sort(var) + n = x.size + y = np.arange(1, n+1) / (n + 1) + return [y, x] + +def ecdf_inverse(p, data, exceedance=False): + """Compute x = F^-1(p) for an empirical distribution.""" + N = len(data) + if exceedance: + p = 1 - p + index = int(np.floor(p*(N + 1))) + x = np.sort(data)[index - 1] + return x + +def semi_log_plots(dist_1, dist_2, exceedance=True): + """Helper function for plot_univariate_comparison. + + dist_1, dist_2: ndarray, list. Empirical distributions. + exceedance: bool. Default (True) plots exceedance, 1 - F(x) + + returns: matplotlib objects fig, ax + """ + fig, ax = plt.subplots(1, 1, figsize=(8, 5)) + + e_dist_1 = ecdf(dist_1) + e_dist_2 = ecdf(dist_2) + if exceedance: + e_dist_1[0] = 1 - e_dist_1[0] + e_dist_2[0] = 1 - e_dist_2[0] + + ax.step(e_dist_1[1], e_dist_1[0], + color='k', label='Data') + ax.step(e_dist_2[1], e_dist_2[0], + color='r', label='MCS Sample') + ax.set_xlabel('$Z(X_1,X_2)$') + ax.set_yscale('log') + ax.legend() + ax.grid() + return fig, ax + +def plot_univariate_comparison(rv_dictionary, dist_key, plot_values): + """Compare univariate plots. + + Assumes model is an empirical distribution (MCS + + rv_dictionary: dict. Created from univariate_RV_dict() + dist_key: str. Name of probability model + plot_values: array, list (size 4). Limits of X and Y, respectively. + returns: none, except printed output. + """ + + data = rv_dictionary["data"] + model = rv_dictionary[dist_key]["sample"] + + fig, ax = plt.subplots(1) + ax.hist([data, model], + bins=plot_values, + density=True, + edgecolor='black'); + ax.legend(['Data', 'MCS Sample']) + ax.set_xlabel('$Z(X_1,X_2)$') + ax.set_ylabel('Empirical Density [--]') + ax.set_title('Comparison of Distributions of $Z$'); + + fig, ax = semi_log_plots(data, model, exceedance=False) + ax.set_ylabel('CDF, $\mathrm{P}[Z < z]$') + ax.set_title('Comparison: CDF (log scale expands lower tail)') + + fig, ax = semi_log_plots(data, model, exceedance=True) + ax.set_ylabel('CDF, $\mathrm{P}[Z < z]$') + ax.set_title('Comparison: CDF (log scale expands lower tail)') \ No newline at end of file diff --git a/figures/template_blank.svg b/figures/template_blank.svg new file mode 100644 index 0000000..39783aa --- /dev/null +++ b/figures/template_blank.svg @@ -0,0 +1,534 @@ +<?xml version="1.0" 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https://__token__:glpat-JduurUdhDczFJzvzZN4G@gitlab.tudelft.nl/api/v4/projects/13957/packages/pypi/simple +citg-jb-stack +--extra-index-url https://gitlab.tudelft.nl/api/v4/projects/17983/packages/pypi/simple +jupyterbook_patches ~= 0.1.3 +--extra-index-url https://gitlab.tudelft.nl/api/v4/projects/11239/packages/pypi/simple +sphinx-thebe == 0.2.1000 + +# lastly any packages you wish to download directly from a Git repository +download_link_replacer @ git+https://gitlab.tudelft.nl/mude/sphinx-download-link-replacer@dlr-0.1.2 \ No newline at end of file