71 lines
2.5 KiB
TeX
71 lines
2.5 KiB
TeX
\documentclass[addpoints,11pt]{exam}
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\usepackage{url}
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\usepackage{color}
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\usepackage{hyperref}
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\pagestyle{headandfoot}
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\runningheadrule
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\firstpageheadrule
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\firstpageheader{Scientific Computing}{Project Assignment}{WS 2016/17}
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%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
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\firstpagefooter{}{}{{\bf Supervisor:} Jan Grewe}
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\runningfooter{}{}{}
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\pointsinmargin
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\bracketedpoints
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%\printanswers
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%\shadedsolutions
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\begin{document}
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%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
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\sffamily
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% \begin{flushright}
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% \gradetable[h][questions]
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% \end{flushright}
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\begin{center}
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\input{../disclaimer.tex}
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\end{center}
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%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
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\section*{Random walk with memory.}
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Some animals perform a random walk when searching for food. In some
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cases this random walk is not completely random. In fact, sometimes
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there is some memory involved. Whenever there is a positive gradient
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in food gain between successive steps the animal will continue in the
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very same direction as before. When the next step leads to a decrease
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in food gain the animal switches back to a random walk.
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\begin{questions}
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\question{} The accompanying dataset (random\_world.mat) contains a
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single variable. This is the world (10000\,m$^2$ area with
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10\,cm spatial resolution) in which there are randomly distributed
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food sources (Gaussian blotches of food).
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\begin{parts}
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\part{} Create a plot of the world.\\[0.5ex]
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\part{} Create a model animal that performs a pure random walk. The
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agent can walk in eight different directions (the cardinal and
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diagonal directions) with a stepsize of 10\,cm
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(approximately). Let the agent start at a random location in the
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world and count how much food it eats in 10000 steps (eaten food
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disappears from the world, of course). If the agent bumps into the
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borders of the world choose a different direction.\\[0.5ex]
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\part{} Plot a typical example walk. (You can also make an animation
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with MATLAB)\\[0.5ex]
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\part{} Same as above, but create a model animal that has some memory,
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i.e. the direction is kept constant as long as there is a positive
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gradient in the food gain. Otherwise, a random walk is performed.\\[0.5ex]
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\part{} Plot a typical example walk also for this agent.\\[0.5ex]
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\part{} Compare the performance of the two agents. Create
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appropriate plots and apply statistical methods. You will need to
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run the simulations several times to get a good estimate of the
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neumbers.
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\end{parts}
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\end{questions}
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\end{document}
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