55 lines
2.3 KiB
TeX
55 lines
2.3 KiB
TeX
\documentclass[a4paper,12pt,pdftex]{exam}
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\newcommand{\ptitle}{Random walk}
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\input{../header.tex}
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\firstpagefooter{Supervisor: Jan Grewe}{phone: 29 74588}%
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{email: jan.grewe@uni-tuebingen.de}
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\begin{document}
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\input{../instructions.tex}
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%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
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\section*{Random walk with memory.}
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The movement pattern of some animals can be described as a random walk when
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searching for food. In some cases this random walk is not completely
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random. In fact, sometimes there is some memory involved. Whenever
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there is a positive gradient in food gain between successive steps the
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animal will continue in the very same direction as in the step before. When the
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next step leads to a decrease in food gain the animal switches back to
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a random walk and changes directions randomly.
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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 using \code{imshow}.\\[0.5ex]
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\part{} Create a model animal (agent) 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, see plotting chapter in the script).\\[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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\part{} Can you think about better search strategies?
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\end{parts}
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\end{questions}
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\end{document}
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