1. Take-Home Exam Questions on ‘Brain and Computation’
Brain and Computation (Spring 2010)
Brain-Mind-Behavior Concentration Program
[Course homepage: http://bi.snu.ac.kr/  Courses  Brain and Computation]
Instructor: Prof. Byoung-Tak Zhang
School of Computer Science and Engineering
Cognitive Science, Brain Science, and Bioinformatics Programs
Seoul National University
April 15, 2010
Due: 1:00 PM, Thursday, April 22, 2009
Submission form: both in electronic and hard copy to
M. G. Kang at mgkang@bi.snu.ac.kr (Room 302-314-1, Tel. 02-880-1847)
Answer the following 5 questions. The length of each answer is limited to two A4 pages, so that the total
number of your answer sheets does not exceed 10 pages. Each question addresses a specific topic or
theme and includes several sub-questions. Try to address the theme in general by using the sub-
questions as hints to guide your answers. Try not to answer the sub-questions piece by piece; they
should be part of your discussion of the general topic. Try also to use as many equations as possible if
you think they will make your answers concise and precise. For some questions, you may also write a
short essay on the topic. The text book can be used for answering your questions, but attempt to formulate
your own sentences and avoid transcribing the sentences in the text.
1. (20 points) Conductance-based models of neurons consider the detailed chemical and
electrical processes in signal transmission within and between neurons. How does an action
potential initiate the synaptic transmission? How are the signals transmitted from the
presynaptic neuron to the postsynaptic membrane? How are the signals propagated from the
postsynaptic membrane to the axon terminal? How are the action potentials generated and
propagated? Explain the mechanisms for ion-channels, the resting potential, depolarization, and
hyperpolarization in neurons.
2. (20 points) Leaky integrate-and-fire neurons are a typical computational model of neurons in
the brain. What kinds of ion-channel dynamics are described by this model and what aspects are
not modeled? Give the equations defining the basic integrate-and-fire (IF) neurons. How do you
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2. model the response of IF neurons to constant input currents? How do you extend this basic
model to the general case for time-varying input currents? How can we include noise in the
neuron models to describe some of the stochastic processes within neuronal responses?
3. (20 points) Networks of many neurons are believed to be necessary to realize higher-order
mental functions in the brain. How are the neuronal networks organized? How is information
transmitted in networks of neurons? What is a chain model of network organization? What is a
random network model of information transmission? How is information transmission modeled
in large random networks? How is the activity of small random networks spread? What are
netlets? What is a population dynamics model of neurons? How does it differ from the models
of spiking neurons? How can population dynamics of neurons be related with neuronal
networks?
4. (20 points) How do neurons learn to build associations? What is the synaptic plasticity? What
are LTP and LTD? What is the spike timing dependant plasticity (STDP) and what types of
STDP are discovered? What is activity-dependent synaptic plasticity? What is Hebbian
learning? Give mathematical formulations of Hebbian learning and explain their meaning. Can
you use the Hebbian learning algorithm to explain the conditioning mechanism?
5. (20 points) Feed-forward mapping networks have been studied with respect to both
computational neuroscience and machine learning. What is a typical mapping function? Give an
example. Give a mathematical description of the computational process of a feed-forward
mapping network, i.e. propagating the signals from the input units to the output units. What does
it mean by that a multilayer feed-forward network is a universal function approximator? What is
generalization in learning? Why is it necessary to design the network structure of a multilayer
mapping network? How do you design the network structure by a genetic algorithm?
The end.
(100 points in total)
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