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Assignment 1:

  1. Give three examples of models and argue briefly what makes them models.
  2. Modify the simulation program for a synapse (Table 2.1) to shows the time course of the EPSP when the synapse is stimulated with neurotransmitters every 20 ms.
  3. Given is a membrane with capacitance 1000µF and a voltage-gated and time-dependent ion channel. This channel has a reversal potential of -1mV and supports an inward current of positive ions with conductance g_0 = 1S in it's base state. When the membrane potential exceeds 0.5mV, then this channel opens for an additional inward current of negative ions with conductance g_vt = 5S for a time window of Δt=1ms. Write a simulation program which shows the time-course of the membrane potential.

Assignment 2:

  1. What is the difference between a conductance-based synaptic model in Chapter 2 and the leaky integrate-and-fire model?
  2. Implement a regular-spiking Izhikevich neuron in Matlab or a comparable programming environmen..
  3. Investigate the point of no return (threshold) of an Izhikevich neuron.
  4. Plot a gain function (the average firing rate versus the input current) for a fast spiking Izhikevich neuron.
  5. Plot the time-course of a dynamic population note that is driven by input which is switched on-and-off in regular intervals.

Assignment 3:

  1. In the example of learning associations shown in Fig.4.2, the unconditioned and conditioned stimuli were always present without noise. Can such a model neuron learn associations with incomplete stimuli, where on average only 1 of the corresponding 3 channels is active?
  2. Is spike timing dependent plasticity (STDP) only dependent on the spike timing?
  3. Write a program that implements STDP for one synapse an show how the synaptic value changes with repeated synaptic events (CSCI6508 only).
  4. The program weightDistribution.m of Table 4.1 uses exponential distributeded rate values of presynaptic neurons and the postsynaptic neuron. What is the resulting weight distribution if these rate values are chosen from a Poisson distribution? Explain.
  5. Replace in program oja.m of Table 4.3. the normalization of weights with the Oja rule by the Willshaw rule. Plot how well the different methods approximate the direction of the first principal component during the learning process.

Assignment 4:

  1. In a network of 1012 neurons, where each neuron is connected to 1000 other neurons, what is the average number of synaptic steps in the path between one neuron and another neuron?
  2. If a neuron has a diameter of 40 micron (µm), and all the neurons in the brain are arranged tightly on the surface of a sphere (ball), what is the diameter of this sphere? Describe your calculation.
  3. Write a program that simulates two simple neurons which are reciprocally connected. Find a condition under which such a network displays oscillatory behavior. (CSCI 6508 only)
  4. For the simulation of Izhikevich neurons in a random network, plot the intantaneous population rate. Compare this to the average rate of the neurons and a smoothened version of the population rate.
  5. Vary the thalamic input to the random network of Izhikevich neurons and plot the resulting rate (gain function). Discuss your results.

Assignment 5:

  1. Implement a single layer perceptron and train it to translate the digital lettersgiven in file pattern1 into the corresponding ASCII representation (NESC 4177 only).
  2. Implement a MLP and train it to translate the digital lettersgiven in file pattern1 into the corresponding ASCII representation (CSCI 6508 only).
  3. Plot a training curve, which is the error rate as a function of training steps.
  4. Investigate how much noise in the pattern the MLP can tolerate before beigunable to recognize a letter. (CSCI 6508 only)
  5. Which letter is represented in file pattern2.

Assignment 6:

  1. What is a tuning curve, and what is a receptive field of a neuron?
  2. In program som.m, measure the distance of the SOM map to an ideal grid and plot the development of this distance measure over time. Interpret your results. Hint: The ideal grid can be set with the variables X and Y in the program (CSCI 6508 only).
  3. Modify the dnf.m program to simulate two simultaneous inputs with the same strength at 1/4*nn and 3/4*nn and observe the network activity. Change the strength of one input and discuss the results. Return to the same strength of input, but choose different locations. Discus your results. (NESCI 4177 only)
  4. Given is a noisy population signal. Estimate the feature value encoded with this signal and explain your choise (CSCI 6508 only).

Assignment 7;

  1. Explain how the deterministic update rule of the fixedpoint version of an ANN, eq. 8.10, is recovered in the noiseless limit, T --> 0, from the probabilistic update rule eq. 8.11 (CSCI 6508 only).

  2. Write an ANN to memorize the letter patterns in file pattern1, which we discussed in chapter 6. How many letters can be memorized by the network? How robust is this network to noise?