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General Neurobiology

• Models of the nervous system come in many forms and types; from abstract to highly realistic (e.g. Hopfield model vs. biophysical detailed networks). Use specific examples to discuss the tradeoffs.
• Discuss the major features of at least two very different nervous systems (i.e. jellyfish, locust, lamprey, octopus, owl, rat, monkey). In what ways might the features of each system affect neural processing?
• Do you know how animals are classified? What are the major phyla? What different types of vertebrates exist?
• Draw an outline of a vertebrate brain and name its major areas.
• What is the limbic system?
• Every sensory system relies on receptor cells that transduce a stimulus into an electrical signal. This clearly requires some significant amplification. Describe two different sensory receptor cells, with attention to the location(s) and the mechanism(s) of this amplification.
• Describe the main pathways between sensory receptors and cortex (including intra-cortical circuits) for mammalian vision, hearing and olfaction.
• What do you know about high-frequency oscillations (20-50 Hz) in invertebrates or vertebrates? What causes them?
• In mammals, somatosensory, visual, auditory, and olfactory sensory systems all project to the cerebral cortex. To what extent does this imply some common form of neural processing? Justify your answer by referring to and comparing specific details of cortical anatomy and physiology.
• Describe several main findings resulting from the study of the crustacean stomatogastric nervous system and their implications for the study and understanding of local circuit function in larger, more complex systems.
• What is the VOR in primates? How does plasticity in the VOR express itself?
• What is a central pattern generator (CPG)?
• What is a transgenic animal? A transgenic knockout mouse? What are the advantages and disadvantages of such animals for neuroscientific studies? Please give one or two specific examples.
• Anatomically, what are the frontal and pre-frontal cortical areas? What do you know about patients with lesions in the orbital-frontal cortex?
• Why do some animals have larger brains than others? Why do animals with larger bodies have larger brains? How does brain size relate to metabolism or to longevity?
• What is a local field potential? What are its underlying causes? What can we learn from such data?
• What is the physical and biological basis of structural and functional MRI for brain imaging?

• What is the central dogma of molecular biology? Click here.
• Explain how a system of chemical reactions can be represented as ODEs and PDEs. What approximations are involved?
• What are the differences between entropy, free energy, and enthalpy?
• Explain the difference between equilibrium and steady-state.
• Give the basic circuits for a current- and voltage-clamp set-up. Click here.
• Describe the main biophysical characteristics of at least one type of ionic channel. How do its biophysical properties contribute to its physiological function? What is thought to be the basis for the channel's ion selectivity? Click here.
• Derive the cable equation (for a uniform cylinder, with optimal boundary conditions). What does it mean for neurons? Click here.
• What is diffusion? How far would a typical molecule diffuse in a millisecond? A second? An hour? How does the diffusion equation differ from the cable equation? Click here.
• Describe and explain the Hodgkin-Huxley model of the action potential. Click here.
• Describe and discuss the two principal models of individual neurons (integrate-and-fire and mean-rate neurons). What assumptions do they make about encoding. In what way are they faithful to real neurons and how do they fall short?
• Explain the concept of "signal to noise," and give a mathematical definition.   How does it relate to information?

• Describe the pre- and post-synaptic events underlying fast synaptic transmission at a central synapse. How do synaptic inputs interact and what sort of computations could be implemented using synaptic input in dendritic trees?
• How random are synaptic events? And why (both from a functional as well as from a biophysical point of view)?
• What are neuromodulators? How do they work and where do they fit in from a computational point of view?
• Describe the serotonergic system in the brain. How does serotonin relate to behavior (for instance, the therapeutic use of the drug Prozac or crustacean behavior and serotonin)?
• List the two principal inhibitory neurotransmitters. How do they work? What are their antagonists (natural or synthetic) and what actions do they have?
• Describe the principles of quantal analysis in the peripheral and central nervous system.
• Consider a surprising visual stimulus in your animal of choice.  How quickly will information arrive at various places in the brain, and what implications does this have for neural coding?

• Describe and contrast NMDA-dependent and NMDA-independent long term potentiation (LTP). What are some of the known presynaptic and postsynaptic events involved in the process?
• What is LTD and how does it differ from LTP?
• Donald Hebb proposed an activity-dependent learning rule for synapses as a basis for neuronal self-organization. In what ways is LTP similar or different from the Hebb rule? What are the potential consequences of the differences?
• What are some of the experiments linking synaptic plasticity with learning and memory in behaving animals?
• What do you know of activity-dependent developmental changes, such as the origin of ocular-dominance pattern in the visual system? Describe how a use-dependent synaptic modification rule can lead to the organization of sensory maps.
• There is evidence for rapid re-organization of sensory receptive fields (Merzenich et al.; Gilbert et al.) in the mammalian cortex. How could such arrangements occur rapidly in adult animals?

• What is a receptive field in visual and auditory cortices? How are they built by the nervous system? What is a non-classical receptive field? What could be its computational significance?
• Provide at least one detailed example of hierarchical and parallel processing in the nervous system.
• What is a "place code"? Describe at least one such place code in the nervous system and its underlying mechanisms.
• Features of the environment appear to be coded in two different ways: either using a Gaussian-type of response (e.g. auditory frequency or binocular disparity turning) or via a sigmoidal type of response (e.g. contrast). Give examples and discuss.
• What do you know about population coding in subcortical (e.g. superior colliculus) or cortical structures? Why would the nervous system use population rather than single cell coding? How would cross-correlation among cells affect this?
• What do you know about information coding in the nervous system? What are some of the different ways in which information could be encoded in spike trains? Can you tell us of one experiment in which this has been done. What are the (dis)-advantages of these different methods with respect to robustness and accuracy?

• What are the two fundamental ways to estimate visual motion in 1-D? To what extent do these methods estimate speed? What experimental support exists for either method in flies or mammals.
• Give a definition of optical flow. What is the "aperture problem"? How can it be solved?
• What is the basic idea inherent in stereo algorithms that use binocular (horizontal) disparity? Describe one or two such algorithms. What is the "stereo correspondence problem"?
• What do you know about the psychophysics (and some physiology) of color processing in primates? Describe briefly the "trichromacy" vs. "opponency" theories of color processing.
• Define a "psychometric curve." How would it look for a spatial hyperacuity task? Can you explain the performance of the system on dot-discrimination and line-alignment (Vernier) tasks in terms of the mechanisms of the retina and the primary visual cortex?
• List all the cues that allow one to perform image segmentation. Describe one algorithm for image segmentation.
• What do you know about the psychophysics and neurophysiology of selective, visual (focal) attention? What could the computational roles of this process be? How might attention relate to visual perception and to visual awareness?
• Describe the two major pathways in the visual system of the primate. Why are there so many visual cortical areas?
• What different types of eye movements exists and what to you know of their underlying neuronal substrate?
• "Neglect" and "Blindsight" patients have specific cortical lesions. Describe their deficits and what we can learn from them, in particular with regards to the neuronal correlate of consciousness.

• Explain the following terms in psychophysics: threshold, Weber's law, and staircase. Also, explain the relationship among them.
• What is "perceptual constancy"? Define it, describe some examples, and explain why it is biologically important.
• Refute the classical view of illusory contour and surface filling-in as "knowledge-based cognitive inference, top-down in its nature." Provide empirical evidence supporting your position.
• Describe how measurements of reaction times can be used to infer brain architecture. Give an example.

• Neural networks for combinatorial optimization, back-propagation learning, and protein folding share a common problem which tends to increase rapidly with size. Describe the generic problem, and approaches to circumvent it in one of these cases.
• Two classic algorithms for training an individual neuron are the "adaline" and the "perceptron" learning algorithm. Describe the differences between the two methods and discuss the practical consequences of these differences.
• Most real-life variational problems have a non-convex energy landscape. Describe stochastic search methods (such as simulated annealing, genetic algorithms) for locating the global minimum. Click here.
• Discuss the role of the nonlinearity in multi-layer neural networks. Compare thresholding versus soft sigmoidal functions and bump functions in terms of network function and learning capability.
• Describe the similarities and differences between backpropagation and radial basis function learning networks.
• Describe the Minimum Description Length framework, and how it relates to Occam's razor.
• What is Bayes' Rule?  Discuss the justification for and against using Bayesian Inference.
• How does Maximum Likelihood inference relate to Minimum Description Length inference and to least-squares error functions?
• Describe the concepts of generalization and of overfitting.  What problem do they address?  Describe some approaches that ameliorate the problem.
• What is the VC dimension?  What is a shattering set?  How do they relate to the inference problem?

• What is a finite state machine? What is a Turing machine? What is the Church/Turing thesis? Click here.
• How many different formal models of computation do you know?  How are they related?
• Explain the idea of simulation, and what is meant by "Turing-universal."
• What is meant by "algorithm A solves problem X"?  What is meant by a problem "instance"?
• Marr described three levels at which an information processing device might be understood: computational, representation/algorithmic, and hardware implementation. Describe, with examples, each level.
• How would you compare the computational power of a cortical pyramidal cell with that of a desktop computer? Be specific about your criteria for computational power.
• Show how to compute the Boolean functions AND and OR using a linear threshold element. Click here.
• Prove that XOR can not be computed by a single linear threshold element. Show how to compute XOR using a two-layered circuit of AND, OR and NOT gates. Is this construction optimal in size? Click here.
• What characterizes "von Neumann" computing? Discuss its plausibility as a metaphor for the human brain.
• We can read everywhere that the brain is a "complex adaptive system". What is meant by this vague statement?  Give at least two formal definitions of complexity.
• Define the asymptotic notation "o(f(n))" and "O(f(n))".   When is an O(n log n)-time algorithm faster than an O(n^2)-time algorithm?
• What do the terms "NP", "P", and "NP-complete" refer to? Click here.
• Give an example of an undecidable problem.  Why is it undecidable?  Are undecidable problems common?

• What is a dynamical system? What is meant by a "stable" dynamical system? An "unstable" system? Give examples of each. Click here.
• Derive the conditions for stability of a two-dimensional linear system.  What qualitative types of behavior are possible?
• What is a state space?  When can trajectories cross in state space?  What is a basin of attraction?  What is a separatrix?  Sketch an illustrative phase portrait or vector field.
• We frequently read statements such as "the electrical activity in brain area XYZ is chaotic"? What does this mean, how can it be tested and what might it imply? Click here.
• What is meant by the term "transfer function"? And "impulse response"? What kinds of dynamical system can be fully characterized by their impulse response (give examples)?
• Explain the idea of white noise analysis for characterizing linear systems.

• What is convolution?  What is an autocorrelation function?  What is the relationship between Fourier transforms and convolution?
• What is the difference between entropy and information?
• Discuss the concept of Shannon information and its application to the nervous system.
• What is Principal Component Analysis and how is it relevant within the context of neural networks?
• A person rolls two fair dice and records the total number of points. You can ask a sequence of yes/no questions to find out this number. The answer to a question may affect your choice of the following questions. Devise and justify a strategy that achieves the minimum possible average number of questions.
• What is the Central Limit Theorem?