## The Graduate Program in Computational Neuroscience

##### Neuroscience Theme

This three quarter sequence introduces the basic concepts that relate the structure and function of the nervous system to behavior. Students typically take the first course in the sequence in their first year in the program and the second two courses in their second year.

CPNS 30107: Behavioral Neurosciences

**Instructor: Daniel Margoliash**

This course is concerned with the structure and function of systems of neurons, and how these are related to behavior. Common patterns of organization are described from the anatomical, physiological, and behavioral perspectives of analysis. The comparative approach is emphasized throughout. Laboratories include exposure to instrumentation and electronics, and involve work with live animals. A central goal of the laboratory is to expose students to in vivo extracellular electrophysiology in vertebrate preparations. Laboratories will be attended only on one day a week but may run well beyond the canonical period.

CPNS 30116: Survey of Systems Neuroscience (also NURB 31600)

**Instructor: Leslie Osborne**

This lab-centered course teaches students the fundamental principles of vertebrate nervous system organization. Students learn the major structures and the basic circuitry of the brain, spinal cord and peripheral nervous system. Somatic, visual, auditory, vestibular and olfactory sensory systems are presented in particular depth. A highlight of this course is that students become practiced at recognizing the nuclear organization and cellular architecture of many regions of brain in rodents, cats and primates.

NURB 31800: Cellular Neurobiology (also CPNS 30000)

**Instructor: Christian Hansel, Philip Lloyd**

This course is concerned with the structure and function of the nervous system at the cellular level. The cellular and subcellular components of neurons and their basic membrane and electrophysiological properties will be described. Cellular and molecular aspects of interactions between neurons will be studied. This will lead to functional analyses of the mechanisms involved in the generation and modulation of behavior in selected model systems.

##### Mathematics Theme

This three quarter sequence introduces mathematical and statistical ideas and techniques used in the analysis of brain mechanisms. Students entering these courses should have some background in linear algebra and ordinary differential equations. Students with this background can take the first two courses in the sequence in their first year in the program. They can take the third, elective course, in either their first or second years.

CPNS 32110: Signal analysis and modeling for neuroscientists

**Instructor: Wim van Drongelen**

The course provides an introduction into signal analysis and modeling for neuroscientists. We cover linear and nonlinear techniques and model both single neurons and neuronal networks. The goal is to provide students with the mathematical background to understand the literature in this field, the principles of analysis and simulation software, and allow them to construct their own tools. Several of the 90-minute lectures include demonstrations and/or exercises in Matlab.

##### Computational Neuroscience Theme

This three quarter sequence brings together the concepts from the neuroscience theme with the quantitative methods from the mathematical theme to discuss current issues in computational neuroscience. Students entering these courses should have completed a one year sequence in calculus. Students take these courses in their first year in the program.

CPNS 3423: Methods in Computational Neuroscience

**Instructor: Sliman Bensmaia**

Topics include (but are not limited to): Hodgkin-Huxley equations, Cable theory, Single neuron models, Information theory, Signal Detection theory, Reverse correlation, Relating neural responses to behavior, and Rate vs. temporal codes.

CPNS 33200: Computational Approaches for Cognitive Neuroscience

**Instructor: Nicholas Hatsopoulos**

This course is concerned with the relationship of the nervous system to higher order behaviors such as perception and encoding, action, attention, and learning and memory. Modern methods of imaging neural activity are introduced, and information theoretic methods for studying neural coding in individual neurons and populations of neurons are discussed.

##### Elective Courses

CPNS 31000: Mathematical Methods for the Biological Sciences I (also BIOS 26210)

**Instructor: Dmitry Kondrashov**

This course builds on the introduction to modeling course biology students take in the first year (BIOS 20151 or 152). It begins with a review of one-variable ordinary differential equations as models for biological processes changing with time, and proceeds to develop basic dynamical systems theory. Analytic skills include stability analysis, phase portraits, limit cycles, and bifurcations. Linear algebra concepts are introduced and developed, and Fourier methods are applied to data analysis. The methods are applied to diverse areas of biology, such as ecology, neuroscience, regulatory networks, and molecular structure. The students learn computations methods to implement the models in MATLAB.

CPNS 31100: Mathematical Methods for the Biolgoical Sciences II (also BIOS 26211)

**Instructor: Dmitry Kondrashov**

This course is a continuation of BIOS 26210. The topics start with optimization problems, such as nonlinear least squares fitting, principal component analysis and sequence alignment. Stochastic models are introduced, such as Markov chains, birth-death processes, and diffusion processes, with applications including hidden Markov models, tumor population modeling, and networks of chemical reactions. In computer labs, students learn optimization methods and stochastic algorithms, e.g., Markov Chain, Monte Carlo, and Gillespie algorithm. Students complete an independent project on a topic of their interest.

CPNS 31200: Mathematical Methods for the Biological Sciences III (also BIOS 26212)

CPNS 32607: Advanced Topics in Theoretical Neuroscience

**Instructor: Jack Cowan**

CPNS 34206: Peering Inside the Black Box: Neocortex (also BIOS 24205)

**Instructor: Jason MacLean**

The neocortex is the multilayered outermost structure of the mammalian brain. It is the site of higher brain functions including reasoning and creativity. However, the complexity of the neocortex—it is comprised of ~20 billion neurons which have 0.15 quadrillion connections between them—seems to preclude any hope of achieving a fundamental understanding of the system. Recent technological innovations have opened novel avenues of investigation making realization of the neocortex an increasingly tractable problem. This course will place particular emphasis on how to critically read scientific papers as we evaluate and discuss current experimental approaches to the neocortex. Integral to this evaluation will be the detailed discussion of the latest technological approaches.

CPNS 34600: Neurobiology of Disease I

**Instructor: Christopher Gomezand Staff**

CPNS 34700: Neurobiology of Disease II

**Instructor: Christopher Gomezand Staff**

CPNS 35510: Theoretical Neuroscience: Single Neuron Dynamics and Computation (also STAT 42510)

**Instructor: Nicolas Bruneland Staff**

This course is the first part of a three-quarter sequence in,theoretical/computational neuroscience. It will focus on mathematical,models of single neurons. Topics will include: basic biophysical,properties of neurons; Hodgkin-Huxley model for action potential,generation; 2D models, phase-plane analysis and bifurcations leading,to action potential generation; integrate-and-fire-type models; noise;,characterization of neuronal activity with stochastic inputs;,spatially extended models; models of synaptic currents and synaptic,plasticity; unsupervised learning; supervised learning; reinforcement,learning.

CPNS 35520: Theoretical Neuroscience: Network Dynamics and Computation. (also STAT 42520)

**Instructor: Nicolas Brunel**

This course is the second part of a three-quarter sequence in,theoretical/computational neuroscience. It will focus on mathematical,models of networks of neurons. Topics will include: firing rate models,for populations of neurons; spatially extended firing rate models;,models of visual cortex; models of brain networks at different levels;,characterization of properties of specific brain networks; models of,networks of binary neurons, mean rates, correlations, reductions to,rate models; learning in networks of binary neurons, associative,memory models; models of networks of spiking neurons: asynchronous vs,synchronous states; oscillations in networks of spiking neurons;,learning in networks of spiking neurons; models of working memory;,models of decision-making.

CPNS 35600: Theoretical Neuroscience: Statistics and Information Theory (also STAT 42600)

**Instructor: Stephanie Palmer**

This course is the third part of a three-quarter sequence in theoretical/computational neuroscience. It begins with the spike sorting problem, used as an introduction to inference and statistical methods in data analysis. We then cover the two main sections of the course: I) Encoding and II) Decoding in single neurons and populations. The encoding section will cover receptive field analysis (STA, STC and non-linear methods such as maximally informative dimensions) and will explore linear-nonlinear-Poisson models of neural encoding as well as generalized linear models and newer population coding models. The decoding section will cover basic methods for inferring the stimulus from spike train data, including both linear and correlational approaches to population decoding. The course will use examples from real data (where appropriate) in the problem sets which students will solve using MATLAB.

##### Neural Engineering Courses

These courses are offered on a semester basis through the Illinois Institute of Technology.

##### Reading and Research Courses

CPNS 39900: Readings in Computational Neuroscience

**Instructor: Staff**

Reading courses on various topics in computational neuroscience.

CPNS 40100: Research in Computational Neuroscience

**Instructor: Staff**

Research credit (varied units) for research undertaken by graduate students under the guidance of a faculty member of the Committee on Computational Neuroscience.