Prof. Anatoli Gorchetchnikov
Office: Rm. 213, 677 Beacon Street
Office hours: Wednesday 10:00-1pm, or by appointment
Email: anatoli (at) bu (dot) edu
Dayan, P. and Abbott, L.F. (2001). Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems.. Cambridge, MA: MIT Press. Referred to as D&A in syllabus and class notes.
Brauer, F. and Nohel, J.A. (1989). The Qualitative Theory of Ordinary Differential Equations: An Introduction. New York: Dover.
Kandel, E., Schwartz, J.H., and Jessell, T.M. (2000). Principles of Neural Science, 4th Edition. New York: McGraw-Hill. Referred to as PNS.
Izhikevich, E.M. (2007). Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting. Cambridge, MA, MIT Press.
Levine, D.S. (2000). Introduction to Neural and Cognitive Modeling, 2nd Edition. Hillsdale, NJ: Erlbaum. Referred to as NCM.
Shepherd, G.M. (2004). Synaptic Organization of the Brain. New York, NY: Oxford University Press.
Useful Matlab references:
CN510 is designed to introduce students to important themes and approaches in the computational modeling of biological neural systems. The class combines systems-level neuroscience, mathematical modeling techniques, and computer simulation techniques. Particular simple neural models will be covered in detail, thus exposing students to mathematical modeling techniques that will serve as the basic building blocks for a number of the sensory, motor, and memory models discussed in the other CN5xx courses. A major theme of CN510 is the use of these modeling techniques to tie together anatomical, physiological, and psychological data, as exemplified by the neural modeling studies covered in the course.
Grades are determined by performance on homework assignments and examinations. The in-class final exam will be worth 30%, and all homework assignments will make up equally the remaining 70% of the grade. It is recommended to type homework reports in LaTeX using this template and this style file. Participation in class discussions will play a role in determining the final letter grade in borderline cases.
Late homework policy: 10% penalty if turned in less than one week late, 20% penalty for 1-2 weeks late, and 30% penalty for > 2+ weeks late. No late homework will be accepted after the final exam.
OTHER USEFUL TEXTS:
Anderson, J.A. and Rosenfeld, E., (Eds.), (1988). Neurocomputing: Foundations of Research. Cambridge, MA: MIT Press. Referred to as NFR. [Out of print, available in CompNet Library.]
Arbib MA (ed.) (1995). The Handbook of Brain Theory and Neural Networks. Cambridge, MA: MIT Press. Referred to as HBT.
Churchland, P. (1986). Neurophilosophy: Toward a Unified Science of the Mind/Brain. Cambridge, MA: MIT Press.
Schwartz, E.L. (1990). Computational Neuroscience. Cambridge, MA: MIT Press.
Carpenter, G.A. and Grossberg, S. (1991). Pattern Recognition by Self-organizing Neural Networks. Cambridge, MA: MIT Press.
Grossberg, S. (1982). Studies of Mind and Brain. Kluwer/Reidel Press. Referred to as SMB. [Out of print, available in CompNet library.]
Koch, C. and Segev, I. (1989). Methods in Neuronal Modeling. Cambridge, MA: MIT Press.
McClelland, J.L. and Rumelhart, D.E. (1988). Explorations in Parallel Distributed Processing: A Handbook of Models, Programs, and Exercises. MIT Press.
Martin, J.H. (1996). Neuroanatomy: Text and Atlas. Stamford, CT: Appleton & Lange.
Lecture 1 (September 2)
Introduction to Brain Structure and Function, Experimental Techniques, and Brain Theories
I will provide an overview of central nervous system's anatomy and functions, including a brief treatment of theories of brain function from the late 18th century to the present. We will discuss experimental techniques for measuring brain anatomy and physiology from the perspective of a theoretical modeler.
Functions of the Human Nervous System, Encyclopedia Britannica.
PNS Chapter 1 [Kandel, E.R. The brain and behavior.]
PNS Chapter 17 [Amaral, D.G. The anatomical organization of the central nervous system.]
NCM Chapter 1 [Levine, D.S. Brain and machine: The same principles?]
NCM Chapter 2 [Levine, D.S. Historical outline.]
Homework Assignment (Due September 9):
Short (1-2 pages) essay describing your background, expectations for the class, and what you want to learn in this class but did not find in the syllabus.
Lecture 2 (September 4)
Introduction to Computational Neuroscience and Various Modeling Scales
We will discuss the goals of computational neuroscience, general approaches to model the nervous systems, and various scales the models can concentrate on. Several example neural models, each defined at a different grain of analysis will be briefly presented. We will also discuss an idea of multiscale modeling, its advantages, and related issues.
Churchland, P.S., Koch, C., and Sejnowski, T.J. (1990). What is computational neuroscience? In E. Schwartz (ed.): Computational Neuroscience. Cambridge, MA: MIT Press.
Guenther, F.H. (2002). Neural networks: Biological models and applications. International Encyclopedia of the Social & Behavioral Sciences (vol. 15, pp. 10534-10537). Oxford: Elsevier Science.
Lecture 3 (September 9)
Mathematical and Computational Concepts Used in Neural Modeling I
Using examples of leaky integrator and leaky Integrate-and-Fire (lIaF) neurons, I will review mathematical concepts used in neural modeling including ordinary differential and difference equations, matrices and eigenvalues. I will point out some issues introduced by discrete digital computers when we simulate these concepts.
D&A Appendix A.1, pp399-403; Appendix A.3
NCM Appendix 2 [Levine, D.S. Difference and differential equations in neural networks.]
Rotter S., and Diesmann M. (1999). Exact digital simulation of time-invariant linear systems with applications to neuronal modeling . Biol. Cybern.. 81: 381-402. (From the beginning up to section 3.1.2 (inclusive)
Essay on your background and goals in CN510 is due before the class starts.
Homework Assignment (Due September 16):
Lecture 4 (September 11)
Mathematical and Computational Concepts Used in Neural Modeling II
We will discuss critical points, stability, and basic phase plane analysis in application to neural models
Izhikevich, E.M. (2007). Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting. Cambridge, MA, MIT Press. Chapter 1
Lecture 5 (September 16)
Biophysics of the Cell Membrane as a Foundation of the Hodgkin-Huxley Equation
I will briefly remind you how electric current flows in ionic solutions, present the concepts behind mapping cell elements into equivalent electrical circuits, and analyze the resulting circuit to produce Hodgkin-Huxley equation.
D&A Chapters 5 (sections 1-4, 6) and 6 (sections 3-4)
Shepherd, G.M. (2004). Synaptic Organization of the Brain. New York, NY. Oxford University Press. Chapter 1.
PNS Chapter 7 [Koester, J. and
PNS Chapter 9 [Koester, J. and
PNS Appendix A [Koester, J. Current flow in neurons.]
PNS Chapter 6 [Siegelbaum, S.A. and Koester, J. Ion channels.]
PNS Chapter 8 [Koester, J. and Siegelbaum, S.A. Local signaling: Passive electrical properties of the neuron.]
Hodgkin, A.L. and Huxley, A.F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiology, 117, 500-544
Leaky integrator assignment is due before the class starts.
Homework Assignment (Due September 23):
Lecture 6 (September 18)
Extensions and Simplifications of the Hodgkin-Huxley Model
We will discuss how to combine neuronal equations into a compartmental model and take a brief look at cable theory for simulations of the cellular structure. We will also discuss how to simplify Hodgkin-Huxley model of spiking to derive Izhikevich neuron.
Izhikevich, E.M. (2007). Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting. Cambridge, MA, MIT Press. Chapter 8
Ermentrout, GB and Kopell, N. (1986). Parabolic bursting in an excitable system coupled with a slow oscillation, SIAM-J.-Appl.-Math, 46, 233-253.
Brette R. and Gerstner W. (2005), Adaptive Exponential Integrate-and-Fire Model as an Effective Description of Neuronal Activity, J. Neurophysiol., 94, 3637-3642.
Lecture 7 (September 23)
Feedforward Shunting Competitive Network
We will discuss how from the need to factorize an input pattern from the total input energy we can derive shunting network. Feedforward shunting network properties of automatic gain control and activity normalization will be discussed.
Appendix C of Grossberg, S. (1980). How does the brain build a cognitive code? Psychological Review, 87, pp. 1-51. [SMB Chapter 1; NFR Chapter 24.]
SMB Chapter 11 [Grossberg, S. Behavioral contrast in short term memory.]
NCM Chapter 4 [Levine, D.S. Competition, lateral inhibition, and short-term memory.]
Furman, G.G. (1965). Comparison of models for subtraction and shunting lateral-inhibition in receptor-neuron fields. Kybernetika, 2, 257-274.
Homework Assignment (Due September 30):
Lecture 8 (September 25)
Shunting Network and Experimental Data
Further properties of feedforward shunting networks are treated, including the shift property and Weber's law. The similarities and differences between the shunting equations and membrane equations from earlier lectures are discussed.
Werblin, F.S. (1971). Adaptation in a vertebrate retina: Intracellular recording in Necturus. Journal of Neurophysiology, 34, pp. 228-241.
Cornsweet, T. (1970). Visual Perception, Chapter 11. New York, NY: Academic Press.
Lecture 9 (September 30)
Recurrent Competitive Shunting Networks (or Fields)
We will discuss pattern preservation and transformations during short-term memory storage in recurrent competitive fields (RCFs). A major issue is the nature and role of the feedback (recurrent) signal. Properties associated with linear, faster-than-linear, slower-than-linear, and sigmoid feedback signal functions will be analyzed and discussed.
Appendix D of Grossberg, S. (1980). How does the brain build a cognitive code? Psychological Review, 87, pp. 1-51.
Grossberg, S. (1973). Contour enhancement, short term memory, and constancies in reverberating neural networks. Studies in Applied Mathematics, LII, pp. 213-257. [SMB Chapter 8.]
NCM Chapter 4 [Levine, D.S. Competition, lateral inhibition, and short-term memory. ]
Grossberg, S. and Levine, D. (1975). Some developmental and attentional biases in the contrast enhancement and short term memory of recurrent neural networks. Journal of Theoretical Biology, 53, pp. 341-380.
Replication of 20 cases of Izhikevich neuron assignment is due before the class starts.
Homework Assignment (Due October 7):
Lecture 10 (October 2)
Synaptic Transmission in the Brain
We will discuss synaptic dynamics from action potential to postsynaptic response and identify the possibilities for plasticity during this process.
Shepherd, G.M. (2004). Synaptic Organization of the Brain. New York, NY. Oxford University Press. Chapter 2.
PNS Chapter 10 [Kandel, E.R. and Siegelbaum, S.A. Overview of synaptic transmission.]
PNS Chapters 12-15 [Kandel, E.R., Siegelbaum, S.A., and Schwartz J.H. Synaptic integration; Modulation of synaptic transmission; Transmitter release; Neurotransmitters.]
Lecture 11 (October 7)
Modeling the Synaptic Response
We will discuss current based and conductance based models of synaptic responses in spiking networks, and possible applications of Rotter-Diessmann approach to these models.
D&A Chapter 5 (sections 8-9).
Rotter S., and Diesmann M. (1999). Exact digital simulation of time-invariant linear systems with applications to neuronal modeling . Biol. Cybern.. 81: 381-402. (From the beginning up to section 3.1.2 (inclusive)
Additive and Shunting Networks assignment is due before the class starts.
Homework Assignment (Due October 16):
Lecture 12 (October 9)
Learning Rules for Continuous Models
We will discuss several learning laws described at the network level and based on neurophysiological findings. Concepts of local and global learning rules are introduced. A set of Hebbian rules is analyzed for stability and properties of resulting weights.
D&A Chapter 8 (section 1-3).
Vasilkoski, Z. et al. (2011). Review of stability properties of neural plasticity rules for implementation on memristive neuromorphic hardware. In: Proceedings of International Joint Conference on Neural Networks. San Jose, CA.
Levy, W.B. and Desmond, N.L. (1985). The rules of elemental synaptic plasticity. In W.B. Levy, J.A. Anderson, and S. Lehmkuhle (Eds.), Synaptic modification, neuron selectivity, and nervous system organization. Hillsdale, NJ: Erlbaum.
NCM Chapter 3 [Levine, D.S. Associative learning and synaptic plasticity.]
PNS Chapter 63 [Kandel, E.R. Cellular mechanisms of learning and the biological basis of individuality.]
No class - Monday schedule (October 14)
Lecture 13 (October 16)
Spike-Timing-Dependent Plasticity I
We will start discussing the experimental findings and modeling using temporally asymmetric learning rules.
Morrison, A, Diesmann, M and Gerstner, W. (2008). Phenomenological models of synaptic plasticity based on spike timing. Biological Cybernetics 98: 459-478.
Izhikevich E.M. and Desai N.S. (2003). Relating STDP to BCM. Neural Computation 15: 1511-1523
Abbott, LF and Nelson SB (2000) Synaptic plasticity: taming the beast. Nat Neurosci. Suppl:1178-83. Review.
Song, S., Miller, KD and Abbott, LF (2000) Competitive Hebbian learning through spike-timing-dependent synaptic plasticity. Nat Neurosci. 3(9):919-26.
G-Q Bi, M-M Poo (2001) Synaptic Modifications by Correlated Activity: Hebb's Postulate Revisited. Ann Rev Neurosci, 24: 139-166
Mehta, MR, Quirk, MC and Wilson, MA. (2000). Experience dependent asymmetric shape of hippocampal receptive fields. Neuron 25: 707-715.
Recurrent Competitive Field assignment is due before the class starts.
Homework Assignment (Due October 23):
Lecture 14 (October 21)
Spike-Timing-Dependent Plasticity II
We will continue discussing modeling of temporally asymmetric learning rules. Spatially and temporally local STDP rule is introduced and analyzed.
Gorchetchnikov, A., Versace, M., and Hasselmo, M.E. (2005). A model of STDP based on spatially and temporally local information: Derivation and combination with gated decay. Neural Networks 18, 458466.
Gorchetchnikov, A. and Grossberg, S. (2007) Space, time and learning in the hippocampus: How fine spatial and temporal scales are expanded into population codes for behavioral control. Neural Netw. 20, 18293.
Lecture 15 (October 23)
Outstar Network and Classical Conditioning
We will look at a classical conditioning model example in terms interactions between neuronal activation and weight changes, the resulting outstar network, and outstar learning theorem.
Appendix B of Grossberg,S. (1980). How does the brain build a cognitive code? Psychological Review, 87, pp. 1-51. [SMB Chapter 1.]
Sections I-IV of Grossberg, S. (1974) Classical and instrumental learning by neural networks. Progress in Theoretical Biology, 3, pp. 51-141. [SMB Chapter 3.]
Communication in spiking network assignment is due before the class starts
Homework Assignment (Due October 30):
Lecture 16 (October 28)
Outstar Network and Spatio-Temporal Sampling
We will discuss the use of a chain of outstars in a model of temporal sequence learning, the associative avalanche.
Section V of Grossberg, S. (1974) Classical and instrumental learning by neural networks. Progress in Theoretical Biology, 3, pp. 51-141. [SMB Chapter 3.]
Lashley, K.S. (1951). The problem of serial order in behavior. Reprinted in F.A. Beach et .al (Eds.), The Neuropsychology of Lashley. New York: McGraw-Hill, 1960.
Lecture 17 (October 30)
Introduction to Neural Pathways and Cortical Organization
We will discuss the main neural pathways of the sensory and motor systems, and the organization of unimodal and association areas of cortex.
PNS Chapter 18 [Amaral, D.G. The functional organization of perception and movement.]
PNS Chapter 19 [Saper, C.B., Iversen, S., and Frackowiak, R. Integration of sensory and motor function: The association areas of the cerebral cortex and the cognitive capabilities of the brain.]
Outstar Network assignment is due before the class starts
Homework Assignment (Due November 6):
Lecture 18 (November 4)
Introduction to Models of Cortical Maps
We will discuss von der Malsburg (1973) and Grossberg (1976) models of the development of neural feature detectors using competitive learning.
D&A Chapter 8 (section 3 reread).
von der Malsburg, C. (1973). Self-organization of orientation sensitive cells in the striate cortex. Kybernetik, 14, pp. 85-100. [NFR Chapter 17.]
Grossberg, S. (1976). Adaptive pattern classification and universal recoding I: Parallel development and coding of neural feature detectors. Biological Cybernetics, 23, pp. 121-134. [SMB Chapter 12; NFR Chapter 19.]
Sutton, G.G. III, Reggia, J.A., Armentrout, S.L., and D'Autrechy, C.L. (1994). Cortical map reorganization as a competitive process. Neural Computation, 6, 1-13.
Grajski, K.A., and Merzenich, M.M. (1990). Hebb-type dynamics is sufficient to account for the inverse magnification rule in cortical somatotopy. Neural Computation, 2, 71-84.
Lecture 19 (November 6)
Introduction to Models of Cortical Maps II
We will continue to discuss competitive learning models of cortical maps by looking at Kohonen (1982) model, comparing all three models and briefly looking at Cohen-Grossberg theorem.
Kohonen, Teuvo (1982). Self-Organized Formation of Topologically Correct Feature Maps. Biological Cybernetics 43(1): 59–69.
Cohen, M. and Grossberg, S. (1983). Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Transactions on Systems, Man, and Cybernetics, 13, pp. 815-826.
Spike-Timing Dependent Plasticity assignment is due before the class starts
Homework Assignment (Due November 13):
Lecture 20 (November 11)
Neuromodulatory Systems and Drug Effects
We will discuss diffusely projecting transmitter systems of the CNS and the implications of these systems in terms of a variety of drug effects.
Pages 84, 86-88 of Martin, J.H. (1996) Neuroanatomy: Text and Atlas. Stamford, CT: Appleton & Lange.
Snyder, S.H. (1996). Drugs and the Brain. New York: Scientific American Library.
Lecture 21 (November 13)
Dopamine and Reinforcement Learning
We will look at the dopamine role in the reinforcement learning from data modeling points of view.
D&A Chapter 9 (sections 1-2).
Schultz, W., Dayan, P. and Montague, PR. (1997). A neural substrate of prediction and reward. Science, 275, pp. 1593-1599.
Schultz, W. (2006). Behavioral theories and the neurophysiology of reward. Annual review of Psychology. 57, pp. 87-115.
Setting up correlated inputs and network architecture for self-organizing STDP assignment is due before the class starts
Lecture 22 (November 18)
Acetylcholine, Memory, and Learning
We will discuss the role of acetylcholine as a diffuse teaching signal and as a modulator of encoding/retrieval switch, including a neurophysiological results and modeling studies.
Hasselmo, M. E. (1999). Neuromodulation: Acetylcholine and memory consolidation. Cogn. Sci. 3: 351-359 .
Kilgard, M.P. and Merzenich, M.M. (1998). Cortical map reorganization enabled by nucleus basalis activity. Science, 279, pp. 1714-1718.
Lecture 23 (November 20)
Adaptive Resonance Theory
We will discuss the basic foundations of Adaptive Resonance Theory.
Grossberg, S. (1980). How does the brain build a cognitive code? Psychological Review, 87, pp. 1-51. [SMB Chapter 1; NFR Chapter 24.]
Baraldi, A., Alpaydin D. (1998). Simplified ART: A new class of ART algorithms Technical report TR-98-004, International Computer Science Institute.
Homework Assignment (Due December 4):
Lecture 24 (November 25)
Spiking Modulated Adaptive Resonance Theory (SMART). Oscillations and Synchrony I
In the first part of the lecture Jesse Palma will present SMART model. In the second part we will discuss the reasons for oscillations in the brain, look at intracellular and extracellular oscillations, and discuss microcircuit models of neuronal oscillations.
Ermentrout, GB, and Kopell, N. (1998). Fine structure of neural spiking and synchronization in the presence of conduction delays. Proc. Nat. Acad. Sci. USA 95: 1259-1264.
C. Chow, J. White, J. Ritt, N. Kopell (1998). Frequency control in synchronous networks of inhibitory neurons, J. Comput. Neurosci. 5:407-420.
D. Pinto, S. Jones, T. Kaper and N. Kopell (2003). Analysis of state-dependent transitions in frequency and long-distance coordination in a model oscillatory cortical circuit, J. Comp. Neurosci. 15(2):283-298.
N. Kopell, C. Borgers, D. Pervouchine, P. Malerba, and A.B.L. Tort. 2010. Gamma and theta rhythms in biophysical models of hippocampal circuits. In Hippocampal Microcircuits: A Computational Modeller's Resource Book. Eds. V. Cutsuridis, B.P. Graham, S. Cobb, I. Vida. Springer. Ch. 15.
No Lecture - Thanksgiving break (November 27)
Lecture 25 (December 2)
Oscillations and Synchrony II
We will discuss an idea of synchronization as a binding element between different cortical areas will be further discussed as a basis for computation with neural assemblies.
Engel, AK, Fries, P. and Singer W. (2001). Dynamic predictions: oscillations and synchrony in top-down processing. Nature Neuroscience Reviews 2: 704.
Lecture 26 (December 4)
We will discuss various tools for neural modeling with an emphasis on result reproducibility and interchange between research groups.
Brette, R. et al (2007). Simulation of networks of spiking neurons: a review. J Comput Neurosci 23(3):349-98.
Versace M., Ames H.M., Leveille J., Fortenberry B., Mhatre H., and Gorchetchnikov A. (2008). KInNeSS: A modular framework for computational neuroscience. Neuroinformatics. 6(4), 291-309.
Carnevale, N.T. and Hines, M.L. The NEURON Book. Cambridge, UK: Cambridge University Press, 2006.
Cornelis, H., Rodrigues, A.L., Coop, A.D., Bower, J.M. (2011). Federated Scripting in GENESIS 3.0 Neural Simulation Platform. University of Texas Health Science Center at San Antonio (submitted to PLOS).
Diesmann, M. & Gewaltig, M. (2002) NEST: An Environment for Neural Systems Simulations. In: Plesser, T. & Macho, V. (ed.) Forschung und wisschenschaftliches Rechnen, Beitrge zum Heinz-Billing-Preis 2001, 58: 43-70, Ges. fr Wiss. Datenverarbeitung
Self-organizing STDP assignment is due before the class starts
Homework Assignment (Due at the Final):
Lecture 27 (December 9)
KInNeSS, Descriptive Languages, GPUs for neurons
We will discuss design of KInNeSS simulator with respect to: 1) Descriptive languages for neural models and concepts underlying NineML and NeuroML 2; 2) CUDA programming of neural models.
Churchland, P.S. (1986).
Theories of brain function.
Chapter 10 in Neurophilosophy: Toward a Unified Science of the
Anderson, J.R. (1987). Methodologies for studying human knowledge. Behavioral and Brain Sciences, 10, 467-505.
Nordlie E, Gewaltig M-O, Plesser HE (2009) Towards Reproducible Descriptions of Neuronal Network Models. PLoS Comput Biol 5(8): e1000456. doi:10.1371/journal.pcbi.1000456.
FINAL EXAM Tuesday December 16, 12:30pm-2:30pm