- Point
distribution
- 80%
for homework
- 20%
final project
Biological
Neural Computation
Spring 2013
Time: Tuesday and Thursday; 4:00-5:30
pm, Location: Whitaker 218
Course Overview:
This
course will consider the computations performed by the biological nervous
system with a particular focus on neural circuits and population-level
encoding/decoding. Topics include, Hodgkin-Huxley equations, phase-plane
analysis, reduction of Hodgkin-Huxley equations, models of neural circuits,
plasticity and learning, and pattern recognition & machine learning algorithms
for analyzing neural data.
Note:
Graduate students in psychology or neuroscience who are in the Cognitive,
Computational, and Systems Neuroscience curriculum pathway may register in L41
5657. For non-BME majors, conceptual
understanding, evaluation and selection of right neural data analysis technique
will be stressed.
L41
5657 prerequisites: Permission from the instructor
Course Goals:
The objectives of
this course are to:
·
To integrate previous math, physical
science, biology and engineering studies into a rigorous investigation of the
quantitative foundations of neurophysiology
·
Provide students with quantitative
tools essential for systems-level investigation of neural circuits
·
Introduce fundamental pattern
recognition and machine learning concepts required for neural data analysis
Prerequisites:
Calculus,
Differential Equations, Basic Probability and Linear Algebra
Optional Textbooks:
There is no
required text book for this course. Some optional books for references are:
Biophysics
of Computation, C. Koch
Theoretical
Neuroscience, L. Abbott & P. Dayan
Pattern
Recognition and Machine Learning, Christopher Bishop
Principles
of Neural Science, E. Kandel
Pattern
Classification, Duda, Hart and Stork
Mathematics
for Neuroscientists, Gabbiani and Cox
Instructor:
Barani Raman, office: Brauer 2007,
email: barani@wustl.edu
Teaching Assistants:
·
Nalin Katta (Email: nk1@wustl.edu;
Office Hours: Monday 5 - 6PM; Brauer Hall 2010, Danforth Campus)
·
Nick Szarama (Email: szraman@wusm.wustl.edu; Office Hours: Tuesday
10 - 11AM; Brauer Hall 2010, Danforth Campus)
Students are
encouraged to attend recitations and Matlab
programming tutorial sessions that will be held by the TAs.
Grading
Grading will be straight scale (91 – 100%: A;
81 – 90%: B; 71 – 80%: C; 61 – 70%: D; < 60%: F)
Homework
submission
Homework assignments
are due at 12:00PM on the due date (soft copy should be uploaded to Telesis by
the deadline; Hard copies should be handed over at the beginning of the class).
I will provide more details when I issue the first homework. With the exception
of MATLAB’s built-in functions (e.g., cov, eig, mvnrnd), you are expected to
write your own implementation of the algorithms; in case of doubt please
consult with the instructor or the TAs.
Paper Reviews
A good habit that every graduate student (or those aspiring to get into grad schools) should
nurture is reading papers and assimilating new ideas. To develop this aspect of graduate
education, we will have a paper(s) associated for reading with each lecture. To facilitate healthy
discussion in the lecture, it is strongly encouraged that you read these papers before each
lecture.
Late submissions
Late submissions will
receive a 15% penalty on the total grade of the assignment; the penalty will
increase by an additional 15% every 24 hours. Hardcopies of late submissions
must be dated and time stamped by the instructor or the teaching assistants. An
assignment is considered submitted when ALL components of the assignment have
been submitted; e.g., late submission of one problem in a homework will cause
your entire homework to be considered as a late submission.
Project
The course involves a semester long project. Interdisciplinary teams of comprising of 2-3
students are supposed to pursue an idea of your choosing. The chosen projects must be at a
systems level and ideally will integrate multiple components of the course: biophysics of
computation, neuron network modeling, data analysis using machine learning algorithms.
For students interested in hands-on work, this year we will make resources in the BME
undergraduate lab (Brauer Hall 2011) available to them.
Collaboration vs.
Academic Dishonesty
In
the spirit of academic openness, students are encouraged to share learning
experiences with one another. Discussion of (NOT collaboration on) homework and
projects is strongly encouraged (write the names of your discussants on each
assignment). All written work must be generated by yourself. Exam work should
be your own with no discussion, even for take-home exams. Violations of
academic integrity by any student will be handled according to the guidelines
laid out for all Washington University students:
http://www.wustl.edu/policies/undergraduate-academic-integrity.html
Exceptions
to any of the policies outlined in this syllabus for an individual student
(e.g., due dates and times) will be handled on a case-by-case basis and
possibly put to the remainder of the class for evaluation. No non-emergency
deadline extension of any sort will be granted without the submission of a
partially completed assignment.
Lecture
Outline:
|
Schedule |
Topic |
Assignments |
|
1/15 |
Overview of the course |
|
|
|
Module
1 – Biophysics of Neural Computation |
|
|
1/17 |
Introduction to nervous systems Associated Reading: 1.
Penfield,
W. & Boldrey, E. (1937). Somatic motor and
sensory representation in the cerebral cortex of man as studied by electrical
stimulation. Brain 60: 389-443. 2.
Koch,
Chapter 1 |
|
|
1/24 |
Electrical properties of a membrane patch, ion
channels, HH equations, multi-compartmental models Associated Reading: 1.
Hodgkin,
A., and Huxley, A. (1952): A quantitative description of membrane current and
its application to conduction and excitation in nerve. J. Physiol.
117:500–544. |
|
|
1/29 |
Introduction to phase-plane analysis Associated Reading: 1.
Koch,
Chapter 7 |
|
|
1/31 |
Reduction of HH models: Simple models of neurons (Morris-Lecar, FitzHugh-Nagumo Model, Izhikevich
model) Associated Reading: 1. Koch, Chapter 7 2. Izhikevich E.M. (2003) Simple Model of Spiking
Neurons. IEEE Transactions on Neural Networks, 14:1569- 1572 |
|
|
2/7 |
Generalized linear models of neurons Associated Reading: 1.
Pillow
JW, Shlens J, Paninski L,
Sher A, Litke AM, Chichilnisky EJ, Simoncelli EP.
(2008) Spatio-temporal correlations and visual
signaling in a complete neuronal population. Nature 454: 995-999 2.
Geffen,
MN, Broome, BM, Laurent, G and Meister, M. (2009). “Neural encoding of
rapidly fluctuating odors.” Neuron
61(4): 570-586 |
|
|
2/12 |
Spike Train Analysis (Binomial and Poisson
distributions) |
|
|
2/14 |
Dendritic Computations Associated Reading: 1.
London,
M. and Hausser, M (2005). “Dendritic computations”.
Annual Review Neuroscience 28: 503-532. |
|
|
2/19 |
Synapse and Plasticity Associated Reading: 2.
Markram H, Lübke J, Frotscher M, Sakmann B (January
1997). "Regulation of synaptic efficacy by coincidence of postsynaptic APs
and EPSPs". Science 275 (5297): 213–5. 3.
Bi
GQ, Poo MM. Synaptic modifications in cultured hippocampal neurons:
dependence on spike timing, synaptic strength, and postsynaptic cell type. J Neurosci.
1998 Dec 15;18(24):10464-72. 4.
Cassenaer, S. and Laurent, G. (2007). “Hebbian
STDP in mushroom bodies facilitates the synchronous flow of olfactory
information.” Nature 448: 709-713 |
|
|
|
|
|
|
|
Module
2 – Artificial Neural Networks |
|
|
2/21 |
Perceptron algorithm Associated Reading: Book Chapter
(will be assigned) |
Homework 1
due Homework 2 assigned |
|
2/26 |
Back-propagation Neural Net Associated Reading: Book chapter (will
be assigned) |
|
|
2/28 |
Self-Organized Maps Associated Reading: 1.
Kohonen (1990), The Self Organizing Maps, Proceedings of the
IEEE, Vol. 78, no. 9, pp: 1464-1479 |
Project proposal due |
|
|
|
|
|
|
Module
3 – Neural Encoding/Decoding |
|
|
3/5 |
Fourier analysis – Analysis of mesoscopic
and macroscopic signals (LFP, EEG and ECOG) Book chapter |
|
|
3/7 |
Analysis of population codes - dimensionality reduction
for neural data (PCA, LLE) Associated Reading: 1.
Neuronal
population coding of movement direction. Georgopoulos
AP, Schwartz AB, Kettner RE. Science. 1986 Sep 26;233(4771):1416-9. 2.
Stopfer, M., Jayaraman, V. and
Laurent, G. (2003). “Intensity versus identity coding in an olfactory
system.” Neuron 39(6): 991-1004. |
Homework 2
due Homework 3 assigned |
|
|
SPRING
BREAK |
|
|
3/19 |
Other linear dimensionality reduction methods
(Canonical Correlation Analysis, Partial Least Squares, LDA) Associated Reading: 1.
Temporally
diverse firing patterns in olfactory receptor neurons underlie spatio-temporal neural codes for odors, B. Raman, J.
Joseph, J. Tang, and M. Stopfer, Journal of
Neuroscience, Vol. 30, no. 6, pp. 1994-2006, February 2010 |
|
|
3/21 |
Independent component analysis and Visual encoding Associated Reading: 1.
Independent
component analysis: A tutorial, Aapo Hyvärinen and Erkki Oja Neural Networks, 13(4-5): 411-430,
2000. 2.
Sparse
Coding of Sensory Inputs, Olshausen BA, Field DJ
(2004). Current Opinion in
Neurobiology, 14: 481-487. 3.
M.
S. Lewicki, Efficient coding of natural sounds,
Nature Neuroscience, 5 (4): 356-363, 2002 4.
Scott
Makeig, Anthony J. Bell, Tzyy-Ping
Jung and Terrence J. Sejnowski, Independent
Component Analysis of EEG data. Advances in Neural Information Processing
Systems 8, 145-151, 1996. |
|
|
3/26 |
Classification Algorithms – Quadratic Classifiers,
Naïve Bayes, k- Nearest Neighbor Associated Reading: M. S. Lewicki, A review of
methods for spike sorting: the detection and classification of neural action
potentials. Network: Computation in Neural Systems, 9 (4): 53-78, 1998. |
|
|
3/28 |
Methods for model
validation |
|
|
4/2 |
Parameter Estimation and Clustering (Mixture Models and
Expectation Maximization) Associated Reading: 1.
Pouzat, C., Mazor, O. and Laurent,
G. (2002). “Using noise signature to optimize spike-sorting and to assess
neuronal classification quality.” J Neurosci
Methods 122(1): 43-57 |
|
|
4/4 |
Kalman filter and Neural decoding Associated Reading: 1.
Connecting
brains with machines: The neural control of 2D cursor movement, Black, M. J.,
Bienenstock, E., Donoghue, J. P., Serruya, M., Wu, W., Gao, Y.,
IEEE/EMBS Conference on Neural Engineering, pp. 580-583, Capri, Italy, March
20-22, 2003. 2.
Neural
decoding of cursor motion using a Kalman filter,
Wu, W., Black, M. J., Gao, Y., Bienenstock,
E., Serruya, M., Shaikhouni,
A., Donoghue, J. P., Advances in Neural Information Processing Systems 15, S.
Becker, S. Thrun and K. Obermayer
(Eds.), MIT Press, pp. 117-124, 2003. |
|
|
|
|
|
|
|
Module
4 – Case Studies |
|
|
4/9 |
Olfactory system Associated Reading: 1.
Laurent,
G. (2002). “Olfactory Network Dynamics and the coding of multidimensional
signals.” Nat Rev Neurosci
3(11): 884-95, 2.
Temporally
diverse firing patterns in olfactory receptor neurons underlie spatio-temporal neural codes for odors, B. Raman, J.
Joseph, J. Tang, and M. Stopfer, Journal of
Neuroscience , Vol. 30, no. 6, pp. 1994-2006, February 2010 |
Homework 4 due |
|
4/11 |
Guest Lecture - TBA |
|
|
4/16 |
Guest Lecture - TBA |
|
|
4/23-5/02 |
Final Project Presentations |
|
TA Recitations Sessions:
(Location Whitaker 218)
Wednesday
5:30-7:00 PM - Nalin Katta or Nick Szarama - Danforth
Session 1/24: Matlab &
Calculus Session 1 - Nick
Session 1/31: Matlab & Calculus Session 2 -
Nick
Session 2/7: Differential Equations in Matlab - Nalin
Session 2/14: Probability & Statistics - Nalin
Session 2/21: Linear Algebra Review - Nick
Session 2/28: Review of Perceptron and Back Propagating Neural Network - Nalin
Session 3/7: Review of SOM and Fourier Analysis - Nick
Session 3/21: Review of Dimensionality Reduction Techniques - Nalin
Session 3/28: Review of ICA and Classification Algorithms - Nick
Session 4/4: Parameter Estimation and Clustering - Nalin