Quantitative Methods in Neuroscience

NEU 366M, Fall 2013
The University of Texas at Austin
 
location: PAR 208
time: Tues/Thurs 12:30-2:00 pm
 
instructor: Professor Ila Fiete (fiete [at] mail.clm.utexas.edu)
teaching Assistant: Kenneth Latimer (latimerk [at] utexas.edu)
office hours:
Dr. Fiete: Mon 1:30-2:30 pm, Thurs 11:30-12:30 (NHB 3.354) and by appt.
Kenneth: Mon 4-5:30, Fri 10-11:30 (SEA 2.122) and by appt.
 
syllabus: PDF, HTML
textbook: Mathematics for Neuroscientists Gabbiani and Cox 2010, @UT Library
MATLAB tutorials: Mathworks tutorial page
basic programming tutorial
plotting basics
Matlab primer (pdf)
Math links: Linear algebra review and some slides
course schedule
DateTopic Reading Homework
Thur 8.29 Preliminaries: Introduction to course aims, mathematical notation, review of basic math objects and operations. Textbook Secs 1.3, 1.4 Homework 1 assigned (pdf)
Fri 8.30, 10:00am and 3:00pm
SEA 2.122
MATLAB tutorial
Tues 9.03 Subthreshold cellular properties: Nernst potential, cell membrane as an RC circuit. Textbook Ch 2 (excluding 2.5), Sec 3.4, slides (pdf)
Thur 9.05 Subthreshold cell voltage equation; numerical integration of functions; steady states. Textbook Section 3.1 Homework 2 assigned (pdf)
Tues 9.10 Exact integration of subthreshold voltage equation, synaptic dynamics. Textbook Sections 2.5, 3.1 Homework 1 solutions (pdf)
Thur 9.12 Synaptic dynamics, numerical integration of differential equations including voltage equation. Textbook Sections 3.5, 3.4
Tues 9.17 Simple spiking model (leaky integrate-and-fire neuron). Textbook Section 10.1 Homework 3 assigned (pdf)
Thur 9.19 The Dirac Delta function; spikes in the synpatic activity equation. Wikipedia page on the Dirac Delta function. For more details on the Dirac Delta, see book: Mathematical Methods for Physicists, by Arfken (7th ed. Elsevier, 2013), Section 1.11, p. 75. Homework 2 solutions (pdf)
Tues 9.24 Synaptic activation with trains of spikes. Method of averaging I: numerical integration of differential equations that involve delta functions. Homework 4 assigned (pdf)
Thurs 9.26 Method of averaging II: deriving a rate-based equation for synaptic activation. Homework 3 solutions (pdf)
Tues 10.1 Stability of fixed points: Graphical stability analysis. Example: The autapse as a bistable switch. Homework 5 assigned (pdf)
Thurs 10.3 Graphical stability analysis continued. Linear stability analysis. The autapse as an integrator. Linear stability notes (pdf) Homework 4 solutions (pdf)
Tues 10.8 Review No new homework; Homework 5 solutions (pdf)
Thur 10.10 Midterm: in-class, closed book.
Tues 10.15 Positive feedback in a mutual inhibition circuit: switches, integrators, perceptual bistability. Slides (pdf), Matlab code mut_inhib_switch.m Homework 6 assigned (pdf)
Thur 10.17 Decoupling coupled linear (differential) equations: heuristic. Homework 6 solutions (pdf)
Tues 10.22 Linear algebra: basis sets, vector spaces. Linear algebra notes by E. Simoncelli (pdf) Homework 7 assigned (pdf)
Thur 10.24 Matrices, pseudo inverse for linear least-squares regression (overconstrained problems). Homework 7 solutions (pdf)
Tues 10.29 Pseudo inverse for underconstrained systems of linear equations; eigenvectors and eigenvalues. Homework 8 assigned (pdf) Related data file (mat)
Thur 10.31 Eigenvector decomposition of systems of linear equations. Homework 8 solutions (pdf)
Tues 11.05 Covariance. PCA. Textbook section 14.2; A tutorial on Principal Components Analysis, by J. Shlens (2009) (pdf) Homework 9 assigned (pdf) Related data and code files (zip)
Thur 11.07 Convolution. Notes by S. Seung (pdf)
Tues 11.12 Convolution: interpretations, examples. Correlation. Homework 9 solutions (pdf)
Thur 11.14 Linear neural coding problem: Wiener-Hopf equations. Notes by S. Seung (pdf)
Tues 11.19 Probability distributions, Maximum Likelihood, GLMs (Professor Pillow) Slides (pdf)
Thur 11.21 Fourier series: sines and cosines as a basis set for periodic functions. Filtering and denoising. PROJECTS.   Homework 10 assigned (pdf) Related code to generate data (m-file)
Tues 11.26 How to write a research report: target audience, style, content. PROJECTS.
Thur 11.28 Thanksgiving
Tues 12.03 Fourier transforms. Identifying frequency content of a signal. Convolution as product. PROJECTS.
Thur 12.05 Course evaluations. PROJECTS.
Fri 12.06, 6 pm Homework # 10 due: drop in office (Ila Fiete) or send by email.
Fri 12.13, 2:30-5 pm Final exam: project presentations.
 
 

page maintained by Kenneth Latimer