# AMATH 342

Instructor
Eric Shea-Brown
325 Lewis Hall
Office hours: Thurs 2-3
TA
Stephen Jonany
Lewis Hall 115

Office hours:

Tues 10:30-11:30
Weds 3-4
Thurs 10:30-11:30
Fri 3-5

NOTE: Please bring a laptop to class for interactive work (see computing notes below).

## Texts

Required text: "Theoretical Neuroscience" by Abbott and Dayan.

Optional supplemental text: "An Introductory Course in Computational Neuroscience" by Miller.

Optional additional MATLAB reference: A student's guide to MATLAB for physical modeling. .pdf provided openly by authors Philip Nelson and Tom Dodson.

For those wanting another, sometimes more mathematical reference with all the derivations, Mathematics for Neuroscientists by Gabbiani and Cox is a wonderful place to head.

## Syllabus, supplemental slides, and readings

(1) Neural coding -- response statistics and signal decoding

TOPICS:

• Introduction to neurons and spike trains
• Tuning curves
• Introduction to probabilty
• Neural responses and response variability
• Response to high-dimensional stimuli: spike triggered averages and effective filters
• The decoding problem, maximum likelihood and signal detection solutions
• Higher, and hierarchical, signal encoding
PROGRAMMING SKILLS:
• MATLAB overview
• Vectors, Matrices
• Loops and logic
• Random numbers + very basic stats
• Plotting, visualization

• (Required) Abbott and Dayan: Ch. 1 (OK to skip parts on autocorrelation)
• (Optional) Miller: Sections 1.1, 1.2, 1.4.2, 1.4.3, 3.1, 3.3, and remainder of Ch. 3
• CLASS MATERIALS:

Weeks 1-2:

Week 3-4:

• Slideset on visual representations. Slideset on neural decoding and variability.
• Rough handwritten notes on fano factor, balanced inputs, and maximum likelihood decoding from class.
• Tutorial notes and practice exercises (not due) on maximum likelihood decoding
• (2) Models of neuron spiking and feature "selection" and coding

(3) Synaptic dynamics and neural netowrks

(4) Population coding: Modern large-scale recordings from cortex and beyond

• Weeks 9-10
• Introduction to Python
• The Allen Brain Observatory, presented by Dr. Saskia deVries

• ## Course structure and grading

Course grades (80%) are based on several extensive Problem Sets handed out in class and due on select Mondays at 3:30. Turn-in will be electronic (scanned, etc) -- details forthcoming. These Sets will combine programming, analytical work, and scientific reasoning. Additionally, very brief in-class quizzes will account for 20% of the grade (example quiz).

Important formatting instructions: in your writeup please present all material for a given problem together -- e.g. under "Problem II" you'd have any and all code that you used for that problem, a written answer, plots that explain and back up your findings and answers, and any analysis. Then we'd go to the next problem. (Not stapling all code for all problems together as an appendix at the end.) You may find the publish(code.m) command in MATLAB helpful. You can print out your codes and plots and intermingle this with handwritten answers and explanations

Late policy: In extenuating circumstances contact instructors.

• Please bring a MATLAB-equpped laptop to class. There is also access to MATLAB at the ICL labs on campus.

#### We'll use Python later into the class. To aid your transition to Python:

Python tutorial, courtesy of Higham and MacMillen: