COURSE SYLLABUS
Computational Neuroscience
Neurl UA 302
Psych UA 300
Fall 2021

Thursdays: 5-7:30pm
Meyer (4-6 Washington Place), room 465

Last updated: Oct 24, 2021

Course Objective

The objective of this course is to master select topics in computational neuroscience, focusing in particular on dynamics of neural activity. This is an interdisciplinary field of science, crossing the boundaries between psychology, biology, physics and engineering. This course is intended for neural science majors and psychology majors that are on track for careers in science and medicine. This course is also appropriate for students in the psychology masters degree program. Topics include: the membrane equation, synaptic input, convolution and receptive fields, recurrent neural nets, neural integrators and working memory. The best way to learn something is to do it. So we will cover each topic by implementing simulations, using spreadsheets (Excel or Numbers) to simulate the dynamics of neural activity over time.

Prerequisites

Intro to Neuroscience (NEURL-UA 100) or Cognitive Neuroscience (PSYCH-UA 25) or Perception (PSYCH-UA 22).

Assignments and Grading

There will be a series of computational lab assignments (see below), using Excel, each of which will be submitted with a written lab report. Most of the work on these assignments will be done in class (bring your computer to class).

Your grade will be determined by: computational lab assignments (80%), attendance and class participation (20%).

Assignments and Grading Readings

Readings are available online through the links provided in the schedule below. These include mostly lecture notes that I've written over the years for teaching computational neuroscience. Some of them are a bit "mathy" but it'll be ok - we'll go through them together.

Schedule

Date Topic Reading
9/2, 9/9 The membrane equation Membrane equation handout
9/16 No class (Yom Kippur)
9/23, 9/30, 10/7 Linear systems and convolution Linear systems handout
10/14, 10/21 & 10/28 Neural integrators and neural oscillators Primer on neural integrators and neural oscillators
11/4, 11/11 V1 physiology Wandell Ch 6;
Carandini & Heeger (2012)
11/25 No class: Thanksgiving
11/18, 12/2, 12/9 Oscillatory Recurrent Gated Neural Integrator Circuits Heeger & Mackey (2019);
Heeger & Zemlianova (2020)

Assignments

Assignment 1 (due 9/23)

Read the membrane equation handout. Use Eq. 5 to implement the membrane equation in Excel (or Numbers). Simulate the membrane potential over time for current steps, and make graphs that look like those in Fig. 2 (using the parameters in the figure caption). We call this the step response. Make another series of graphs for current inputs that vary sinusoidally over time. We call this the frequency response. You will note that the frequency response is also sinusoidal (i.e., if the injected current varies sinusoidally over time then the membrane potential also varies sinusoidally over time).

Use your simulations to answer the following questions:

(1) What happens to the step response when you double the value of C, when you double the value of g, and when you double both C and g? Use Eq. 6 and Fig. 2 as a guide.

(2) What happens to the frequency response when you change the frequency of the injected current? In what way does the frequency of the sinusoidal membrane potential depend on the frequency of injected current? In what way does the amplitude of the sinusoidal membrane potential depend on the frequency of injected current? In what way does the phase of the sinusoidal membrane potential depend on the frequency of injected current? Use Eqs. 9 and 10, and Fig. 4 as a guide.

Write a lab report consisting of a couple pages of text and a few figures showing the results of your simulations. Copy/paste the graphs from Excel/Numbers into either Word or Pages. Please make the figures legible and comprehensible: label the axes, add figure captions, etc. Make a PDF of your lab report and send it to me by email. I will accept only PDF files.

Assignment 2 (due 10/14)

Download the Linear systems tutorial. Work through this spreadsheet to understand what it does and how it works. Write up a lab report that answers the questions in red in the tutorial, including graphs.

Assignment 3 (due 11/4)

Read the Primer on neural integrators and neural oscillators. Use Eq. 1 (with tau = 10 msec) to recreate Fig. 1. Use the same equation but with the value of lambda changing over time to recreate Fig. 2. Use Eqs. 7, 8, and 9 to recreate Fig. 3.

Write a lab report consisting of a couple pages of text and a few figures showing the results of your simulations. Copy/paste the graphs from Excel/Numbers into either Word or Pages. Please make the figures legible and comprehensible: label the axes, add figure captions, etc. Make a PDF of your lab report and send it to me by email. I will accept only PDF files.

Assignment 4 (due 11/18)

Download the V1 tutorial. Work through this spreadsheet to understand what it does and how it works. Write up a lab report that answers the questions in red in the tutorial, including graphs.

Assignment 5 (due 12/16)

Read the ORGaNICs papers: Heeger, PNAS, 2019; Heeger & Zemlianova, PNAS, 2020.

Follow the instructions in the Assignment 5 handout.

Academic integrity policy

Students must adhere to NYU's principles of academic integrity, and the CAS Honor Code. Academic integrity means that all of the work that you submit is original.

Violations of academic integrity include: Consequences of a single violation of the principles of academic integrity are a grade of F on the scored assessment, and a formal report to the Dean's Office. The grade of F must be factored into the course's final grade. In cases of serious violation(s) of these standards, the department will seek dismissal of the student from the university.

Health and safety policy

Please plan to attend class in person as long as you are healthy. If you feel ill (even slightly ill) or if you think you might have been exposed (e.g., you attended at a party that was more crowded than you expected it to be), please skip class and get yourself tested. I will meet with you 1:1 via zoom to make sure that you don't get behind and/or give you extra time on the next assignment.

Please stay home even if you think you don't have COVID (i.e., you got a negative test result). Think of the consequences. If you come to class with a cold and transmit it to someone else, they will have to assume that they might have COVID. So they will need to get tested which can take several days and in the meantime they will need to quarantine, skip classes and cancel all their plans, risk infecting their friends and family. So...

STAY HOME IF YOU FEEL ILL - EVEN IF YOU ARE CERTAIN THAT YOU DON'T HAVE COVID.

At this point in time, everyone should know how to wear a mask. But just in case... Wearing a mask is effective only if it covers both your mouth and your nose. There's little metal strip at the top of the mask that should be pinched over your nose to the shape of your face, so that the mask doesn't slide down. We should not be able to see the tip of your nose. I will have to ask you to leave if your nose is not covered.

david.heeger@nyu.edu