## Intro to Theory

**Computational Neuroscience, Fall 2021**

**Larry Abbott, Ken Miller, Ashok Litwin Kumar, Stefano Fusi, Sean Escola**

**TAs: Elom Amematsro, Ramin Khajeh, Minni Sun, Denis Turcu**

**Meetings: **Tuesdays & Thursdays 2:00-3:30

**Text **- Theoretical Neuroscience by P. Dayan and L.F. Abbott (MIT Press)

**Webpage **- https://ctn.zuckermaninstitute.columbia.edu/courses

**September**

9 (Larry) Introduction to Course and to Computational Neuroscience

14 (Larry) Electrical Properties of Neurons, Integrate-and-Fire Model

16 (Stefano) Adaptation, Synapses, Synaptic Plasticity

21 (Larry) The Hodgkin-Huxley Model (Assignment 1)

23 (Larry) Types of Neuron Models and Networks

28 (Larry) Numerical Methods, Filtering (Assignment 2)

29 Assignment 1 Due

30 (Sean) Generalized Linear Models

**October**

5 (Ken) Linear Algebra (Assignment 3)

6 Assignment 2 Due

7 (Ken) PCA and Dimensionality Reduction

12 (Ken) Rate Networks/E-I networks I (Assignment 4)

13 Assignment 3 Due

14 (Ken) Rate Networks/E-I networks II

19 (Ken) Unsupervised/Hebbian Learning, Developmental Models (Assignment 5)

20 Assignment 4 Due

21 (Ashok) Introduction to Probability, Encoding, Decoding

26 (Ashok) Decoding, Fisher Information I

27 Assignment 5 Due

28 (Ashok) Decoding, Fisher Information II (Assignment 6)

**November**

2 Holiday

4 (Ashok) Information Theory

9 (Ashok) Optimization I (Assignment 7)

10 Assignment 6 Due

11 (Ashok) Optimization II

16 (Stefano) The Perceptron (Assignment 8)

17 Assignment 7 Due

18 (Stefano) Multilayer Perceptrons and Mixed Selectivity

23 Holiday

25 Holiday

30 (Stefano) Deep Learning (Assignment 8)

**December**

1 Assignment 8 Due

2 (Sean) Learning in Recurrent Networks

7 (Stefano) Continual Learning and Catastrophic Forgetting (Assignment 10)

8 Assignment 9 Due

9 (Stefano) Reinforcement Learning

15 Assignment 10 Due

Introduction to Theoretical Neuroscience (Spring 2021)

Introduction to Theoretical Neuroscience (Spring 2020)

## Statistical analysis of neural data

Statistical analysis of neural data (GR8201), Fall 2021

**This is a Ph.D.-level topics course in statistical analysis of neural data. Students from statistics, neuroscience, and engineering are all welcome to attend. A link to the last iteration of this course is here.****Time**: F 10-11:30**Place**: JLG L8-084**Professor**: Liam Paninski; Office: Zoom. Email: [email protected]. Hours by appointment.

View Schedule**Prerequisite**: A good working knowledge of basic statistical concepts (likelihood, Bayes' rule, Poisson processes, Markov chains, Gaussian random vectors), including especially linear-algebraic concepts related to regression and principal components analysis, is necessary. No previous experience with neural data is required.

**Evaluation**: Final grades will be based on class participation and a student project. Additional informal exercises will be suggested, but not required. The project can involve either the implementation and justification of a novel analysis technique, or a standard analysis applied to a novel data set. Students can work in pairs or alone (if you work in pairs, of course, the project has to be twice as impressive). See this page for some links to available datasets; or talk to other students in the class, many of whom have collected their own datasets.

**Course goals**: We will introduce a number of advanced statistical techniques relevant in neuroscience. Each technique will be illustrated via application to problems in neuroscience. The focus will be on the analysis of single and multiple spike train and calcium imaging data, with a few applications to analyzing intracellular voltage and dendritic imaging data. Note that this class will not focus on MRI or EEG data. A brief list of statistical concepts and corresponding neuroscience applications is below.

## Mathematical Tools

**Mathematical Tools for Theoretical Neuroscience (NBHV GU4359)**

**Spring 2021**

**Lecturer**: Dan Tyulmankov ([email protected])**Faculty contact**: Prof. Ken Miller ([email protected])***Time**: Tuesdays, Thursdays 11:40a-12:55p**Place**: Zoom**Webpage:** CourseWorks (announcements, assignments, readings) and Piazza (Q&A, discussion)**Credits:** 3 **(Please contact Prof. Miller to sign add/drop forms and other items which require faculty permission)*

**Description**: An introduction to mathematical concepts used in theoretical neuroscience aimed to give a minimal requisite background for NBHV G4360, Introduction to Theoretical Neuroscience. The target audience is students with limited mathematical background who are interested in rapidly acquiring the vocabulary and basic mathematical skills for studying theoretical neuroscience, or who wish to gain a deeper exposure to mathematical concepts than offered by NBHV G4360. Topics include single- and multivariable calculus, linear algebra, differential equations, dynamical systems, and probability. Examples and applications are drawn primarily from theoretical and computational neuroscience.

**Registration**:

*Undergraduate and graduate students*: Must register** on SSOL and on Piazza*All others*: Please fill out this form and register on Piazza

*(******If you’re only interested in attending a subset of lectures, register anyways and contact Dan) *

**Prerequisites**: Basic prior exposure to trigonometry, calculus, and vector/matrix operations at the high school level

**Mathematical Tools for Theoretical Neuroscience (Spring 2020)**

## Advanced Theory

**Special Virtual Edition, Summer/Fall 2020**

**Meetings:** Wednesdays, 10.00 am

**Location:** Zoom, contact **[email protected]** for details

**Schedule:**

7/15/2020 Time-dependent mean-field theory for mathematical streetfighters **(Rainer Engelken)**

7/22/2020 Predictive coding in balanced neural networks with noise, chaos, and delays, Article **(Everyone) **

7/29/2020 A solution to the learning dilemma for recurrent networks of spiking neurons, Article **(Everyone) **

8/5/2020 Canceled

8/12/2020 Artificial neural networks for neuroscientists: A primer, Article **(Robert Yang)**

8/19/2020 A mechanism for generating modular activity in the cerebral cortex **(Bettina Hein)**

8/26/2020 Dynamic representations in networked neural systems, Article **(Kaushik Lakshminarasimhan)**

9/2/2020 Network principles predict motor cortex population activity across movement speeds **(Shreya Saxena)**

9/9/2020 Modeling neurophysiological mechanisms of language production **(Serena Di Santo)**

9/16/2020 How single rate unit properties shape chaotic dynamics and signal transmission in random neural networks, Article **(Samuel Muscinelli)**

9/23/2020 Shaping dynamics with multiple populations in low-rank recurrent networks, Article **(Laureline Logiaco)**

9/30/2020 Deep Graph Pose: a semi-supervised deep graphical model for improved animal pose tracking, Article **(Anqi Wu)**

10/7/2020 Decoding and mixed selectivity, Article, Article, Article **(Fabio Stefanini)**

10/14/2020 Theory of gating in recurrent neural networks, Article, Article **(Kamesh Krishnamurthy)**

10/21/2020 Decentralized motion inference and registration of neuropixel data **(Erdem Varol)**

10/28/2020 Decision, interrupted **(NaYoung So)**

11/4/2020 Abstract rules implemented via neural dynamics **(Kenny Kay)**

11/11/2020 Canceled for Holiday

11/18/2020 "Rodent paradigms for the study of volition (free will)" **(Cat Mitelut)**

11/25/2020 Gaussian process inference **(Geoff Pleiss)**

12/2/2020 Canceled

12/9/2020 Structure and variability of optogenetic responses in multiple cell-type cortical circuits **(Agostina Palmigiano)**

12/16/2020 ** **Manifold GPLVMs for discovering non-Euclidean latent structure in neural data, Article **(Josh Glaser)**

Advanced Theory Seminar (Spring 2020) website

Advanced Theory Seminar (Spring 2019) website

*Page Last Updated: 9/16/2021*