Physics 178/278

(Truth is much too complicated to allow anything but approximations.*)

Course overview

This course explores the cellular and synaptic basis for neuronal control of animal behavior. The emphasis in on analytically tractable models of network dynamics and neuronal computation. We provide a path from the dynamics of single neurons to three forms of network activity, each of which involves models where the description of a neuron is reduced to a single state-variable. The first involves networks of weakly coupled neuronal oscillators in which each neuron is described by the phase in its limit cycle. These networks provide a natural means to discuss collective dynamics, such as oscillations and waves in networks of inhibitory neurons. The second and third forms of activity involve circuits of asynchronous neurons in which each cell is described by its Poisson firing rate. Recurrent architectures provide a natural means to discuss attractor-based circuits for motor control, sensory processing and memory. Feedfoward architectures provide a means to formalize the logic of both single cells with large dendritic fields and motivate the concept of receptive fields. Aspects of applied mathematics and experimental procedures are discussed as needed.

Class meets in room 2623 Mayer Hall. Lectures are every Tuesday and Thursday from 8:00 to 9:20 AM. Ms. Sravya Alluri and Ms. Mendy Hsu, the class teaching assistants, will run a discussion section, which includes pedagogical lectures, and homework review on Wednesdays from 6:00 to 8:00 PM in room 2623 Mayer Hall. Office hours with Ms. Alluri and Ms. Hsu are 9:30 to 10:30 AM (directly after class in 2702 Mayer Hall) on both Tuesday sand Thursdays, or by appointment.

Preliminary lecture schedule, notes, and source material for Winter 2017

(Week 1) 10, 12 Jan - Basic neuronal anatomy, electrical dynamics, and computation
DK lecture notes and graphics (7.3 Mb PDF)
Connectomics - Kleinfeld et al. reprint (7.7 Mb PDF)
Connectomics - Kasthuri et al. reprint (5.3 Mb PDF)
Cortical connectivity - Data of Mrsic-Flogle (1.5 Mb PDF)
Action potentials - Bean reprint (0.7 Mb PDF)
(Week 2) 17, 19 Jan - Biophysical basis of action potentials: Insight through reduced neuronal dynamics
DK lecture notes and graphics on Hodgkin-Huxley model (2.8 Mb PDF)
DK lecture notes and graphics on reduced models (1.5 Mb PDF)
Threshold gain curves and neuronal computation (3.5 Mb PDF)
Dimensional reduction - Rinzel reprint (1.8 Mb PDF)
(Week 3) 24, 26 Jan - What makes neurons spike? Noise and "balanced" networks
DK preliminary lecture notes and graphics (1.0 Mb PDF)
Noise driven spiking and neuronal noise (3.5 Mb PDF)
van Vreeswijk & Sompolinsky reprint (0.8 Mb PDF)
Barral and Reyes reprint (1.7 Mb PDF)
(Week 4) 31 Jan, 2 Feb - Pairs and networks of neuronal oscillators and coupled phase dynamics
DK lecture notes and graphics on phase dynamics (13.0 Mb PDF)
Coupled oscillators - Ermentrout & Kleinfeld reprint (0.9 Mb PDF)
Rhythms of the Brain - Buzsaki book (5.4 Mb PDF)
(Week 5) 7, 9 Feb - Linear recurrent networks: Basis of integration in motor control (line attractors)
DK lecture notes and graphics on linear networks (2.0 Mb PDF)
Line attractors - Seung reprint (0.5 Mb PDF)
Integrator networks - Major & Tank reprint (1.1 Mb PDF)
Integrator networks - Seelig & Jayaraman reprint (5.7 Mb PDF)
Integrator networks - Mante, Sussillo, Shenoy & Newsome reprint (3.2 Mb PDF)
Head direction - Peyrache, Lacroix, Petersen & Buzsáki reprint (3.1 Mb PDF)
(Week 6) 14, 16 Feb - Rate-based recurrent networks: Basis for associative memory and application to motor programs
Discussion of group projects
DK lecture notes and graphics on associative networks (4.9 Mb PDF)
Central pattern generators - Kleinfeld & Sompolinsky reprint (1.4 Mb PDF)
(Week 7) 21, 23 Feb - Rate-based recurrent networks: Derivation from conductance models and application to sensory selection
DK lecture notes and graphic on deriving rate-based networks (0.1 Mb PDF)
Gain curves - Chance, Abbott & Reyes reprint (0.2 Mb PDF)
DK notes and graphic on ring attractor (1.9 Mb PDF)
Invariant tuning - Shapley & Sompolinsky reprint (1.1 Mb PDF)
Bump attractors - Wimmer, Nykamp, Constantinidis & Compte reprint (1.2 Mb PDF)
(Week 8) 28 Feb, 2 Mar - Feed forward computation with Perceptrons and layered networks
DK lecture notes on layered networks (0.4 Mb PDF)
MATLAB code for Perceptron learning from Seung (0.1 Mb M)
MATLAB Data (3.3 Mb Mat)
Dendrites - Polsky, Mel & Schiller reprint (1.3 Mb PDF)
Vision and gaze - Zipser & Andersen reprint (0.8 Mb PDF)
Vision-based identification - Serre, Oliva & Poggio reprint (0.9 Mb PDF)
Vision-based identification - Yamins, Hong, Cadieu, Solomon, Seibert & DeCarlo reprint (1.8 Mb PDF)
Layered Networks - Chapter 6 of Haykin (11.5 Mb PDF)
(Week 9) 7, 9 Mar - Complicated neurons: Dendritic gain, filtering, and cellular logic
DK lecture notes and graphics on dendritic attenuation and gain (3.0 Mb PDF)
Dendrites - London & Häusser reprint (0.8 Mb PDF)
Dendrites - Magee reprint (0.9 Mb PDF)
(Week 10) 14, 16 Mar - Tools of the trade: Measurements and data analysis
Functional measurements - Scanziani & Häusser reprint (2.1 Mb PDF)
YA lecture notes and graphic on reverse correlation stimulus design and analysis (7.7 Mb PDF)
Analysis of spike trains - Aljadeff, Lansdell, Fairhall & Kleinfeld reprint (7.8 Mb PDF)
Spectral methods - Kleinfeld & Mitra reprint (5.3 Mb PDF)

Homework (e-mail a type set or scanned PDF to Ms. Mendy Hsu)

Number 1: Available on 12 Jan and due midnight on 23 Jan (0.3 Mb ZIP)
Number 2: Available on 26 Jan and due midnight on 6 Feb (0.3 Mb PDF)
Number 3: Available on 9 Feb and due midnight on 20 Feb (0.3 Mb ZIP)
Number 4: Available on 2 Mar and due midnight on 20 Mar (0.2 Mb ZIP)
Group project: Available on 14 Feb and presented on 23 Mar Topics (0.2 Mb PDF)
Materials (52.5 Mb ZIP)

Background material

Review of diffusion. Notes and graphics of DK (0.3 Mb PDF)
Review of electrodiffusion across membranes. Notes and graphics of DK (3.8 Mb PDF)
Review of electrotonic properties of dendrites and axons. Notes and graphics of DK. (0.7 Mb PDF)
Review of Hodgkin Huxley formalism: Chapter 6 from "Biophysics of Computation" by Christoff Koch. (28.0 Mb PDF)
Review of mammalian CNS anatomy. MBL Neuroinformatics graphics of Helen Basbas. (1.7 Mb PDF)
Review of linear algebra. MBL Neuroinformatics notes of DK. (2.1 Mb PDF)
Stability analysis of a two dimensiona dynamical system. Notes of Yonitan Aljadef. (0.1 Mb PDF)
Review of Fourier transforms. Notes of DK. (0.1 Mb PDF)
Review of Poisson distribution. Notes of John Cooper. (0.1 Mb PDF)
Review of neuronal variability and Poisson statistics. Notes of Yonitan Aljadef. (0.1 Mb PDF)
Receptive fields and predicting stimuli from spike trains. Notes of DK. (5.7 Mb PDF)
Basic MATLAB tutorial: Notes of Douglas Rubino. (0.1 Mb M-code)
Advanced Matlab tutorial (0.1 Mb zipped M-code)

*John von Neumann (1903-1957)