Supplementary Materials Help Center Learn more.

This page contains supplementary materials such as additional notes on lecture slides, tutorials, documents, and links useful for understanding the lectures and solving quiz questions.

• Week 1:
  • Lecture Notes
• Week 2:
  • Lecture Notes
  • Math Notes: Vectors and Functions
  • Quiz 2: Spike Triggered Average Tutorial
  • Video tutorial: functions are vectors (note: there is a small error at 14:06 -- I write that $x_3 = (4, -4)$ but draw it as $(-4, 4)$ -- it should be drawn four units to the right and four units down instead)
  • Video tutorial: convolutions and linear systems
• Week 3:
  • Lecture Notes
  • Video tutorial: Gaussians in one dimension
  • Math notes: A quick run-down on basis functions
• Week 4:
  • Lecture Notes
  • Video tutorial: What's up with entropy?
  • Video tutorial: Information theory? That's crazy!
  • Derivation of definition of entropy.
  • Maximum likelihood tutorial (from the mathematicalmonk Youtube channel)
  • Maximum a posteriori tutorial (from the mathematicalmonk Youtube channel)
• Week 5:
  • Lecture Notes
  • RC circuits and solving first-order differential equations
  • Video Tutorial: Probability distributions in 2D and Bayes' Rule
  • Video Tutorial: Dynamical Systems Theory Intro Part 1: Fixed points
  • Video Tutorial: Dynamical Systems Theory Intro Part 2: Nullclines
• Week 6:
• Lecture Notes
• Video tutorial: Changing basis
• Video tutorial: Welcome to eigenworld
• Dr. Rao's Notes on Recurrent Networks!
• Week 7:
  • Lecture Notes
  • Papers relevant to this week's lectures:
    • Olshausen & Field (1996)
    • Rao (1999)
    • Rao & Ballard (1999)
    • Koch & Poggio (1999)
    • Huang & Rao (2011)
  • Video tutorial: Gradient ascent and descent
• Week 8: 
• Lecture Notes
• Backpropagation Algorithm for Multilayer Networks (PDF file)
• Reinforcement Learning textbook by Sutton and Barto (free online book)
• Actor-critic models of brain function
• Barto's 1995 article on the model
• Scholarpedia review article by Jim Houk
• Recent probabilistic model (Rao,  2010)
• Reinforcement learning of autonomous helicopter flight

A computational neuroscientist's library: Some recommended additional textbooks:

• Anastasio. Tutorial on Neural Systems Modeling. Gentle introduction to neural modeling; comes with Matlab code for examples in the book.
• Johnston and Wu, Foundations of Cellular Neurophysiology. The classic text for quantitative neurophysiology.
• Koch, The Biophysics of Computation. A compendium of neuronal hardware, its dynamics and functional implications for coding.
• Izhikevich, Dynamical systems in neuroscience. A highly recommended introduction to nonlinear dynamics applied to neuronal excitability.
• Rieke et al. Spikes: Exploring the Neural Code. Classic introductory book on neural coding.

Some cool and informative videos:

• Center-surround receptive field: In this video, the experimenter presents a circle of light on a screen in front of an anesthetized animal. This circle of light falls upon the circular receptive field, drawn upon the screen, of a particular cell in the lateral geniculate nucleus (LGN, of the thalamus, the sensory waypoint of the brain) which is connected to a particular retinal ganglion cell (within the retina). When the light is localized to that area, the cell spikes furiously; each individual 'pop' heard is a single action potential being recorded. As you can hear, neurons have the ability to fire quickly! This particular cell has an on-center receptive field: when the light is shown within the circular receptive field, the firing rate of the cell increases. However, when darkness occurs within the circle with a ring of light around it, the cell is inhibited and its firing rate is reduced. As the receptive field is simply a circle, any light over that area, be it a bar or spot, can elicit a response in the cell. Note that a given cell's center-surround receptive field does not take up the entire screen, but rather is localized to a few degrees of visual angle.


• Mapping an oriented receptive field: This video demonstrates the process by which the oriented receptive field of a visual cortical neuron is determined. Unlike the video above demonstrating a center-surround receptive field, this visual cortical neuron requires a full bar of light at a specific orientation in order to be activated. Once again, each 'pop' is an action potential recorded electrically and converted to a sound to be heard.

Useful papers relevant to course lectures:

• Two-Dimensional Time Coding in the Auditory Brainstem. Slee, S. J., et al. The Journal of Neuroscience, October 26, 2005•25(43):9978 –9988
• Selectivity for Multiple Stimulus Features in Retinal Ganglion Cells. Fairhall, A. L. (November 01, 2006). Journal of Neurophysiology, 96, 5.
• Characterization of neural responses with stochastic stimuli. Simoncelli, E. P., Paninski, L., Pillow, J., & Schwartz, O. (2004). The cognitive neurosciences, 3, 327-338.
• Analyzing Neural Responses to Natural Signals: Maximally Informative Dimensions. Sharpee, Tatyana, Nicole C. Rust, and William Bialek. Neural computation 16.2 (2004): 223-250.
• A Mathematical Theory of Communication. Shannon, C. E. The Bell System Technical Journal 27 (1948): 379-423, 623-656.
• A Neural Substrate of Prediction and Reward. Shultz, W., et al. Science 275 1593 (1997).
• Adaptation and Natural Stimulus Statistics.  Fairhall, in Cognitive Neuroscience, ed. Gazzaniga (2014)
  

Links to some helpful resources: 

• Eero Simoncelli's linear algebra notes. 

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