9.29 Introduction to Computational Neuroscience

Lecture schedule

• Lecture 1 (T 2/5) (html, pdf, video)
  • Introduction
  • Examples of neural coding. Simple linear regression.
  • Dayan and Abbott, Section 1.1
  • R. Wessel, C. Koch, F. Gabbiani, Coding of time-varying electric field amplitude modulations in a wave-type electric fish, J. of Neurophysiology, 75(6), 2280-93 (1996).
  • Fitting Data to a Straight Line, Numerical Recipes in C
• Lecture 2 (Th 2/7) (html, pdf, video)
  • Convolution, correlation. Firing rate. Spike-triggered average.
  • Wiener-Hopf equations and white noise analysis
  • Dayan and Abbott, Sections 1.2-1.3
  • Convolution and Deconvolution Using the FFT, Numerical Recipes in C
  • Correlation and Autocorrelation Using the FFT, Numerical Recipes in C
• Optional Lecture 1 (Th 2/7) (video)
  • Initializing and using matrices in MATLAB. Linear modelling in a sample data set.
• Lecture 3 (T 2/12) (html, pdf, video) Assignment #1 due!
  • More about convolution and correlation.
  • Dayan and Abbott, Sections 2.1-2.2
• Optional Lecture 2 (W 2/13) (pdf)
  • Basic linear algebra in MATLAB. Vector and matrix addition and multiplication. Solving sets of linear equations using matrices.
• Lecture 4 (Th 2/14) (video)
  • Visual receptive fields I.
  • Basics of the visual system. Center-surround receptive fields. Difference of Gaussians model.
  • S. E. Palmer, Vision Science - photons to phenomenology, 146-154, The MIT Press, Cambridge, Massachusetts (1999).
  • Dayan and Abbott, Sections 2.3 and 2.6
• no class (T 2/19) Assignment #2 due!
• Lecture 5 (Th 2/21) (video)
  • Visual receptive fields II.
  • Simple cortical cells, separable and nonseparable.
  • Dayan and Abbott, Sections 2.4 and 2.5.
  • Website: Space-Time Receptive Fields of Visual Neurons
• Lecture 6 (T 2/26) (video) Assignment #3 due!
  • Discrete Fourier series
  • G. Strang, Introduction to Applied Mathematics 4.2, 290-308, Wellesley-Cambridge Press, Wellesley, Massachusetts (1990)
    
• Lecture 7 (Th 2/28) (video)
  • Fourier series. Pure tones. Perception of periodic complex tones.
  • G. Strang, Introduction to Applied Mathematics, 4.1, 263-289, Wellesley-Cambridge Press, Wellesley, Massachusetts (1990)
  • D. Deutsch, Paradoxes of Musical Pitch, Scientific American, 88-95, August 1992.
    
• Lecture 8 (T 3/5) (video)
  • Fourier transform. Spectral analysis. The cochlea as a Fourier analyzer.
  • G. Strang, Introduction to Applied Mathematics 4.3, 309-329, Wellesley-Cambridge Press, Wellesley, Massachusetts (1990)
    
• Lecture 9 (Th 3/7) (video) Assignment #4 due!
  • Features and filters in vision
  • S. E. Palmer, Vision Science - photons to phenomenology, 4.2, 4.3, The MIT Press, Cambridge, Massachusetts (1999).
• Lecture 10 (T 3/12) (video)
  • Probability theory and Bernoulli processes.
  • Dayan and Abbott, Sections 1.4 and 1.5
• Lecture 11 (Th 3/14) (video) Assignment #5 due!
  • Poisson processes and spike train statistics.
  • Dayan and Abbott, Sections 3.1 and 3.2
• Lecture 12 (T 3/19) (video) Assignment #6 due!
  Review
• Midterm (Th 3/21)
• Spring break
• Lecture 13 (T 4/2) (video)
  • Midterm post-mortem
• Lecture 14 (Th 4/4) (video)
  • Ion channels. Nernst equation. Passive electrical properties of neurons.
  • Dayan and Abbott, Section 5.2.
  • D. Johnston and S. Miao-Sin Wu, Foundations of Cellular Neurophysiology, Chapter 2, The MIT Press, Cambridge, Massachusetts, London, England (1995)
• Lecture 15 (T 4/9) (video)
  • The action potential. Hodgkin-Huxley model.
  • Dayan and Abbott, Sections 5.3 and 5.5.
• Lecture 16 (Th 4/11) (video) Assignment #7 due!
  • Hodgkin-Huxley model. Numerical methods for differential equations.
  • Dayan and Abbott, Section 5.6
  • Dayan and Abbott, Section 5.11 (Appendices A and B).
  • C. Koch, Biophysics of Computation, Information Processing in Single Neurons, Chapter 6, Oxford University Press, New York, Oxford (1999)
  • A. Sherman, Lecture Notes and Lab Problems on Numerical Methods.
  • Arthur Sherman's web page on Numerical Methods in Neuronal Modeling
• Patriot's Day (T 4/16)
• Lecture 17 (Th 4/18) (video) Assignment #8 due!
  • A-type potassium channels, calcium-dependent potassium channels.
  • Dayan and Abbott, Section 6.2.
• Lecture 18 (T 4/23) (video)
  • Phase plane analysis of the Morris-Lecar model.
  • B. Ermentrout and J. Rinzel. Analysis of neural excitability and oscillations.
• Lecture 19 (Th 4/25) (video) Assignment #9 due!
  • Bifurcation theory
  • S. Strogatz, Nonlinear dynamics and chaos, Sections 3.1, 3.4, 4.3, 5.1, 5.2, and 8.2
• Lecture 20 (T 4/30) (video)
  • Cable theory
  • Dayan and Abbott, Sections 5.2, 6.3, and 6.4.
• Lecture 21 (Th 5/2) (video) Assignment #10 due!
  • Ion channels and Markov processes.
  • Dayan and Abbott, Section 5.7.
• Lecture 22 (T 5/7) (video)
  • Diffusion and calcium dynamics.
  • C. Koch, Biophysics of Computation: Information Processing in Single Neurons, from Chapter 11, Oxford University Press, New York, Oxford (1999)
• Lecture 23 (Th 5/9) (video) Assignment #11 due!
  • Synaptic transmission.
  • Dayan and Abbott, Section 5.8
• Lecture 24 (T 5/14) (video)
  • Synaptic plasticity. Long-term potentiation
• (Th 5/16) Final review (video)
• (T 5/21) Final exam, 1:30pm-4:30pm, E51-085