9.29_sp2003 Introduction to Computational Neuroscience

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Lecture schedule

• Lecture 1 (T 2/4) (pdf, realvideo)
  • 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 2/6) ( pdf, realvideo)
  • Convolution and correlation I.
  • Firing rate.
  • 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 (M 2/10, 66-160) (pdf, realvideo)
  • Initializing and using vectors and matrices in MATLAB. Matrix shortcuts. Plots in MATLAB. Useful commands.
  • Simple statistics and linear regression.
• Lecture 3 (T 2/11) ( pdf, realvideo)
  • Convolution and correlation II.
  • Spike-triggered average.
  • Wiener-Hopf equations and white noise analysis
  • Dayan and Abbott, Sections 2.1-2.2
• Lecture 4 (Th 2/13) (realvideo) Assignment #1 due!
  • Visual receptive fields I.
  • Basics of the visual system. Center-surround receptive fields.
  • 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 2/18, M schedule)
• Optional Lecture 2 (W 2/19, 66-168) (realvideo)
  • Geometric and algebraic treatment of least-squares fitting.
  • Discrete/continuous convolution and correlation.
  • Lagrange multipliers.
• Lecture 5 (Th 2/20) (realvideo) Assignment #2 due!
• Visual receptive fields II.
• Difference of Gaussians model.
• Simple cortical cells, separable.
• Dayan and Abbott, Sections 2.4 and 2.5.
• Website: Space-Time Receptive Fields of Visual Neurons
• Optional Lecture 3 (M 2/24, E25-202) (pdf, realvideo)
  • Eigenvectors and eigenvalues. Diagonalization and the eigenvector basis.
• Lecture 6 (T 2/25) (realvideo)
  • Visual receptive fields III.
  • Simple cortical cells, nonseparable.
  • Complex cortical cells.
• Lecture 7 (Th 2/27) (realvideo) Assignment #3 due!
  • Fourier series and integrals. Spectral analysis.
  • Pure tones. Perception of periodic complex tones.
  • The cochlea as a Fourier analyzer.
  • 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.
    
  • G. Strang, Introduction to Applied Mathematics 4.3, 309-329, Wellesley-Cambridge Press, Wellesley, Massachusetts (1990)
    
• Lecture 8 (F 2/28) (realvideo)
  • Discrete Fourier series
  • G. Strang, Introduction to Applied Mathematics 4.2, 290-308, Wellesley-Cambridge Press, Wellesley, Massachusetts (1990)
    
• Optional Lecture 4 (M 3/03, E25-202) (realvideo)
  • Cumulative review of problem sets.
• Lecture 9 (Th 3/6) (realvideo) 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).
• Optional Lecture 5 (M 3/10) (pdf, realvideo)
  • Poisson processes and spike train statistics.
• Project meeting 1 (T 3/11) (realvideo)
  Discussion of topics; choice of projects; work begins.
• Project meeting 2 (Th 3/13) Assignment #5 due!
• Project meeting 3 (T 3/18)
• Project meeting 4 (Th 3/20)
• Spring break, 3/24-28
• Project presentations (T 4/1) (realvideo)
• Lecture 10 (Th 4/3) (realvideo)
  • 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 11 (F 4/4) (realvideo)
  • The action potential. Hodgkin-Huxley model.
  • Dayan and Abbott, Sections 5.3, 5.5, and 5.6
  • C. Koch, Biophysics of Computation, Information Processing in Single Neurons, Chapter 6, Oxford University Press, New York, Oxford (1999)
• Optional Lecture 6 (M 4/7) (realvideo)
  • Numerical methods for differential equations.
  • Dayan and Abbott, Section 5.11 (Appendices A and B).
  • A. Sherman, Lecture Notes and Lab Problems on Numerical Methods.
  • Arthur Sherman's web page on Numerical Methods in Neuronal Modeling
• Optional Lecture 7 (Th 4/10) (pdf, realvideo)
  • Introduction to nonlinear dynamics.
  • Linear and nonlinear dynamical systems.
  • Stability analysis.
• Lecture 12 (M 4/14) (realvideo) Assignment #6 due!
  • A-type potassium channels, calcium-dependent potassium channels.
  • Dayan and Abbott, Section 6.2.
• Lecture 13 (T 4/15) (realvideo)
  • Phase plane analysis and bifurcation theory.
  • B. Ermentrout and J. Rinzel. Analysis of neural excitability and oscillations.
  • S. Strogatz, Nonlinear dynamics and chaos, Sections 3.1, 3.4, 4.3, 5.1, 5.2, and 8.2
• Lecture 14 (Th 4/17) (realvideo) Assignment #7 due!
  • Cable theory
  • Dayan and Abbott, Sections 5.2, 6.3, and 6.4.
• Patriot's Day (T 4/22)
• Optional Lecture 8 (Wed 4/23) (pdf, realvideo)
  • Probability theory
• Lecture 15 (Th 4/24) (realvideo) Assignment #8 due!
  • Ion channels and Markov processes.
  • Dayan and Abbott, Section 5.7.
• Lecture 16 (F 4/25) (realvideo)
  • 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 17 (Th 5/1) (realvideo) Assignment #9 due!
  • Synapses.
  • Dayan and Abbott, Section 5.8
• Project Meeting 5 (T 5/6)
• Project Meeting 6 (Th 5/8)
• Project Meeting 7 (T 5/13)
• Project Meeting 8 (Th 5/15)