2009 Program Syllabus

Title: Reception

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Title: Introduction
Presenters: Mitra
(Saturday evening) (materials)

Title: Linear Algebra
Presenters: Rolston, Kleinfeld
(Sunday morning) (materials)
     

1. Linear algebra (OBD ref: P.56-70)
   1. vector spaces: motivation, definition; angles, distances. Functions of time as vectors
   2. basis expansions, subspaces, projections. Basis expansions of functions of time
   3. Matrices as linear transformations; geometrical interpretation; eigenvectors of square matrices; Eigenvectors do not always exist; Singular vectors; Matrix operations: conjugate, transpose, determinant. Matrix rank
   4. Matrix decompositions: Eigenvalue decomposition; Singular Value Decomposition; SVD = EVD of HH; mention LU and other decompositions
   5. Biology example: SVD of a spacetime matrix; SV distribution.

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Title: Sinusoids, Ordinary Differential Equations
Presenters: Rolston, Kleinfeld
(Sunday morning) (materials)
     

1. Complex numbers: Necessity (origin: solving algebraic equations; signal processing: compact notation for dealing simultaneously with sines and cosines); Euler relation [eix = cos(x) + i sin(x)]; complex oscillation; time translation = phase shift for single sinusoid; meaning of amplitude, phase; visualization in complex plane: phasors. Example: sinusoidal output driven by sinusoidal input in a biological example; line noise.
2. Linear Ordinary Differential Equations (ODEs); Complex exponentials as solutions to ODEs; Linear ODEs as linear systems or input/output relationships; Simple effect of linear systems on complex exponentials; Brief comments on nonlinear ODEs. Example: Visual system, rodent somatosensory system

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Title: Probability Theory
Presenters: Iyengar
(Sunday afternoon) (materials)
     

1. Probability Theory (OBD ref: P.98-112)
   1. Basic definitions: sample space, events, probability axioms
   2. Conditional probability, Bayes rule
   3. Univariate random variables, probability distribution functions: discrete and continuous; define moments, cumulants.
   4. Examples: Bernoulli, binomial, Poisson, Gaussian; Bio Examples: Bernoulli: choice expts; Poisson: spike counts; Gaussian: LFP
   5. Multivariate example: multivariate Gaussian
   6. Law of large numbers, CLT: motivate and state.

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Title: Probability Theory
Presenters: Iyengar
(Sunday afternoon) (materials)

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Title: Math/Stat Tutorials
Presenters: Rolston, Iyengar
(Sunday evening) (materials)
     MATLAB based tutorial + analytical problems: complex exponentials amplitude and phase; Linear algebra: EVD, SVD; probability theory exercises

Title: Exploratory Data Analysis, Estimation
Presenters: Iyengar
(Monday morning) (materials)
     

1. Exploratory data analysis: Brief intro: define/motivate; Histograms, Box plots
2. Estimation (OBD Refs. P.154-160, P.171-172, P.181-183)
   1. Point estimation: Bias, Variance. Estimating moments, or distribution parameters. Maximum Likelihood Estimation; Fisher information. Biology examples
   2. Interval estimation
   3. Bayesian estimation of parameters
3. Inference (OBD Ref: P.172-178)
   1. Binary hypotheses; Type I and II errors; Test statistics; Likelihood Ratio test, Chi-Square test.

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Title: Inference Test Statistics
Presenters: Iyengar
(Monday morning) (materials)
     

1. Linear Model: univariate, multivariate. Goodness of fit testing + statistics.
2. Generalized linear model: Logistic regression.
3. Classification and clustering; analysis of variance.
4. Lab: Morning lectures (Estimation, Inference), Afternoon lecture (Linear Model) - *using neural data examples*

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Title: Linear Models
Presenters: Iyengar
(Monday afternoon) (materials)

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Title: MATLAB Tutorial
Presenters: Iyengar, Rolston
(Monday afternoon) (materials)

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Title: Harvey Karten lecture. Lab: Chronux Intro
Presenters: Bokil, Rolston
(Monday evening) (materials)

Title: Nonparametric function estimation and regression
Presenters: Bokil, Eden
(Tuesday morning) (materials)
     

1. Local regression (OBD ref: P.323-332)
   1. LOWESS
   2. Advantages/disadvantages
2. Local likelihood
3. Examples
   1. Local Poisson
   2. Local logistic
   3. Density estimation
   4. Rate estimation
   5. PSTH
4. Diagnostics
   1. Residuals
   2. Confidence bands
   3. Bias/variance
   4. Cross-validation
   5. DOF
5. Regression splines
6. B-splines, natural splines
7. Knot selection
   1. Bayesian knot selection
8. Smoothing

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Title: Lab Splines Locfit
Presenters: Bokil, Eden
(Tuesday morning) (materials)

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Title: Signal Processing Basics
Presenters: Kleinfeld
(Tuesday afternoon) (materials)
     (OBD Ref: P.77-82, P.84-98)

1. Fourier series expansions. Truncation of Fourier series and Gibbs ripples.
2. Tapering Fourier series to reduce Gibbs ripples.
3. Bandlimited functions, sampling theorem and aliasing. [Neuro example]
4. DFT and FFT [Neuro example]
5. Truncation of Fourier series; Broadband and Narrowband Bias
6. Spectral Concentration Problem; Slepian Functions

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Title: Stochastic Process Theory and Spectral Estimation (continuous processes)
Presenters: Pesaran
(Tuesday afternoon) (materials)
     (OBD Refs: P.114-122, 189-194)

1. Defining Stochastic processes.
2. Time Translation Invariance; Ergodicity
3. Moments (Correlation functions) and spectra.
4. Example: Gaussian Processes Ornstein-Uhlenbeck process; Wiener Process.
5. Spectral Estimation: Periodogram bias and variance
6. Nonparametric quadratic estimators: Tapering
7. Quadratic estimates as multitaper estimates
8. Multitaper estimates using Slepians: Spectrum, coherence

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Title: Lab: Signal Processing, Spectra, Coherence Lab
Presenters: Pesaran, Bokil, Kleinfeld
(Tuesday evening) (materials)

Title: Spectrogram/ Coherogram Statistics,Permutations, Jackknife
Presenters: Bokil
(Wednesday morning) (materials)
     Dynamic spectral analysis; statistical comparisons and hypotheses testing (OBD Refs: P.194-197, 283-290)

1. Revisit Multitaper estimates of spectrum and coherence; time and bandwidth parameters.
2. Harmonic analysis and F-ratio test for sinusoids.
3. Variance of spectral estimate; Chi-square distribution of S, variance of log(S); distribution of coherence (under Gaussian assumptions; magnitude and phase).
4. Units for spectra, coherence.
5. Confidence bands, local + global (under asymptotic Gaussian assumptions)
6. Comparing spectra, coherences across conditions tests.
7. Permutation/Jackknife procedures for confidence bands, and for significance levels in comparing spectra/coherences across conditions

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Title: Lab: Dynamic Spectra
Presenters: Bokil
(Wednesday morning) (materials)

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Title: Point Process Theory
Presenters: Eden, Sarma
(Wednesday afternoon) (materials)
     (OBD Ref: P.124-140)

1. Different ways of specifying point processes
2. Poisson Process
3. Inhomogeneous Poisson
4. Doubly Stochastic Poisson
5. General Point process models
6. Conditional Intensity Process

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Title: Point Process Models
Presenters: Eden, Sarma
(Wednesday afternoon) (materials)
     Conditional intensity process-based modeling of neural data

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Title: Point Process Lab (GLM)
Presenters: Eden, Sarma
(Wednesday evening) (materials)
     Fitting point process models

Title: Point Process Spectral Methods
Presenters: Pesaran
(Thursday morning) (materials)
     

1. Specifying Point Processes in terms of moments
2. Factorial Moments
3. Nonstationary Measures: JPSTH
4. Spectra; Asymptotic properties; Relation to Fano Factor
5. Interval Spectrum
6. Hybrid moments: Spike-triggered average; Spike-LFP coherence
7. Periodic Processes; F-test

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Title: Point Process Spectral Lab
Presenters: Pesaran
(Thursday morning) (materials)
     Point process spectral analysis

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Title: Multivariate time series, SVD Denoising
Presenters: Pesaran
(Thursday afternoon) (materials)
     

1. SVD: space x time data.
2. SV distribution for random matrices noise tail; SVD truncation to denoise
3. SVD: space x frequency (factorization of cross spectral matrix).
4. Global coherence.
5. Coherence phase: phase shifts, time delays, traveling waves.
6. Harmonic analysis to remove periodic artifact and to reconstruct periodized signals

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Title: Application: EEG, Optical Imaging
Presenters: Pesaran, Kleinfeld
(Thursday afternoon) (materials)
     EEG (Pesaran)
Optical imaging data (Kleinfeld)

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Title: Lab: Optical Imaging
Presenters: Kleinfeld, Sornborger, Pesaran
(Thursday evening) (materials)
     Applications of multivariate time-series analysis
Optical imaging data
Denoising EEG data

Title: fMRI Data Analysis
Presenters: Bohland
(Friday morning) (materials)
     (OBD Ref: P.306-312)

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Title: EEG/MEG Source Localization Methods
Presenters: Hamalainen
(Friday morning) (materials)
     

1. EEG and MEG: Commonalities and differences
2. Brief introduction to MEG (and EEG) measurement techniques
3. Overview of the EEG/MEG source localization problem
4. Time-varying current dipole models (with examples)
5. Anatomically constrained l2 minimum-norm solutions (with examples)
6. EEG/MEG solutions constrained by fMRI
7. Summary

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Title: Behavioral data analysis : Ethological
Presenters: Golani
(Friday afternoon) (materials)
     Physiological reflex; classical Conditioning; operant conditioning; biological constraints on learning

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Title: Behavioral data analysis : Expt Psych
Presenters: Golani, TBD
(Friday afternoon) (materials)
     Ethological description of whole-animal behavior. Using computational ethology, continuous kinematic variables, robust data preparation for analysis, segmentation based on intrinsic properties of the data, and developmental dynamics, to improve the description of behavior.

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Title: fMRI, EEG and MEG Data Analysis Lab
Presenters: Pesaran, Bokil, Bohland
(Friday evening) (materials)

Title: Spike Sorting Tutorial
Presenters: Hill
(Saturday morning) (materials)

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Title: Lunch: Introduction to the Data Analysis Challenge
Presenters: Sornborger
(Saturday morning) (materials)

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Title: Data analysis challenge
Presenters: Hill
(Saturday afternoon) (materials)

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Title: Data analysis challenge
Presenters: Hill
(Saturday afternoon) (materials)

Title: Connectivity architecture overview
Presenters: Barbas, TBA
(Monday morning) (materials)

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Title: Lab: Mouse brain gene expression atlas
Presenters: Bernard, TBA
(Monday morning) (materials)

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Title: Primate Atlases. Cortical flatmaps
Presenters: Van Essen
(Monday afternoon) (materials)
     Primate atlases; Cortical flatmaps

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Title: Lab (Caret,Freesurfer)
Presenters: Van Essen, Bohland
(Monday afternoon) (materials)
     Software packages: Caret, Freesurfer

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Title: Data challenge

Title: Lab:RDBMs, MySQL, MATLAB
Presenters: Andrews
(Tuesday morning) (materials)
     RDBMs, MySQL/MATLAB, Examples

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Title: Web Programming Basics Lab
Presenters: Bohland, Andrews
(Tuesday morning) (materials)
     TBA

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Title: Machine Learning SVMs, CART, Boosting
Presenters: Belkin
(Tuesday afternoon) (materials)
     Learning machines: SVMs, CART, Boosting

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Title: Manifolds Spectral Methods
Presenters: Belkin
(Tuesday afternoon) (materials)
     Manifold learning methods, Spectral methods, semi-supervised learning.

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Title: Data challenge

Title: Information Theory Lecture/Lab
Presenters: Victor
(Wednesday morning) (materials)
     Entropy and mutual information based measures

1. Why might one want to compute (Shannon) information?
   1. Neural coding
   2. Nonparametric measure of association
2. Definition of entropy and information
   1. Discrete distributions
   2. Continuous distributions
3. Basic properties of entropy and information
   1. Information in independent channels
   2. The Data Processing Inequality
4. Simple, important examples
5. Entropy of a Poisson spike train
6. Entropy of a Gaussian process
7. Mutual information in a linear Gaussian channel with additive noise
8. The fundamental difficulty with applying information theory to laboratory data
9. Strategies for addressing these difficulties (and their drawbacks)
   1. Bias correction methods
   2. Regularization methods: weak and strong models
10. Examples
11. Maximum entropy methods: brief introduction

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Title: Biomedical Applications of Signal Processing
Presenters: Schiff
(Wednesday morning) (materials)
     TBA

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Title: Data challenge

     TBA

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Title: Data challenge

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Title: Data challenge

Title: Image processing 1
Presenters: Whitaker
(Thursday morning) (materials)
     TBA

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Title: Neuroanatomy workshops
Presenters: Whitaker, Wang, Kleinfeld
(Thursday morning) (materials)
     TBA

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Title: Neuroanatomy workshops
Presenters: Turaga, Chklovskii
(Thursday afternoon) (materials)
     TBA

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Title: Neuroanatomy workshops
Presenters: Zikopoulos, Mikula
(Thursday afternoon) (materials)
     TBA

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Title: Course Banquet

Title: Data challenge

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Title: Data challenge

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Title: Data challenge

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Title: Data challenge

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Title: Data challenge

Title: Data challenge

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Title: Challenge Presentations