Linear Algebra Preliminaries

Make sure that you are comfortable with basic linear Algebra: Vector & matrix operations, transpose, inverse, and eigenvalues:

• Summary Sheet 1: Be familiar with at least Pt 1-2
• Summary Sheet 2: Be familiar at least up to pt 3.7.

If you find you need a refresher, here is an excellent resource:

• Khan Academy: Linear algebra Lectures

For more advanced people, here are two excellent cheat-sheets that contain really all you need to know:

• Matrix Identities by Sam Roweis
• Gaussian Identities by Sam Roweis

Brain Basics

Make sure you are familiar with some basic Neuroscience, including Neurons, Synpases, and the overall structure of the human brain

• Khan Academy: Central Nervous system introduction

General text on fMRI

• Huettel, Song, and McCarthy. (2008). Functional magentic resonance imaging.

Origins of BOLD signal

Video Lectures

• BOLD Basics
• Neural activity and Energy demand
• Vasodialation and Blood Flow
• Flow, CMRO2 and the negativeBOLD Signal
• Blood Volume and the Balloon model

Further reading

• Ogawa S, Lee TM, Kay AR, Tank DW (1990) Brain magnetic resonance imaging with contrast dependent on blood oxygenation. Proc Natl Acad Sci U S A 87:9868-9872.
• Shmuel A, Yacoub E, Pfeuffer J, Van de Moortele PF, Adriany G, Hu X, Ugurbil K (2002) Sustained negative BOLD, blood flow and oxygen consumption response and its coupling to the positive response in the human brain. Neuron 36:1195-1210.

Timeseries Models

Video Lectures

• Convolution and Hemodynamic response functions
• Transfer function & temporal resolution of fMRI
• Linearity of BOLD signal
• Simple regression
• Multiple regression (OLS)
• Collinearity
• Squared residual image and time series
• t-contrasts for OLS

External Video Lectures

• Multivariate Gaussian Distribution
• Derivation of OLS in matrix form (part 1, part 2, part 3).
• Derivation of variance of OLS Estimators
• Derivation of GLS in matrix form (part 1, part 2, part 3).

Further reading

• Friston KJ, Holmes AP, Poline JB, Grasby PJ, Williams SC, Frackowiak RS, Turner R (1995) Analysis of fMRI time-series revisited. Neuroimage 2:45-53.
• Worsley KJ, Friston KJ (1995) Analysis of fMRI time-series revisited--again. Neuroimage 2:173-181.
• Diedrichsen, J., & Shadmehr, R. (2005). Detecting and adjusting for artifacts in fMRI time series data. Neuroimage, 27(3), 624-634.

Data formats

Video Lectures

• Voxels and Affine Transformation matrices
• Nifti Format

Further reading

• Nift Project Webpage
• Nifti Package for R
• Matlab Package for R (reading matlab files)
• SPM book Chapter 2, Rigid Body transformations

Group analysis

Video Lectures

• Group analysis
• Anatomical normalisation I
• Anatomical normalisation II
• The multiple testing problem
• Permutation methods

Further reading

• Eklund et al. (2016). Why fMRI inference for spatial extent have inflated false-positive rates. PNAS.

Multivariate analysis

Video Lectures

• Classification: Linear Discriminant Analysis
• Spatial prewhitening
• Crossvalidated distances
• Second moment matrix
• Encoding models without a prior
• Encoding models with a prior

Further reading

• Walther, A., Nilli, H., Ejaz, N., Alink, A., Kriegeskorte, N., Diedrichsen, J. (2016). Reliability of dissimilarity measures for multivariate fMRI pattern analysis.
• Diedrichsen, J., & Kriegeskorte, N. (2017). Representational models: A common framework for understanding encoding, pattern-component, and representational-similarity analysis. PLoS Computational Biology.

Independent component analysis

Reading

• Hyvarinen, A., & Oja, E. (2000). Independent component analysis: algorithms and applications. Neural Netw, 13(4-5), 411-430.
• Calhoun VD, Liu J, Adali T (2009) A review of group ICA for fMRI data and ICA for joint inference of imaging, genetic, and ERP data. Neuroimage 45:S163-172.