Pascal Wallisch

Chapter 31 – Decision Theory

In this chapter, you will learn how to implement progressively more comprehensive mathematical models of decision making using MATLAB®. The exploration of decision models will introduce solving partial differential equations as finite differences, focusing on the diffusion equation. A simple model accounting for perceptual decisions and corresponding activity in cortical areas LIP and MT will be discussed.

Functional Magnetic Imaging

This chapter focuses on functional magnetic imaging (fMRI) as a fundamental noninvasive tool in understanding brain functioning in humans. It describes the basic physics behind structural and functional magnetic resonance imaging, and after that it explains the major experimental paradigms used in fMRI research and the kinds of data that are collected in an fMRI experiment. Functional magnetic resonance imaging has emerged as the dominant form of noninvasive functional imaging in humans. Although it is a relatively young technology that began in the early 1990s, it now plays a major role in many subfields of psychology, cognitive science, and neuroscience. It is even creeping up in other disciplines such as sociology and economics. As of the beginning of 2008, a quick online search of articles on PubMed revealed over 180,000 papers that reference the use of fMRI. Some have criticized fMRI as a scientific tool, claiming that it is little more than modern phrenology. Finally, using existing fMRI data from a simple finger-tapping task, it shows how to analyze and visualize the data to come up with a statistical parametric map of activation in the brain.

Fitzhugh-Nagumo Model

This chapter describes how to model traveling waves in an excitable media. This entails the solution of a partial differential equation involving a first derivative in time coordinates and a second derivative in spatial coordinates. It helps in learning how to compute a second derivative in the MATLAB® software and use a modification of the Fitzhugh- Nagumo model. The Fitzhugh-Nagumo model is often used as a generic model for excitable media because it is analytically tractable. It as a simple model to generate traveling waves by the addition of a diffusion term: a second derivative in spatial coordinates. The chapter also introduces the most practical and commonly used built-in ODE solvers in MATLAB: the function ode45. This solver is based on an explicit Runge-Kutta formula and is optimized to adaptively find the most efficient time steps to produce a solution within a certain allowed relative error tolerance and absolute error tolerance.

Frequency Analysis Part II

This chapter defines the most common method of decomposing a time series into frequency components, Fourier analysis. It also describes the MATLAB implementation of the Fast Fourier Transform (FFT), an efficient algorithm for calculating Fourier transformations and application to the analysis of human speech sounds. With a few special tricks, a faster algorithm, the FFT, that scales in N log N time can be formulated. One of these tricks involves taking advantage of datasets exactly 2N elements long. The increase in processing speed has made the FFT ubiquitous in signal processing. The chapter illustrates the project that defines Fourier decomposition to analyze vowel sounds produced by human speakers. The human vocal tract has multiple cavities in which speech sounds resonate. As such, most sounds have multiple strong frequency components. In classifying speech sounds, the lowest strong frequency band is termed the first formant. The next highest is termed the second formant, and so on. Vowels lend themselves to a particularly simple characterization through their formants. Typically, vowel sounds have distinguishable first and second formants.

Neural Networks Part I

This chapter deals with neural networks using Neural Networks Toolbox built into the MATLAB® software to address a particular problem. The major goal is to become familiar with the general concept of unsupervised neural networks and how they may relate to certain forms of synaptic plasticity in the nervous system. Neural networks have assumed a central role in a variety of fields. They are actually quite abstract computing structures. In fact, they are sometimes referred to as artificial neural networks. The nature of this role is fundamentally dualistic. On the one hand, neural networks can provide powerful models of elementary processes in the brain, including processes of plasticity and learning. On the other hand, they provide solutions to a broad range of specific problems in applied engineering, such as speech recognition, financial forecasting, or object classification.

Chapter 10 – Signal Detection Theory

This chapter will mostly concern the use of signal detection theory to analyze data generated in psychophysical—and hypothetical neurophysiological—experiments. We will do this in MATLAB®.

Psychophysics with GUIs

This chapter pursues dual goals. First, we want to build on the data collection within a psychophysical paradigm approach. Second, and more importantly, this chapter will introduce the concept of a graphical user interface (GUI) within MATLAB® and demonstrate its gainful use.

Chapter 37 – Neural Networks Part II: Supervised Learning

This chapter has two primary goals. The first goal is to be introduced to the concept of supervised learning and how it may relate to synaptic plasticity in the nervous system, particularly in the cerebellum. The second goal is to learn to implement single-layer and multi-layer neural network architectures using supervised learning rules to solve particular problems.

Chapter 36 – Neural Networks Part I: Unsupervised Learning

This chapter has two goals that are of equal importance. The first goal is to become familiar with the general concept of unsupervised neural networks and how they may relate to certain forms of synaptic plasticity in the nervous system. The second goal is to learn how to build two common forms of unsupervised neural networks to solve a classification problem.

Chapter 33 – Modeling Spike Trains as a Poisson Process

This chapter focuses on point process models for characterizing and simulating trains of actions potentials generated by neurons. Initially, a simple homogeneous Poisson process model will be introduced to capture fundamental characteristics. Models with greater sophistication will be introduced to incorporate more complex activity, such as refractory periods and bursting.