P A R T I

FUNDAMENTALS

C H A P T E R

1

Introduction

Neuroscience is at a critical juncture. In the past few decades, the essentially biologicalnature of the field has been infused by the tools provided by mathematics. At first, theuse of mathematics was mostly methodological in nature—primarily aiding the analysisof data. Soon, this influence turned conceptual, framing the very issues that characterizemodern neuroscience today. Naturally, this development has not remained uncontroversial.Some neurobiologists of yore resent what they perceive to be a hostile takeover of the field,as many quantitative methods applied to neurobiology were pioneered by nonbiologistswith a background in physics, engineering, mathematics, statistics, and computer science.Their concerns are not entirely without merit. For example, Hubel and Wiesel (2004) warnof the faddish nature that the idol of “computation” has taken on, even likening it to a dan-gerous disease that has befallen the field and that we should overcome quickly in order torestore its health.

While these concerns are valid to some degree and while excesses do happen, westrongly believe that—all in all—the effect of mathematics in the neurosciences has beenvery positive. Moreover, we believe that our science is and will continue to be one that iscomputational at its very core. Historically, this notion stems in part from the influence thatcognitive psychology has had in the study of the mind. Cognitive psychology and cognitivescience, more generally, posited that the mind and, by extension, the brain should beviewed as an information processing device that receives inputs and transforms theseinputs into intermediate representations which ultimately generate observable outputs. Atthe same time that cognitive science was taking hold in psychology in the 1950s and1960s, computer science was developing beyond mere number crunching and consideringthe possibility that intelligence could be modeled computationally, leading to the birth ofartificial intelligence. The information processing perspective, in turn, ultimately influencedthe study of the brain and is best exemplified by an influential book by David Marr titledVision, published in 1982. In that book, Marr proposed that vision and, more generally,the brain should be studied at three levels of analysis: the computational, algorithmic,and implementational levels. The challenge at the computational level is to determine whatcomputational problem a neuron, neural circuit, or part of the brain is solving. The

3

algorithmic level identifies the inputs, the outputs, their representational format, and thealgorithm that takes the input representation and transforms it into an output representa-tion. Finally, the implementational level identifies the neural “hardware” and biophysicalmechanisms that underlie the algorithm which solves the problem. Today, this perspectivehas permeated not only cognitive neuroscience but also systems, cellular, and even molec-ular neuroscience.

Importantly, such a conceptualization of our field places chief importance on the issuessurrounding scientific computing. For someone to participate in or even appreciate stateof the art debates in modern neuroscience, that person has to be well versed in the languageof computation. Of course, it is the task of education—if it is to be truly liberal—to enablestudents to do so. Yet, this poses a quite formidable challenge.

For most students interested in neuroscience, mathematics amounts to what is essentiallya foreign language. Similarly, the language of scientific computing is typically as foreign tostudents as it is powerful. The prospects of learning both at the same time can be dauntingand—at times—overwhelming. So what is a student or educator to do?

Immersion has been shown to be a powerful way to learn foreign languages (Genesee,1985). Hence, it is imperative that students are using these languages as often as possiblewhen facing a problem in the field. For immersion to work, the learning experience hasto be positive, yielding useful results that solve some real or perceived problem. Unfortu-nately, the inherent complexity as well as the seemingly arcane formalisms that characterizeboth are usually very off-putting to students, requiring much effort with little tangibleyield, reducing the likelihood of further voluntary immersion.

To break this catch-22, the utility of learning these languages has to be drasticallyincreased while making the learning process more accessible and manageable at the sametime, even during the learning process itself. As we alluded to previously, this is a tallorder. Fortunately, there is a way out of this conundrum. Recent advances in software, aswell as hardware, have instantiated scientific computing within the framework of a unifiedcomputational environment. One of these environments is provided by the MATLABW

software. For reasons that will become readily apparent in this book, MATLAB fulfills therequirements that are necessary to meet and overcome the challenges outlined earlier.In addition—and partly for these reasons—MATLAB has become the de facto standard ofscientific computing in our field. More strongly, MATLAB really has become the linguafranca that all serious students of neuroscience are expected to understand in the very nearfuture, if not already today.

This, in turn, introduces a new—albeit more tractable—problem. How does one teachMATLAB to a useful level of proficiency without making the study of MATLAB itself anadditional problem and simply another chore for students? Overcoming this problem as akey to reaching the deeper goals of fluency in mathematics and scientific computing isa crucial goal of this book. We reason that a gentle introduction to MATLAB with a specialemphasis on immediate results will computationally empower you to such a degree that thepractice of MATLAB becomes self-sustaining by the end of the book. We carefully pickedthe content such that the result constitutes a confluence of ease (gradually increasingsophistication and complexity) and relevance. We are confident that at the end of the bookyou will be at a level where you will be able to venture out on your own, convinced of theutility of MATLAB as a tool as well as your abilities to harness this power henceforth. We

4 1. INTRODUCTION

have tested the various parts of the contents of this book on our students and believe thatour approach has been successful. It is our sincere wish and hope that the materialcontained will be as beneficial to you as it was to those students.

With this in mind, we would like to outline two additional specific goals of this book.First, the material covered in the chapters to follow gives a MATLAB perspective on manytopics within computational neuroscience across multiple levels of neuroscientific inquiryfrom decision-making and attentional mechanisms to retinal circuits and ion channels. Itis well known that an active engagement with new material facilitates both understandingand long-time retention of said material. The secondary aim of this book is to acquire pro-ficiency in programming using MATLAB while going through the chapters. If you arealready proficient in MATLAB, you can go right to the chapters following the tutorial.For the rest, the tutorial chapter will provide a gentle introduction to the empowering qua-lities that the mastery of a language of scientific computing affords.

We take a project-based approach in each chapter so that you will be encouraged to writea MATLAB program that implements the ideas introduced in the chapter. Each chapterbegins with background information related to a particular neuroscientific or psychologicalproblem, followed by an introduction to the MATLAB concepts necessary to address thatproblem with sample code and output included in the text. You are invited to modify,expand, and improvise on these examples in a set of exercises. Finally, the project assign-ment introduced at the end of the chapter requires integrating the exercises. Most of theprojects will involve genuine experimental data that are either collected as part of the projector were collected through experiments in research labs. In some rare cases, we use publisheddata from classical papers to illustrate important concepts, giving you a computationalunderstanding of critically important research.

In addition, solutions to exercises as well as executable code can be found in the onlinerepository accompanying this book.

Finally, we would like to point out that we are well aware that there is more than oneway to teach—and learn—MATLAB in a reasonably successful and efficient manner. Thisbook represents a manifestation of our approach; it is the path we chose, for the reasonswe outlined here.

51. INTRODUCTION