Introduction
In the past few decades, the essentially biological nature of the study of neuroscience has been infused by the tools provided by mathematics. At first, the use of mathematics was mostly methodological in nature—primarily aiding the analysis of data. Soon, this influence turned conceptual, framing the very issues that characterize modern neuroscience today. This development has not remained uncontroversial; some neurobiologists resent what they perceive to be a hostile takeover of the field, as many quantitative methods applied to neurobiology were pioneered by nonbiologists with a background in physics, engineering, mathematics, statistics, and computer science. While these concerns are valid to some degree, and while excesses do happen, the authors strongly believe that—all in all—the effect of mathematics in the neurosciences has been very positive, and that neuroscience is and will continue to be a discipline that is computational at its very core.
Keywords
neuroscience; MATLAB; cognitive psychology; cognitive science; mathematics
Neuroscience is at a critical juncture. In the past few decades, the essentially biological nature of the field has been infused by the tools provided by mathematics. At first, the use of mathematics was mostly methodological in nature—primarily aiding the analysis of data. Soon, this influence turned conceptual, framing the very issues that characterize modern 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 nonbiologists with a background in physics, engineering, mathematics, statistics, and computer science. Their concerns are not entirely without merit. For example, Hubel and Wiesel (2004) warn of the faddish nature that the idol of “computation” has taken on, even likening it to a dangerous disease that has befallen the field that we should overcome quickly in order to restore its health.
While these concerns are valid to some degree, and while excesses do happen, we strongly believe that—all in all—the effect of mathematics in the neurosciences has been very positive. Moreover, we believe that our science is and will continue to be one that is computational at its very core. The reason for this is that—as pointed out by Konrad Körding (http://www.nature.com/news/neuroscience-solving-the-brain-1.13382)—the human brain produces in 30 seconds as much data as the Hubble Space Telescope has produced in its lifetime. That is a staggering number, given that Hubble has been in operation for well over 23 years and generates more than 100 GB of data each week. Eventually, we will develop experimental methods that will fully tap this wellspring of data. We expect that computational methods to tackle this data will be developed in parallel. Put differently, not only is a computational perspective on neuroscience here to stay, we are likely only at the very beginning of this process. Historically, this notion stems in part from the influence that cognitive psychology has had in the study of the mind. Cognitive psychology and cognitive science—more generally—posited that the mind and, by extension, the brain should be viewed as information processing devices that receive inputs and transform these inputs into intermediate representations that ultimately generate observable outputs. At the same time that cognitive science was taking hold in psychology in the 1950s and 1960s, computer science was developing beyond mere number crunching and considering the possibility that intelligence could be modeled computationally, leading to the birth of artificial intelligence. The information processing perspective, in turn, ultimately influenced the study of the brain, and is best exemplified by an influential book by David Marr titled Vision, 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 what computational problem a neuron, neural circuit, or part of the brain is solving. The algorithmic level identifies the inputs, the outputs, their representational format, and the algorithm that takes the input representation and transforms it into an output representation. Finally, the implementational level identifies the neural “hardware” and biophysical mechanisms underlying the algorithm that solves the problem. Today this perspective has permeated not only cognitive neuroscience, but also systems, cellular, and even molecular neuroscience.
Importantly, such a conceptualization of our field places chief importance on the issues surrounding scientific computing. For someone to participate in or even appreciate state of the art debates in modern neuroscience, that person has to be well-versed in the language of computation. Of course, it is the task of education—if it is to be truly liberal—to enable students to do so. Yet, this poses a quite formidable challenge. The point of a truly liberal education is to free the recipient from the most severe bondage—ignorance and accidents of birth. The situation is akin to that of the prisoners in Plato’s cave (see Figure 1.1). Those prisoners are chained to rocks in a cave (in actuality, probably a stone quarry in Syracuse) and only see the shadows, never the forms. Of course, these prisoners are actually better off than the ignorant. At least they know that they are prisoners. In contrast, the shackles of ignorance often seem light, and even quite comfortable. Once freed, the recipient of a liberal education can walk out of the cave and take part in the life of the mind.
Figure 1.1 The prisoners in Plato’s cave. Contemporary neuroscientists without profound scientific computing skills are arguably in a much more desperate situation, even if it doesn’t feel like it.
For most students interested in neuroscience, mathematics amounts to what is essentially a foreign language. Similarly, the language of scientific computing is typically as foreign to students as it is powerful. The prospects of learning both at the same time can be daunting and—at times—overwhelming. So what is a student or educator to do? To quote from Alfred North Whitehead’s Aims of Education essay:
There is only one subject-matter for education, and that is Life in all its manifestations. Instead of this single unity, we offer children—Algebra, from which nothing follows; Geometry, from which nothing follows; Science, from which nothing follows; History, from which nothing follows; a Couple of Languages, never mastered; and lastly, most dreary of all, Literature, represented by plays of Shakespeare, with philological notes and short analyses of plot and character to be in substance committed to memory.
p. 194
Whitehead makes two points. First, teaching should not be disjointed. It is crucial to make connections between subjects. Second, teaching “inert ideas” is worse than useless; it is paralyzing. The tonic is to provide actionable information that allows the pursuit of relevant goals. This will tie the information together and make it come to life.
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 possible when facing a problem in the field. For immersion to work, the learning experience has to be positive, yielding useful results that solve some real or perceived problem. Unfortunately, the inherent complexity as well as the seemingly arcane formalisms that characterize both are usually very off-putting to students, requiring much effort with little tangible yield and reducing the likelihood of further voluntary immersion.
To break this catch-22, the utility of learning these languages has to be drastically increased while making the learning process more accessible and manageable at the same time, even during the learning process itself. As we alluded to previously, this is a tall order. Fortunately, there is a way out of this conundrum. Recent advances in software as well as hardware have instantiated scientific computing within the framework of a unified computational environment. One of these environments is provided by the MATLAB® software. For reasons that will become readily apparent in this book, MATLAB fulfills the requirements 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 of scientific computing in our field. Stated more strongly, MATLAB really has become the lingua franca that all serious students of neuroscience are expected to understand in the very near future, if not already today.
This, in turn, introduces a new—albeit more tractable—problem. How does one teach MATLAB to a useful level of proficiency without making the study of MATLAB itself an additional problem and simply another chore for students? Overcoming this problem as a key to reaching the deeper goals of fluency in mathematics and scientific computing is a crucial goal of this book. We reason that a gentle introduction to MATLAB with a special emphasis on immediate results will computationally empower you to such a degree that the practice of MATLAB becomes self-sustaining by the end of the book. We carefully picked the content such that the result constitutes a confluence of ease (gradually increasing sophistication and complexity) and relevance. We are confident that at the end of the book you will be at a level where you will be able to venture out on your own, convinced of the utility of MATLAB as a tool and of your ability to harness this power henceforth. We have tested the various parts of the contents of this book on our students, and believe that our approach has been successful. It is our sincere wish and hope that the material contained 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 many topics within computational neuroscience across multiple levels of neuroscientific inquiry from decision-making and attentional mechanisms to retinal circuits and ion channels. It is well known that an active engagement with new material facilitates both understanding and long-time retention of said material. The secondary aim of this book is to acquire proficiency in programming using MATLAB while going through the chapters. If you are already 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 qualities 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 write a MATLAB program that implements the ideas introduced in the chapter. Each chapter begins with background information related to a particular neuroscientific or psychological problem, followed by an introduction to the MATLAB concepts necessary to address that problem 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 assignment introduced at the end of the chapter requires integrating the exercises. Most of the projects will involve genuine experimental data that are either collected as part of the project or were collected through experiments in research labs. In rare cases, we use published data from classical papers to illustrate important concepts, giving you a computational understanding of critically important research.
In addition, solutions to exercises and executable code can be found in the online repository accompanying this book (booksite.elsevier.com/9780123838360).
Finally, we would like to point out that we are well aware that there is more than one way to teach—and learn—MATLAB in a reasonably successful and efficient manner. This book represents a manifestation of our approach; it is the path we chose, for the reasons we outlined here.