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Theoretical neuroscience provides a quantitative basis for describing what nervous systems do, determining how they function, and uncovering the general principles by which they operate. This text introduces the basic mathematical and computational methods of theoretical neuroscience and presents applications in a variety of areas including vision, sensory-motor integration, development, learning, and memory. The book is divided into three parts. Part I discusses the relationship between sensory stimuli and neural responses, focusing on the representation of information by the spiking activity of neurons. Part II discusses the modeling of neurons and neural circuits on the basis of cellular and synaptic biophysics. Part III analyzes the role of plasticity in development and learning. An appendix covers the mathematical methods used, and exercises are available on the book's Web site.
This volume gathers contributions from theoretical, experimental and computational researchers who are working on various topics in theoretical/computational/mathematical neuroscience. The focus is on mathematical modeling, analytical and numerical topics, and statistical analysis in neuroscience with applications. The following subjects are considered: mathematical modelling in Neuroscience, analytical and numerical topics; statistical analysis in Neuroscience; Neural Networks; Theoretical Neuroscience. The book is addressed to researchers involved in mathematical models applied to neuroscience.
The new edition of Fundamentals of Computational Neuroscience build on the success and strengths of the first edition. Completely redesigned and revised, it introduces the theoretical foundations of neuroscience with a focus on the nature of information processing in the brain.
This solid introduction uses the principles of physics and the tools of mathematics to approach fundamental questions of neuroscience.
Computational neuroscience is a relatively new but rapidly expanding area of research which is becoming increasingly influential in shaping the way scientists think about the brain. Computational approaches have been applied at all levels of analysis, from detailed models of single-channel function, transmembrane currents, single-cell electrical activity, and neural signaling to broad theories of sensory perception, memory, and cognition. This book provides a snapshot of this exciting new field by bringing together chapters on a diversity of topics from some of its most important contributors. This includes chapters on neural coding in single cells, in small networks, and across the entire cerebral cortex, visual processing from the retina to object recognition, neural processing of auditory, vestibular, and electromagnetic stimuli, pattern generation, voluntary movement and posture, motor learning, decision-making and cognition, and algorithms for pattern recognition. Each chapter provides a bridge between a body of data on neural function and a mathematical approach used to interpret and explain that data. These contributions demonstrate how computational approaches have become an essential tool which is integral in many aspects of brain science, from the interpretation of data to the design of new experiments, and to the growth of our understanding of neural function.• Includes contributions by some of the most influential people in the field of computational neuroscience• Demonstrates how computational approaches are being used today to interpret experimental data• Covers a wide range of topics from single neurons, to neural systems, to abstract models of learning
A textbook for students with limited background in mathematics and computer coding, emphasizing computer tutorials that guide readers in producing models of neural behavior. This introductory text teaches students to understand, simulate, and analyze the complex behaviors of individual neurons and brain circuits. It is built around computer tutorials that guide students in producing models of neural behavior, with the associated Matlab code freely available online. From these models students learn how individual neurons function and how, when connected, neurons cooperate in a circuit. The book demonstrates through simulated models how oscillations, multistability, post-stimulus rebounds, and chaos can arise within either single neurons or circuits, and it explores their roles in the brain. The book first presents essential background in neuroscience, physics, mathematics, and Matlab, with explanations illustrated by many example problems. Subsequent chapters cover the neuron and spike production; single spike trains and the underlying cognitive processes; conductance-based models; the simulation of synaptic connections; firing-rate models of large-scale circuit operation; dynamical systems and their components; synaptic plasticity; and techniques for analysis of neuron population datasets, including principal components analysis, hidden Markov modeling, and Bayesian decoding. Accessible to undergraduates in life sciences with limited background in mathematics and computer coding, the book can be used in a “flipped” or “inverted” teaching approach, with class time devoted to hands-on work on the computer tutorials. It can also be a resource for graduate students in the life sciences who wish to gain computing skills and a deeper knowledge of neural function and neural circuits.
Neural network research often builds on the fiction that neurons are simple linear threshold units, completely neglecting the highly dynamic and complex nature of synapses, dendrites, and voltage-dependent ionic currents. Biophysics of Computation: Information Processing in Single Neurons challenges this notion, using richly detailed experimental and theoretical findings from cellular biophysics to explain the repertoire of computational functions available to single neurons. The author shows how individual nerve cells can multiply, integrate, or delay synaptic inputs and how information can be encoded in the voltage across the membrane, in the intracellular calcium concentration, or in the timing of individual spikes.Key topics covered include the linear cable equation; cable theory as applied to passive dendritic trees and dendritic spines; chemical and electrical synapses and how to treat them from a computational point of view; nonlinear interactions of synaptic input in passive and active dendritic trees; the Hodgkin-Huxley model of action potential generation and propagation; phase space analysis; linking stochastic ionic channels to membrane-dependent currents; calcium and potassium currents and their role in information processing; the role of diffusion, buffering and binding of calcium, and other messenger systems in information processing and storage; short- and long-term models of synaptic plasticity; simplified models of single cells; stochastic aspects of neuronal firing; the nature of the neuronal code; and unconventional models of sub-cellular computation.Biophysics of Computation: Information Processing in Single Neurons serves as an ideal text for advanced undergraduate and graduate courses in cellular biophysics, computational neuroscience, and neural networks, and will appeal to students and professionals in neuroscience, electrical and computer engineering, and physics.
Explains the relationship of electrophysiology, nonlinear dynamics, and the computational properties of neurons, with each concept presented in terms of both neuroscience and mathematics and illustrated using geometrical intuition. In order to model neuronal behavior or to interpret the results of modeling studies, neuroscientists must call upon methods of nonlinear dynamics. This book offers an introduction to nonlinear dynamical systems theory for researchers and graduate students in neuroscience. It also provides an overview of neuroscience for mathematicians who want to learn the basic facts of electrophysiology. Dynamical Systems in Neuroscience presents a systematic study of the relationship of electrophysiology, nonlinear dynamics, and computational properties of neurons. It emphasizes that information processing in the brain depends not only on the electrophysiological properties of neurons but also on their dynamical properties. The book introduces dynamical systems, starting with one- and two-dimensional Hodgkin-Huxley-type models and continuing to a description of bursting systems. Each chapter proceeds from the simple to the complex, and provides sample problems at the end. The book explains all necessary mathematical concepts using geometrical intuition; it includes many figures and few equations, making it especially suitable for non-mathematicians. Each concept is presented in terms of both neuroscience and mathematics, providing a link between the two disciplines. Nonlinear dynamical systems theory is at the core of computational neuroscience research, but it is not a standard part of the graduate neuroscience curriculum—or taught by math or physics department in a way that is suitable for students of biology. This book offers neuroscience students and researchers a comprehensive account of concepts and methods increasingly used in computational neuroscience. An additional chapter on synchronization, with more advanced material, can be found at the author's website, www.izhikevich.com.
Comprehensive introduction to the neural network models currently under intensive study for computational applications. It also provides coverage of neural network applications in a variety of problems of both theoretical and practical interest.
An integrative overview of network approaches to neuroscience explores the origins of brain complexity and the link between brain structure and function. Over the last decade, the study of complex networks has expanded across diverse scientific fields. Increasingly, science is concerned with the structure, behavior, and evolution of complex systems ranging from cells to ecosystems. In Networks of the Brain, Olaf Sporns describes how the integrative nature of brain function can be illuminated from a complex network perspective. Highlighting the many emerging points of contact between neuroscience and network science, the book serves to introduce network theory to neuroscientists and neuroscience to those working on theoretical network models. Sporns emphasizes how networks connect levels of organization in the brain and how they link structure to function, offering an informal and nonmathematical treatment of the subject. Networks of the Brain provides a synthesis of the sciences of complex networks and the brain that will be an essential foundation for future research.