An Introduction to Modeling Neuronal Dynamics


Book Description

This book is intended as a text for a one-semester course on Mathematical and Computational Neuroscience for upper-level undergraduate and beginning graduate students of mathematics, the natural sciences, engineering, or computer science. An undergraduate introduction to differential equations is more than enough mathematical background. Only a slim, high school-level background in physics is assumed, and none in biology. Topics include models of individual nerve cells and their dynamics, models of networks of neurons coupled by synapses and gap junctions, origins and functions of population rhythms in neuronal networks, and models of synaptic plasticity. An extensive online collection of Matlab programs generating the figures accompanies the book.




Neuronal Dynamics


Book Description

This solid introduction uses the principles of physics and the tools of mathematics to approach fundamental questions of neuroscience.




Dynamical Systems in Neuroscience


Book Description

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.




An Introduction to the Modeling of Neural Networks


Book Description

This book is a beginning graduate-level introduction to neural networks which is divided into four parts.




Brain Dynamics


Book Description

This is an excellent introduction for graduate students and nonspecialists to the field of mathematical and computational neurosciences. The book approaches the subject via pulsed-coupled neural networks, which have at their core the lighthouse and integrate-and-fire models. These allow for highly flexible modeling of realistic synaptic activity, synchronization and spatio-temporal pattern formation. The more advanced pulse-averaged equations are discussed.




An Introductory Course in Computational Neuroscience


Book Description

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.




Spiking Neuron Models


Book Description

Neurons in the brain communicate by short electrical pulses, the so-called action potentials or spikes. How can we understand the process of spike generation? How can we understand information transmission by neurons? What happens if thousands of neurons are coupled together in a seemingly random network? How does the network connectivity determine the activity patterns? And, vice versa, how does the spike activity influence the connectivity pattern? These questions are addressed in this 2002 introduction to spiking neurons aimed at those taking courses in computational neuroscience, theoretical biology, biophysics, or neural networks. The approach will suit students of physics, mathematics, or computer science; it will also be useful for biologists who are interested in mathematical modelling. The text is enhanced by many worked examples and illustrations. There are no mathematical prerequisites beyond what the audience would meet as undergraduates: more advanced techniques are introduced in an elementary, concrete fashion when needed.




Biophysics of Computation


Book Description

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.




Principles of Computational Modelling in Neuroscience


Book Description

Learn to use computational modelling techniques to understand the nervous system at all levels, from ion channels to networks.




Biologically Inspired Computer Vision


Book Description

As the state-of-the-art imaging technologies became more and more advanced, yielding scientific data at unprecedented detail and volume, the need to process and interpret all the data has made image processing and computer vision increasingly important. Sources of data that have to be routinely dealt with today's applications include video transmission, wireless communication, automatic fingerprint processing, massive databanks, non-weary and accurate automatic airport screening, robust night vision, just to name a few. Multidisciplinary inputs from other disciplines such as physics, computational neuroscience, cognitive science, mathematics, and biology will have a fundamental impact in the progress of imaging and vision sciences. One of the advantages of the study of biological organisms is to devise very different type of computational paradigms by implementing a neural network with a high degree of local connectivity. This is a comprehensive and rigorous reference in the area of biologically motivated vision sensors. The study of biologically visual systems can be considered as a two way avenue. On the one hand, biological organisms can provide a source of inspiration for new computational efficient and robust vision models and on the other hand machine vision approaches can provide new insights for understanding biological visual systems. Along the different chapters, this book covers a wide range of topics from fundamental to more specialized topics, including visual analysis based on a computational level, hardware implementation, and the design of new more advanced vision sensors. The last two sections of the book provide an overview of a few representative applications and current state of the art of the research in this area. This makes it a valuable book for graduate, Master, PhD students and also researchers in the field.