Author : David Sterratt
Publisher : Cambridge University Press
Page : 553 pages
File Size : 45,96 MB
Release : 2023-10-05
Category : Science
ISBN : 1108483143
Learn to use computational modelling techniques to understand the nervous system at all levels, from ion channels to networks.
Author : Christoph Börgers
Publisher : Springer
Page : 445 pages
File Size : 46,60 MB
Release : 2017-04-17
Category : Mathematics
ISBN : 3319511718
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.
Author : D. Alistair Steyn-Ross
Publisher : Springer Science & Business Media
Page : 325 pages
File Size : 43,36 MB
Release : 2010-03-14
Category : Medical
ISBN : 1441907963
Foreword by Walter J. Freeman. The induction of unconsciousness using anesthetic agents demonstrates that the cerebral cortex can operate in two very different behavioral modes: alert and responsive vs. unaware and quiescent. But the states of wakefulness and sleep are not single-neuron properties---they emerge as bulk properties of cooperating populations of neurons, with the switchover between states being similar to the physical change of phase observed when water freezes or ice melts. Some brain-state transitions, such as sleep cycling, anesthetic induction, epileptic seizure, are obvious and detected readily with a few EEG electrodes; others, such as the emergence of gamma rhythms during cognition, or the ultra-slow BOLD rhythms of relaxed free-association, are much more subtle. The unifying theme of this book is the notion that all of these bulk changes in brain behavior can be treated as phase transitions between distinct brain states. Modeling Phase Transitions in the Brain contains chapter contributions from leading researchers who apply state-space methods, network models, and biophysically-motivated continuum approaches to investigate a range of neuroscientifically relevant problems that include analysis of nonstationary EEG time-series; network topologies that limit epileptic spreading; saddle--node bifurcations for anesthesia, sleep-cycling, and the wake--sleep switch; prediction of dynamical and noise-induced spatiotemporal instabilities underlying BOLD, alpha-, and gamma-band Hopf oscillations, gap-junction-moderated Turing structures, and Hopf-Turing interactions leading to cortical waves.
Author : Tohru Ozaki
Publisher : CRC Press
Page : 561 pages
File Size : 12,66 MB
Release : 2012-01-26
Category : Mathematics
ISBN : 1420094610
Recent advances in brain science measurement technology have given researchers access to very large-scale time series data such as EEG/MEG data (20 to 100 dimensional) and fMRI (140,000 dimensional) data. To analyze such massive data, efficient computational and statistical methods are required.Time Series Modeling of Neuroscience Data shows how to
Author : Eugene M. Izhikevich
Publisher : MIT Press
Page : 459 pages
File Size : 19,55 MB
Release : 2010-01-22
Category : Medical
ISBN : 0262514206
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.
Author : Paul Miller
Publisher : MIT Press
Page : 405 pages
File Size : 49,72 MB
Release : 2018-10-09
Category : Science
ISBN : 0262347563
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.
Author : Wulfram Gerstner
Publisher : Cambridge University Press
Page : 591 pages
File Size : 22,25 MB
Release : 2014-07-24
Category : Computers
ISBN : 1107060834
This solid introduction uses the principles of physics and the tools of mathematics to approach fundamental questions of neuroscience.
Author : Robert B. Northrop
Publisher : CRC Press
Page : 490 pages
File Size : 13,4 MB
Release : 2000-11-27
Category : Medical
ISBN : 142004172X
Although neural modeling has a long history, most of the texts available on the subject are quite limited in scope, dealing primarily with the simulation of large-scale biological neural networks applicable to describing brain function. Introduction to Dynamic Modeling of Neuro-Sensory Systems presents the mathematical tools and methods that can de
Author : Grace Lindsay
Publisher : Bloomsbury Publishing
Page : 401 pages
File Size : 14,51 MB
Release : 2021-03-04
Category : Science
ISBN : 1472966457
The human brain is made up of 85 billion neurons, which are connected by over 100 trillion synapses. For more than a century, a diverse array of researchers searched for a language that could be used to capture the essence of what these neurons do and how they communicate – and how those communications create thoughts, perceptions and actions. The language they were looking for was mathematics, and we would not be able to understand the brain as we do today without it. In Models of the Mind, author and computational neuroscientist Grace Lindsay explains how mathematical models have allowed scientists to understand and describe many of the brain's processes, including decision-making, sensory processing, quantifying memory, and more. She introduces readers to the most important concepts in modern neuroscience, and highlights the tensions that arise when the abstract world of mathematical modelling collides with the messy details of biology. Each chapter of Models of the Mind focuses on mathematical tools that have been applied in a particular area of neuroscience, progressing from the simplest building block of the brain – the individual neuron – through to circuits of interacting neurons, whole brain areas and even the behaviours that brains command. In addition, Grace examines the history of the field, starting with experiments done on frog legs in the late eighteenth century and building to the large models of artificial neural networks that form the basis of modern artificial intelligence. Throughout, she reveals the value of using the elegant language of mathematics to describe the machinery of neuroscience.
Author : Thomas J. Anastasio
Publisher : Sinauer
Page : 0 pages
File Size : 41,40 MB
Release : 2010-03-01
Category : Medical
ISBN : 9780878933396
For students of neuroscience and cognitive science who wish to explore the functioning of the brain further, but lack an extensive background in computer programming or maths, this new book makes neural systems modelling truly accessible. Short, simple MATLAB computer programs give readers all the experience necessary to run their own simulations.
