*Computational And Mathematical Modeling of Neural Systems*

**Author**: Peter Dayan

**Publisher:**Mit Press

**ISBN:**9780262541855

**Category:**Medical

**Page:**460

**View:**8692

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# Search Results for: theoretical-neuroscience-computational-and-mathematical-modeling-of-neural-systems-computational-neuroscience-series

*Computational And Mathematical Modeling of Neural Systems*

**Author**: Peter Dayan

**Publisher:** Mit Press

**ISBN:** 9780262541855

**Category:** Medical

**Page:** 460

**View:** 8692

The construction and analysis of mathematical and computational models of neural systems.

**Author**: Thomas Trappenberg

**Publisher:** Oxford University Press

**ISBN:** 0199568413

**Category:** Mathematics

**Page:** 390

**View:** 7615

The new edition of Fundamentals of Computational Neuroscience build on the success and strengths of the first edition. It introduces the theoretical foundations of neuroscience with a focus on the nature of information processing in the brain. The book covers the introduction and motivation of simplified models of neurons that are suitable for exploring information processing in large brain-like networks. Additionally, it introduces several fundamental networkarchitectures and discusses their relevance for information processing in the brain, giving some examples of models of higher-order cognitive functions to demonstrate the advanced insight that can begained with such studies.

**Author**: Eugene M. Izhikevich

**Publisher:** MIT Press

**ISBN:** 0262090430

**Category:** Medical

**Page:** 441

**View:** 5361

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.
*A First Course*

**Author**: Hanspeter Mallot

**Publisher:** Springer Science & Business Media

**ISBN:** 3319008617

**Category:** Computers

**Page:** 135

**View:** 9956

Computational Neuroscience - A First Course provides an essential introduction to computational neuroscience and equips readers with a fundamental understanding of modeling the nervous system at the membrane, cellular, and network level. The book, which grew out of a lecture series held regularly for more than ten years to graduate students in neuroscience with backgrounds in biology, psychology and medicine, takes its readers on a journey through three fundamental domains of computational neuroscience: membrane biophysics, systems theory and artificial neural networks. The required mathematical concepts are kept as intuitive and simple as possible throughout the book, making it fully accessible to readers who are less familiar with mathematics. Overall, Computational Neuroscience - A First Course represents an essential reference guide for all neuroscientists who use computational methods in their daily work, as well as for any theoretical scientist approaching the field of computational neuroscience.

**Author**: David Sterratt,Bruce Graham,Andrew Gillies,David Willshaw

**Publisher:** Cambridge University Press

**ISBN:** 1139500791

**Category:** Medical

**Page:** N.A

**View:** 5770

The nervous system is made up of a large number of interacting elements. To understand how such a complex system functions requires the construction and analysis of computational models at many different levels. This book provides a step-by-step account of how to model the neuron and neural circuitry to understand the nervous system at all levels, from ion channels to networks. Starting with a simple model of the neuron as an electrical circuit, gradually more details are added to include the effects of neuronal morphology, synapses, ion channels and intracellular signalling. The principle of abstraction is explained through chapters on simplifying models, and how simplified models can be used in networks. This theme is continued in a final chapter on modelling the development of the nervous system. Requiring an elementary background in neuroscience and some high school mathematics, this textbook is an ideal basis for a course on computational neuroscience.

**Author**: G. Bard Ermentrout,David H. Terman

**Publisher:** Springer Science & Business Media

**ISBN:** 0387877088

**Category:** Mathematics

**Page:** 422

**View:** 7773

This book applies methods from nonlinear dynamics to problems in neuroscience. It uses modern mathematical approaches to understand patterns of neuronal activity seen in experiments and models of neuronal behavior. The intended audience is researchers interested in applying mathematics to important problems in neuroscience, and neuroscientists who would like to understand how to create models, as well as the mathematical and computational methods for analyzing them. The authors take a very broad approach and use many different methods to solve and understand complex models of neurons and circuits. They explain and combine numerical, analytical, dynamical systems and perturbation methods to produce a modern approach to the types of model equations that arise in neuroscience. There are extensive chapters on the role of noise, multiple time scales and spatial interactions in generating complex activity patterns found in experiments. The early chapters require little more than basic calculus and some elementary differential equations and can form the core of a computational neuroscience course. Later chapters can be used as a basis for a graduate class and as a source for current research in mathematical neuroscience. The book contains a large number of illustrations, chapter summaries and hundreds of exercises which are motivated by issues that arise in biology, and involve both computation and analysis. Bard Ermentrout is Professor of Computational Biology and Professor of Mathematics at the University of Pittsburgh. David Terman is Professor of Mathematics at the Ohio State University.

**Author**: Fabrizio Gabbiani,Steven James Cox

**Publisher:** Academic Press

**ISBN:** 0128019069

**Category:** Science

**Page:** 628

**View:** 7374

Mathematics for Neuroscientists, Second Edition, presents a comprehensive introduction to mathematical and computational methods used in neuroscience to describe and model neural components of the brain from ion channels to single neurons, neural networks and their relation to behavior. The book contains more than 200 figures generated using Matlab code available to the student and scholar. Mathematical concepts are introduced hand in hand with neuroscience, emphasizing the connection between experimental results and theory. Fully revised material and corrected text Additional chapters on extracellular potentials, motion detection and neurovascular coupling Revised selection of exercises with solutions More than 200 Matlab scripts reproducing the figures as well as a selection of equivalent Python scripts
*Mathematical Modeling of Mental Illness*

**Author**: Alan Anticevic,John D Murray

**Publisher:** Academic Press

**ISBN:** 0128098260

**Category:** Medical

**Page:** 332

**View:** 6728

Computational Psychiatry: Mathematical Modeling of Mental Illness is the first systematic effort to bring together leading scholars in the fields of psychiatry and computational neuroscience who have conducted the most impactful research and scholarship in this area. It includes an introduction outlining the challenges and opportunities facing the field of psychiatry that is followed by a detailed treatment of computational methods used in the service of understanding neuropsychiatric symptoms, improving diagnosis and guiding treatments. This book provides a vital resource for the clinical neuroscience community with an in-depth treatment of various computational neuroscience approaches geared towards understanding psychiatric phenomena. Its most valuable feature is a comprehensive survey of work from leaders in this field. Offers an in-depth overview of the rapidly evolving field of computational psychiatry Written for academics, researchers, advanced students and clinicians in the fields of computational neuroscience, clinical neuroscience, psychiatry, clinical psychology, neurology and cognitive neuroscience Provides a comprehensive survey of work from leaders in this field and a presentation of a range of computational psychiatry methods and approaches geared towards a broad array of psychiatric problems

**Author**: John A. Hertz

**Publisher:** CRC Press

**ISBN:** 0429979290

**Category:** Science

**Page:** 352

**View:** 7217

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.
*Probabilistic Approaches to Neural Coding*

**Author**: Kenji Doya

**Publisher:** MIT Press

**ISBN:** 026204238X

**Category:** Medical

**Page:** 326

**View:** 8843

Experimental and theoretical neuroscientists use Bayesian approaches to analyze the brain mechanisms of perception, decision-making, and motor control.
*From Ions to Networks*

**Author**: Christof Koch,Idan Segev

**Publisher:** MIT Press

**ISBN:** 9780262112314

**Category:** Medical

**Page:** 671

**View:** 8169

This book serves as a handbook of computational methods and techniques for modeling the functional properties of single and groups of nerve cells.

**Author**: Patricia S. Churchland,Terrence J. Sejnowski

**Publisher:** MIT Press

**ISBN:** 0262339668

**Category:** Science

**Page:** 568

**View:** 2987

Before The Computational Brain was published in 1992, conceptual frameworks for brain function were based on the behavior of single neurons, applied globally. In The Computational Brain, Patricia Churchland and Terrence Sejnowski developed a different conceptual framework, based on large populations of neurons. They did this by showing that patterns of activities among the units in trained artificial neural network models had properties that resembled those recorded from populations of neurons recorded one at a time. It is one of the first books to bring together computational concepts and behavioral data within a neurobiological framework. Aimed at a broad audience of neuroscientists, computer scientists, cognitive scientists, and philosophers, The Computational Brain is written for both expert and novice. This anniversary edition offers a new preface by the authors that puts the book in the context of current research.This approach influenced a generation of researchers. Even today, when neuroscientists can routinely record from hundreds of neurons using optics rather than electricity, and the 2013 White House BRAIN initiative heralded a new era in innovative neurotechnologies, the main message of The Computational Brain is still relevant.
*Foundations of Computational Neuroscience*

**Author**: William W. Lytton

**Publisher:** Springer Science & Business Media

**ISBN:** 0387227334

**Category:** Mathematics

**Page:** 364

**View:** 7069

Biology undergraduates, medical students and life-science graduate students often have limited mathematical skills. Similarly, physics, math and engineering students have little patience for the detailed facts that make up much of biological knowledge. Teaching computational neuroscience as an integrated discipline requires that both groups be brought forward onto common ground. This book does this by making ancillary material available in an appendix and providing basic explanations without becoming bogged down in unnecessary details. The book will be suitable for undergraduates and beginning graduate students taking a computational neuroscience course and also to anyone with an interest in the uses of the computer in modeling the nervous system.

**Author**: Erik De Schutter

**Publisher:** Mit Press

**ISBN:** 9780262013277

**Category:** Computers

**Page:** 419

**View:** 4691

A guide to computational modeling methods in neuroscience, covering a range of modeling scales from molecular reactions to large neural networks. This book offers an introduction to current methods in computational modeling in neuroscience. The book describes realistic modeling methods at levels of complexity ranging from molecular interactions to large neural networks. A "how to" book rather than an analytical account, it focuses on the presentation of methodological approaches, including the selection of the appropriate method and its potential pitfalls. It is intended for experimental neuroscientists and graduate students who have little formal training in mathematical methods, but it will also be useful for scientists with theoretical backgrounds who want to start using data-driven modeling methods. The mathematics needed are kept to an introductory level; the first chapter explains the mathematical methods the reader needs to master to understand the rest of the book. The chapters are written by scientists who have successfully integrated data-driven modeling with experimental work, so all of the material is accessible to experimentalists. The chapters offer comprehensive coverage with little overlap and extensive cross-references, moving from basic building blocks to more complex applications. Contributors Pablo Achard, Haroon Anwar, Upinder S. Bhalla, Michiel Berends, Nicolas Brunel, Ronald L. Calabrese, Brenda Claiborne, Hugo Cornelis, Erik De Schutter, Alain Destexhe, Bard Ermentrout, Kristen Harris, Sean Hill, John R. Huguenard, William R. Holmes, Gwen Jacobs, Gwendal LeMasson, Henry Markram, Reinoud Maex, Astrid A. Prinz, Imad Riachi, John Rinzel, Arnd Roth, Felix Schürmann, Werner Van Geit, Mark C. W. van Rossum, Stefan Wils

**Author**: Thomas J. Anastasio

**Publisher:** Sinauer Associates Incorporated

**ISBN:** 9780878933396

**Category:** Medical

**Page:** 553

**View:** 1346

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.

**Author**: Paul Miller

**Publisher:** MIT Press

**ISBN:** 0262347563

**Category:** Science

**Page:** 408

**View:** 6062

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**: Michael A. Arbib,James J. Bonaiuto

**Publisher:** MIT Press

**ISBN:** 0262335271

**Category:** Science

**Page:** 808

**View:** 1664

This textbook presents a wide range of subjects in neuroscience from a computational perspective. It offers a comprehensive, integrated introduction to core topics, using computational tools to trace a path from neurons and circuits to behavior and cognition. Moreover, the chapters show how computational neuroscience -- methods for modeling the causal interactions underlying neural systems -- complements empirical research in advancing the understanding of brain and behavior. The chapters -- all by leaders in the field, and carefully integrated by the editors -- cover such subjects as action and motor control; neuroplasticity, neuromodulation, and reinforcement learning; vision; and language -- the core of human cognition.The book can be used for advanced undergraduate or graduate level courses. It presents all necessary background in neuroscience beyond basic facts about neurons and synapses and general ideas about the structure and function of the human brain. Students should be familiar with differential equations and probability theory, and be able to pick up the basics of programming in MATLAB and/or Python. Slides, exercises, and other ancillary materials are freely available online, and many of the models described in the chapters are documented in the brain operation database, BODB (which is also described in a book chapter).ContributorsMichael A. Arbib, Joseph Ayers, James Bednar, Andrej Bicanski, James J. Bonaiuto, Nicolas Brunel, Jean-Marie Cabelguen, Carmen Canavier, Angelo Cangelosi, Richard P. Cooper, Carlos R. Cortes, Nathaniel Daw, Paul Dean, Peter Ford Dominey, Pierre Enel, Jean-Marc Fellous, Stefano Fusi, Wulfram Gerstner, Frank Grasso, Jacqueline A. Griego, Ziad M. Hafed, Michael E. Hasselmo, Auke Ijspeert, Stephanie Jones, Daniel Kersten, Jeremie Knuesel, Owen Lewis, William W. Lytton, Tomaso Poggio, John Porrill, Tony J. Prescott, John Rinzel, Edmund Rolls, Jonathan Rubin, Nicolas Schweighofer, Mohamed A. Sherif, Malle A. Tagamets, Paul F. M. J. Verschure, Nathan Vierling-Claasen, Xiao-Jing Wang, Christopher Williams, Ransom Winder, Alan L. Yuille
*A Student's Introduction to Methods and Procedures*

**Author**: Britt Anderson

**Publisher:** SAGE

**ISBN:** 1446297373

**Category:** Psychology

**Page:** 240

**View:** 2927

"For the neuroscientist or psychologist who cringes at the sight of mathematical formulae and whose eyes glaze over at terms like differential equations, linear algebra, vectors, matrices, Bayes’ rule, and Boolean logic, this book just might be the therapy needed." - Anjan Chatterjee, Professor of Neurology, University of Pennsylvania "Anderson provides a gentle introduction to computational aspects of psychological science, managing to respect the reader’s intelligence while also being completely unintimidating. Using carefully-selected computational demonstrations, he guides students through a wide array of important approaches and tools, with little in the way of prerequisites...I recommend it with enthusiasm." - Asohan Amarasingham, The City University of New York This unique, self-contained and accessible textbook provides an introduction to computational modelling neuroscience accessible to readers with little or no background in computing or mathematics. Organized into thematic sections, the book spans from modelling integrate and firing neurons to playing the game Rock, Paper, Scissors in ACT-R. This non-technical guide shows how basic knowledge and modern computers can be combined for interesting simulations, progressing from early exercises utilizing spreadsheets, to simple programs in Python. Key Features include: Interleaved chapters that show how traditional computing constructs are simply disguised versions of the spread sheet methods. Mathematical facts and notation needed to understand the modelling methods are presented at their most basic and are interleaved with biographical and historical notes for contex. Numerous worked examples to demonstrate the themes and procedures of cognitive modelling. An excellent text for postgraduate students taking courses in research methods, computational neuroscience, computational modelling, cognitive science and neuroscience. It will be especially valuable to psychology students.
*Models, Methods and Applications*

**Author**: Alonso, Eduardo

**Publisher:** IGI Global

**ISBN:** 1609600231

**Category:** Computers

**Page:** 396

**View:** 3615

"This book argues that computational models in behavioral neuroscience must be taken with caution, and advocates for the study of mathematical models of existing theories as complementary to neuro-psychological models and computational models"--
*A Foundation for Motor Learning*

**Author**: Reza Shadmehr,Steven P. Wise,National Institute of Mental Health in Bethesda Maryland Steven P Wise

**Publisher:** MIT Press

**ISBN:** 9780262195089

**Category:** Medical

**Page:** 575

**View:** 2070

An introduction to the computational biology of reaching and pointing, with an emphasis on motor learning. Neuroscience involves the study of the nervous system, and its topics range from genetics to inferential reasoning. At its heart, however, lies a search for understanding how the environment affects the nervous system and how the nervous system, in turn, empowers us to interact with and alter our environment. This empowerment requires motor learning. The Computational Neurobiology of Reaching and Pointing addresses the neural mechanisms of one important form of motor learning. The authors integrate material from the computational, behavioral, and neural sciences of motor control that is not available in any other single source. The result is a unified, comprehensive model of reaching and pointing. The book is intended to be used as a text by graduate students in both neuroscience and bioengineering and as a reference source by experts in neuroscience, robotics, and other disciplines. The book begins with an overview of the evolution, anatomy, and physiology of the motor system, including the mechanisms for generating force and maintaining limb stability. The sections that follow, "Computing Locations and Displacements", "Skills, Adaptations, and Trajectories", and "Predictions, Decisions, and Flexibility", present a theory of sensorially guided reaching and pointing that evolves organically based on computational principles rather than a traditional structure-by-structure approach. The book also includes five appendixes that provide brief refreshers on fundamentals of biology, mathematics, physics, and neurophysiology, as well as a glossary of relevant terms. The authors have also made supplemental materials available on the Internet. These web documents provide source code for simulations, step-by-step derivations of certain mathematical formulations, and expanded explanations of some concepts.

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