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Dynamics Of Small Neural Populations
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Book Synopsis Dynamics of Small Neural Populations by : John Milton
Download or read book Dynamics of Small Neural Populations written by John Milton and published by American Mathematical Soc.. This book was released on 1996 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book arose from a series of lectures presented at the CRM Summer School in Mathematical Biology held at the University of British Columbia in the summer of 19934 by John Milton, a clinical neurologist and biomathematician. In this work, three themes are explored: time-delayed feedback control, noise, and statistical properties of neurons and large neural populations. This volume focuses on systems composed of 2-3 neurons. Such neural populations are small enough to permit experimental manipulation while at the same time being well enough characterized so that plausible mathematical models can be posed. Thus direct comparisons between theory and observation are in principle possible.
Book Synopsis Neuronal Dynamics by : Wulfram Gerstner
Download or read book Neuronal Dynamics written by Wulfram Gerstner and published by Cambridge University Press. This book was released on 2014-07-24 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: This solid introduction uses the principles of physics and the tools of mathematics to approach fundamental questions of neuroscience.
Book Synopsis Metastable Dynamics of Neural Ensembles by : Emili Balaguer-Ballester
Download or read book Metastable Dynamics of Neural Ensembles written by Emili Balaguer-Ballester and published by Frontiers Media SA. This book was released on 2018-03-19 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: A classical view of neural computation is that it can be characterized in terms of convergence to attractor states or sequential transitions among states in a noisy background. After over three decades, is this still a valid model of how brain dynamics implements cognition? This book provides a comprehensive collection of recent theoretical and experimental contributions addressing the question of stable versus transient neural population dynamics from complementary angles. These studies showcase recent efforts for designing a framework that encompasses the multiple facets of metastability in neural responses, one of the most exciting topics currently in systems and computational neuroscience.
Book Synopsis Applications of Nonlinear Dynamics, and Critical Phenomena to Measure Neural Populations Using Inputs to Single Neurons by : James Kenneth Johnson
Download or read book Applications of Nonlinear Dynamics, and Critical Phenomena to Measure Neural Populations Using Inputs to Single Neurons written by James Kenneth Johnson and published by . This book was released on 2020 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: A compelling vision for the future of neuroscience is the ability to sense neural activity throughout the bulk of the brain with exquisite resolution. Popular visions usually include intricate electrode technology intruding into the neuropil, meandering along nerve tracts, and sensing the whole brain. These popular visions stem from the belief that we must always have an outsider's perspective of neural activity. According to this belief the closest thing neuroscientists can achieve to an insider's perspective is to shadow every neuron (or almost every neuron) with an electrical or optical recording device. Yet, the brain naturally has an expansive sensor network. The brain already aggregates and organizes neural activity according to computational function. The brain does this through the operation of single neurons, which have arrays of many dendrites to process inputs arriving from far and wide. These processed inputs are concentrated at the soma of the neuron where they drive rich dynamics, and where the neuron translates these inputs into outputs. One of the most venerable methods in neuroscience, the patch-clamp intracellular recording technique, can record these rich input driven dynamics. Neuroscience has long held the goal of patching into the full network dynamics with patch-clamp, but it is difficult to reconstruct network dynamics information. Fortunately, the neural criticality hypothesis provides a justification for expecting to find network dynamics information, and the modern field of nonlinear dynamics provides tools for reconstructing full dynamics from scant information. The neural criticality hypothesis is the idea that the brain can exhibit phase transitions, but tunes itself to sit at a point (called a "critical point") between two phases where the most dynamical complexity arises. One of the key phenomena of critical systems is "scale-freeness" which is widely observed in the brain. One implication of Scale-freeness is that some statistics are always the same whether observed at very small scales or very large. For critical phenomena scale-freeness is both extensive and precise, if scale-freeness is limited in a system then it suggests that system is not a critical system. We adopt condensed matter physics' rigorous standards for experimentally identifying critical systems. We show that we can meet these standards with long intracellular recordings. We also show that our findings agree with large scale population recordings. After establishing this proof-of-concept, we then use new methods for modeling nonlinear dynamical systems to extract small details about visual stimulus from short intracellular recordings. These details were too small to be reliably detected in the output of neurons. We use models of nonlinear dynamics because of their relationship to a neural coding paradigm: Attractor network theory. Thus, we also have novel evidence of dynamical attractor based neural code in primary visual cortex. Therefore, we have advanced both the neural criticality hypothesis and the attractor network theory of neural coding while demonstrating that we can patch into in-situ neural communication networks and get information that previously required electrode arrays or other population recording methods.
Book Synopsis Foundations and Tools for Neural Modeling by : Jose Mira
Download or read book Foundations and Tools for Neural Modeling written by Jose Mira and published by Springer. This book was released on 2006-12-08 with total page 890 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes, together with its compagnion LNCS 1607, the refereed proceedings of the International Work-Conference on Artificial and Natural Neural Networks, IWANN'99, held in Alicante, Spain in June 1999. The 89 revised papers presented were carefully reviewed and selected for inclusion in the book. This volume is devoted to foundational issues of neural computation and tools for neural modeling. The papers are organized in parts on neural modeling: biophysical and structural models; plasticity phenomena: maturing, learning, and memory; and artificial intelligence and cognitive neuroscience.
Book Synopsis Foundations and Tools for Neural Modeling by : Jose Mira
Download or read book Foundations and Tools for Neural Modeling written by Jose Mira and published by Springer Science & Business Media. This book was released on 1999-05-19 with total page 900 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes, together with its compagnion LNCS 1606, the refereed proceedings of the International Work-Conference on Artificial & Neural Networks, IWANN'99, held in Alicante, Spain in June 1999. The 91 revised papers presented were carefully reviewed & selected for inclusion in the book. This volume is devoted to applications of biologically inspired artificial neural networks in various engineering disciplines. The papers are organized in parts on artificial neural nets simulation & implementation, image processing & engineering applications.
Book Synopsis Reduced Representations of Neural Networks by : Roxana A. Stefanescu
Download or read book Reduced Representations of Neural Networks written by Roxana A. Stefanescu and published by . This book was released on 2009 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Experimental and computational investigations addressing how various neural functions are achieved in the brain converged in recent years to a unified idea that the neural activity underlying most of the cognitive functions is distributed over large scale networks comprising various cortical and subcortical areas. Modeling approaches represent these areas and their connections using diverse models of neurocomputational units engaged in graph-like or neural field-like structures. Regardless of the manner of network implementation, simulations of large scale networks have encountered significant difficulties mainly due to the time delay introduced by the long range connections. To decrease the computational effort, it is common to assume severe approximations to simplify the descriptions of the neural dynamics associated with the system's units. In this dissertation we propose an alternative framework allowing the prevention of such strong assumptions while efficiently representing the dynamics of a complex neural network. First, we consider the dynamics of small scale networks of globally coupled non-identical excitatory and inhibitory neurons, which could realistically instantiate a neurocomputational unit. We identify the most significant dynamical features the neural population exhibits in different parametric configuration, including multi-cluster dynamics, multi-scale synchronization and oscillator death. Then, using mode decomposition techniques, we construct analytically low dimensional representations of the network dynamics and show that these reduced systems capture the dynamical features of the entire neural population. The cases of linear and synaptic coupling are discussed in detail. In chapter 5, we extend this approach for spatially extended neural networks. We consider the dynamical behavior of a neural field-like network, which incorporates many biologically realistic characteristics such as heterogeneous local and global connectivity as well as dispersion in the neural membrane excitability. We show that in this case as well, we can construct a reduced representation, which may capture well the dynamical features of the full system. The method outlined in this dissertation provides a consistent way to represent complex dynamical features of various neural networks in a computationally efficient manner.
Book Synopsis Self-Organized Biological Dynamics and Nonlinear Control by : Jan Walleczek
Download or read book Self-Organized Biological Dynamics and Nonlinear Control written by Jan Walleczek and published by Cambridge University Press. This book was released on 2006-04-20 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: The growing impact of nonlinear science on biology and medicine is fundamentally changing our view of living organisms and disease processes. This book introduces the application to biomedicine of a broad range of interdisciplinary concepts from nonlinear dynamics, such as self-organization, complexity, coherence, stochastic resonance, fractals and chaos. It comprises 18 chapters written by leading figures in the field and covers experimental and theoretical research, as well as the emerging technological possibilities such as nonlinear control techniques for treating pathological biodynamics, including heart arrhythmias and epilepsy. This book will attract the interest of professionals and students from a wide range of disciplines, including physicists, chemists, biologists, sensory physiologists and medical researchers such as cardiologists, neurologists and biomedical engineers.
Book Synopsis Neuronal Stochastic Variability: Influences on Spiking Dynamics and Network Activity by : Mark D. McDonnell
Download or read book Neuronal Stochastic Variability: Influences on Spiking Dynamics and Network Activity written by Mark D. McDonnell and published by Frontiers Media SA. This book was released on 2016-07-18 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic fluctuations are intrinsic to and unavoidable at every stage of neural dynamics. For example, ion channels undergo random conformational changes, neurotransmitter release at synapses is discrete and probabilistic, and neural networks are embedded in spontaneous background activity. The mathematical and computational tool sets contributing to our understanding of stochastic neural dynamics have expanded rapidly in recent years. New theories have emerged detailing the dynamics and computational power of the balanced state in recurrent networks. At the cellular level, novel stochastic extensions to the classical Hodgkin-Huxley model have enlarged our understanding of neuronal dynamics and action potential initiation. Analytical methods have been developed that allow for the calculation of the firing statistics of simplified phenomenological integrate-and-fire models, taking into account adaptation currents or temporal correlations of the noise. This Research Topic is focused on identified physiological/internal noise sources and mechanisms. By "internal", we mean variability that is generated by intrinsic biophysical processes. This includes noise at a range of scales, from ion channels to synapses to neurons to networks. The contributions in this Research Topic introduce innovative mathematical analysis and/or computational methods that relate to empirical measures of neural activity and illuminate the functional role of intrinsic noise in the brain.
Book Synopsis Handbook of Brain Connectivity by : Viktor K. Jirsa
Download or read book Handbook of Brain Connectivity written by Viktor K. Jirsa and published by Springer. This book was released on 2007-08-16 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our contemporary understanding of brain function is deeply rooted in the ideas of the nonlinear dynamics of distributed networks. Cognition and motor coordination seem to arise from the interactions of local neuronal networks, which themselves are connected in large scales across the entire brain. The spatial architectures between various scales inevitably influence the dynamics of the brain and thereby its function. But how can we integrate brain connectivity amongst these structural and functional domains? Our Handbook provides an account of the current knowledge on the measurement, analysis and theory of the anatomical and functional connectivity of the brain. All contributors are leading experts in various fields concerning structural and functional brain connectivity. In the first part of the Handbook, the chapters focus on an introduction and discussion of the principles underlying connected neural systems. The second part introduces the currently available non-invasive technologies for measuring structural and functional connectivity in the brain. Part three provides an overview of the analysis techniques currently available and highlights new developments. Part four introduces the application and translation of the concepts of brain connectivity to behavior, cognition and the clinical domain.
Download or read book Neural Fields written by Stephen Coombes and published by Springer. This book was released on 2014-06-17 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neural field theory has a long-standing tradition in the mathematical and computational neurosciences. Beginning almost 50 years ago with seminal work by Griffiths and culminating in the 1970ties with the models of Wilson and Cowan, Nunez and Amari, this important research area experienced a renaissance during the 1990ties by the groups of Ermentrout, Robinson, Bressloff, Wright and Haken. Since then, much progress has been made in both, the development of mathematical and numerical techniques and in physiological refinement und understanding. In contrast to large-scale neural network models described by huge connectivity matrices that are computationally expensive in numerical simulations, neural field models described by connectivity kernels allow for analytical treatment by means of methods from functional analysis. Thus, a number of rigorous results on the existence of bump and wave solutions or on inverse kernel construction problems are nowadays available. Moreover, neural fields provide an important interface for the coupling of neural activity to experimentally observable data, such as the electroencephalogram (EEG) or functional magnetic resonance imaging (fMRI). And finally, neural fields over rather abstract feature spaces, also called dynamic fields, found successful applications in the cognitive sciences and in robotics. Up to now, research results in neural field theory have been disseminated across a number of distinct journals from mathematics, computational neuroscience, biophysics, cognitive science and others. There is no comprehensive collection of results or reviews available yet. With our proposed book Neural Field Theory, we aim at filling this gap in the market. We received consent from some of the leading scientists in the field, who are willing to write contributions for the book, among them are two of the founding-fathers of neural field theory: Shun-ichi Amari and Jack Cowan.
Book Synopsis Nonlinear Dynamics and Chaos by : J Hogan
Download or read book Nonlinear Dynamics and Chaos written by J Hogan and published by CRC Press. This book was released on 2002-08-01 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear dynamics has been successful in explaining complicated phenomena in well-defined low-dimensional systems. Now it is time to focus on real-life problems that are high-dimensional or ill-defined, for example, due to delay, spatial extent, stochasticity, or the limited nature of available data. How can one understand the dynamics of such sys
Book Synopsis Mathematics as a Laboratory Tool by : John Milton
Download or read book Mathematics as a Laboratory Tool written by John Milton and published by Springer. This book was released on 2014-09-18 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory textbook is based on the premise that the foundation of good science is good data. The educational challenge addressed by this introductory textbook is how to present a sampling of the wide range of mathematical tools available for laboratory research to well-motivated students with a mathematical background limited to an introductory course in calculus.
Book Synopsis Quantitative Neuroscience by : Panos M. Pardalos
Download or read book Quantitative Neuroscience written by Panos M. Pardalos and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in the field of signal processing, nonlinear dynamics, statistics, and optimization theory, combined with marked improvement in instrumenta tion and development of computers systems, have made it possible to apply the power of mathematics to the task of understanding the human brain. This verita ble revolution already has resulted in widespread availability of high resolution neuroimaging devices in clinical as well as research settings. Breakthroughs in functional imaging are not far behind. Mathematical tech niques developed for the study of complex nonlinear systems and chaos already are being used to explore the complex nonlinear dynamics of human brain phys iology. Global optimization is being applied to data mining expeditions in an effort to find knowledge in the vast amount of information being generated by neuroimaging and neurophysiological investigations. These breakthroughs in the ability to obtain, store and analyze large datasets offer, for the first time, exciting opportunities to explore the mechanisms underlying normal brain func tion as well as the affects of diseases such as epilepsy, sleep disorders, movement disorders, and cognitive disorders that affect millions of people every year. Ap plication of these powerful tools to the study of the human brain requires, by necessity, collaboration among scientists, engineers, neurobiologists and clini cians. Each discipline brings to the table unique knowledge, unique approaches to problem solving, and a unique language.
Book Synopsis Nonlinear Dynamics in Human Behavior by : Raoul Huys
Download or read book Nonlinear Dynamics in Human Behavior written by Raoul Huys and published by Springer. This book was released on 2010-12-09 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Humans engage in a seemingly endless variety of different behaviors, of which some are found across species, while others are conceived of as typically human. Most generally, behavior comes about through the interplay of various constraints – informational, mechanical, neural, metabolic, and so on – operating at multiple scales in space and time. Over the years, consensus has grown in the research community that, rather than investigating behavior only from bottom up, it may be also well understood in terms of concepts and laws on the phenomenological level. Such top down approach is rooted in theories of synergetics and self-organization using tools from nonlinear dynamics. The present compendium brings together scientists from all over the world that have contributed to the development of their respective fields departing from this background. It provides an introduction to deterministic as well as stochastic dynamical systems and contains applications to motor control and coordination, visual perception and illusion, as well as auditory perception in the context of speech and music.
Book Synopsis Handbook of Developmental Systems Theory and Methodology by : Peter C. M. Molenaar
Download or read book Handbook of Developmental Systems Theory and Methodology written by Peter C. M. Molenaar and published by Guilford Publications. This book was released on 2013-12-09 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developmental systems theory provides powerful tools for predicting complex, dynamic interactions among biological and environmental processes in human behavior and health. This groundbreaking handbook provides a roadmap for integrating key concepts of developmental systems theory (such as self-organization, reciprocal dynamic interaction, and probabilistic epigenesis) and simulation models (connectionist and agent-based models) with advanced dynamic modeling approaches for testing these theories and models. Internationally renowned developmental science scholars present innovations in research design, measurement, and analysis that offer new means of generating evidence-based decisions to optimize the course of health and positive functioning across the life span. Topics include epigenetic development and evolution; the relationship between neural systems growth and psychological development; the role of family environments in shaping children's cognitive skills and associated adult outcomes, and more.
Book Synopsis Moduli Spaces and Arithmetic Dynamics by : Joseph H. Silverman
Download or read book Moduli Spaces and Arithmetic Dynamics written by Joseph H. Silverman and published by American Mathematical Soc.. This book was released on with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt:
