This book is devoted to the study of the functional architecture of the visual cortex. Its geometrical structure is the differential geometry of the connectivity between neural cells. This connectivity is building and shaping the hidden brain structures underlying visual perception. The story of the problem runs over the last 30 years, since the discovery of Hubel and Wiesel of the modular structure of the primary visual cortex, and slowly cams towards a theoretical understanding of the experimental data on what we now know as functional architecture of the primary visual cortex. Experimental data comes from several domains: neurophysiology, phenomenology of perception and neurocognitive imaging. Imaging techniques like functional MRI and diffusion tensor MRI allow to deepen the study of cortical structures. Due to this variety of experimental data, neuromathematematics deals with modelling both cortical structures and perceptual spaces. From the mathematical point of view, neuromathematical call for new instruments of pure mathematics: sub-Riemannian geometry models horizontal connectivity, harmonic analysis in non commutative groups allows to understand pinwheels structure, as well as non-linear dimensionality reduction is at the base of many neural morphologies and possibly of the emergence of perceptual units. But at the center of the neurogeometry is the problem of harmonizing contemporary mathematical instruments with neurophysiological findings and phenomenological experiments in an unitary science of vision. The contributions to this book come from the very founders of the discipline.
This volume includes contributions from diverse disciplines including electrical engineering, biomedical engineering, industrial engineering, and medicine, bridging a vital gap between the mathematical sciences and neuroscience research. Covering a wide range of research topics, this volume demonstrates how various methods from data mining, signal processing, optimization and cutting-edge medical techniques can be used to tackle the most challenging problems in modern neuroscience.
The thirty original contributions in this book provide a working definition of"computational neuroscience" as the area in which problems lie simultaneously within computerscience and neuroscience. They review this emerging field in historical and philosophical overviewsand in stimulating summaries of recent results. Leading researchers address the structure of thebrain and the computational problems associated with describing and understanding this structure atthe synaptic, neural, map, and system levels.The overview chapters discuss the early days of thefield, provide a philosophical analysis of the problems associated with confusion between brainmetaphor and brain theory, and take up the scope and structure of computationalneuroscience.Synaptic-level structure is addressed in chapters that relate the properties ofdendritic branches, spines, and synapses to the biophysics of computation and provide a connectionbetween real neuron architectures and neural network simulations.The network-level chapters take upthe preattentive perception of 3-D forms, oscillation in neural networks, the neurobiologicalsignificance of new learning models, and the analysis of neural assemblies and local learningrides.Map-level structure is explored in chapters on the bat echolocation system, cat orientationmaps, primate stereo vision cortical cognitive maps, dynamic remapping in primate visual cortex, andcomputer-aided reconstruction of topographic and columnar maps in primates.The system-level chaptersfocus on the oculomotor system VLSI models of early vision, schemas for high-level vision,goal-directed movements, modular learning, effects of applied electric current fields on corticalneural activity neuropsychological studies of brain and mind, and an information-theoretic view ofanalog representation in striate cortex.Eric L. Schwartz is Professor of Brain Research and ResearchProfessor of Computer Science, Courant Institute of Mathematical Sciences, New York UniversityMedical Center. Computational Neuroscience is included in the System Development FoundationBenchmark Series.
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
Helping us understand our complex world, this book presents key findings in quantitative complex system science. Its approach is modular and phenomenology driven. Examples of phenomena treated in the book include the small world phenomenon in social and scale-free networks; life at the edge of chaos; the concept of living dynamical systems; and emotional diffusive control within cognitive system theory. Each chapter includes exercises to test your grasp of new material. Written at an introductory level, the author provides an accessible entry for graduate students in physics, mathematics, and theoretical computer science.
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.
In this issue of Neurosurgery Clinics, Drs. Chang and Barbaro provide a thorough look at epilepsy, with sections focusing on devices in epilepsy surgery, open loop systems, closed loop systems, and non-stimulation. Topics in this issue include history and overview of stimulation for epilepsy, trigeminal nerve stimulation, anterior thalamus DBS, hippocampal stimulation, neuropace RNS, seizure detection/prediction algorithms, cooling, seizure prediction and its applications, stimulation paradigms, and experimental stimulation.