Spectral Analysis Differential Equations And Mathematical Physics A Festschrift In Honor Of Fritz Gesztesy S 60th Birthday

Autor: Helge Holden
Publisher: American Mathematical Soc.
ISBN: 0821875744
File Size: 57,65 MB
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This volume contains twenty contributions in the area of mathematical physics where Fritz Gesztesy made profound contributions. There are three survey papers in spectral theory, differential equations, and mathematical physics, which highlight, in particu

Introduction To Theoretical Neurobiology Volume 1 Linear Cable Theory And Dendritic Structure

Autor: Henry C. Tuckwell
Publisher: Cambridge University Press
ISBN: 9780521350969
File Size: 22,23 MB
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The human brain contains billions of nerve cells whose activity plays a critical role in the way we behave, feel, perceive, and think. This two-volume set explains the basic properties of a neuron--an electrically active nerve cell--and develops mathematical theories for the way neurons respond to the various stimuli they receive. Volume 1 contains descriptions and analyses of the principle mathematical models that have been developed for neurons in the past thirty years. It provides a brief review of the basic neuroanatomical and neurophysiological facts that will form the focus of the mathematical treatment. Tuckwell discusses the mathematical theories, beginning with the theory of membrane potentials. He then goes on to treat the Lapicque model, linear cable theory, and time-dependent solutions of the cable equations. He concludes with a description of Rall's model nerve cell. Because the level of mathematics increases steadily upward from Chapter Two some familiarity with differential equations and linear algebra is desirable.

Mathematics Of Bioinformatics

Autor: Matthew He
Publisher: John Wiley & Sons
ISBN: 9781118099520
File Size: 78,66 MB
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Mathematics of Bioinformatics: Theory, Methods, and Applications provides a comprehensive format for connecting and integrating information derived from mathematical methods and applying it to the understanding of biological sequences, structures, and networks. Each chapter is divided into a number of sections based on the bioinformatics topics and related mathematical theory and methods. Each topic of the section is comprised of the following three parts: an introduction to the biological problems in bioinformatics; a presentation of relevant topics of mathematical theory and methods to the bioinformatics problems introduced in the first part; an integrative overview that draws the connections and interfaces between bioinformatics problems/issues and mathematical theory/methods/applications.

Principles Of Computational Modelling In Neuroscience

Autor: David Sterratt
Publisher: Cambridge University Press
ISBN: 1139500791
File Size: 40,29 MB
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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.

Handbook On Biological Networks

Autor: Stefano Boccaletti
Publisher: World Scientific
ISBN: 9812838791
File Size: 22,60 MB
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Networked systems are all around us. The accumulated evidence of systems as complex as a cell cannot be fully understood by studying only their isolated constituents, giving rise to a new area of interest in research ? the study of complex networks. In a broad sense, biological networks have been one of the most studied networks, and the field has benefited from many important contributions. By understanding and modeling the structure of a biological network, a better perception of its dynamical and functional behavior is to be expected. This unique book compiles the most relevant results and novel insights provided by network theory in the biological sciences, ranging from the structure and dynamics of the brain to cellular and protein networks and to population-level biology.

Epidemic Modelling

Autor: D. J. Daley
Publisher: Cambridge University Press
ISBN: 9780521014670
File Size: 80,86 MB
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This is a general introduction to the mathematical modelling of diseases.

Introduction To Theoretical Neurobiology Volume 2 Nonlinear And Stochastic Theories

Autor: Henry C. Tuckwell
Publisher: Cambridge University Press
ISBN: 9780521019323
File Size: 11,26 MB
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The second part of this two-volume set contains advanced aspects of the quantitative theory of the dynamics of neurons. It begins with an introduction to the effects of reversal potentials on response to synaptic input. It then develops the theory of action potential generation based on the seminal Hodgkin-Huxley equations and gives methods for their solution in the space-clamped and nonspaceclamped cases. The remainder of the book discusses stochastic models of neural activity and ends with a statistical analysis of neuronal data with emphasis on spike trains. The mathematics is more complex in this volume than in the first volume and involves numerical methods of solution of partial differential equations and the statistical analysis of point processes.

Analysis Of Parallel Spike Trains

Autor: Sonja Grün
Publisher: Springer Science & Business Media
ISBN: 9781441956750
File Size: 36,26 MB
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Solid and transparent data analysis is the most important basis for reliable interpretation of experiments. The technique of parallel spike train recordings using multi-electrode arrangements has been available for many decades now, but only recently gained wide popularity among electro physiologists. Many traditional analysis methods are based on firing rates obtained by trial-averaging, and some of the assumptions for such procedures to work can be ignored without serious consequences. The situation is different for correlation analysis, the result of which may be considerably distorted if certain critical assumptions are violated. The focus of this book is on concepts and methods of correlation analysis (synchrony, patterns, rate covariance), combined with a solid introduction into approaches for single spike trains, which represent the basis of correlations analysis. The book also emphasizes pitfalls and potential wrong interpretations of data due to violations of critical assumptions.

Ultimate Computing

Autor: S.R. Hameroff
Publisher: Elsevier
ISBN: 0444600094
File Size: 54,10 MB
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The possibility of direct interfacing between biological and technological information devices could result in a merger of mind and machine - Ultimate Computing. This book, a thorough consideration of this idea, involves a number of disciplines, including biochemistry, cognitive science, computer science, engineering, mathematics, microbiology, molecular biology, pharmacology, philosophy, physics, physiology, and psychology.