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Mathematics For Neuroscientists

Author: Fabrizio Gabbiani
Publisher: Academic Press
ISBN: 0128019069
Size: 28.97 MB
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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 Foundations Of Neuroscience

Author: G. Bard Ermentrout
Publisher: Springer Science & Business Media
ISBN: 0387877088
Size: 33.32 MB
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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.

Der Zahlensinn Oder Warum Wir Rechnen K Nnen

Author: Stanislas Dehaene
Publisher: Springer-Verlag
ISBN: 3034878257
Size: 28.12 MB
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Wir sind umgeben von Zahlen. Ob auf Kreditkarten gestanzt oder auf Münzen geprägt, ob auf Schecks gedruckt oder in den Spalten computerisierter Tabellen aufgelistet, überall beherrschen Zahlen unser Leben. Sie sind auch der Kern unserer Technologie. Ohne Zahlen könnten wir weder Raketen starten, die das Sonnensystem erkunden, noch Brücken bauen, Güter austauschen oder Rech nungen bezahlen. In gewissem Sinn sind Zahlen also kulturelle Erfindungen, die sich ihrer Bedeutung nach nur mit der Landwirtschaft oder mit dem Rad vergleichen lassen. Aber sie könnten sogar noch tiefere Wurzeln haben. Tausende von Jahren vor Christus benutzten babylonische Wissenschaftler Zahlzeichen, um erstaun lich genaueastronomische Tabellen zu berechnen. Zehntausende von Jahren zuvor hatten Menschen der Steinzeit die ersten geschriebenen Zahlenreihen geschaffen, indem sie Knochen einkerbten oder Punkte auf Höhlenwände malten. Und, wie ich später überzeugend darzustellen hoffe, schon vor weiteren Millionen von Jahren, lange bevor es Menschen gab, nahmen Tiere aller Arten Zahlen zur Kenntnis und stellten mit ihnen einfache Kopfrechnungen an. Sind Zahlen also fast so alt wie das Leben selbst? Sind sie in der Struktur unseres Gehirns verankert? Besitzen wir einen Zahlensinn, eine spezielle Intuition, die uns hilft, Zahlen und Mathematik mit Sinn zu erfüllen? Ich wurde vor fünfzehn Jahren, während meiner Ausbildung zum Mathema tiker, fasziniert von den abstrakten Objekten, mit denen ich umzugehen lernte, vor allem von den einfachsten von ihnen- den Zahlen.

Mathematical Neuroscience

Author: Stanislaw Brzychczy
Publisher: Academic Press
ISBN: 0124104827
Size: 28.50 MB
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Mathematical Neuroscience is a book for mathematical biologists seeking to discover the complexities of brain dynamics in an integrative way. It is the first research monograph devoted exclusively to the theory and methods of nonlinear analysis of infinite systems based on functional analysis techniques arising in modern mathematics. Neural models that describe the spatio-temporal evolution of coarse-grained variables—such as synaptic or firing rate activity in populations of neurons —and often take the form of integro-differential equations would not normally reflect an integrative approach. This book examines the solvability of infinite systems of reaction diffusion type equations in partially ordered abstract spaces. It considers various methods and techniques of nonlinear analysis, including comparison theorems, monotone iterative techniques, a truncation method, and topological fixed point methods. Infinite systems of such equations play a crucial role in the integrative aspects of neuroscience modeling. The first focused introduction to the use of nonlinear analysis with an infinite dimensional approach to theoretical neuroscience Combines functional analysis techniques with nonlinear dynamical systems applied to the study of the brain Introduces powerful mathematical techniques to manage the dynamics and challenges of infinite systems of equations applied to neuroscience modeling

Invited Lectures From The 13th International Congress On Mathematical Education

Author: Gabriele Kaiser
Publisher: Springer
ISBN: 3319721704
Size: 15.15 MB
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The book presents the Invited Lectures given at 13th International Congress on Mathematical Education (ICME-13). ICME-13 took place from 24th- 31st July 2016 at the University of Hamburg in Hamburg (Germany). The congress was hosted by the Society of Didactics of Mathematics (Gesellschaft für Didaktik der Mathematik - GDM) and took place under the auspices of the International Commission on Mathematical Instruction (ICMI). ICME-13 – the biggest ICME so far - brought together about 3500 mathematics educators from 105 countries, additionally 250 teachers from German speaking countries met for specific activities. The scholars came together to share their work on the improvement of mathematics education at all educational levels.. The papers present the work of prominent mathematics educators from all over the globe and give insight into the current discussion in mathematics education. The Invited Lectures cover a wide spectrum of topics, themes and issues and aim to give direction to future research towards educational improvement in the teaching and learning of mathematics education. This book is of particular interest to researchers, teachers and curriculum developers in mathematics education.

Signal Processing For Neuroscientists

Author: Wim van Drongelen
Publisher: Academic Press
ISBN: 012810483X
Size: 45.67 MB
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Signal Processing for Neuroscientists, Second Edition provides an introduction to signal processing and modeling for those with a modest understanding of algebra, trigonometry and calculus. With a robust modeling component, this book describes modeling from the fundamental level of differential equations all the way up to practical applications in neuronal modeling. It features nine new chapters and an exercise section developed by the author. Since the modeling of systems and signal analysis are closely related, integrated presentation of these topics using identical or similar mathematics presents a didactic advantage and a significant resource for neuroscientists with quantitative interest. Although each of the topics introduced could fill several volumes, this book provides a fundamental and uncluttered background for the non-specialist scientist or engineer to not only get applications started, but also evaluate more advanced literature on signal processing and modeling. Includes an introduction to biomedical signals, noise characteristics, recording techniques, and the more advanced topics of linear, nonlinear and multi-channel systems analysis Features new chapters on the fundamentals of modeling, application to neuronal modeling, Kalman filter, multi-taper power spectrum estimation, and practice exercises Contains the basics and background for more advanced topics in extensive notes and appendices Includes practical examples of algorithm development and implementation in MATLAB Features a companion website with MATLAB scripts, data files, figures and video lectures

Educational Neuroscience

Author: Kathryn E. Patten
Publisher: John Wiley & Sons
ISBN: 144434580X
Size: 45.21 MB
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Educational Neuroscience provides an overview of the wide range of recent initiatives in educational neuroscience, examining a variety of methodological concerns, issues, and directions. Encourages interdisciplinary perspectives in educational neuroscience Contributions from leading researchers examine key issues relating to educational neuroscience and mind, brain, and education more generally Promotes a theoretical and empirical base for the subject area Explores a range of methods available to researchers Identifies agencies, organizations, and associations facilitating development in the field Reveals a variety of on-going efforts to establish theories, models, methods, ethics, and a common language

Grundlagen Zur Neuroinformatik Und Neurobiologie

Author: Patricia S. Churchland
Publisher: Springer-Verlag
ISBN: 3322868214
Size: 23.57 MB
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The Computational Brain, das außergewöhnliche Buch über vergleichende Forschung in den Bereichen von menschlichem Gehirn und neuesten Möglichkeiten der Computertechnologie, liegt hiermit erstmals in deutscher Sprache vor. Geschrieben von einem führenden Forscherteam in den USA, ist es eine Fundgrube für alle, die wissen wollen, was der Stand der Wissenschaft auf diesem Gebiet ist. Die Autoren führen die Bereiche der Neuroinformatik und Neurobiologie mit gut ausgesuchten Beispielen und der gebotenen Hintergrundinformation gekonnt zusammen. Das Buch wird somit nicht nur dem Fachwissenschaftler sondern auch dem interdisziplinären Interesse des Informatikers und des Biologen auf eine hervorragende Weise gerecht. Übersetzt wurde das Buch von Prof. Dr. Steffen Hölldobler und Dipl.-Biol. Claudia Hölldobler, einem Informatiker und einer Biologin. Rezension in Spektrum der Wissenschaft nr. 10, S. 122 f. im Oktober 1997 (...) Die 1992 erschienene amerikanische Originalausgabe des vorliegenden Werkes ist so erfolgreich, daß man bereits von einem Klassiker reden kann. (...) (...) das Buch sehr zu empfehlen. In Verbindung von Neurobiologie und Neuroinformatik konkurrenzlos, vermittelt es einiges von der Faszination theoretischer Hirnforschung, die auch in Deutschland zunehmend mehr Wissenschaftler in ihren Bann schlägt. Rezension erschienen in: Computer Spektrum 3/1997, S. 2 (...)Das Buch wird somit nicht nur dem Fachwissenschaftler, sondern auch den interdisziplinären Interesse des Informatikers und des Biologen auf eine hervorragende Weise gerecht(...)