Weakly Connected Neural Networks

Devoted to local and global analysis of weakly connected systems with applications to neurosciences, this book uses bifurcation theory and canonical models as the major tools of analysis.

Author: Frank C. Hoppensteadt

Publisher: Springer Science & Business Media

ISBN: 9781461218289

Category: Mathematics

Page: 402

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Devoted to local and global analysis of weakly connected systems with applications to neurosciences, this book uses bifurcation theory and canonical models as the major tools of analysis. It presents a systematic and well motivated development of both weakly connected system theory and mathematical neuroscience, addressing bifurcations in neuron and brain dynamics, synaptic organisations of the brain, and the nature of neural codes. The authors present classical results together with the most recent developments in the field, making this a useful reference for researchers and graduate students in various branches of mathematical neuroscience.
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Ground State Coding in Partially Connected Neural Networks

The codes associated with lattice-structured and hierarchical networks are discussed in some detail. Baram, Yoram Ames Research Center NASA-TM-102239, A-89256, NAS 1.15:102239 RTOP 505-67-21.

Author: National Aeronautics and Space Adm Nasa

Publisher: Independently Published

ISBN: 1792747322

Category:

Page: 38

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Patterns over (-1,0,1) define, by their outer products, partially connected neural networks, consisting of internally strongly connected, externally weakly connected subnetworks. The connectivity patterns may have highly organized structures, such as lattices and fractal trees or nests. Subpatterns over (-1,1) define the subcodes stored in the subnetwork, that agree in their common bits. It is first shown that the code words are locally stable stares of the network, provided that each of the subcodes consists of mutually orthogonal words or of, at most, two words. Then it is shown that if each of the subcodes consists of two orthogonal words, the code words are the unique ground states (absolute minima) of the Hamiltonian associated with the network. The regions of attraction associated with the code words are shown to grow with the number of subnetworks sharing each of the neurons. Depending on the particular network architecture, the code sizes of partially connected networks can be vastly greater than those of fully connected ones and their error correction capabilities can be significantly greater than those of the disconnected subnetworks. The codes associated with lattice-structured and hierarchical networks are discussed in some detail. Baram, Yoram Ames Research Center NASA-TM-102239, A-89256, NAS 1.15:102239 RTOP 505-67-21...
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Weakly Connected Nonlinear Systems

Izhikevich E.M., Hoppensteadt F.C. [1] Weakly connected neural networks. New York: Springer, 1997. Kamenkov G.V. [1] Stability of motion. Oscillations.

Author: Anatoly Martynyuk

Publisher: CRC Press

ISBN: 9781466570870

Category: Mathematics

Page: 228

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Weakly Connected Nonlinear Systems: Boundedness and Stability of Motion provides a systematic study on the boundedness and stability of weakly connected nonlinear systems, covering theory and applications previously unavailable in book form. It contains many essential results needed for carrying out research on nonlinear systems of weakly connected
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The Handbook of Brain Theory and Neural Networks

Weakly Connected Neural Networks The assumption of weak neuronal connections is based on the observation that the typical size of a postsynaptic potential ...

Author: Michael A. Arbib

Publisher: MIT Press

ISBN: 9780262011976

Category: Computers

Page: 1290

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This second edition presents the enormous progress made in recent years in the many subfields related to the two great questions : how does the brain work? and, How can we build intelligent machines? This second edition greatly increases the coverage of models of fundamental neurobiology, cognitive neuroscience, and neural network approaches to language. (Midwest).
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Advances in Information Processing and Protection

AfrB ) the network afferent subset connected by arcs with node B . Similarly ... Morphological invariant of weakly-connected neural network may be expressed ...

Author: Jerzy Pejas

Publisher: Springer Science & Business Media

ISBN: 9780387731377

Category: Computers

Page: 460

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This book contains a selection of the best papers given at an international conference on advanced computer systems. The Advanced Computer Systems Conference was held in October 2006, in Miedzyzdroje, Poland. The book is organized into four topical areas: Artificial Intelligence; Computer Security and Safety; Image Analysis, Graphics and Biometrics; and Computer Simulation and Data Analysis.
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Advances in Neural Networks ISNN 2005

Second International Symposium on Neural Networks, Chongqing, China, ... E.M.: Class 1 Neural Excitability, Conventional Synapses, Weakly Connected Networks ...

Author: Jun Wang

Publisher: Springer Science & Business Media

ISBN: 9783540259121

Category: Computers

Page: 1055

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This book and its sister volumes constitute the proceedings of the 2nd International Symposium on Neural Networks (ISNN 2005). ISNN 2005 was held in the beautiful mountain city Chongqing by the upper Yangtze River in southwestern China during May 30-June 1, 2005, as a sequel of ISNN 2004 successfully held in Dalian, China. ISNN emerged as a leading conference on neural computation in the region with - creasing global recognition and impact. ISNN 2005 received 1425 submissions from authors on ?ve continents (Asia, Europe, North America, South America, and Oc- nia), 33 countries and regions (Mainland China, Hong Kong, Macao, Taiwan, South Korea, Japan, Singapore, Thailand, India, Nepal, Iran, Qatar, United Arab Emirates, Turkey, Lithuania, Hungary, Poland, Austria, Switzerland, Germany, France, Sweden, Norway, Spain, Portugal, UK, USA, Canada, Venezuela, Brazil, Chile, Australia, and New Zealand). Based on rigorous reviews, 483 high-quality papers were selected by the Program Committee for presentation at ISNN 2005 and publication in the proce- ings, with an acceptance rate of less than 34%. In addition to the numerous contributed papers, 10 distinguished scholars were invited to give plenary speeches and tutorials at ISNN 2005.
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Natural Biodynamics

7.5.6 Weakly Connected and Canonical Neural Nets The assumption of weak neuronal connections is based on the observation that the typical size of a ...

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Publisher:

ISBN: 9789814479110

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Page:

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Replication of Chaos in Neural Networks Economics and Physics

Neurocomputing 101, 370–374 (2013) F.C. Hoppensteadt, E.M. Izhikevich, Weakly Connected Neural Networks (Springer, New York, 1997) F. Pasemann, M. Hild, ...

Author: Marat Akhmet

Publisher: Springer

ISBN: 9783662475003

Category: Science

Page: 457

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This book presents detailed descriptions of chaos for continuous-time systems. It is the first-ever book to consider chaos as an input for differential and hybrid equations. Chaotic sets and chaotic functions are used as inputs for systems with attractors: equilibrium points, cycles and tori. The findings strongly suggest that chaos theory can proceed from the theory of differential equations to a higher level than previously thought. The approach selected is conducive to the in-depth analysis of different types of chaos. The appearance of deterministic chaos in neural networks, economics and mechanical systems is discussed theoretically and supported by simulations. As such, the book offers a valuable resource for mathematicians, physicists, engineers and economists studying nonlinear chaotic dynamics.
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The Relevance of the Time Domain to Neural Network Models

Rev Mod Phys 77:137–185 Hoppensteadt FC, Izhikevich EM (1997) Weakly connected neural networks. Springer, New York Hirose A (ed) (2003) Complex-valued ...

Author: A. Ravishankar Rao

Publisher: Springer Science & Business Media

ISBN: 1461407249

Category: Medical

Page: 226

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A significant amount of effort in neural modeling is directed towards understanding the representation of information in various parts of the brain, such as cortical maps [6], and the paths along which sensory information is processed. Though the time domain is integral an integral aspect of the functioning of biological systems, it has proven very challenging to incorporate the time domain effectively in neural network models. A promising path that is being explored is to study the importance of synchronization in biological systems. Synchronization plays a critical role in the interactions between neurons in the brain, giving rise to perceptual phenomena, and explaining multiple effects such as visual contour integration, and the separation of superposed inputs. The purpose of this book is to provide a unified view of how the time domain can be effectively employed in neural network models. A first direction to consider is to deploy oscillators that model temporal firing patterns of a neuron or a group of neurons. There is a growing body of research on the use of oscillatory neural networks, and their ability to synchronize under the right conditions. Such networks of synchronizing elements have been shown to be effective in image processing and segmentation tasks, and also in solving the binding problem, which is of great significance in the field of neuroscience. The oscillatory neural models can be employed at multiple scales of abstraction, ranging from individual neurons, to groups of neurons using Wilson-Cowan modeling techniques and eventually to the behavior of entire brain regions as revealed in oscillations observed in EEG recordings. A second interesting direction to consider is to understand the effect of different neural network topologies on their ability to create the desired synchronization. A third direction of interest is the extraction of temporal signaling patterns from brain imaging data such as EEG and fMRI. Hence this Special Session is of emerging interest in the brain sciences, as imaging techniques are able to resolve sufficient temporal detail to provide an insight into how the time domain is deployed in cognitive function. The following broad topics will be covered in the book: Synchronization, phase-locking behavior, image processing, image segmentation, temporal pattern analysis, EEG analysis, fMRI analyis, network topology and synchronizability, cortical interactions involving synchronization, and oscillatory neural networks. This book will benefit readers interested in the topics of computational neuroscience, applying neural network models to understand brain function, extracting temporal information from brain imaging data, and emerging techniques for image segmentation using oscillatory networks
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Handbook of Dynamical Systems

G.B. Ermentrout and N. Kopell, Frequency plateaus in a chain of weakly coupled oscillators, ... Weakly Connected Neural Networks, Springer, New York (1997).

Author: B. Fiedler

Publisher: Gulf Professional Publishing

ISBN: 9780080532844

Category: Science

Page: 1098

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This handbook is volume II in a series collecting mathematical state-of-the-art surveys in the field of dynamical systems. Much of this field has developed from interactions with other areas of science, and this volume shows how concepts of dynamical systems further the understanding of mathematical issues that arise in applications. Although modeling issues are addressed, the central theme is the mathematically rigorous investigation of the resulting differential equations and their dynamic behavior. However, the authors and editors have made an effort to ensure readability on a non-technical level for mathematicians from other fields and for other scientists and engineers. The eighteen surveys collected here do not aspire to encyclopedic completeness, but present selected paradigms. The surveys are grouped into those emphasizing finite-dimensional methods, numerics, topological methods, and partial differential equations. Application areas include the dynamics of neural networks, fluid flows, nonlinear optics, and many others. While the survey articles can be read independently, they deeply share recurrent themes from dynamical systems. Attractors, bifurcations, center manifolds, dimension reduction, ergodicity, homoclinicity, hyperbolicity, invariant and inertial manifolds, normal forms, recurrence, shift dynamics, stability, to name just a few, are ubiquitous dynamical concepts throughout the articles.
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Advances in Neural Networks isnn 2006

Hoppensteadt, F.C., Izhikevich, E.M.: Weakly Connected Neural Networks. Springer- Verlag, New York (1997) 11. Gerstner, W., Kistler, W.M.: Spiking Neuron ...

Author:

Publisher: Springer Science & Business Media

ISBN: 9783540344391

Category: Artificial intelligence

Page: 4288

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Neural Networks with Discontinuous Impact Activations

Birkhäuser, Boston Haykin S (2001) Neural networks: A comprehensive foundations, 2nd edn. ... Izhikevich EM (1997) Weakly connected neural networks.

Author: Marat Akhmet

Publisher: Springer Science & Business Media

ISBN: 9781461485667

Category: Technology & Engineering

Page: 168

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This book presents as its main subject new models in mathematical neuroscience. A wide range of neural networks models with discontinuities are discussed, including impulsive differential equations, differential equations with piecewise constant arguments, and models of mixed type. These models involve discontinuities, which are natural because huge velocities and short distances are usually observed in devices modeling the networks. A discussion of the models, appropriate for the proposed applications, is also provided.
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Neural Nets WIRN09

... (1997) Weakly Connected Neural Networks. Springer-Verlag, New York. Izhikevich E.M. (1999) IEEE Transactions On Neural Networks, 10:508-526 [13] Z. Yu, ...

Author: Bruno Apolloni

Publisher: IOS Press

ISBN: 9781607500728

Category: Computers

Page: 342

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This book reports the proceedings of WIRN09, the 19th Italian Workshop of the Italian Society for Neural Networks (SIREN). Neural networks explore thought mechanisms that efficient computational tools and a representative physics of our brain share together and that ultimately produce the loops of our thoughts. The general approach is to see how these loops run and which tracks they leave.
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Advances in Neural Networks Research

Weakly connected neural networks . New York : Springer . Huerta , P. , & Lisman , J. ( 1993 ) . Heightened synaptic plasticity of hippocampal cal neurons ...

Author: M. Hasselmo

Publisher: Elsevier

ISBN: 0080443206

Category: Computers

Page: 434

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IJCNN is the flagship conference of the INNS, as well as the IEEE Neural Networks Society. It has arguably been the preeminent conference in the field, even as neural network conferences have proliferated and specialized. As the number of conferences has grown, its strongest competition has migrated away from an emphasis on neural networks. IJCNN has embraced the proliferation of spin-off and related fields (see the topic list, below), while maintaining a core emphasis befitting its name. It has also succeeded in enforcing an emphasis on quality.
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Artificial Neural Networks and Machine Learning ICANN 2013

Hoppensteadt, F.C., Izhikevich, E.M.: Weakly Connected Neural Networks. Springer, New York (1997) 9. Hodgkin, A.L., Huxley, A.F.: A Quantitative Description ...

Author: Valeri Mladenov

Publisher: Springer

ISBN: 9783642407284

Category: Computers

Page: 643

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The book constitutes the proceedings of the 23rd International Conference on Artificial Neural Networks, ICANN 2013, held in Sofia, Bulgaria, in September 2013. The 78 papers included in the proceedings were carefully reviewed and selected from 128 submissions. The focus of the papers is on following topics: neurofinance graphical network models, brain machine interfaces, evolutionary neural networks, neurodynamics, complex systems, neuroinformatics, neuroengineering, hybrid systems, computational biology, neural hardware, bioinspired embedded systems, and collective intelligence.
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Neuroscience From Neural Networks to Artificial Intelligence

471-492. 6. Zak, M., (1990a), “Weakly Connected Neural Nets”, Appl. Math. Letters, Vol. 3, No. 3. 7. Zak, M., (1990b), “Creative Dynamics Approach to Neural ...

Author: Pablo Rudomin

Publisher: Springer Science & Business Media

ISBN: 9783642781025

Category: Computers

Page: 579

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The Central Nervous System can be considered as an aggregate of neurons specialized in both the transmission and transformation of information. Information can be used for many purposes, but probably the most important one is to generate a representation of the "external" world that allows the organism to react properly to changes in its external environment. These functions range from such basic ones as detection of changes that may lead to tissue damage and eventual destruction of the organism and the implementation of avoidance reactions, to more elaborate representations of the external world implying recognition of shapes, sounds and textures as the basis of planned action or even reflection. Some of these functions confer a clear survival advantage to the organism (prey or mate recognition, escape reactions, etc. ). Others can be considered as an essential part of cognitive processes that contribute, to varying degrees, to the development of individuality and self-consciousness. How can we hope to understand the complexity inherent in this range of functionalities? One of the distinguishing features of the last two decades has been the availability of computational power that has impacted many areas of science. In neurophysiology, computation is used for experiment control, data analysis and for the construction of models that simulate particular systems. Analysis of the behavior of neuronal networks has transcended the limits of neuroscience and is now a discipline in itself, with potential applications both in the neural sciences and in computing sciences.
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Spiking Neuron Models

Weakly Connected Neural Networks . Springer - Verlag , Berlin . Horn , D. and Usher , M. ( 1989 ) . Neural networks with dynamical thresholds . Phys . Rev.

Author: Wulfram Gerstner

Publisher: Cambridge University Press

ISBN: 0521890799

Category: Computers

Page: 480

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This is an introduction to spiking neurons for advanced undergraduate or graduate students. It can be used with courses in computational neuroscience, theoretical biology, neural modeling, biophysics, or neural networks. It focuses on phenomenological approaches rather than detailed models in order to provide the reader with a conceptual framework. No prior knowledge beyond undergraduate mathematics is necessary to follow the book. Thus it should appeal to students or researchers in physics, mathematics, or computer science interested in biology; moreover it will also be useful for biologists working in mathematical modeling.
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Quantum Neural Computation

represent the hyperbolic tangent (sigmoid) neural activation functions. ... in the form of weakly-connected neural networks (see [HI97]), respectively, ...

Author: Vladimir G. Ivancevic

Publisher: Springer Science & Business Media

ISBN: 9048133505

Category: Computers

Page: 929

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Quantum Neural Computation is a graduate–level monographic textbook. It presents a comprehensive introduction, both non-technical and technical, into modern quantum neural computation, the science behind the fiction movie Stealth. Classical computing systems perform classical computations (i.e., Boolean operations, such as AND, OR, NOT gates) using devices that can be described classically (e.g., MOSFETs). On the other hand, quantum computing systems perform classical computations using quantum devices (quantum dots), that is devices that can be described only using quantum mechanics. Any information transfer between such computing systems involves a state measurement. This book describes this information transfer at the edge of classical and quantum chaos and turbulence, where mysterious quantum-mechanical linearity meets even more mysterious brain’s nonlinear complexity, in order to perform a super–high–speed and error–free computations. This monograph describes a crossroad between quantum field theory, brain science and computational intelligence.
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Handbook of Parkinson s Disease

Weakly Connected Neural Networks in Applied Mathematical Sciences Vol. 126, New York: Springer-Verlag, 1997. 67. Hoppensteadt FC, Izhikevich EM.

Author: Rajesh Pahwa

Publisher: CRC Press

ISBN: 9781420019995

Category: Medical

Page: 520

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This blue-ribbon guide has long prevailed as one of the leading resources on Parkinson's Disease (PD). Fully updated with practical and engaging chapters on pathology, neurochemistry, etiology, and breakthrough research, this source spans every essential topic related to the identification, assessment, and treatment of PD. Reflecting the many advan
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Dynamics of Coupled Map Lattices and of Related Spatially Extended Systems

B. Ermentrout , Neural networks as spatio - temporal pattern - forming systems ... F.C. Hoppensteadt , E.M. Izhikevich , Weakly Connected Neural Networks ...

Author: Jean-René Chazottes

Publisher: Springer Science & Business Media

ISBN: 3540242899

Category: Science

Page: 362

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This book is about the dynamics of coupled map lattices (CML) and of related spatially extended systems. It will be useful to post-graduate students and researchers seeking an overview of the state-of-the-art and of open problems in this area of nonlinear dynamics. The special feature of this book is that it describes the (mathematical) theory of CML and some related systems and their phenomenology, with some examples of CML modeling of concrete systems (from physics and biology). More precisely, the book deals with statistical properties of (weakly) coupled chaotic maps, geometric aspects of (chaotic) CML, monotonic spatially extended systems, and dynamical models of specific biological systems.
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