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Maximum-Entropy Networks

Author : Tiziano Squartini

Publisher : Springer

Page : 125 pages

File Size : 16,37 MB

Release : 2017-11-22

Category : Science

ISBN : 3319694383

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Book Description

This book is an introduction to maximum-entropy models of random graphs with given topological properties and their applications. Its original contribution is the reformulation of many seemingly different problems in the study of both real networks and graph theory within the unified framework of maximum entropy. Particular emphasis is put on the detection of structural patterns in real networks, on the reconstruction of the properties of networks from partial information, and on the enumeration and sampling of graphs with given properties. After a first introductory chapter explaining the motivation, focus, aim and message of the book, chapter 2 introduces the formal construction of maximum-entropy ensembles of graphs with local topological constraints. Chapter 3 focuses on the problem of pattern detection in real networks and provides a powerful way to disentangle nontrivial higher-order structural features from those that can be traced back to simpler local constraints. Chapter 4 focuses on the problem of network reconstruction and introduces various advanced techniques to reliably infer the topology of a network from partial local information. Chapter 5 is devoted to the reformulation of certain “hard” combinatorial operations, such as the enumeration and unbiased sampling of graphs with given constraints, within a “softened” maximum-entropy framework. A final chapter offers various overarching remarks and take-home messages.By requiring no prior knowledge of network theory, the book targets a broad audience ranging from PhD students approaching these topics for the first time to senior researchers interested in the application of advanced network techniques to their field.



Maximum Entropy Analysis of Queuing Systems and Networks

Author : D. Kouvatsos

Publisher :

Page : pages

File Size : 30,40 MB

Release : 1993-01

Category :

ISBN : 9780632030118

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Book Description

Examines performance analysis of general queuing network models of computer and communications systems using the principle of maximum entropy, its extensions and the generalized exponential distributions.



Ay's Neuroanatomy of C. Elegans for Computation

Author : Theodore B. Achacoso

Publisher : CRC Press

Page : 298 pages

File Size : 18,29 MB

Release : 1991-11-22

Category : Science

ISBN : 9780849342349

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Book Description

AY's Neuroanatomy of C. elegans for Computation provides the neural circuitry database of the nematode Caenorhabditis elegans, both in printed form and in ASCII files on 5.25-inch diskettes (for use on IBM® and compatible personal computers, Macintosh® computers, and higher level machines). Tables of connections among neuron classes, synapses among individual neurons, gap junctions among neurons, worm cells and their embryonic origin, and synthetically derived neuromuscular connections are presented together with the references from which the data were compiled and edited. Sample data files and source codes of FORTRAN and BASIC programs are provided to illustrate the use of mathematical tools for any researcher or student interested in examining a natural neural network and discovering what makes it tick.



Entropy Measures, Maximum Entropy Principle and Emerging Applications

Author : Karmeshu

Publisher : Springer

Page : 300 pages

File Size : 34,88 MB

Release : 2012-10-01

Category : Technology & Engineering

ISBN : 3540362126

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Book Description

The last two decades have witnessed an enormous growth with regard to ap plications of information theoretic framework in areas of physical, biological, engineering and even social sciences. In particular, growth has been spectac ular in the field of information technology,soft computing,nonlinear systems and molecular biology. Claude Shannon in 1948 laid the foundation of the field of information theory in the context of communication theory. It is in deed remarkable that his framework is as relevant today as was when he 1 proposed it. Shannon died on Feb 24, 2001. Arun Netravali observes "As if assuming that inexpensive, high-speed processing would come to pass, Shan non figured out the upper limits on communication rates. First in telephone channels, then in optical communications, and now in wireless, Shannon has had the utmost value in defining the engineering limits we face". Shannon introduced the concept of entropy. The notable feature of the entropy frame work is that it enables quantification of uncertainty present in a system. In many realistic situations one is confronted only with partial or incomplete information in the form of moment, or bounds on these values etc. ; and it is then required to construct a probabilistic model from this partial information. In such situations, the principle of maximum entropy provides a rational ba sis for constructing a probabilistic model. It is thus necessary and important to keep track of advances in the applications of maximum entropy principle to ever expanding areas of knowledge.



Maximum-Entropy and Bayesian Methods in Science and Engineering

Author : G. Erickson

Publisher : Springer Science & Business Media

Page : 338 pages

File Size : 24,95 MB

Release : 1988-08-31

Category : Mathematics

ISBN : 9789027727930

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Book Description

This volume has its origin in the Fifth, Sixth and Seventh Workshops on and Bayesian Methods in Applied Statistics", held at "Maximum-Entropy the University of Wyoming, August 5-8, 1985, and at Seattle University, August 5-8, 1986, and August 4-7, 1987. It was anticipated that the proceedings of these workshops would be combined, so most of the papers were not collected until after the seventh workshop. Because all of the papers in this volume are on foundations, it is believed that the con tents of this volume will be of lasting interest to the Bayesian community. The workshop was organized to bring together researchers from different fields to critically examine maximum-entropy and Bayesian methods in science and engineering as well as other disciplines. Some of the papers were chosen specifically to kindle interest in new areas that may offer new tools or insight to the reader or to stimulate work on pressing problems that appear to be ideally suited to the maximum-entropy or Bayesian method. A few papers presented at the workshops are not included in these proceedings, but a number of additional papers not presented at the workshop are included. In particular, we are delighted to make available Professor E. T. Jaynes' unpublished Stanford University Microwave Laboratory Report No. 421 "How Does the Brain Do Plausible Reasoning?" (dated August 1957). This is a beautiful, detailed tutorial on the Cox-Polya-Jaynes approach to Bayesian probability theory and the maximum-entropy principle.





Maximum Entropy and Ecology

Author : John Harte

Publisher : OUP Oxford

Page : 282 pages

File Size : 26,8 MB

Release : 2011-06-23

Category : Science

ISBN : 0191621161

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Book Description

This pioneering graduate textbook provides readers with the concepts and practical tools required to understand the maximum entropy principle, and apply it to an understanding of ecological patterns. Rather than building and combining mechanistic models of ecosystems, the approach is grounded in information theory and the logic of inference. Paralleling the derivation of thermodynamics from the maximum entropy principle, the state variable theory of ecology developed in this book predicts realistic forms for all metrics of ecology that describe patterns in the distribution, abundance, and energetics of species over multiple spatial scales, a wide range of habitats, and diverse taxonomic groups. The first part of the book is foundational, discussing the nature of theory, the relationship of ecology to other sciences, and the concept of the logic of inference. Subsequent sections present the fundamentals of macroecology and of maximum information entropy, starting from first principles. The core of the book integrates these fundamental principles, leading to the derivation and testing of the predictions of the maximum entropy theory of ecology (METE). A final section broadens the book's perspective by showing how METE can help clarify several major issues in conservation biology, placing it in context with other theories and highlighting avenues for future research.



Maximum Entropy Discrimination Markov Networks

Author : Jun Zhu

Publisher :

Page : 27 pages

File Size : 50,30 MB

Release : 2008

Category : Entropy (Information theory)

ISBN :

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Book Description

Abstract: "Standard max-margin structured prediction methods concentrate directly on the input-output mapping, and the lack of an elegant probabilistic interpretation causes limitations. In this paper, we present a novel framework called Maximum Entropy Discrimination Markov Networks (MaxEntNet) to do Bayesian max-margin structured learning by using expected margin constraints to define a feasible distribution subspace and applying the maximum entropy principle to choose the best distribution from this subspace. We show that MaxEntNet subsumes the standard max-margin Markov networks (M3N) as a spacial case where the predictive model is assumed to be linear and the parameter prior is a standard normal. Based on this understanding, we propose the Laplace max-margin Markov networks (LapM3N) which use the Laplace prior instead of the standard normal. We show that the adoption of a Laplace prior of the parameter makes LapM3N enjoy properties expected from a sparsified M3N. Unlike the L1-regularized maximum likelihood estimation which sets small weights to zeros to achieve sparsity, LapM3N posteriorly weights the parameters and features with smaller weights are shrunk more. This posterior weighting effect makes LapM3N more stable with respect to the magnitudes of the regularization coefficients and more generalizable. To learn a LapM3N, we present an efficient iterative learning algorithm based on variational approximation and existing convex optimization methods employed in M3N. The feasibility and promise of LapM3N are demonstrated on both synthetic and real OCR data sets.



Maximum Entropy and Ecology

Author : John Harte

Publisher : Oxford University Press

Page : 274 pages

File Size : 24,59 MB

Release : 2011-06-23

Category : Computers

ISBN : 0199593418

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Book Description

Provides readers with the concepts and practical tools required to understand the maximum entropy principle, and apply it to an understanding of ecological patterns. The theory developed predicts realistic forms for all metrics of ecology that describe patterns in the distribution, abundance, and energetics of species.



Maximum Entropy and Bayesian Methods

Author : W.T. Grandy Jr.

Publisher : Springer Science & Business Media

Page : 356 pages

File Size : 48,31 MB

Release : 2012-12-06

Category : Mathematics

ISBN : 940113460X

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Book Description

The 10th International Workshop on Maximum Entropy and Bayesian Methods, MaxEnt 90, was held in Laramie, Wyoming from 30 July to 3 August 1990. This volume contains the scientific presentations given at that meeting. This series of workshops originated in Laramie in 1981, where the first three of what were to become annual workshops were held. The fourth meeting was held in Calgary. the fifth in Laramie, the sixth and seventh in Seattle, the eighth in Cambridge, England, and the ninth at Hanover, New Hampshire. It is most appropriate that the tenth workshop, occurring in the centennial year of Wyoming's statehood, was once again held in Laramie. The original purpose of these workshops was twofold. The first was to bring together workers from diverse fields of scientific research who individually had been using either some form of the maximum entropy method for treating ill-posed problems or the more general Bayesian analysis, but who, because of the narrow focus that intra-disciplinary work tends to impose upon most of us, might be unaware of progress being made by others using these same techniques in other areas. The second was to introduce to those who were somewhat aware of maximum entropy and Bayesian analysis and wanted to learn more, the foundations, the gestalt, and the power of these analyses. To further the first of these ends, presenters at these workshops have included workers from area. s as varied as astronomy, economics, environmenta.