Mean Field Theories And Dual Variation A Mathematical Profile Emerged In The Nonlinear Hierarchy Atlantis Studies In Mathematics For Engineering And Science

Mean Field Theories And Dual Variation A Mathematical Profile Emerged In The Nonlinear Hierarchy Atlantis Studies In Mathematics For Engineering And Science Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Mean Field Theories And Dual Variation A Mathematical Profile Emerged In The Nonlinear Hierarchy Atlantis Studies In Mathematics For Engineering And Science book. This book definitely worth reading, it is an incredibly well-written.

MEAN FIELD THEORIES AND DUAL VARIATION

Takashi Suzuki
MEAN FIELD THEORIES AND DUAL VARIATION Book PDF

Author : Takashi Suzuki
Publisher : Springer Science & Business Media
Page : 299 pages
File Size : 52,6 Mb
Release : 2009-01-01
Category : Mathematics
ISBN : 9789491216220

Get Book

MEAN FIELD THEORIES AND DUAL VARIATION by Takashi Suzuki Pdf

A mathematical theory is introduced in this book to unify a large class of nonlinear partial differential equation (PDE) models for better understanding and analysis of the physical and biological phenomena they represent. The so-called mean field approximation approach is adopted to describe the macroscopic phenomena from certain microscopic principles for this unified mathematical formulation. Two key ingredients for this approach are the notions of “duality” according to the PDE weak solutions and “hierarchy” for revealing the details of the otherwise hidden secrets, such as physical mystery hidden between particle density and field concentration, quantized blow up biological mechanism sealed in chemotaxis systems, as well as multi-scale mathematical explanations of the Smoluchowski–Poisson model in non-equilibrium thermodynamics, two-dimensional turbulence theory, self-dual gauge theory, and so forth. This book shows how and why many different nonlinear problems are inter-connected in terms of the properties of duality and scaling, and the way to analyze them mathematically.

Mean Field Theories and Dual Variation ; a Mathematical Profile Emerged in the Nonlinear Hierarchy. Atlantis Studies in Mathematics for Engineering and Science

T. Suzuki
Mean Field Theories and Dual Variation a Mathematical Profile Emerged in the Nonlinear Hierarchy Atlantis Studies in Mathematics for Engineering and Science Book PDF

Author : T. Suzuki
Publisher : Unknown
Page : 128 pages
File Size : 53,9 Mb
Release : 2008
Category : Electronic
ISBN : OCLC:671748783

Get Book

Mean Field Theories and Dual Variation ; a Mathematical Profile Emerged in the Nonlinear Hierarchy. Atlantis Studies in Mathematics for Engineering and Science by T. Suzuki Pdf

A mathematical theory is introduced in this book to unify a large class of nonlinear partial differential equation (PDE) models for better understanding and analysis of the physical and biological phenomena they represent. The so-called mean field approximation approach is adopted to describe the macroscopic phenomena from certain microscopic principles for this unified mathematical formulation. Two key ingredients for this approach are the notions of “duality†according to the PDE weak solutions and “hierarchy†for revealing the details of the otherwise hidden secrets, such as physical mystery hidden between particle density and field concentration, quantized blow up biological mechanism sealed in chemotaxis systems, as well as multi-scale mathematical explanations of the Smoluchowskiâ€"Poisson model in non-equilibrium thermodynamics, two-dimensional turbulence theory, self-dual gauge theory, and so forth. This book shows how and why many different nonlinear problems are inter-connected in terms of the properties of duality and scaling, and the way to analyze them mathematically.

Advanced Mean Field Methods

Manfred Opper,David Saad
Advanced Mean Field Methods Book PDF

Author : Manfred Opper,David Saad
Publisher : MIT Press
Page : 300 pages
File Size : 41,7 Mb
Release : 2001
Category : Computers
ISBN : 0262150549

Get Book

Advanced Mean Field Methods by Manfred Opper,David Saad Pdf

This book covers the theoretical foundations of advanced mean field methods, explores the relation between the different approaches, examines the quality of the approximation obtained, and demonstrates their application to various areas of probabilistic modeling. A major problem in modern probabilistic modeling is the huge computational complexity involved in typical calculations with multivariate probability distributions when the number of random variables is large. Because exact computations are infeasible in such cases and Monte Carlo sampling techniques may reach their limits, there is a need for methods that allow for efficient approximate computations. One of the simplest approximations is based on the mean field method, which has a long history in statistical physics. The method is widely used, particularly in the growing field of graphical models. Researchers from disciplines such as statistical physics, computer science, and mathematical statistics are studying ways to improve this and related methods and are exploring novel application areas. Leading approaches include the variational approach, which goes beyond factorizable distributions to achieve systematic improvements; the TAP (Thouless-Anderson-Palmer) approach, which incorporates correlations by including effective reaction terms in the mean field theory; and the more general methods of graphical models. Bringing together ideas and techniques from these diverse disciplines, this book covers the theoretical foundations of advanced mean field methods, explores the relation between the different approaches, examines the quality of the approximation obtained, and demonstrates their application to various areas of probabilistic modeling.

Solitons in Field Theory and Nonlinear Analysis

Yisong Yang
Solitons in Field Theory and Nonlinear Analysis Book PDF

Author : Yisong Yang
Publisher : Springer
Page : 0 pages
File Size : 54,8 Mb
Release : 2011-08-18
Category : Mathematics
ISBN : 1441929193

Get Book

Solitons in Field Theory and Nonlinear Analysis by Yisong Yang Pdf

There are two approaches in the study of differential equations of field theory. The first, finding closed-form solutions, works only for a narrow category of problems. Written by a well-known active researcher, this book focuses on the second, which is to investigate solutions using tools from modern nonlinear analysis.

Topological Nonlinear Analysis II

Michele Matzeu,Alfonso Vignoli
Topological Nonlinear Analysis II Book PDF

Author : Michele Matzeu,Alfonso Vignoli
Publisher : Birkhäuser
Page : 605 pages
File Size : 48,6 Mb
Release : 2011-10-29
Category : Mathematics
ISBN : 1461241278

Get Book

Topological Nonlinear Analysis II by Michele Matzeu,Alfonso Vignoli Pdf

The main purpose of the present volume is to give a survey of some of the most significant achievements obtained by topological methods in nonlin ear analysis during the last three decades. It is intended, at least partly, as a continuation of Topological Nonlinear Analysis: Degree, Singularity and Varia tions, published in 1995. The survey articles presented are concerned with three main streams of research, that is topological degree, singularity theory and variational methods, They reflect the personal taste of the authors, all of them well known and distinguished specialists. A common feature of these articles is to start with a historical introduction and conclude with recent results, giving a dynamic picture of the state of the art on these topics. Let us mention the fact that most of the materials in this book were pre sented by the authors at the "Second Topological Analysis Workshop on Degree, Singularity and Variations: Developments of the Last 25 Years," held in June 1995 at Villa Tuscolana, Frascati, near Rome. Michele Matzeu Alfonso Vignoli Editors Topological Nonlinear Analysis II Degree, Singularity and Variations Classical Solutions for a Perturbed N-Body System Gianfausto Dell 'A ntonio O. Introduction In this review I shall consider the perturbed N-body system, i.e., a system composed of N point bodies of masses ml, ... mN, described in cartesian co ordinates by the system of equations (0.1) where f) V'k,m == -£l--' m = 1, 2, 3.

Emerging Technologies in Distance Education

George Veletsianos
Emerging Technologies in Distance Education Book PDF

Author : George Veletsianos
Publisher : Athabasca University Press
Page : 351 pages
File Size : 42,5 Mb
Release : 2010
Category : Education
ISBN : 9781897425763

Get Book

Emerging Technologies in Distance Education by George Veletsianos Pdf

Highlighted are the pedagogical, organizational, cultural, social, and economic factors that influence the adoption and integration of emerging technologies in distance education. Advice is offered on how educators can launch effective and engaging distance education initiatives, in response to technological advancements, changing mindsets, and economic and organizational pressures.

Handbook of Mathematical Methods in Imaging

Otmar Scherzer
Handbook of Mathematical Methods in Imaging Book PDF

Author : Otmar Scherzer
Publisher : Springer Science & Business Media
Page : 1626 pages
File Size : 50,7 Mb
Release : 2010-11-23
Category : Mathematics
ISBN : 9780387929194

Get Book

Handbook of Mathematical Methods in Imaging by Otmar Scherzer Pdf

The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.

New Atlantis Revisited

Paul R. Josephson
New Atlantis Revisited Book PDF

Author : Paul R. Josephson
Publisher : Unknown
Page : 351 pages
File Size : 42,8 Mb
Release : 1997
Category : Science
ISBN : 0691044546

Get Book

New Atlantis Revisited by Paul R. Josephson Pdf

In 1958 construction began on Akademgorodok, a scientific utopian community modeled after Francis Bacon's vision of a "New Atlantis." The city, carved out of a Siberian forest 2,500 miles east of Moscow, was formed by Soviet scientists with Khrushchev's full support. They believed that their rational science, liberated from ideological and economic constraints, would help their country surpass the West in all fields. In a lively history of this city, a symbol of de-Stalinization, Paul Josephson offers the most complete analysis available of the reasons behind the successes and failures of Soviet science--from advances in nuclear physics to politically induced setbacks in research on recombinant DNA. Josephson presents case studies of high energy physics, genetics, computer science, environmentalism, and social sciences. He reveals that persistent ideological interference by the Communist Party, financial uncertainties, and pressures to do big science endemic in the USSR contributed to the failure of Akademgorodok to live up to its promise. Still, a kind of openness reigned that presaged the glasnost of Gorbachev's administration decades later. The openness was rooted in the geographical and psychological distance from Moscow and in the informal culture of exchange intended to foster the creative impulse. Akademgorodok is still an important research center, having exposed physics, biology, sociology, economics, and computer science to new investigations, distinct in pace and scope from those performed elsewhere in the Soviet scientific establishment.

Integral Biomathics

Plamen L. Simeonov,Leslie S. Smith,Andrée C. Ehresmann
Integral Biomathics Book PDF

Author : Plamen L. Simeonov,Leslie S. Smith,Andrée C. Ehresmann
Publisher : Springer Science & Business Media
Page : 424 pages
File Size : 54,6 Mb
Release : 2012-07-13
Category : Technology & Engineering
ISBN : 9783642281112

Get Book

Integral Biomathics by Plamen L. Simeonov,Leslie S. Smith,Andrée C. Ehresmann Pdf

Perhaps the most distinct question in science throughout the ages has been the one of perceivable reality, treated both in physics and philosophy. Reality is acting upon us, and we, and life in general, are acting upon reality. Potentiality, found both in quantum reality and in the activity of life, plays a key role. In quantum reality observation turns potentiality into reality. Again, life computes possibilities in various ways based on past actions, and acts on the basis of these computations. This book is about a new approach to biology (and physics, of course!). Its subtitle suggests a perpetual movement and interplay between two elusive aspects of modern science — reality/matter and potentiality/mind, between physics and biology — both captured and triggered by mathematics — to understand and explain emergence, development and life all the way up to consciousness. But what is the real/potential difference between living and non-living matter? How does time in potentiality differ from time in reality? What we need to understand these differences is an integrative approach. This book contemplates how to encircle life to obtain a formal system, equivalent to the ones in physics. Integral Biomathics attempts to explore the interplay between reality and potentiality.

From Newspeak to Cyberspeak

Slava Gerovitch
From Newspeak to Cyberspeak Book PDF

Author : Slava Gerovitch
Publisher : MIT Press
Page : 386 pages
File Size : 53,8 Mb
Release : 2004-09-17
Category : History
ISBN : 0262572257

Get Book

From Newspeak to Cyberspeak by Slava Gerovitch Pdf

In this book, Slava Gerovitch argues that Soviet cybernetics was not just an intellectual trend but a social movement for radical reform in science and society as a whole. Followers of cybernetics viewed computer simulation as a universal method of problem solving and the language of cybernetics as a language of objectivity and truth. With this new objectivity, they challenged the existing order of things in economics and politics as well as in science. The history of Soviet cybernetics followed a curious arc. In the 1950s it was labeled a reactionary pseudoscience and a weapon of imperialist ideology. With the arrival of Khrushchev's political "thaw," however, it was seen as an innocent victim of political oppression, and it evolved into a movement for radical reform of the Stalinist system of science. In the early 1960s it was hailed as "science in the service of communism," but by the end of the decade it had turned into a shallow fashionable trend. Using extensive new archival materials, Gerovitch argues that these fluctuating attitudes reflected profound changes in scientific language and research methodology across disciplines, in power relations within the scientific community, and in the political role of scientists and engineers in Soviet society. His detailed analysis of scientific discourse shows how the Newspeak of the late Stalinist period and the Cyberspeak that challenged it eventually blended into "CyberNewspeak."

THEORY OF CAUSAL DIFFERENTIAL EQUATIONS

S. Leela,V. Lakshmikantham
THEORY OF CAUSAL DIFFERENTIAL EQUATIONS Book PDF

Author : S. Leela,V. Lakshmikantham
Publisher : Springer Science & Business Media
Page : 208 pages
File Size : 54,9 Mb
Release : 2010-01-01
Category : Mathematics
ISBN : 9789491216251

Get Book

THEORY OF CAUSAL DIFFERENTIAL EQUATIONS by S. Leela,V. Lakshmikantham Pdf

The problems of modern society are both complex and inter-disciplinary. Despite the - parent diversity of problems, however, often tools developed in one context are adaptable to an entirely different situation. For example, consider the well known Lyapunov’s second method. This interesting and fruitful technique has gained increasing signi?cance and has given decisive impetus for modern development of stability theory of discrete and dynamic system. It is now recognized that the concept of Lyapunov function and theory of diff- ential inequalities can be utilized to investigate qualitative and quantitative properties of a variety of nonlinear problems. Lyapunov function serves as a vehicle to transform a given complicated system into a simpler comparison system. Therefore, it is enough to study the properties of the simpler system to analyze the properties of the complicated system via an appropriate Lyapunov function and the comparison principle. It is in this perspective, the present monograph is dedicated to the investigation of the theory of causal differential equations or differential equations with causal operators, which are nonanticipative or abstract Volterra operators. As we shall see in the ?rst chapter, causal differential equations include a variety of dynamic systems and consequently, the theory developed for CDEs (Causal Differential Equations) in general, covers the theory of several dynamic systems in a single framework.

THE HYBRID GRAND UNIFIED THEORY

E. Escultura,V. Lakshmikantham
THE HYBRID GRAND UNIFIED THEORY Book PDF

Author : E. Escultura,V. Lakshmikantham
Publisher : Springer Science & Business Media
Page : 132 pages
File Size : 47,9 Mb
Release : 2009-03-01
Category : Science
ISBN : 9789491216237

Get Book

THE HYBRID GRAND UNIFIED THEORY by E. Escultura,V. Lakshmikantham Pdf

In this book, an attempt is made to provide a hybrid grand unified theory to understand the universe, both in its micro/quantum aspects as well as macro/galactic aspects. The book describes a truly hybrid theory as it encompasses both the modern and ancient theories of the universe, together with its functioning at all levels of human comprehension. One of its authors, Dr Escultura, was nominated in 2005 for a Nobel Prize for his flux theory of gravitation. From then on this theory has been improved, clarified and is now known as the hybrid grand unified theory. This book deals with this new bold theory, unifying mathematics and physics, and answering some open fundamental questions and paradoxes in these disciplines. The book also describes what the ancient scientists knew about these matters.

Chaos and Order

N. Katherine Hayles
Chaos and Order Book PDF

Author : N. Katherine Hayles
Publisher : University of Chicago Press
Page : 317 pages
File Size : 40,6 Mb
Release : 2014-12-10
Category : Literary Criticism
ISBN : 9780226230047

Get Book

Chaos and Order by N. Katherine Hayles Pdf

The scientific discovery that chaotic systems embody deep structures of order is one of such wide-ranging implications that it has attracted attention across a spectrum of disciplines, including the humanities. In this volume, fourteen theorists explore the significance for literary and cultural studies of the new paradigm of chaotics, forging connections between contemporary literature and the science of chaos. They examine how changing ideas of order and disorder enable new readings of scientific and literary texts, from Newton's Principia to Ruskin's autobiography, from Victorian serial fiction to Borges's short stories. N. Katherine Hayles traces shifts in meaning that chaos has undergone within the Western tradition, suggesting that the science of chaos articulates categories that cannot be assimilated into the traditional dichotomy of order and disorder. She and her contributors take the relation between order and disorder as a theme and develop its implications for understanding texts, metaphors, metafiction, audience response, and the process of interpretation itself. Their innovative and diverse work opens the interdisciplinary field of chaotics to literary inquiry.

Natural Climate Variability on Decade-to-Century Time Scales

National Research Council,Division on Earth and Life Studies,Commission on Geosciences, Environment and Resources,Climate Research Committee
Natural Climate Variability on Decade to Century Time Scales Book PDF

Author : National Research Council,Division on Earth and Life Studies,Commission on Geosciences, Environment and Resources,Climate Research Committee
Publisher : National Academies Press
Page : 645 pages
File Size : 50,9 Mb
Release : 1996-08-30
Category : Science
ISBN : 9780309054492

Get Book

Natural Climate Variability on Decade-to-Century Time Scales by National Research Council,Division on Earth and Life Studies,Commission on Geosciences, Environment and Resources,Climate Research Committee Pdf

This volume reflects the current state of scientific knowledge about natural climate variability on decade-to-century time scales. It covers a wide range of relevant subjects, including the characteristics of the atmosphere and ocean environments as well as the methods used to describe and analyze them, such as proxy data and numerical models. They clearly demonstrate the range, persistence, and magnitude of climate variability as represented by many different indicators. Not only do natural climate variations have important socioeconomic effects, but they must be better understood before possible anthropogenic effects (from greenhouse gas emissions, for instance) can be evaluated. A topical essay introduces each of the disciplines represented, providing the nonscientist with a perspective on the field and linking the papers to the larger issues in climate research. In its conclusions section, the book evaluates progress in the different areas and makes recommendations for the direction and conduct of future climate research. This book, while consisting of technical papers, is also accessible to the interested layperson.

Proceedings of the Twelfth International Conference on Management Science and Engineering Management

Jiuping Xu,Fang Lee Cooke,Mitsuo Gen,Syed Ejaz Ahmed
Proceedings of the Twelfth International Conference on Management Science and Engineering Management Book PDF

Author : Jiuping Xu,Fang Lee Cooke,Mitsuo Gen,Syed Ejaz Ahmed
Publisher : Springer
Page : 1795 pages
File Size : 41,7 Mb
Release : 2018-06-25
Category : Technology & Engineering
ISBN : 9783319933511

Get Book

Proceedings of the Twelfth International Conference on Management Science and Engineering Management by Jiuping Xu,Fang Lee Cooke,Mitsuo Gen,Syed Ejaz Ahmed Pdf

This proceedings book is divided in 2 Volumes and 8 Parts. Part I is dedicated to Decision Support System, which is about the information system that supports business or organizational decision-making activities; Part II is on Computing Methodology, which is always used to provide the most effective algorithm for numerical solutions of various modeling problems; Part III presents Information Technology, which is the application of computers to store, study, retrieve, transmit and manipulate data, or information in the context of a business or other enterprise; Part IV is dedicated to Data Analysis, which is a process of inspecting, cleansing, transforming, and modeling data with the goal of discovering useful information, suggesting conclusions, and supporting decision-making; Part V presents papers on Operational Management, which is about the plan, organization, implementation and control of the operation process; Part VI is on Project Management, which is about the initiating, planning, executing, controlling, and closing the work of a team to achieve specific goals and meet specific success criteria at the specified time in the field of engineering; Part VII presents Green Supply Chain, which is about the management of the flow of goods and services based on the concept of “low-carbon”; Part VIII is focused on Industry Strategy Management, which refers to the decision-making and management art of an industry or organization in a long-term and long-term development direction, objectives, tasks and policies, as well as resource allocation.