Correlated Random Systems: Five Different Methods


Book Description

This volume presents five different methods recently developed to tackle the large scale behavior of highly correlated random systems, such as spin glasses, random polymers, local times and loop soups and random matrices. These methods, presented in a series of lectures delivered within the Jean-Morlet initiative (Spring 2013), play a fundamental role in the current development of probability theory and statistical mechanics. The lectures were: Random Polymers by E. Bolthausen, Spontaneous Replica Symmetry Breaking and Interpolation Methods by F. Guerra, Derrida's Random Energy Models by N. Kistler, Isomorphism Theorems by J. Rosen and Spectral Properties of Wigner Matrices by B. Schlein. This book is the first in a co-edition between the Jean-Morlet Chair at CIRM and the Springer Lecture Notes in Mathematics which aims to collect together courses and lectures on cutting-edge subjects given during the term of the Jean-Morlet Chair, as well as new material produced in its wake. It is targeted at researchers, in particular PhD students and postdocs, working in probability theory and statistical physics.




Advances in Disordered Systems, Random Processes and Some Applications


Book Description

This book offers a unified perspective on the study of complex systems with contributions written by leading scientists from various disciplines, including mathematics, physics, computer science, biology, economics and social science. It is written for researchers from a broad range of scientific fields with an interest in recent developments in complex systems.




Statistical Mechanics of Classical and Disordered Systems


Book Description

These proceedings of the conference Advances in Statistical Mechanics, held in Marseille, France, August 2018, focus on fundamental issues of equilibrium and non-equilibrium dynamics for classical mechanical systems, as well as on open problems in statistical mechanics related to probability, mathematical physics, computer science, and biology. Statistical mechanics, as envisioned more than a century ago by Boltzmann, Maxwell and Gibbs, has recently undergone stunning twists and developments which have turned this old discipline into one of the most active areas of truly interdisciplinary and cutting-edge research. The contributions to this volume, with their rather unique blend of rigorous mathematics and applications, outline the state-of-the-art of this success story in key subject areas of equilibrium and non-equilibrium classical and quantum statistical mechanics of both disordered and non-disordered systems. Aimed at researchers in the broad field of applied modern probability theory, this book, and in particular the review articles, will also be of interest to graduate students looking for a gentle introduction to active topics of current research.




Random Walks, Random Fields, and Disordered Systems


Book Description

Focusing on the mathematics that lies at the intersection of probability theory, statistical physics, combinatorics and computer science, this volume collects together lecture notes on recent developments in the area. The common ground of these subjects is perhaps best described by the three terms in the title: Random Walks, Random Fields and Disordered Systems. The specific topics covered include a study of Branching Brownian Motion from the perspective of disordered (spin-glass) systems, a detailed analysis of weakly self-avoiding random walks in four spatial dimensions via methods of field theory and the renormalization group, a study of phase transitions in disordered discrete structures using a rigorous version of the cavity method, a survey of recent work on interacting polymers in the ballisticity regime and, finally, a treatise on two-dimensional loop-soup models and their connection to conformally invariant systems and the Gaussian Free Field. The notes are aimed at early graduate students with a modest background in probability and mathematical physics, although they could also be enjoyed by seasoned researchers interested in learning about recent advances in the above fields.




Sojourns in Probability Theory and Statistical Physics - I


Book Description

Charles M. (Chuck) Newman has been a leader in Probability Theory and Statistical Physics for nearly half a century. This three-volume set is a celebration of the far-reaching scientific impact of his work. It consists of articles by Chuck’s collaborators and colleagues across a number of the fields to which he has made contributions of fundamental significance. This publication was conceived during a conference in 2016 at NYU Shanghai that coincided with Chuck's 70th birthday. The sub-titles of the three volumes are: I. Spin Glasses and Statistical Mechanics II. Brownian Web and Percolation III. Interacting Particle Systems and Random Walks The articles in these volumes, which cover a wide spectrum of topics, will be especially useful for graduate students and researchers who seek initiation and inspiration in Probability Theory and Statistical Physics.




Viral Fitness and Evolution


Book Description

This book unifies general concepts of plant and animal virus evolution and covers a broad range of topics related to theoretical and experimental aspects of virus population dynamics and viral fitness. Timely topics such as viral mechanisms to cope with antiviral agents, the adaptability of the virus to new hosts, emergence of new viral phenotypes, and the connections between short- and long-term virus evolution are included. By comparing plant and animal viruses, universal mechanisms responsible for fitness variations, viral emergence and disease mechanisms are explored. Although emphasis is put on specific plant and human viral pathogens, relevant similarities and differences to other viruses are highlighted. Additionally, readers will learn more about the adaptability of coronaviruses, including the recently emerged SARS-CoV-2, the causative agent of the COVID-19 pandemic. The book is aimed at students and scientists interested in basic and applied aspects of plant and animal virus population dynamics and evolution.




Artificial Neural Networks - ICANN 2008


Book Description

This two volume set LNCS 5163 and LNCS 5164 constitutes the refereed proceedings of the 18th International Conference on Artificial Neural Networks, ICANN 2008, held in Prague Czech Republic, in September 2008. The 200 revised full papers presented were carefully reviewed and selected from more than 300 submissions. The first volume contains papers on mathematical theory of neurocomputing, learning algorithms, kernel methods, statistical learning and ensemble techniques, support vector machines, reinforcement learning, evolutionary computing, hybrid systems, self-organization, control and robotics, signal and time series processing and image processing.




Diffusion in Crystalline Solids


Book Description

Diffusion in Crystalline Solids addresses some of the most active areas of research on diffusion in crystalline solids. Topics covered include measurement of tracer diffusion coefficients in solids, diffusion in silicon and germanium, atom transport in oxides of the fluorite structure, tracer diffusion in concentrated alloys, diffusion in dislocations, grain boundary diffusion mechanisms in metals, and the use of the Monte Carlo Method to simulate diffusion kinetics. This book is made up of eight chapters and begins with an introduction to the measurement of diffusion coefficients with radioisotopes. The following three chapters consider diffusion in materials of substantial technological importance such as silicon and germanium. Atomic transport in oxides of the fluorite structure is described, and diffusion in concentrated alloys, including intermetallic compounds, is analyzed. The next two chapters delve into diffusion along short-circuiting paths, focusing on the effect of diffusion down dislocations on the form of the tracer concentration profile. The book also discusses the mechanisms of diffusion in grain boundaries in metals by invoking considerable work done on grain-boundary structure. The last two chapters are concerned with computer simulation, paying particular attention to machine calculations and the Monte Carlo method. The book concludes by exploring the fundamental atomic migration process and presenting some state-of-the-art calculations for defect energies and the topology of the saddle surface. Students and researchers of material science will find this book extremely useful.




Biomechanical Systems Technology (A 4-volume Set): (1) Computational Methods


Book Description

Because of rapid developments in computer technology and computational techniques, advances in a wide spectrum of technologies, coupled with cross-disciplinary pursuits between technology and its application to human body processes, the field of biomechanics continues to evolve. Many areas of significant progress include dynamics of musculoskeletal systems, mechanics of hard and soft tissues, mechanics of bone remodeling, mechanics of blood and air flow, flow-prosthesis interfaces, mechanics of impact, dynamics of man-machine interaction, and more. Thus, the great breadth and significance of the field in the international scene require a well integrated set of volumes to provide a complete coverage of the exciting subject of biomechanical systems technology. World-renowned contributors tackle the latest technologies in an in-depth and readable manner.




Dramatic Effect of Cross-Correlations in Random Vibrations of Discrete Systems, Beams, Plates, and Shells


Book Description

This volume explains the dramatic effect of cross-correlations in forming the structural response of aircraft in turbulent excitation, ships in rough seas, cars on irregular roads, and other dynamic regimes. It brings into sharp focus the dramatic effect of cross correlations often neglected due to the analytical difficulty of their evaluation. Veteran author Professor Isaac Elishakoff illustrates how neglect of cross correlations could result in underestimation of the response by tens or hundreds of percentages the effect of the random vibrations of structures’ main elements, including beams, plates, and shells.