Gaussian processes can be viewed as a far-reaching infinite-dimensional extension of classical normal random variables. Their theory presents a powerful range of tools for probabilistic modelling in various academic and technical domains such as Statistics, Forecasting, Finance, Information Transmission, Machine Learning - to mention just a few. The objective of these Briefs is to present a quick and condensed treatment of the core theory that a reader must understand in order to make his own independent contributions. The primary intended readership are PhD/Masters students and researchers working in pure or applied mathematics. The first chapters introduce essentials of the classical theory of Gaussian processes and measures with the core notions of reproducing kernel, integral representation, isoperimetric property, large deviation principle. The brevity being a priority for teaching and learning purposes, certain technical details and proofs are omitted. The later chapters touch important recent issues not sufficiently reflected in the literature, such as small deviations, expansions, and quantization of processes. In university teaching, one can build a one-semester advanced course upon these Briefs.
This volume first introduces the mathematical tools necessary for understanding and working with a broad class of applied stochastic models. The toolbox includes Gaussian processes, independently scattered measures such as Gaussian white noise and Poisson random measures, stochastic integrals, compound Poisson, infinitely divisible and stable distributions and processes.Next, it illustrates general concepts by handling a transparent but rich example of a “teletraffic model”. A minor tuning of a few parameters of the model leads to different workload regimes, including Wiener process, fractional Brownian motion and stable Lévy process. The simplicity of the dependence mechanism used in the model enables us to get a clear understanding of long and short range dependence phenomena. The model also shows how light or heavy distribution tails lead to continuous Gaussian processes or to processes with jumps in the limiting regime. Finally, in this volume, readers will find discussions on the multivariate extensions that admit a variety of completely different applied interpretations.The reader will quickly become familiar with key concepts that form a language for many major probabilistic models of real world phenomena but are often neglected in more traditional courses of stochastic processes.
It is well known that the normal distribution is the most pleasant, one can even say, an exemplary object in the probability theory. It combines almost all conceivable nice properties that a distribution may ever have: symmetry, stability, indecomposability, a regular tail behavior, etc. Gaussian measures (the distributions of Gaussian random functions), as infinite-dimensional analogues of tht
We consider the Volterra integral operator $T_{\rho,\psi}:L_p(0,\infty)\to L_q(0,\infty)$ for $1\leq p,q\leq \infty$, defined by $(T_{\rho,\psi}f)(s) =\rho(s)\int_0^s \psi(t) f(t) dt$ and investigate its degree of compactness in terms of properties of the kernel functions $\rho$ and $\psi$. In particular, under certain optimal integrability conditions the entropy numbers $e_n(T_{\rho,\psi})$ satisfy $c_1\Vert{\rho\,\psi}\Vert_r\leq \liminf_{n\to\infty} n\, e_n(T_{\rho,\psi}) \leq \limsup_{n\to\infty} n\, e_n(T_{\rho,\psi})\leq c_2\Vert{\rho\,\psi}\Vert_r$ where $1/r = 1- 1/p +1/q >0$. We also obtain similar sharp estimates for the approximation numbers of $T_{\rho,\psi}$, thus extending former results due to Edmunds et al. and Evans et al.. The entropy estimates are applied to investigate the small ball behaviour of weighted Wiener processes $\rho\, W$ in the $L_q(0,\infty)$-norm, $1\leq q\leq \infty$. For example, if $\rho$ satisfies some weak monotonicity conditions at zero and infinity, then $\lim_{\varepsilon\to 0}\,\varepsilon^2\,\log\mathbb{P}(\Vert{\rho\, W}\Vert_q\leq \varepsilon) = -k_q\cdot\Vert{\rho}\Vert_{{2q}/{2+q}}^2$.
This groundbreaking work by one of the world's foremost theoreticians of Russian literature, culture, and thought gives for the first time an extensive and detailed examination of the development of Russian thought during the late Soviet period. Countering the traditional view of an intellectual wilderness under the Soviet regime, Mikhail Epstein offers a systematic account of Russian thought in the second half of the 20th century. In doing so, he provides new insights into previously ignored areas such as Russian liberalism, personalism, structuralism, neo–rationalism, and culturology. Epstein shows how Russian philosophy and culture has long been trapped in an intellectual prison of its own making as it sought to create its own utopia. However, he demonstrates that it is time to reappraise Russian philosophical thought and cultural theory, now freed from the bonds of totalitarianism. We are left with not only a new and exciting interpretation of Russian thought, but also an opportunity to rethink our own intellectual heritage.
This book features the refereed proceedings of the 2nd International Symposium on Computer Science in Russia held in September 2007. The 35 papers cover theory track deals with algorithms, protocols, and data structures; complexity and cryptography; formal languages, automata and their applications to computer science; computational models and concepts; proof theory; and applications of logic to computer science. Many applications are presented.
In Der Nister's Soviet Years, author Mikhail Krutikov focuses on the second half of the dramatic writing career of Soviet Yiddish writer Der Nister, pen name of Pinhas Kahanovich (1884–1950). Krutikov follows Der Nister's painful but ultimately successful literary transformation from his symbolist roots to social realism under severe ideological pressure from Soviet critics and authorities. This volume reveals how profoundly Der Nister was affected by the destruction of Jewish life during WWII and his own personal misfortunes. While Der Nister was writing a history of his generation, he was arrested for anti-government activities and died tragically from a botched surgery in the Gulag. Krutikov illustrates why Der Nister's work is so important to understandings of Soviet literature, the Russian Revolution, and the catastrophic demise of the Jewish community under Stalin.
Space exploration and advanced astronomy have dramatically expanded our knowledge of outer space and made it possible to study the indepth mechanisms underlying various natural phenomena caused by complex interaction of physical-chemical and dynamical processes in the universe. Huge breakthroughs in astrophysics and the planetary s- ences have led to increasingly complicated models of such media as giant molecular clouds giving birth to stars, protoplanetary accretion disks associated with the solar system’s formation, planetary atmospheres and circumplanetary space. The creation of these models was promoted by the development of basic approaches in modern - chanics and physics paralleled by the great advancement in the computer sciences. As a result, numerous multidimensional non-stationary problems involving the analysis of evolutionary processes can be investigated using wide-range numerical experiments. Turbulence belongs to the most widespread and, at the same time, the most complicated natural phenomena, related to the origin and development of organized structures (- dies of different scale) at a definite flow regime of fluids in essentially non-linear - drodynamic systems. This is also one of the most complex and intriguing sections of the mechanics of fluids. The direct numerical modeling of turbulent flows encounters large mathematical difficulties, while the development of a general turbulence theory is hardly possible because of the complexity of interacting coherent structures. Three-dimensional non-steady motions arise in such a system under loss of la- nar flow stability defined by the critical value of the Reynolds number.
This volume first introduces the mathematical tools necessary for understanding and working with a broad class of applied stochastic models. The toolbox includes Gaussian processes, independently scattered measures such as Gaussian white noise and Poisson random measures, stochastic integrals, compound Poisson, infinitely divisible and stable distributions and processes.Next, it illustrates general concepts by handling a transparent but rich example of a “teletraffic model”. A minor tuning of a few parameters of the model leads to different workload regimes, including Wiener process, fractional Brownian motion and stable Lévy process. The simplicity of the dependence mechanism used in the model enables us to get a clear understanding of long and short range dependence phenomena. The model also shows how light or heavy distribution tails lead to continuous Gaussian processes or to processes with jumps in the limiting regime. Finally, in this volume, readers will find discussions on the multivariate extensions that admit a variety of completely different applied interpretations.The reader will quickly become familiar with key concepts that form a language for many major probabilistic models of real world phenomena but are often neglected in more traditional courses of stochastic processes.
From Kabbalah to Class Struggle is an intellectual biography of Meir Wiener (1893–1941), an Austrian Jewish intellectual and a student of Jewish mysticism who emigrated to the Soviet Union in 1926 and reinvented himself as a Marxist scholar and Yiddish writer. His dramatic life story offers a fascinating glimpse into the complexities and controversies of Jewish intellectual and cultural history of pre-war Europe. Wiener made a remarkable career as a Yiddish scholar and writer in the Stalinist Soviet Union and left an unfinished novel about Jewish intellectual bohemia of Weimar Berlin. He was a brilliant intellectual, a controversial thinker, a committed communist, and a great Yiddish scholar—who personally knew Lenin and Rabbi Kook, corresponded with Martin Buber and Hugo von Hofmannsthal, and argued with Gershom Scholem and Georg Lukács. His intellectual biography brings Yiddish to the forefront of the intellectual discourse of interwar Europe.
Each year a large number of first rate articles on the physics and technology of semiconductor devices, written by Soviet experts in the field, are published. However, due to the lack of exchange and personal contact, most of these, unfortunately, are neglected by many scientists from the United States, Japan as well as Western Europe. Consequently, many important developments in semiconductor physics are missed by the Western world.This book is a serious attempt to bridge the gap between the Soviet and Western scientific communities. Most of all, it is an effort towards facilitating the communication and sharing of knowledge amongst people from different parts of the world. Ultimately, the aim is to contribute towards the building of a better world for all ? one where the knowledge of advanced technology and scientific discoveries is used to improve the quality of life and not the pursuit of selfish mutually destructive behavior. For those in the field who wish to partake in this exchange of knowledge and as a gesture of support for their Soviet counterparts, the reading of this book provides the first step.
Mikhail Lifshitz is a major forgotten figure in the tradition of Marxist philosophy and art history. A significant influence on Lukács, and the dedicatee of his The Young Hegel, as well as an unsurpassed scholar of Marx and Engels’s writings on art and a lifelong controversialist, Lifshitz’s work dealt with topics as various as the philosophy of Marx and the pop aesthetics of Andy Warhol. The Crisis of Ugliness (originally published in Russian by Iskusstvo, 1968), published here in English for the first time, and with a detailed introduction by its translator David Riff, is a compact broadside against modernism in the visual arts that nevertheless resists the dogmatic complacencies of Stalinist aesthetics. Its reentry into English debates on the history of Soviet aesthetics promises to re-orient our sense of the basic coordinates of a Marxist art theory.
This landmark monograph presents the most recent mathematical developments in the analysis of ionospheric distortions of SAR images and offers innovative new strategies for their mitigation. As a prerequisite to addressing these topics, the book also discusses the radar ambiguity theory as it applies to synthetic aperture imaging and the propagation of radio waves through the ionospheric plasma, including the anisotropic and turbulent cases. In addition, it covers a host of related subjects, such as the mathematical modeling of extended radar targets (as opposed to point-wise targets) and the scattering of radio waves off those targets, as well as the theoretical analysis of the start-stop approximation, which is used routinely in SAR signal processing but often without proper justification. The mathematics in this volume is clean and rigorous – no assumptions are hidden or ambiguously stated. The resulting work is truly interdisciplinary, providing both a comprehensive and thorough exposition of the field, as well as an accurate account of a range of relevant physical processes and phenomena. The book is intended for applied mathematicians interested in the area of radar imaging or, more generally, remote sensing, as well as physicists and electrical/electronic engineers who develop/operate spaceborne SAR sensors and perform the data processing. The methods in the book are also useful for researchers and practitioners working on other types of imaging. Moreover, the book is accessible to graduate students in applied mathematics, physics, engineering, and related disciplines. Praise for Transionospheric Synthetic Aperture Imaging: “I perceive that this text will mark a turning point in the field of synthetic aperture radar research and practice. I believe this text will instigate a new era of more rigorous image formation relieving the research, development and practitioner communities of inconsistent physical assumptions and numerical approaches.” – Richard Albanese, Senior Scientist, Albanese Defense and Energy Development LLC
Gaussian processes can be viewed as a far-reaching infinite-dimensional extension of classical normal random variables. Their theory presents a powerful range of tools for probabilistic modelling in various academic and technical domains such as Statistics, Forecasting, Finance, Information Transmission, Machine Learning - to mention just a few. The objective of these Briefs is to present a quick and condensed treatment of the core theory that a reader must understand in order to make his own independent contributions. The primary intended readership are PhD/Masters students and researchers working in pure or applied mathematics. The first chapters introduce essentials of the classical theory of Gaussian processes and measures with the core notions of reproducing kernel, integral representation, isoperimetric property, large deviation principle. The brevity being a priority for teaching and learning purposes, certain technical details and proofs are omitted. The later chapters touch important recent issues not sufficiently reflected in the literature, such as small deviations, expansions, and quantization of processes. In university teaching, one can build a one-semester advanced course upon these Briefs.
This text considers a specific Volterra integral operator and investigates its degree of compactness in terms of properties of certain kernel functions. In particular, under certain optimal integrability conditions the entropy numbers $e_n(T_{\rho, \psi})$ satisfy $c_1\norm{\rho\psi}_r0$.
This second edition reflects significant progress in tsunami research, monitoring and mitigation within the last decade. Primarily meant to summarize the state-of-the-art knowledge on physics of tsunamis, it describes up-to-date models of tsunamis generated by a submarine earthquake, landslide, volcanic eruption, meteorite impact, and moving atmospheric pressure inhomogeneities. Models of tsunami propagation and run-up are also discussed. The book investigates methods of tsunami monitoring including coastal mareographs, deep-water pressure gauges, GPS buoys, satellite altimetry, the study of ionospheric disturbances caused by tsunamis and the study of paleotsunamis. Non-linear phenomena in tsunami source and manifestations of water compressibility are discussed in the context of their contribution to the wave amplitude and energy. The practical method of calculating the initial elevation on a water surface at a seismotectonic tsunami source is expounded. Potential and eddy traces of a tsunamigenic earthquake in the ocean are examined in terms of their applicability to tsunami warning. The first edition of this book was published in 2009. Since then, a few catastrophic events occurred, including the 2011 Tohoku tsunami, which is well known all over the world. The book is intended for researchers, students and specialists in oceanography, geophysics, seismology, hydro-acoustics, geology, and geomorphology, including the engineering and insurance industries.
This groundbreaking work by one of the world's foremost theoreticians of culture and scholars of Russian philosophy gives for the first time a systematic examination of the development of Russian philosophy during the late Soviet period. Countering the traditional view of an intellectual wilderness under the Soviet regime, Mikhail Epstein provides a comprehensive account of Russian thought of the second half of the 20th century that is highly sophisticated without losing clarity. It provides new insights into previously mostly ignored areas such as late-Soviet Russian nationalism and Eurasianism, religious thought, cosmism and esoterism, and postmodernism and conceptualism. Epstein shows how Russian philosophy has long been trapped in an intellectual prison of its own making as it sought to create its own utopia. However, he demonstrates that it is time to reappraise Russian thought, now freed from the bonds of Soviet totalitarianism and ideocracy but nevertheless dangerously engaged into new nationalist aspirations and metaphysical radicalism. We are left with not only a new and exciting interpretation of recent Russian intellectual history, but also the opportunity to rethink our own philosophical heritage.
This book treats a new, far-from-fully-developed area of molecular biophysics-enzyme physics. An attempt is made to survey this field, but primary consideration is given tothreeprob lems under investigation in the Polymer Structure Labaratory of the Institue of High-Molecular Compounds, Academy of Seiences ofthe USSR. The first problern is the genetic coding of the biologically fun.ctional structure of proteins. Its solution is based on physical theories of hydrophobic interactions. The second problern is the conformational properties of pro teins as the factor governing enzyme activity. The most direct methods for experimental investigation of questions in this area are optical, principally those involving natural and magnetic rota tion of the plane of polarization. A substantial portion of the book concerns optical activity; the Faraday effect is discussed in an appendix. The third problern is the manifestation of the cooperative properties of enzymes in the kinetics of enzymatic reactions and the solution of complex kinetic problems. This problern is espe cially pressing in connection with research on allosteric enzymes, which are responsible for feedback in metabolic processes. An appendix describes a new method for solving kinetic problems, based on the theory of graphs. This volume extends and details certain of the ideas ex pressed in my previous book, Molecules and Life: An Introduction to Molecular Biophysics, which was published in this series in 1965.
This monograph describes mathematical models that enable prediction of phase compositions for various technological processes, as developed on the base of a complex physico-chemical analysis of reaction. It studies thermodynamics and kinetics of specific stages of complex pyrometallurgical processes involving boron, carbon, sulfur, tungsten, phosphorus, and many more, as well as their exposure to all sorts of factors. First and foremost, this enables to optimize processes and technologies at the stage of design, while traditional empirical means of development of new technologies are basically incapable of providing an optimal solution. Simulation results of metals and alloys production, welding and coating technologies allow obtaining materials with pre-given composition, structure and properties in a cost-saving and conscious manner. Moreover, a so-called "inverse problem", i.e., selecting source materials which would ensure the required results, cannot be solved by any other means.
This book presents an extensive analysis of the dynamics of discrete and distributed baroclinic vortices in a multi-layer fluid that characterizes the main features of the large and mesoscales dynamics of the atmosphere and the ocean. It widely covers the case of hetonic situations as well as the case of intrathermocline vortices that are familiar in oceanographic and of recognized importance for heat and mass transfers. Extensive typology of such baroclinic eddies is made and analysed with the help of theoretical development and numerical computations. As a whole it gives an overview and synthesis of all the many situations that can be encountered based on the long history of the theory of vortex motion and on many new situations. It gives a renewed insight on the extraordinary richness of vortex dynamics and open the way for new theoretical, observational and experimental advances. This volume is of interest to experts in physical oceanography, meteorology, hydrodynamics, dynamic systems, involved in theoretical, experimental and applied research and lecturers, post-graduate students, and students in these fields.
Mikhail Alexandrovich Krivoglaz died unexpectedly when he was preparing the English edition of his two-volume monograph on diffraction and diffuse scatter ing of X-rays and neutrons in imperfect crystals. His death was a heavy blow to all who knew him, who had worked with him and to the world science community as a whole. The application of the diffraction techniques for the study of imperfections of crystal structures was the major field of Krivoglaz' work throughout his career in science. He started working in the field in the mid-fifties and since then made fundamental contributions to the theory of real crystals. His results have largely determined the current level of knowledge in this field for more than thirty years. Until the very last days of his life, Krivoglaz continued active studies in the physics of diffraction effects in real crystals. His interest in the theory aided in the explanation of the rapidly advancing experimental studies. The milestones marking important stages of his work were the first mono graph on the theory of X-ray and neutron scattering in real crystals which was published in Russian in 1967 (a revised English edition in 1969), and the two volume monograph published in Russian in 1983-84 (this edition is the revised translation of the latter).
Dynamics of Topological Magnetic Solitons gives a theoretical and experimental review of the dynamics of high-speed domain walls and Bloch lines. After the introduction of magnetic solitons, experimental methods for the observation of the dynamics of domain walls are presented. Further chapters discuss main features of the stimulated motion of domain walls, their magnetoelastic interaction, stability and relaxation. Finally, the dynamics of domain walls in weak ferromagnets with more than one dimension is treated. The last chapter presents the dynamics of Bloch lines and their clusters. More than 230 references guide the reader to the literature. Physicists will gain new insights in interesting applications of soliton theory in condensed matter physics. Engineers will find new information on magnetooptical effects for further applications.
For almost two decades Prof. Shifman, a clear and pedagogical expositor, has been giving review lectures on frontier topics in theoretical high energy physics. This two-volume book is a collection of some of the best of those lectures. The lectures written in the 1980's and early 1990's have been revised and updated specifically for this publication. The lectures in this book are intended for beginners - graduate students and young researchers - who are about to delve into the intricacies of the theory. They were used by the author in his course ';Advanced Modern Field Theory and Its Applications';, given in the academic year 1994/95 at the University of Minnesota.A wide range of key topics is covered. In Volume 1, the first two chapters are devoted to quantum chromodynamics as the theory of hadrons. The author gives an in-depth discussion of a variety ofpowerful methods based on Wilson's operator product expansion. Chapter 3 (written together with V Novikov, A Vainshtein, and V Zakharov) is the most systematic and pedagogical presentation of instantons in the gauge theories one can find in the literature. Chapter 4 introduces supersymmetry. Chapter 5, concluding this volume, reviews the fascinating dynamics of supersymmetric gauge theories in the strong coupling regime. Chapter 6, which opens Volume 2, is a culmination of the supersymmetric theme. It gives a state-of-the-art description of the breakthrough developments in supersymmetric gauge theories. It has been written specifically for this book by A Vainshtein and the author. Chapter 7 is designed as a primer of two-dimensional conformal field theory, which constitutes the basis of modern string theory. Chapter 8, the last, presents remarkable new findings in quantum mechanics. Every chapter contains exercises and a list of recommended literature.Prof. Shifman has been an active participant and significant contributor in the development of the ideas presented in this book. This accounts for the historical remarks and digressions interspersed in the book, enhancing its pedagogical role. The book will serve as a comprehensive reference and textbook for all graduate students and researchers interested in modern particle physics. It will also be a useful guide for lecturers.
Shrouded by the thick clouds of hot, dense atmosphere, the planet Venus - Earth's closest neighbour in space - remained mysterious until recent decades. Today, with data from contemporary observations and from Russian and American spacecraft, Venus has moved into sharper focus. This comprehensive book provides an up-to-date and detailed analysis of the nature of Venus. The authors, experts in planetary science from Russia and the United States, examine all the principal aspects of Venus, with particular attention paid to the planet's formation, the development of a runaway greenhouse effect, and Venus' evolution into a planet completely different from others in our solar system. Integrating data from Galileo, Magellan, Pioneer-Venus, Venera sand other space missions, this book summarizes the history of Venus, covers the atmosphere, geomorphology and tectonic history of the planet, and considers its geology.
This book concerns testing hypotheses in non-parametric models. Generalizations of many non-parametric tests to the case of censored and truncated data are considered. Most of the test results are proved and real applications are illustrated using examples. Theories and exercises are provided. The incorrect use of many tests applying most statistical software is highlighted and discussed.
Mr. Wolkenstein's Physical Approaches to Biological Evolution, whether or not it proves to give the ultimate truth on the matters with which it deals, certainly deserves, by its breadth and scope and profundity, to be considered an impor tant event in the philosophical world." This is a quotation from an introduction written by Bertrand Russell for Ludwig Wittgenstein's Tractatus Logico-Philosophicus. I exchanged only name and subject. As for the rest, I could continue quoting Russell, but I would rather say something myself. As Wittgenstein did with formal logic, Wolkenstein rectifies our views on how to approach the logic of life from a formal theoretical basis. Many bio logists do not believe that their subject lends itself to the scrutiny of physical theory. They certainly admit that one can simulate biological phenomena by models that can be expressed in a mathematical form. However, they do not believe that biology can be given a theoretical foundation that is defined within the general framework of physics. Rather, they insist on a holistic approach, banning any reduction to fundamental principles subject to physical theory.
This book is devoted to the study of the dynamics of rotating bodies with cavities containing liquid. Two basic classes of motions are analyzed: rotation and libration. Cases of complete and partial filling of cavities with ideal liquid and complete filling with viscous liquid are treated. The volume presents a method for obtaining relations betwee
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