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Burdzy Krzysztof: Hypocrisy++: On
Philosophy Of Probability And Sociology

Hypocrisy++: On Philosophy Of Probability And Sociology Of Ideologies

Series On Analysis, Applications And Computation

The book is devoted to rigorous mathematical results on discrete nonlinear Schrödinger equations (DNLS), including the initial value problem of the time-dependent DNLS and the standing wave of the stationary DNLS.The stationary DNLS equations emerge as equations for the profile of the standing wave in evolutionary DNLS. The book mainly presents well-localized, finite-energy solutions that represent solitary standing waves (breathers in the terminology of nonlinear science), while some other types of solutions are considered as well. The approach accepted in this book is variational, based on various critical point theorems of the mountain pass and linking type, as well as constrained minimization.The book covers the existence of solutions and their properties under various physically reasonable assumptions on linear and nonlinear potentials. It also contains a number of open problems which might be thesis topics for fresh PhD students. The results presented are scattered over a large number of research articles and have never been presented in a monograph form. In addition, there is necessary material from the spectral theory of discrete Schrödinger operators, time-dependent DNLS, and a brief presentation of critical point theorems used in the book.

Discrete Nonlinear Schrodinger Equation: Beyond Complete Integrability

This book illustrates statistics with the R programming language, an emerging tool in data science. Filled with techniques for data science and analytics programming, the book is written for students and professionals. It is focused on learning outcomes and problem solving.

This book illustrates statistics with the R programming language, an emerging tool in data science. Filled with techniques for data science and analytics programming, the book is written for students and professionals. It is focused on learning outcomes and problem solving.

Demystifying Probability and Statistics for Data Scientists with R

A Statistical Guide to Certainty in an Uncertain World

What Are the Odds?

This text focuses on the parts of stochastic theory that are particularly relevant to applications. It begins with a description of Brownian motion and the associated stochastic calculus, including the relationship to partial differential equations. It then solves stochastic differential equations by a variety of methods. The author also studies in detail the one-dimensional case. The book concludes with a treatment of semigroups and generators, applying the theory of Harris chains to diffusions as well as weak convergence of Markov chains to diffusions.

This text focuses on the parts of stochastic theory that are particularly relevant to applications. It begins with a description of Brownian motion and the associated stochastic calculus, including the relationship to partial differential equations. It then solves stochastic differential equations by a variety of methods. The author also studies in detail the one-dimensional case. The book concludes with a treatment of semigroups and generators, applying the theory of Harris chains to diffusions as well as weak convergence of Markov chains to diffusions.

An Elementary Introduction Emphasizing Applications

Stochastic Calculus

This book deals with the problem of bounding numerical invariants of nonsingular projective algebraic varieties from a unified point of view. Starting with a new insightful proof of the Castelnuovo theorem, the author proceeds with giving (sharp) bounds for basic numerical invariants (such as Betti, Hodge, and Chern numbers) of algebraic varieties of arbitrary dimension and classifying the varieties on the boundary. Many important results are proved in several different ways underlining different aspects of the topic. However, studying numerical invariants is just a pretext for the exploration of the rich and versatile interplay between geometry and topology of projective algebraic varieties which forms the core of the book. A special role in this study is played by the dual varieties and their degrees classically called classes. While making an extensive use of Lefschetz theory (which is now also available for varieties over an algebraically closed field of positive characteristic), the author also develops a new variant of Morse theory which yields statements (including bounds) on the level of CW-complexes and provides bounds for the homology of real algebraic varieties. In this way one also gets stronger forms of some classical results on the topology of projective varieties, such as weak and hard Lefschetz theorems, Hopf type formula etc. A detailed outline of the exciting centennial history of this topic and a list of intriguing open problems contribute to the value of the book. The exposition is accessible to students with only basic knowledge of algebraic geometry and topology.

Bounding Numerical Invariants Of Algebraic Varieties

A Hybrid Texas Style Approach

An Introduction to Point-Set Topology

Series on Knots & Everything

Shape And Energies Of Geometric Objects

Stochastic Finite Element Modeling in Electronic Packaging

This comprehensive compendium addresses a critical need in the AI and machine learning era by bridging foundational information theory (IT) concepts with practical applications in statistical learning. Unlike traditional IT textbooks, this volume emphasizes how IT principles, such as entropy and source coding, underpin modern machine learning techniques like cross-entropy, decision trees, and evidence-lower bounds.This unique book connects IT with probabilistic inference, illustrated through real-world applications, such as decoding LDPC codes for error correction. The inclusion of the Lea probabilistic programming package is particularly valuable for pedagogy, offering students a hands-on tool to solve numerical problems and reinforce theoretical concepts.The useful reference text benefits professionals, researchers, academics and students in the fields of calculus and probability, communications and information sciences.

Introduction To Information Theory And Probabilistic Inference, An

The book is devoted to contemporary variance reduction methods for Monte Carlo and Markov Chain (MCMC) with Machine Learning and Finance applications. We present new approaches based on martingale representations, and Stein control variates besides the standard techniques. In addition, the book focuses on developing new variance reduction algorithms in MCMC and their theoretical analysis. Readers will find numerical examples that illustrate all proposed algorithms.

Advanced Variance Reduction Techniques For Mcmc

Series In Algebraic And Differential Geometry

Unstable Homotopy Decompositions

An Introduction to Stochastic Modeling

Hypocrisy++: On Philosophy Of Probability And Sociology Of Ideologies

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