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Solan Eilon: Borel Games

Borel Games

These lecture notes offer a general overview of a two-dimensional topological field theory called the Poisson Sigma Model. It is based on a series of talks given by the author at the University of California, Berkeley and the University of Massachusetts, Amherst in the fall of 2018 and the spring of 2019. This book contains an introduction to symplectic, Poisson and graded geometry, the path space construction for Lie algebroids via the reduced phase space of the Poisson Sigma Model, and the Cattaneo-Felder interpretation of Kontsevich's star product via Feynman diagrams. It also describes in detail particular cases of the Poisson Sigma Model, including constant, linear (2-dimensional BF-theory) and quadratic Poisson structures. The target audience of this book is graduate students and researchers with an interest in the mathematical aspects of classical and quantum field theory. No prior exposure to physics or Poisson geometry is required.

Introduction To The Poisson Sigma Model, An

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

Problem Solving in Mathematics and Beyond

Learning Geometry Through Problem Solving

Smart Thinking

Mathematical answers to life’s key questions

Why Don’t Rabbits Rule The World?

Causal Inference and Machine Learning

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

Chapman & Hall/CRC Monographs on Statistics and Applied Probability

This book presents an overview of the diverse literature on change-point methodology and describes some unifying themes and recent breakthroughs. It can be used as a second-year Ph.D. level course in statistics. It is expected to be useful to researchers and graduate students, not only in statistics but also in engineering, biomedicine, economics and finance.

This book presents an overview of the diverse literature on change-point methodology and describes some unifying themes and recent breakthroughs. It can be used as a second-year Ph.D. level course in statistics. It is expected to be useful to researchers and graduate students, not only in statistics but also in engineering, biomedicine, economics and finance.

Change-point Methodology and Applications

There is an increasing prevalence of large and complex datasets within the social sciences, and notably criminology in recent years. This data explosion has led to the development of specialized techniques for extracting information from such data. This book presents an introduction to "Big Data Science" for criminology and the social sciences, taking a case study-based approach to explaining the concepts. The theory is introduced as needed to answer scientific questions based on real data problems in the application areas. Some R and Python code is included to give support with implementation of the methods.

There is an increasing prevalence of large and complex datasets within the social sciences, and notably criminology in recent years. This data explosion has led to the development of specialized techniques for extracting information from such data. This book presents an introduction to "Big Data Science" for criminology and the social sciences, taking a case study-based approach to explaining the concepts. The theory is introduced as needed to answer scientific questions based on real data problems in the application areas. Some R and Python code is included to give support with implementation of the methods.

From Case Studies to Theory

Big Data Science for Criminology and the Social Sciences

This book presents a comprehensive treatment of pricing and hedging soccer betting contracts using the modern techniques of probability, statistics, finance, and portfolio management. It introduces betting in general and then addresses the probabilistic intuition needed in the more complex world of soccer betting. The author presents an innovative perspective by thinking about betting odds in terms of the expected number of goals of both teams. In addition, when the betting market is in play, the book treats betting before the game and during the game separately.

This book presents a comprehensive treatment of pricing and hedging soccer betting contracts using the modern techniques of probability, statistics, finance, and portfolio management. It introduces betting in general and then addresses the probabilistic intuition needed in the more complex world of soccer betting. The author presents an innovative perspective by thinking about betting odds in terms of the expected number of goals of both teams. In addition, when the betting market is in play, the book treats betting before the game and during the game separately.

Science of Soccer Statistics

Soccermetrics

Chapman & Hall/CRC Biostatistics Series

Age-Period-Cohort Models

Differential algebra explores properties of solutions of systems of (ordinary or partial, linear or non-linear) differential equations from an algebraic point of view. It includes as special cases algebraic systems as well as differential systems with algebraic constraints. This algebraic theory of Joseph F Ritt and Ellis R Kolchin is further enriched by its interactions with algebraic geometry, Diophantine geometry, differential geometry, model theory, control theory, automatic theorem proving, combinatorics, and difference equations. Differential algebra now plays an important role in computational methods such as symbolic integration and symmetry analysis of differential equations. These proceedings consist of tutorial and survey papers presented at the Second International Workshop on Differential Algebra and Related Topics at Rutgers University, Newark in April 2007. As a sequel to the proceedings of the First International Workshop, this volume covers more related subjects, and provides a modern and introductory treatment to many facets of differential algebra, including surveys of known results, open problems, and new, emerging, directions of research. It is therefore an excellent companion and reference text for graduate students and researchers.

Differential Algebra and Related Topics II

This unique compendium develops a general approach to building models of economic and financial processes, with a focus on statistical learning techniques that scale to large data sets. It introduces the key elements of a parametric statistical model: likelihood, prior, and posterior, and show how to use them to make predictions.The book covers classical techniques such as multiple regression and the Kalman filter in a clear, accessible style that has been popular with students, but also includes detailed treatments of state-of-the-art models, highlighting tree-based methods, support vector machines and kernel methods, deep learning, and reinforcement learning. Theories are supplemented by real-world examples.This reference text is useful for undergraduate, graduate and even PhD students in quantitative finance, and also to practitioners who are facing the reality that data science and machine learning are disrupting the industry.

Statistical Machine Learning With Applications In Finance

Borel Games

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