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Solan Eilon: Borel Games

Borel Games

'Games offer me the joys of complete absorption in a precise, well-defined world... and within those strictures, I find freedom.'Scoring systems are everywhere. They underpin our daily lives - from social media to education and health - they have become pervasive and increasingly dangerous, warping our desires and outsourcing our values to external institutions. Scores are instructional manuals for behaviour. Instead of encouraging us to be more playful, to take pleasure in the journey of striving towards a goal, institutions weaponize scoring to impose their own interests. In The Score, philosopher C. Thi Nguyen shows us how games and their scoring systems, such as likes on social media or university rankings, have fundamentally changed our value systems, prioritising what can be measured and monetized over what is truly meaningful to us. In this love-letter to the immersive and profound power of games, Nguyen charts a way we might be able to break free from these constraints to lead more creative and joyful lives. To start playing our own game.

How to Stop Playing Someone Else’s Game

The Score

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

Scaling (zooming in or out) is taking a close or distant view of an object. Infinite scaling (the scaling parameter tends to zero or infinity) may lead to a limit which is self-similar and much simpler than the original object. For instance, the classical Donsker's theorem says that all weakly dependent stationary processes with finite variance scale to Brownian motion at large scales. In the case of a random field indexed by two-dimensional parameter, both types of scaling can be anisotropic, meaning that the horizontal and vertical axes are scaled at different rate determined by the ratio γ&gt;0 of the scaling exponents along the axes. The natural questions under such scaling are whether the scaling limits exist for any γ&gt;0, and what are these limits are. The book tries to answer these questions. It introduces the concept of scaling transition and discusses its existence for a natural class of planar random fields including Gaussian, linear and some nonlinear ones. The scaling limits are identified and exhibit a surprising trichitomy at a critical point γ0, with 'unbalanced' limits having unusual path properties and dependence structure along one of the coordinate axes. Scaling transition occurs in applied sciences (telecommunications and econometrics) when aggregating independent processes with long-range dependence in which case 'unbalanced' limits are classical Gaussian or stable random fields.

Anisotropic Scaling Of Random Fields With Long-range Dependence: Scaling Limits Of Random Fields With Applications

Annals of Mathematics Studies

A comprehensive new theory of adelic line bundles on quasi-projective varieties over finitely generated fieldsThis book introduces a comprehensive theory of adelic line bundles on quasi-projective varieties over finitely generated fields, developed in both geometric and arithmetic contexts. In the geometric setting, adelic line bundles are defined as limits of line bundles on projective compactifications under the boundary topology. In the arithmetic setting, they are defined as limits of Hermitian line bundles on projective arithmetic compactifications, also under the boundary topology. After establishing these foundational definitions, the book uses the theory to explore key concepts such as intersection theory, effective sections, volumes, and positivity of adelic line bundles. It also applies these results to study height functions of algebraic points and prove an equidistribution theorem on quasi-projective varieties. This theory has broad applications in the study of numerical, dynamical, and Diophantine properties of moduli spaces, quasi-projective varieties, and varieties over finitely generated fields.

Adelic Line Bundles on Quasi-projective Varieties

How the Quest for the Biggest, Fewest and Weirdest Makes Maths

Reaching for the Extreme

Chapman & Hall/CRC Monographs on Statistics and Applied Probability

Significant new challenges to the use of likelihood-based methods for inference have helped to generate considerable interest in alternative inference methods that are not based on a full likelihood specification. This book provides a comprehensive survey of likelihood methods in statistics, with an emphasis on developments to inference functions for use in complex data. These inference functions are usually motivated by considerations related to likelihood-type arguments and have a variety of names, including composite likelihood, quasi-likelihood and pseudo-likelihood.

Significant new challenges to the use of likelihood-based methods for inference have helped to generate considerable interest in alternative inference methods that are not based on a full likelihood specification. This book provides a comprehensive survey of likelihood methods in statistics, with an emphasis on developments to inference functions for use in complex data. These inference functions are usually motivated by considerations related to likelihood-type arguments and have a variety of names, including composite likelihood, quasi-likelihood and pseudo-likelihood.

Likelihood and its Extensions

An Introduction to Point-Set Topology

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

Problem Solving in Mathematics and Beyond

Learning Geometry Through Problem Solving

This lecture notes is based on a sequence of lectures on Reidemeister torsions by V Turaev.J Milnor showed that Reidemeister torsions and the Alexander polynomials are deeply related. By the surgery formulas of Reidemeister torsions, we can apply them to Dehn surgery problems, namely to lens and Seifert surgery problems, and to amphicheirality problem of a link. Since Reidemeister torsions of rational homology 3-spheres are elements in cyclotomic fields, we need algebraic number theoretical studies.Recently P Ozsvath and Z Szabo defined the Heegaard Floer homology which is a powerful invariant to study 3-manifolds. It induces the Reidemeister-Turaev torsion. We also explain it here.

Applications Of Reidemeister Torsions To 3-dimensional Topology

Meta-analysis Using R

Borel Games

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