Related papers: Functional Inequalities: New Perspectives and New …
In a companion article we have introduced a notion of multiscale functional inequalities for functions $X(A)$ of an ergodic stationary random field $A$ on the ambient space $\mathbb R^d$. These inequalities are multiscale weighted versions…
The rapid trend of deploying artificial intelligence (AI) and machine learning (ML) systems in socially consequential domains has raised growing concerns about their trustworthiness, including potential discriminatory behaviours. Research…
We report an inconsistency found in probability theory (also referred to as measure-theoretic probability). For probability measures induced by real-valued random variables, we deduce an "equality" such that one side of the "equality" is a…
Educational technologies, and the systems of schooling in which they are deployed, enact particular ideologies about what is important to know and how learners should learn. As artificial intelligence technologies -- in education and beyond…
The main subject of the book is an up-to-date and in-depth survey of the theory of normal frames and coordinates in differential geometry. The book can be used as a reference manual, review of the existing results and introduction to some…
Efforts to promote equitable public policy with algorithms appear to be fundamentally constrained by the "impossibility of fairness" (an incompatibility between mathematical definitions of fairness). This technical limitation raises a…
Two kinds of novel generalizations of Nesbitt's inequality are explored in various cases regarding dimensions and parameters in this article. Some other cases are also discussed elaborately by using the semiconcave-semiconvex theorem. The…
[Taken from the "README" in the book] My goal with this book is to provide some kind of bridge for mathematics between the high-school-level and college-level for physics students. From my perspective, our job as physicists is to observe…
In the present paper a new concept of representability is introduced, which can be applied to not total and also to intransitive relations (semiorders in particular). This idea tries to represent the orderings in the simplest manner,…
People's experiences of discrimination are often shaped by multiple intersecting factors, yet algorithmic fairness research rarely reflects this complexity. While intersectionality offers tools for understanding how forms of oppression…
Recommender systems are effective tools for mitigating information overload and have seen extensive applications across various domains. However, the single focus on utility goals proves to be inadequate in addressing real-world concerns,…
In this paper, we propose a novel fairness framework grounded in the concept of happiness, a measure of the utility each group gains fromdecisionoutcomes. Bycapturingfairness through this intuitive lens, we not only offer a more…
One of my recent papers transforms an NP-Complete problem into the question of whether or not a feasible real solution exists to some Linear Program. The unique feature of this Linear Program is that though there is no explicit bound on the…
The standard assumptions that underlie many conceptual and quantitative frameworks do not hold for many complex physical, biological, and social systems. Complex systems science clarifies when and why such assumptions fail and provides…
This is the first of a series of papers that we intend to publish about the epistemology of fundamental physics in its current state. One of the main objectives of these papers is to improve our understanding of fundamental physics (and…
Empirical likelihood is an attractive inferential framework that respects natural parameter boundaries, but existing approaches typically require smoothness of the functional and miscalibrate substantially when these assumptions are…
Fair allocation of indivisible items among agents is a fundamental and extensively studied problem. However, fairness does not have a single universally accepted definition, leading to a variety of competing fairness notions. Some of these…
This book is concerned with the various aspects of hierarchical collective behaviour which is manifested by most complex systems in nature. From the many of the possible topics, we plan to present a selection of those that we think are…
In this work, we consider the problem of intersectional group fairness in the classification setting, where the objective is to learn discrimination-free models in the presence of several intersecting sensitive groups. First, we illustrate…
The aim of this note is to prove a new discrepancy principle. The advantage of the new discrepancy principle compared with the known one consists of solving a minimization problem approximately, rather than exactly, and in the proof of a…