Related papers: What is Cost?
We present a variation of quasi-isometry to approach the problem of defining a geometric notion equivalent to commensurability. In short, this variation can be summarized as "quasi-isometry with uniform parameters for a large enough family…
This is a very basic introduction to some notions related to logic and complexity.
This note concerns a search for publications in which one can find statements that explain the concept of an operating system, reasons for introducing operating systems, a formalization of the concept of an operating system or theory about…
Fair resource allocation is an important problem in many real-world scenarios, where resources such as goods and chores must be allocated among agents. In this survey, we delve into the intricacies of fair allocation, focusing specifically…
This paper is devoted to a new approach of the arithmetic of intervals. We present the set of intervals as a normed vector space. We define also a four-dimensional associative algebra whose product gives the product of intervals in any…
Quantum entanglement is the quantum information processing resource. Thus it is of importance to understand how much of entanglement particular quantum states have, and what kinds of laws entanglement and also transformation between…
This thesis investigates on measure theoretic aspects of fluctuations of error terms appearing in various asymptotic formulas.
We offer an insight into our mathematical endeavors, which aim to advance the foundational understanding of energy systems in a broad context, encompassing facets such as charge transport, energy storage, markets, and collective behavior.…
We describe an investigation of the use of probabilistic models and cost-benefit analyses to guide resource-intensive procedures used by a Web-based question answering system. We first provide an overview of research on question-answering…
The paper has 2 main goals: 1. We propose a variant of the CAPM based on coherent risk. 2. In addition to the real-world measure and the risk-neutral measure, we propose the third one: the extreme measure. The introduction of this measure…
We introduced the concept of a metric value set (MVS) in an earlier paper \cite{GM}. In this paper we study the algebraic structure of MVSs. For an MVS $M$ we define the concept of $M$-metrizability of a topological space and prove some…
This paper is a rather informal guide to some of the basic theory of 2-categories and bicategories, including notions of limit and colimit, 2-dimensional universal algebra, formal category theory, and nerves of bicategories. As is the way…
Fair division is the problem of dividing one or several goods amongst two or more agents in a way that satisfies a suitable fairness criterion. These Notes provide a succinct introduction to the field. We cover three main topics. First, we…
We address the problem of measuring the relative angle between two "quantum axes" made out of N1 and N2 spins. Closed forms of our fidelity-like figure of merit are obtained for an arbitrary number of parallel spins. The asymptotic regimes…
The purpose of this note is to raise two different questions, which are rarely if ever considered, and to which, it seems, we lack convincing, systematic answers. These questions can be posed as: - Why do we compute? - What do we compute?…
This essay, originally published in the Sept 1990 Notices of the AMS, discusses problems of our mathematical education system that often stem from widespread misconceptions by well-meaning people of the process of learning mathematics. The…
A review of various definitions of "compatibility" expressed in terms of ordinary probability, and a discussion of the occurrence of incompatibility (and the related phenomenon of interference) in non-quantal probabilistic systems.
We give a survey of some known results and of the many open questions in the study of generic phenomena in geometrically interesting groups.
This is a draft of an article to appear in the October 2022 issue of the Notices of the AMS. In this survey article we explore a fascinating area called descriptive combinatorics and its recently discovered connections to distributed…
This is a lecture notes for a mini-course in Department of Mathematics, Ghent University, 14 Mar.-25 Mar. 2023.