Related papers: What is Cost?
This is a short survey of amenable equivalence relations.
An equivalence relation in the symmetric group, where is a positive integer has been considered. An algorithm for calculation of the number of the equivalence classes by this relation for arbitrary integer has been described.
This habilitation thesis is intended to be a good introduction to enumeration, the problem of listing solutions. It focuses on the different ways of measuring complexity in enumeration, with a particular emphasis on my contributions to the…
Work in progress concerning alternative formalizations of arithmetic.
We discuss the paper "Citation Statistics" by the Joint Committee on Quantitative Assessment of Research [arXiv:0910.3529]. In particular, we focus on a necessary feature of "good" measures for ranking scientific authors: that good measures…
This paper deals with the comparison of two common types of equivalence groups of differential equations, and this gives rise to a number of results presented in the form of theorems. It is shown in particular that one type can be…
Analogical proportions compare pairs of items (a, b) and (c, d) in terms of their differences and similarities. They play a key role in the formalization of analogical inference. The paper first discusses how to improve analogical inference…
The openCost project aims to enhance transparency in research funding by making publication-related costs publicly accessible, following FAIR principles. It introduces a metadata schema for cost data, allowing aggregation and analysis…
A brief overview and history of the American Mathematics Competitions.
Table of contents: Editorial 1 Correspondents 3 Some recent work in general relativistic Astrophysics 4 Two dimensional black holes 6 Resonant-mass gravitational wave detectors: an update 8 Universality and scaling in gravitational collapse…
The purpose of this note is to give a number of open problems on matching theory and their relation to the well-known results in this area. We also give a linear analogue of the acyclic matchings.
This paper presents a set of general strategies for the analysis of structure in amorphous materials and a general approach to assessing the utility of a selected structural description. Measures of structural diversity and utility are…
This paper discusses the distributions of missing sums and differences.
ECM survey article discussing the structure of subsets of Abelian groups which behave `a bit like' cosets (of subgroups).
In this paper, we provide an approach to clustering relational matrices whose entries correspond to either similarities or dissimilarities between objects. Our approach is based on the value of information, a parameterized,…
Several questions of scientometrics parameters organization are considered. Two new indices for scientific works citation analysis are proposed. They provide more detailed and reliable scientific significance assessment of individual…
In this paper, we study three matching problems all of which came up quite recently in the field of machine teaching. The cost of a matching is defined in such a way that, for some formal model of teaching, it equals (or bounds) the number…
Measure Equivalence (ME) is the measure theoretic counterpart of quasi-isometry. This field grew considerably during the last years, developing tools to distinguish between different ME classes of countable groups. On the other hand,…
Recognizing non-standard entity types and relations, such as B2B products, product classes and their producers, in news and forum texts is important in application areas such as supply chain monitoring and market research. However, there is…
The article introduces the concept of uniformity, which is formulated as a scheme of axioms. The connection of this concept with ordered sets is studied. The effectiveness of using axiom schemes as a convenient and short way of replacing…