Related papers: Presentations with negative deficiency and largene…
This note being devoted to some aspects of the inverse problem of representation theory contains a new insight into it illustrated by two topics. The attention is concentrated on the manner of representation of abstract objects by the…
We consider largeness of groups given by a presentation of deficiency 1, where the group is respectively free-by-cyclic, LERF or 1-relator. We give the first examples of (finitely generated free)-by-(infinite cyclic) word hyperbolic groups…
Necessary and sufficient conditions for the exactness (in the algebraic sense) of certain sequences of continuous group homomorphisms are established.
We present four generalized small cancellation conditions for finite presentations and solve the word- and conjugacy problem in each case. Our conditions $W$ and $W^*$ contain the non-metric small cancellation cases C(6), C(4)T(4), C(3)T(6)…
In this paper we study obstructions to presentability by products for finitely generated groups. Along the way we develop both the concept of acentral subgroups, and the relations between presentability by products on the one hand, and…
Commensurable groups are bi-interpretable, under suitable definability conditions.
Small sample sizes are common in many disciplines, which necessitates pooling roughly similar datasets across multiple institutions to study weak but relevant associations between images and disease outcomes. Such data often manifest…
Group fairness definitions such as Demographic Parity and Equal Opportunity make assumptions about the underlying decision-problem that restrict them to classification problems. Prior work has translated these definitions to other machine…
Contrastive representation learning encourages data representation to make semantically similar pairs closer than randomly drawn negative samples, which has been successful in various domains such as vision, language, and graphs. Recent…
We provide new group presentations for surface braid groups which are positive. We study some properties of such presentations and we solve the conjugacy problem in a particular case.
A minor improvement is made to the calculation of the inhomogeneity term. The new calculation gives better agreement with the observations of Daoud et al. and Cheng-Graessley-Melnichenko.
We derive sufficient conditions for exponential decay of solutions of the delay negative feedback equation with distributed delay. The conditions are written in terms of exponential moments of the distribution. Our method only uses…
This is a survey of results on random group presentations, and on random subgroups of certain fixed groups. Being a survey, this paper does not contain new results, but it offers a synthetic view of a part of this very active field of…
Learning from imbalanced data is one of the most significant challenges in real-world classification tasks. In such cases, neural networks performance is substantially impaired due to preference towards the majority class. Existing…
In this paper, we characterize the extreme points of a class of multidimensional monotone functions. This result is then applied to large contests, where it provides a useful representation of optimal allocation rules under a broad class of…
We establish both sufficient and necessary conditions for weighted Hardy inequalities in metric spaces in terms of Assouad (co)dimensions. Our sufficient conditions in the case where the complement is thin are new even in Euclidean spaces,…
Self-similar groups provide a rich source of groups with interesting properties; e.g., infinite torsion groups (Burnside groups) and groups with an intermediate word growth. Various self-similar groups can be described by a recursive…
In this series of papers we study subspaces of de Branges spaces of entire functions which are generated by majorization on subsets $D$ of the closed upper half-plane. The present, first, part is addressed to the question which subspaces of…
Let G be an additive abelian group whose finite subgroups are all cyclic. Let A_1,...,A_n (n>1) be finite subsets of G with cardinality k>0, and let b_1,...,b_n be pairwise distinct elements of G with odd order. We show that for every…
For any given finite abelian group, we give factorizations of the group determinant in the group algebra of any subgroup. The factorizations are an extension of Dedekind's theorem. The extension leads to a generalization of Dedekind's…