Related papers: Concave Distortion Semigroups
Computational Group Theory is applied to indexed objects (tensors, spinors, and so on) with dummy indices. There are two groups to consider: one describes the intrinsic symmetries of the object and the other describes the interchange of…
This survey is based on a series of lectures that we gave at MSRI in Spring 2015 and on a series of papers, mostly written jointly with Joan Porti. Our goal here is to: 1. Describe a class of discrete subgroups $\Gamma<G$ of higher rank…
Semi-supervised medical image segmentation aims to leverage minimal expert annotations, yet remains confronted by challenges in maintaining high-quality consistency learning. Excessive perturbations can degrade alignment and hinder precise…
A canonical desideratum for prediction problems is that performance guarantees should hold not just on average over the population, but also for meaningful subpopulations within the overall population. But what constitutes a meaningful…
Prediction-correction algorithms are a highly effective class of methods for solving pseudo-convex optimization problems. The descent direction of these algorithms can be viewed as an adjustment to the gradient direction based on the…
We study isometric representations of the semigroup $\mathbb{Z}_+\backslash \{1\}$. Notion of an inverse representation is introduced and a complete description (up to unitary equivalence) of such representations is given. Also, we study a…
We generalize the notion of an approximate indicator for a closed subgroup $H$ of a locally compact group $G$ introduced by Aristov, Runde, and Spronk and extend their characterization of the existence of such nets in terms of the…
Given a finite group with a generating subset there is a well-established notion of length for a group element given in terms of its minimal length expression as a product of elements from the generating set. Recently, certain quantities…
We define Conditional quasi concave Performance Measures (CPMs), on random variables bounded from below, to accommodate for additional information. Our notion encompasses a wide variety of cases, from conditional expected utility and…
A semiorder is a model of preference relations where each element $x$ is associated with a utility value $\alpha(x)$, and there is a threshold $t$ such that $y$ is preferred to $x$ iff $\alpha(y) > \alpha(x)+t$. These are motivated by the…
Over the past several decades, geometric mapping methods have been extensively developed and utilized for many practical problems in science and engineering. To assess the quality of geometric mappings, one common consideration is their…
A proportionally modular affine semigroup is the set of nonnegative integer solutions of a modular Diophantine inequality $f_1x_1+\cdots +f_nx_n \mod b \le g_1x_1+\cdots +g_nx_n$ where $g_1,\dots,g_n,$ $f_1,\ldots ,f_n\in \mathbb{Z}$ and…
Estimates of densities of convolution semigroups of probability measures are given under specific assumptions on the corresponding L\'evy measure and the L\'evy--Khinchin exponent. The assumptions are satisfied, e.g., by tempered stable…
The main aim of this work is to introduce and justify the study of semi-covarities. A {\it semi-covariety} is a non-empty family $\mathcal{F}$ of numerical semigroups such that it is closed under finite intersections, has a minimum,…
This is an expostion of various aspects of amenability and paradoxical decompositions for groups, group actions and metric spaces. First, we review the formalism of pseudogroups, which is well adapted to stating the alternative of Tarski,…
In this paper, the notion of semi-compact perturbation of a closed linear subspace is introduced. Then for a of pair of closed linear subspace of a Banach space such that one is a semi-compact perturbation of the other, it is proved that…
Group equivariant neural networks have been explored in the past few years and are interesting from theoretical and practical standpoints. They leverage concepts from group representation theory, non-commutative harmonic analysis and…
The quasiconformal method provides us with a unified approach to the construction of minimal unitary representations (minrep) of noncompact groups, their deformations as well as their supersymmetric extensions. We review the quasiconformal…
Let $C$ be a proper convex cone generated by a compact set which supports a measure $\mu$. A construction due to A.Barvinok, E.Veomett and J.B. Lasserre produces, using $\mu$, a sequence $(P_k)_{k\in \mathbb{N}}$ of nested spectrahedral…
The relation between representations and positive definite functions is a key concept in harmonic analysis on topological groups. Recently this relation has been studied on topological groupoids. This is the first in a series of papers in…