Related papers: Topics in hidden symmetries. V
At a first glance, the problem of illuminating the boundary of a convex body by external light sources and the problem of covering a convex body by its smaller positive homothetic copies appear to be quite different. They are in fact two…
The main result of this article is an application of the theory of invariant convex cones of Lie algebras to the study of unitary representations of Lie supergroups. It also includes an exposition of recent results of the second author on…
A monoid structure on families of representations of a quiver is introduced by taking extensions of representations in families, i.e. subvarieties of the varieties of representations. The study of this monoid leads to interesting…
This paper studies a fundamental mechanism of how to detect a conflict between arguments given sentiments regarding acceptability of the arguments. We introduce a concept of the inverse problem of the abstract argumentation to tackle the…
Inverse problems are concerned with the reconstruction of unknown physical quantities using indirect measurements and are fundamental across diverse fields such as medical imaging, remote sensing, and material sciences. These problems serve…
Geometric symmetry induces symmetries of function spaces, and the latter yields a clue to global analysis via representation theory. In this note we summarize recent developments on the general theory about how geometric conditions affect…
Many fundamental questions in theoretical computer science are naturally expressed as special cases of the following problem: Let $G$ be a complex reductive group, let $V$ be a $G$-module, and let $v,w$ be elements of $V$. Determine if $w$…
Isotopic pairs and their representations are considered in a general framework of the vector superalgebra. Numerous examples of finite-dimensional and infinite-dimensional isotopic pairs are discussed. Several types of their representations…
We survey recent results on the representation theory of symplectic reflection algebras, focusing particularly on connections with symplectic quotient singularities and their resolutions, spaces of representations of quivers, and on…
The Bayesian approach to inverse problems provides a practical way to solve ill-posed problems by augmenting the observation model with prior information. Due to the measure-theoretic underpinnings, the approach has raised theoretical…
These notes illustrates the power of formulating ideas of commutative algebra in a homotopy invariant form. They can then be applied to derived categories of rings or ring spectra. These ideas are powerful in classical algebra, in…
The general concept of symmetry is realized in manifold ways in different realms of reality, such as plants, animals, minerals, mathematical objects or human artefacts in literature, fine arts and society. In order to arrive at a common…
Invariant representations are core to representation learning, yet a central challenge remains: uncovering invariants that are stable and transferable without suppressing task-relevant signals. This raises fundamental questions, requiring…
The connection between symmetries and linearizations of discrete-time dynamical systems is being inverstigated. It is shown, that existence of semigroup structures related to the vector field and having linear representations enables…
Achieving disentangled representations of information is one of the key goals of deep network based machine learning system. Recently there are more discussions on this issue. In this paper, by comparing the geometric structure of…
We study the problem of learning permutation invariant representations that can capture "flexible" notions of containment. We formalize this problem via a measure theoretic definition of multisets, and obtain a theoretically-motivated…
In this paper, we introduce new representation and characterization of the weighted core inverse of matrices. Several properties of these inverses and their interconnections with other generalized inverses are also explored. Through…
It is argued that the occurrence of disproportionately ("un-natural") large (or small) numbers, as well as deep cancellations, are comparatively natural traits of the way Nature is geared to operate in most complex systems. The idea is…
This paper is devoted to a discussion of specific properties of invariants in the theory of forms.
We explain how recent developments in the fields of realisability models for linear logic -- or geometry of interaction -- and implicit computational complexity can lead to a new approach of implicit computational complexity. This…