arXiv research

Choosing a reference group in Oaxaca-Blinder decomposition can reverse conclusions.

In this paper the introduction of notion of reference vector paves the way for a combination of classical and social approaches in the framework of referential preferences given by matrix groups. It is shown that individual demand issue from rational decision does not depend on that reference.

Survey on finite group actions on manifolds.

In this paper we consider the problem of group invariant subspace clustering where the data is assumed to come from a union of group-invariant subspaces of a vector space, i.e. subspaces which are invariant with respect to action of a given group. Algebraically, such group-invariant subspaces are also referred to as su…

For simply connected compact exceptional Lie groups $G = F_4, E_6$ and $E_7$, we consider two involutions $σ, γ$ and determine the group structure of subgroups $G^{σ,γ}$ of $G$ which are the intersection $G^σ\cap G^γ$ of the fixed points subgroups of $G^σ$ and $G^γ$. The motivation is as follows. In [1](see the Referen…

This document contains tables with the classification of prehomogeneous modules for reductive algebraic groups with up to two simple factors due to Sato, Kimura and many others, as well as corresponding tables of the étale modules appearing in this list, determined by the author. It is intended as a convenient referenc…

In this note we point out an error in the above paper and refer to some papers where this error is corrected and a more general theorem is proved.

Active-GRPO improves molecular optimization by actively deciding when to imitate or self-improve.

We give results on when a finitely generated group has only indiscrete embeddings in SL(2,C), with particular reference to 3-manifold groups. For instance if we glue two copies of the figure 8 knot along its torus boundary then the fundamental group of the resulting closed 3-manifold sometimes embeds in SL(2,C) and som…

The paper corrects a previous work on manifold groups.

The purpose of this contribution is to point out connections between recent ideas about gerbes and gerbal actions (as higher categorical extension of representation theory) and old discussion in quantum field theory on commutator anomalies, gauge group extensions, and 3-cocycles. The unifying concept is the classical o…

Let B_n be the braid group on n strands, with n at least 4, and let Mod(S) be the extended mapping class group of the sphere with n+1 punctures. We show that the abstract commensurator of B_n is isomorphic to a semidirect product of Mod(S) with a group we refer to as the transvection subgroup, Tv(B_n). We also show tha…

We establish a relation between higher contact-like structures on supermanifolds and the N = 1 super-Poincare group via its superspace realisation. To do this we introduce a vector-valued contact structure, which we refer to as a polycontact structure.

The paper connects function theory, dynamics, and ergodic theory via Thurston's theory.

This is a survey article with a limited list of references (as required by the publisher) which appears in the Encyclopedia of Mathematical Physics, eds. J.-P. Francoise, G.L. Naber and Tsou S.T. Oxford: Elsevier, 2006. vol.4, pp.94--104.

New measures on orbit spaces for orthogonal groups identified.

In this paper we study the right-angled Coxeter groups that acts geometrically on the Salvetti complex of a certain right-angled Artin group, which we refer to as Croke-Kleiner spaces. We prove that any right-angled Coxeter group that acts geometrically on the Croke-Kleiner spaces acts with $π/2$ angles between reflect…

Calibrating classifiers reduces grouping loss using sufficiency criteria.

Authors compute Weingarten map and curvatures for SL(n, R).

Exponential proportion of pseudo-Anosovs in mapping class groups.

The pants graph of a free group is constructed and studied.

In this paper we introduce distinct approaches to loop braid groups, a generalisation of braid groups, and unify all the definitions that have appeared so far in literature, with a complete proof of the equivalence of these definitions. These groups have in fact been an object of interest in different domains of mathem…

Classifies 3D manifolds with specific structures and automorphisms.

The paper proposes a method to improve sales forecasts by selecting optimal reference classes.

We introduce a representation theory for risk operations on locally compact groups in a partition of unity on a topological manifold for Markowitz-Tversky-Kahneman (MTK) reference points. We identify (1) risk torsion induced by the flip rate for risk averse and risk seeking behaviour, and (2) a structure constant or co…

The Greenberg-Shalom hypothesis connects subgroup properties to lattice structures in Lie groups.

Study continuous paths in discrete subgroups of hyperbolic space, proving combination and decomposition theorems.

GRPO optimizes LLMs with verifiable rewards, amplifying policy success.

Study of equivariant scalar curvature groups for proper group actions.

Equivariant neural networks are a class of neural networks designed to preserve symmetries inherent in the data. In this paper, we introduce a general method for modifying a neural network to enforce equivariance, a process we refer to as equivarification. We further show that group convolutional neural networks (G-CNN…

We investigated the temporally evolving network structures of the Japanese and Korean stock markets through the minimum spanning trees composed of listed stocks. We tested the validity of conventional grouping by industrial categories, and found a common trend of decrease for Japan and Korea. This phenomenon supports t…

We discuss how quantitative cohomological informations could provide qualitative properties on complex and symplectic manifolds. In particular we focus on the Bott-Chern and the Aeppli cohomology groups in both cases, since they represent useful tools in studying non Kähler geometry. We give an overview on the comparis…

Optimizes group testing for COVID-19 to reduce test numbers.

Novel method solves group synchronization with robust corruption tolerance.

Study left invariant spray structures on Lie groups, calculating curvature and geodesics.

In this work, we describe how to obtain the structure of an infinite-dimensional Lie group on the group of compactly carried bundle automorphisms Autc(P) for a locally convex prinicpal bundle P over a finite-dimensional smooth sigma-compact base M. This is a generalization of previous work by Wockel, where the base M w…

We study the problem of multivariate regression where the data are naturally grouped, and a regression matrix is to be estimated for each group. We propose an approach in which a dictionary of low rank parameter matrices is estimated across groups, and a sparse linear combination of the dictionary elements is estimated…

LLoCa makes any network Lorentz-equivariant, achieving high accuracy and efficiency.

New methods improve LLM preference optimization by intelligently weighting multiple reference models.

Optimal quantization of measures on Carnot groups

In this paper we provide a method capable of producing an infinite number of solutions for Einstein's equation on static spacetimes with perfect fluid as a matter field. All spacetimes of this type which are symmetric with respect to a given group of translations and whose spatial factor is conformally flat, are charac…

Screening is the problem of finding a superset of the set of non-zero entries in an unknown p-dimensional vector β* given n noisy observations. Naturally, we want this superset to be as small as possible. We propose a novel framework for screening, which we refer to as Multiple Grouping (MuG), that groups variables, pe…

In current paper we refer to the geometrical classification of the Einstein equations which has been developed by one of the authors of this paper. This classification was based on the classical theory for decomposition of the tensor product of representations into irreducible components, which is studied in the elemen…

This paper gives an exposition of relative weight filtrations on completions of mapping class groups associated to a stable degeneration of marked genus g curves. These relative weight filtrations have been constructed using Galois theory (with Matsumoto) and Hodge theory (with Pearlstein and Terasoma). It is shown tha…

Let $Σ$ be a closed surface, $G$ a compact Lie group, not necessarily connected, with Lie algebra $g$, endowed with an adjoint action invariant scalar product, let $ξ\colon P \to Σ$ be a principal $G$-bundle, and pick a Riemannian metric and orientation on $Σ$, so that the corresponding Yang-Mills equations $$d_A*K_A =…

Let $Σ$ be a closed surface, $G$ a compact Lie group, with Lie algebra $g$, $ξ\colon P \to Σ$ a principal $G$-bundle, let $N(ξ)$ denote the moduli space of central Yang-Mills connections on $ξ$, for suitably chosen additional data, and let $\roman{Rep}_ξ(Γ,G)$ be the space of representations of the universal central ex…

Given a compact Lie group, endowed with a bi-invariant Riemannian metric, its complexification inherits a Kaehler structure having twice the kinetic energy of the metric as its potential, and Kaehler reduction with reference to the adjoint action yields a stratified Kaehler structure on the resulting adjoint quotient. …

In prior work the authors introduced a parabolic flow for pluriclosed metrics, referred to as pluriclosed flow. We also demonstrated that this flow, after certain gauge transformations, gives a class of solutions to the renormalization group flow of the nonlinear sigma model with B-field. Using these transformations, w…