arXiv research

New (co)homology theory for symmetric quandles developed.

Classifies invariant differential operators on a specific geometric space.

Innovative rack theory applied to Legendrian links.

Enhances count process modelling with Markov-modulated non-homogeneous Poisson process.

New CNN architecture improves pediatric image segmentation by homogenizing pose and size.

Holomorphic structures on quantum flag manifolds uniquely defined.

A space is created to realize a specific cohomology module, showing PL structure but not smoothability.

We present a novel approach to the classification of conformally equivariant differential operators on spinors in the case of homogeneous conformal geometry. It is based on the classification of solutions for a vector-valued system of partial differential equations, associated to $\mathcal{D}$-modules for the homogeneo…

We investigate homogeneous geodesics in a class of homogeneous spaces called $M$-spaces, which are defined as follows. Let $G/K$ be a generalized flag manifold with $K=C(S)=S\times K_1$, where $S$ is a torus in a compact simple Lie group $G$ and $K_1$ is the semisimple part of $K$. Then the {\it associated $M$-space} i…

In the present article, we combine some techniques in the harmonic analysis together with the geometric approach given by modules over sheaves of rings of twisted differential operators ($\mathcal{D}$-modules), and reformulate the composition series and branching problems for objects in the Bernstein-Gelfand-Gelfand pa…

Method constructs 2-bundles over homogeneous spaces.

We show that the category of affine bundles over a smooth manifold M is equivalent to the category of affine spaces modelled on projective finitely generated C^\infty(M)-modules. Using this equivalence of categories, we are able to give an alternate proof of the main result of [13], showing that the characterization of…

Let V be the pseudo-Euclidean vector space of signature (p,q), p>2 and W a module over the even Clifford algebra Cl^0 (V). A homogeneous quaternionic manifold (M,Q) is constructed for any spin(V)-equivariant linear map Π: \wedge^2 W \to V. If the skew symmetric vector valued bilinear form Πis nondegenerate then (M,Q) i…

In order to facilitate the comparison of Riemannian homogeneous spaces of compact Lie groups with noncommutative geometries ("quantizations") that approximate them, we develop here the basic facts concerning equivariant vector bundles and Dirac operators over them in a way that uses only global constructions and argume…

Study geodesic orbit property on pseudo-Riemannian H-type nilmanifolds.

Bi-directional Curriculum Learning improves graph anomaly detection by considering both homogeneity and heterogeneity.

A new generalization of Grassmannians in supergeometry, called $ν-$Grassmannians, are constructed by gluing $ν-$domains. By a $ν-$domain, we mean a superdomain with an odd involution say $ν$ on its structure sheaf, as morphism of modules. Then we show that $ν-$Grassmannians are homogeneous superspaces. In addition, in …

Explains algebraic tools for understanding invariant differential operators in curved geometries.

Noncommutative Kähler structures were recently introduced as an algebraic framework for studying noncommutative complex geometry on quantum homogeneous spaces. In this paper, we introduce the notion of a \emph{compact quantum homogeneous Kähler space} which gives a natural set of compatibility conditions between covari…

We study the existence of invariant Einstein metrics on real flag manifolds associated to simple and non-compact split real forms of complex classical Lie algebras whose isotropy representation decomposes into two or three irreducible sub-representations. In this situation, one can have equivalent sub-modules, leading …

MixFT re-partitions data into sub-domains for better TSFM fine-tuning.

Study deformations of compact Calabi-Yau conifolds with singularities.

Achieving machine intelligence requires a smooth integration of perception and reasoning, yet models developed to date tend to specialize in one or the other; sophisticated manipulation of symbols acquired from rich perceptual spaces has so far proved elusive. Consider a visual arithmetic task, where the goal is to car…

This is an introduction to the author's recent work on constrained systems. Firstly, a generalization of the Marsden-Weinstein reduction procedure in symplectic geometry is presented - this is a reformulation of ideas of Mikami-Weinstein and Xu. Secondly, it is shown how this procedure is quantized by Rieffel induction…

Paper connects knot invariants and Morse flow loops.

A typical domain adaptation approach is to adapt models trained on the annotated data in a source domain (e.g., sunny weather) for achieving high performance on the test data in a target domain (e.g., rainy weather). Whether the target contains a single homogeneous domain or multiple heterogeneous domains, existing wor…

A central problem in analyzing networks is partitioning them into modules or communities. One of the best tools for this is the stochastic block model, which clusters vertices into blocks with statistically homogeneous pattern of links. Despite its flexibility and popularity, there has been a lack of principled statist…

Based on the Lie theoretical methods of algebraic Fourier transformation, we classify in the case of generic values of inducing parameters the scalar singular vectors corresponding to the diagonal branching rules for scalar generalized Verma modules in the case of orthogonal Lie algebra and its conformal parabolic suba…

In this paper, we show the existence of a sequence of invariant differential operators on a particular homogeneous model $G/P$ of a Cartan geometry. The first operator in this sequence can be locally identified with the Dirac operator in $k$ Clifford variables, $D=(D_1,..., D_k)$, where $D_i=\sum_j e_j\cdot \partial_{i…

Enhances Ponzi scheme detection on Ethereum using time-aware metapaths.

Estimating fundamental matrices is a classic problem in computer vision. Traditional methods rely heavily on the correctness of estimated key-point correspondences, which can be noisy and unreliable. As a result, it is difficult for these methods to handle image pairs with large occlusion or significantly different cam…

The paper studies how certain surfaces evolve in space without collapsing.

Classifies modules of surface-knots in terms of their properties.

Proves finiteness and holonomicity of skein modules for 3-manifolds.

Defines super projective modules and explores their properties.

Let (V,(.,.)) be a pseudo-Euclidean vector space and S an irreducible Cl(V)-module. An extended translation algebra is a graded Lie algebra m = m_{-2}+m_{-1} = V+S with bracket given by ([s,t],v) = b(v.s,t) for some nondegenerate so(V)-invariant reflexive bilinear form b on S. An extended Poincaré structure on a manifo…

We introduce higher skein modules of links generalizing the Conway skein module. We show that these modules are closely connected to the HOMFLY polynomial.

A new method to derive presentations of skein modules is developed. For the case of homotopy skein modules it will be shown how the topology of a 3-manifold is reflected in the structure of the module. The freeness problem for q-homotopy skein modules is solved, and a natural skein module related to linking numbers is …

Neural Module Networks, originally proposed for the task of visual question answering, are a class of neural network architectures that involve human-specified neural modules, each designed for a specific form of reasoning. In current formulations of such networks only the parameters of the neural modules and/or the or…

Paper compares skein modules to Kauffman bracket modules.

Skein modules are the main objects of an algebraic topology based on knots (or position). In the same spirit as Leibniz we would call our approach "algebra situs." When looking at the panorama of skein modules we see, past the rolling hills of homologies and homotopies, distant mountains - the Kauffman bracket skein mo…

Generalized Steinberg module presentation for Gaussian and Eisenstein integers.

Enhanced Alexander module detects linking numbers in links.

We define 2-crossed module bundle 2-gerbes related to general Lie 2-crossed modules and discuss their properties. A 2-crossed module bundle 2-gerbe over a manifold is defined in terms of a so called 2-crossed module bundle gerbe, which is a crossed module bundle gerbe equipped with an extra sructure. It is shown that s…

Combinatorial approach to compute satellite knot invariants using graph theory.

New sl(2) action defined on a mathematical module.

Introduces admissible skein modules for non-semisimple categories.

Studies modules over a category of Jacobi diagrams in handlebodies.