arXiv research

Researchers confirm scalar-flatness for critical metrics in 5-9 dimensions.

The classification work [5], [9] left unsettled only those anomalous isoparametric hypersurfaces with four principal curvatures and multiplicity pair $\{4,5\},\{6,9\}$ or $\{7,8\}$ in the sphere. By systematically exploring the ideal theory in commutative algebra in conjunction with the geometry of isoparametric hypers…

The paper connects polygon spaces with quotient spaces using spin actions and normed division algebras.

We construct Yang-Mills connections on SO(n)-bundles over spheres equipped with the Euclidean metric. We use a cohomogeneity one group action on the bundle to reduce the Yang-Mills-equation to a system of ordinary differential equations. The system is shown to have solutions by variational methods, using ideas from har…

Study surgeries between lens spaces using Heegaard Floer d-invariant.

Let $M_1$ and $M_2$ be two Kähler manifolds. One says that $M_1$ and $M_2$ are "relatives" if they share a non-trivial Kähler submanifold $S$, namely, if there exist two holomorphic and isometric immersions (Kähler immersions) $h_1: S -> M_1$ and $h_2: S -> M_2$. In this paper we show that a bounded homogeneous domain …

Graph convolutional networks (GCNs) have been successfully applied in node classification tasks of network mining. However, most of these models based on neighborhood aggregation are usually shallow and lack the "graph pooling" mechanism, which prevents the model from obtaining adequate global information. In order to …

We consider orientation-preserving actions of finite groups $G$ on pairs $(S^3, Σ)$, where $Σ$ denotes a compact connected surface embedded in $S^3$. In a previous paper, we considered the case of closed, necessarily orientable surfaces, determined for each genus $g>1$ the maximum order of such a $G$ for all embeddings…

The paper links labor income risk to stock returns using industry portfolio returns.

Genome-wide association studies (GWAS) offer new opportunities to identify genetic risk factors for Alzheimer's disease (AD). Recently, collaborative efforts across different institutions emerged that enhance the power of many existing techniques on individual institution data. However, a major barrier to collaborative…

This paper completes the classification of certain surface singularities with rational homology disk smoothings.

Islamophobic hate speech on social media inflicts considerable harm on both targeted individuals and wider society, and also risks reputational damage for the host platforms. Accordingly, there is a pressing need for robust tools to detect and classify Islamophobic hate speech at scale. Previous research has largely ap…

CoT-UQ improves LLM uncertainty quantification by integrating reasoning steps.

Genome-wide association studies (GWAS) have achieved great success in the genetic study of Alzheimer's disease (AD). Collaborative imaging genetics studies across different research institutions show the effectiveness of detecting genetic risk factors. However, the high dimensionality of GWAS data poses significant cha…

Ivansic's link of five tori in $S^4$ has hyperbolic complement and many symmetrical properties.

Study estimates personalized effects of maternal PM2.5 exposure on birth weight.

Study improves stock return prediction by switching between economic states, outperforming traditional methods.

The study uses transfer learning to compare surgical outcomes across racial/ethnic subgroups.

To draw inferences about gamma-ray burst (GRB) source populations based on Swift observations, it is essential to understand the detection efficiency of the Swift burst alert telescope (BAT). This study considers the problem of modeling the Swift/BAT triggering algorithm for long GRBs, a computationally expensive proce…

Paper proposes MTL for weakly labelled SED, improving performance with 2-step attention.

TinyBayes detects crop diseases from images on edge devices with high accuracy and minimal resources.

Defines and classifies Thurston geometries and connects simplicial volume to Kodaira dimension.

Paper relates asymptotic dimension to cofinal dimension using coarse proximities.

We study the Assouad dimension and the Nagata dimension of metric spaces. As a general result, we prove that the Nagata dimension of a metric space is always bounded from above by the Assouad dimension. Most of the paper is devoted to the study of when these metric dimensions of a metric space are locally given by the …

Our goal in this paper is to develop an effective estimator of fractal dimension. We survey existing ideas in dimension estimation, with a focus on the currently popular method of Grassberger and Procaccia for the estimation of correlation dimension. There are two major difficulties in estimation based on this method. …

We establish cohomological and extension dimension versions of the Hurewicz dimension-raising theorem

Study on CR structures in 7D, proving maximal symmetry dimension.

We introduce a new quasi-isometry invariant of metric spaces called the hyperbolic dimension, hypdim, which is a version of the Gromov's asymptotic dimension, asdim. The hyperbolic dimension is at most the asymptotic dimension, however, unlike the asymptotic dimension, the hyperbolic dimension of any Euclidean space R^…

In the first part of the paper we show how to relate several dimension theories (asymptotic dimension with Higson property, asymptotic dimension of Gromov, and capacity dimension of Buyalo \cite{Buyalo1}) to Nagata-Assouad dimension. This is done by applying two functors on the Lipschitz category of metric spaces: micr…

This paper studies three aspects around dimension datum: (1), a generalization of the dimension datum, which we call the tau-dimension datum; (2), dimension data of disconnected subgroups; (3), compactness of isospectral sets of normal homogeneous spaces.

Thurston's spine dimension exceeds virtual cohomological dimension.

Random walks on Fuchsian Schottky groups have harmonic measures with lower dimension.

Short note shows unbounded dimensions in Fano K-moduli spaces.

Investigates CR structures in 7D, showing 8 is max symmetry dimension.

Given a metric space $X$ of finite asymptotic dimension, we consider a quasi-isometric invariant of the space called dimension function. The space is said to have asymptotic Assouad-Nagata dimension less or equal $n$ if there is a linear dimension function in this dimension. We prove that if $X$ is a tree-graded space …

The study finds limits on dimensions of certain scales and fields for conformal manifolds.

Model complexity is an important factor to consider when selecting among graphical models. When all variables are observed, the complexity of a model can be measured by its standard dimension, i.e. the number of independent parameters. When hidden variables are present, however, standard dimension might no longer be ap…

Many 0/1 datasets have a very large number of variables; on the other hand, they are sparse and the dependency structure of the variables is simpler than the number of variables would suggest. Defining the effective dimensionality of such a dataset is a nontrivial problem. We consider the problem of defining a robust m…

Classified spaces in low dimensions.

We prove that for geometrically finite groups cohomological dimension of the direct product of a group with itself equals 2 times the cohomological dimension dimension of the group.

Estimates dimension of subsets from random samples, proving consistency.

The action dimension of a group G is the minimal dimension of a contractible manifold that G acts on properly discontinuously. We show that if G acts properly and cocompactly on a thick Euclidean building, then the action dimension is bounded below by twice the dimension of the building. We also compute the action dime…

We discuss a variation of Gromov's notion of asymptotic dimension that was introduced and named Nagata dimension by Assouad. The Nagata dimension turns out to be a quasisymmetry invariant of metric spaces. The class of metric spaces with finite Nagata dimension includes in particular all doubling spaces, metric trees, …

We study piecewise linear co-dimension two embeddings of closed oriented manifolds in Euclidean space, and show that any such embedding can always be isotoped to be a closed braid as long as the ambient dimension is at most five, extending results of Alexander (in ambient dimension three), and Viro and independently Ka…

Proves a theorem for Assouad dimension with applications to distance sets and radial projections.

New examples show non-integer Hausdorff dimensions in collapsing spaces.

We introduce a quasi-symmetry invariant of a metric space Z called the capacity dimension. Our main result says that for a visual Gromov hyperbolic space X the asymptotic dimension of X is at most the capacity dimension of its boundary at infinity plus 1.

The paper aims to develop new combinatorial dimensions for bounded memory learning.