arXiv research

Study weakly weighted Einstein-Finsler metrics, showing specific curvature properties and characterizing them.

The paper studies weighted Ricci curvatures and characterizes Randers metrics.

Let $X$ be an infinite Riemann surface equipped with its conformal hyperbolic metric such that the action of the covering group $π_1(X)$ on $\tilde{X}$ is of the first kind-i.e., the surface $X$ is equal to its convex core. We first prove that any geodesic lamination on $X$ is nowhere dense. Given a fixed geodesic pant…

TrustNet robustly learns noise patterns from trusted data to improve weakly-supervised classification.

Localization of chest pathologies in chest X-ray images is a challenging task because of their varying sizes and appearances. We propose a novel weakly supervised method to localize chest pathologies using class aware deep multiscale feature learning. Our method leverages intermediate feature maps from CNN layers at di…

This paper studies the topological properties of the World Trade Web (WTW) and its evolution over time by employing a weighted network analysis. We show that the WTW, viewed as a weighted network, displays statistical features that are very different from those obtained by using a traditional binary-network approach. I…

We compute global log canonical thresholds of a large class of quasismooth well-formed del Pezzo weighted hypersurfaces in $\mathbb{P}(a_{1},a_{2},a_{3},a_{4})$. As a corollary we obtain the existence of orbifold Kähler--Einstein metrics on many of them, and classify exceptional and weakly exceptional quasismooth well-…

Weakly supervised learning aims at coping with scarce labeled data. Previous weakly supervised studies typically assume that there is only one kind of weak supervision in data. In many applications, however, raw data usually contains more than one kind of weak supervision at the same time. For example, in user experien…

Schur theorem proven for weakly Landsberg Finsler metrics.

In this paper, we show that if the optimization function is restricted-strongly-convex (RSC) and restricted-smooth (RSM) -- a rich subclass of weakly submodular functions -- then a streaming algorithm with constant factor approximation guarantee is possible. More generally, our results are applicable to any monotone we…

We provide a Hilbert manifold structure {à} la Bartnik for the space of asymptotically hyperbolic initial data for the vacuum constraint equations. The adaptation led us to prove new weighted Poincar{é} and Korn type inequalities for AH manifolds with inner boundary and weakly regular metric.

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

Method identifies change points in high-dimensional models using sample weights.

Weakly Einstein Kähler surfaces are characterized and classified.

The study examines weakly Einstein Lie groups and proves non-existence for certain types.

Classifies weakly Einstein submanifolds in space forms satisfying specific equalities.

The study explores weakly $p$-Kähler hyperbolic manifolds.

This paper classifies strongly nilpotent special multi-flags and their Goursat counterparts.

The paper provides examples of keen weakly reducible bridge spheres for links in b-bridge position.

Model learns image-word associations from captions using contrastive learning.

As a model problem for clustering, we consider the densest k-disjoint-clique problem of partitioning a weighted complete graph into k disjoint subgraphs such that the sum of the densities of these subgraphs is maximized. We establish that such subgraphs can be recovered from the solution of a particular semidefinite re…

Minimal displacement set in weakly systolic complexes is systolic and embeds isometrically.

Study on extended weakly symmetric spaces, classifying and providing an example.

There is a well developed theory of weakly symmetric Riemannian manifolds. Here it is shown that several results in the Riemannian case are also valid for weakly symmetric pseudo-Riemannian manifolds, but some require additional hypotheses. The topics discussed are homogeneity, geodesic completeness, the geodesic orbit…

Classifies weakly Einstein hypersurfaces in spaces of constant curvature.

We introduce the notion of a weakly reflective submanifold, which is an austere submanifold with a certain global condition, and study its fundamental properties. Using these, we determine weakly reflective orbits and austere orbits of s-representations.

The paper examines Randers metrics with isotropic scalar curvature properties.

Bayesian PROCOVA uses AI to adjust for covariates in RCTs.

New examples of weakly Einstein conformal products are constructed.

In this article we study almost contact manifolds admitting weakly Einstein metrics. We first prove that if a (2n+1)-dimensional Sasakian manifold admits a weakly Einstein metric then its scalar curvature $s$ satisfies $-6\leqslant s \leqslant 6$ for $n=1$ and $-2n(2n+1)\frac{4n^2-4n+3}{4n^2-4n-1}\leqslant s \leqslant …

We study the computational capacity of a model neuron, the Tempotron, which classifies sequences of spikes by linear-threshold operations. We use statistical mechanics and extreme value theory to derive the capacity of the system in random classification tasks. In contrast to its static analog, the Perceptron, the Temp…

Characterizes weakly linked pairs of complete graphs in 3D space.

The object of the present note is to discuss about the defining condition of weakly cyclic Ricci symmetric manifolds and weakly cyclic $Z$-symmetric manifolds \cite{DMS15} and the existence of such notion by proper examples.

Classifies weakly Einstein curvature tensors in 4D Euclidean space.

ROTS improves sentence similarity by incorporating structural information.

We introduce and study a new class of representations of surface groups into Lie groups of Hermitian type, called {\em weakly maximal} representations. We prove that weakly maximal representations are discrete and injective and we describe the structure of the Zariski closure of their image. Furthermore we prove that t…

The Bergman-Szegő kernel is analyzed for weakly pseudoconvex CR manifolds of finite type.

In applications of supervised learning applied to medical image segmentation, the need for large amounts of labeled data typically goes unquestioned. In particular, in the case of brain anatomy segmentation, hundreds or thousands of weakly-labeled volumes are often used as training data. In this paper, we first observe…

Geodesic orbit and weakly symmetric properties in spray geometry.

New families of weakly symmetric nilmanifolds discovered.

We derive a diffusion approximation for the kinetic Vlasov-Fokker-Planck equation in bounded spatial domains with specular reflection type boundary conditions. The method of proof involves the construction of a particular class of test functions to be chosen in the weak formulation of the kinetic model. This involves t…

Weakly convex polyhedra which are star-shaped with respect to one of their vertices are infinitesimally rigid. This is a partial answer to the question whether every decomposable weakly convex polyhedron is infinitesimally rigid. The proof uses a recent result of Izmestiev on the geometry of convex caps.

A Heegaard splitting which admits a unique pair of disjoint compression disks on distinct sides is said to be keen weakly reducible. This paper provides an construction of keen weakly reducible Heegaard splittings of arbitrary genus except 2. Furthermore, critical Heegaard splittings may yield if we change some conditi…

The study shows how to regularize weakly harmonic maps using Sobolev norms and Coulomb frames.

The goal of this paper is to study weakly Einstein critical metrics of the volume functional on a compact manifold $M$ with smooth boundary $\partial M$. Here, we will give the complete classification for an $n$-dimensional, $n=3$ or $4,$ weakly Einstein critical metric of the volume functional with nonnegative scalar …

Study extends reflective submanifold theory to compact homogeneous spaces.

Study shows expanding Ricci solitons from specific metric cones.

The study classifies weakly almost Fuchsian manifolds and proves geometric properties.