arXiv research

We exploit altered patterns in brain functional connectivity as features for automatic discriminative analysis of neuropsychiatric patients. Deep learning methods have been introduced to functional network classification only very recently for fMRI, and the proposed architectures essentially focused on a single type of…

In this paper, we proved the mass angular momentum inequality\cite{D1}\cite{ChrusLiWe}\cite{SZ} for axisymmetric, asymptotically flat, vacuum constraint data sets with small trace. Given an initial data set with small trace, we construct a boost evolution spacetime of the Einstein vacuum equations as \cite{ChOM}. Then …

Sz\H ucs proved in 2000 that the $r$-tuple-point manifold of a generic immersion is cobordant to the $Σ^{1_{r-1}}$-point manifold of its generic projection. Here we slightly extend this by showing that the natural mappings of these manifolds are bordant to each other. The main novelty of our approach is that we constru…

This paper provides an explicit formula for complex structures in embeddings of manifolds.

The purpose of this paper is to study gradient estimate of Hamilton - Souplet - Zhang type for the general heat equation $u_t=Δ_V u + au\log u+bu$ on noncompact Riemannian manifolds. As its application, we show a Harnak inequality for the heat solution and a Liouville type theorem for a nonlinear elliptic equation.…

O. Plamenevskaya associated to each transverse knot K an element of the Khovanov homology of K. In this paper, we give two refinements of Plamenevskaya's invariant, one valued in Bar-Natan's deformation of the Khovanov complex and another as a cohomotopy element of the Khovanov spectrum. We show that the first of these…

New method captures multimodal disconnectivity in schizophrenia.

We study general conditions under which the computations of the index of a perturbed Dirac operator $D_{s}=D+sZ$ localize to the singular set of the bundle endomorphism $Z$ in the semi-classical limit $s\to \infty$. We show how to use Witten's method to compute the index of $D$ by doing a combinatorial computation inv…

We prove a conjecture due to M. Kazarian, connecting two classifying spaces in singularity theory. These spaces are: - Kazarian's space (generalizing Vassiliev's algebraic complex and) showing which cohomology classes are represented by singularity strata. - Author's space $X_τ$ giving homotopy representation of cobord…

A new convex loss function optimizes set predictions with balanced size and coverage.

The paper analyzes skewness and kurtosis measures for skew-elliptical distributions.

Energy statistics was proposed by Sz\' ekely in the 80's inspired by Newton's gravitational potential in classical mechanics and it provides a model-free hypothesis test for equality of distributions. In its original form, energy statistics was formulated in Euclidean spaces. More recently, it was generalized to metric…

Empirical risk minimization frequently employs convex surrogates to underlying discrete loss functions in order to achieve computational tractability during optimization. However, classical convex surrogates can only tightly bound modular loss functions, sub-modular functions or supermodular functions separately while …

The Lichnerowicz conjecture asserts that all harmonic manifolds are either flat or locally symmetric spaces of rank~1. This conjecture has been proved by Z. Szabó \cite{Sz} for harmonic manifolds with compact universal cover. E. Damek and F. Ricci \cite{DR} provided examples showing that in the noncompact case the conj…

Researchers prove zero solutions for certain p-Laplacian equations in convex cones.

BCAE-2D compresses 3D data from a time projection chamber at high speed.