arXiv research

New findings on stable commutator lengths in recursively presented groups.

The paper estimates Betti numbers for graphs with specific curvatures, proving bounds and characterizing rigidity.

Study on Kähler manifolds with non-negative mixed curvature, proving splitting and structure theorems.

Vanishing theorem on CR manifolds with non-negative curvature.

Formal manifolds with non-negative Ricci curvature have formal covers.

Non-negative curvature affects Markov chains' mixing and expansion properties.

BN^2MF identifies unknown exposure patterns in environmental mixtures.

We classify manifolds of small dimension that admit both, a Riemannian metric of non-negative scalar curvature, and a -- a priori different -- metric for which all wedge products of harmonic forms are harmonic. For manifolds whose first Betti numbers are sufficiently large, this classification extends to higher dimensi…

Non-Negative Matrix Factorization, NMF, attempts to find a number of archetypal response profiles, or parts, such that any sample profile in the dataset can be approximated by a close profile among these archetypes or a linear combination of these profiles. The non-negativity constraint is imposed while estimating arch…

A novel method relaxes binary constraints to non-negative spheres for multi-matching and clustering.

Study reveals flatness of Hessian metrics with non-negative Ricci curvature on foliation leaves.

We consider a problem of grouping multiple graphs into several clusters using singular value thesholding and non-negative factorization. We derive a model selection information criterion to estimate the number of clusters. We demonstrate our approach using "Swimmer data set" as well as simulated data set, and compare i…

We find a local solution to the Ricci flow equation under a negative lower bound for many known curvature conditions. The flow exists for a uniform amount of time, during which the curvature stays bounded below by a controllable negative number. The curvature conditions we consider include 2-non-negative and weakly $\t…

The past decade has seen substantial work on the use of non-negative matrix factorization and its probabilistic counterparts for audio source separation. Although able to capture audio spectral structure well, these models neglect the non-stationarity and temporal dynamics that are important properties of audio. The re…

Efficiently reduces rank of non-negative matrices with quadratic time complexity.

Let $V_i$ be a finite dimensional Hermitian vector space of holomorphic sections of a line bundle $L_i$ on a complex $n$-dimensional manifold $X$. We associate to $V_i$ the non-negative Hermitian quadratic form $g_i$ on $X,$ define a Hermitian mixed volume of $X$ for a "mixing tuple" of $n$ non-negative Hermitian forms…

Paper connects Fenchel-Willmore and Sobolev inequalities for submanifolds in curved spaces.

Interpretability has become an important issue in the machine learning field, along with the success of layered neural networks in various practical tasks. Since a trained layered neural network consists of a complex nonlinear relationship between large number of parameters, we failed to understand how they could achie…

Quantum annealing solves matrix factorization for large datasets.

We use quantum invariants to define a 3-manifold invariant j_p which lies in the non-negative integers. We relate j_p to the Heegard genus, and the cut number. We show that j_$ is an invariant of weak p-congruence.

Least squares fitting is in general not useful for high-dimensional linear models, in which the number of predictors is of the same or even larger order of magnitude than the number of samples. Theory developed in recent years has coined a paradigm according to which sparsity-promoting regularization is regarded as a n…

This work creates a CS for non-negative heavy-tailed data with bounded mean.

The paper proves a gap theorem for almost non-negatively curved manifolds.

New findings on neural networks with non-negative weights and low training error.

This work is concerned with the non-negative rank-1 robust principal component analysis (RPCA), where the goal is to recover the dominant non-negative principal components of a data matrix precisely, where a number of measurements could be grossly corrupted with sparse and arbitrary large noise. Most of the known techn…

DeepMP improves non-negative sparse recovery performance.

Study shows non-negative curvature on 4-manifolds with torus symmetry.

Sharp inequality in spaces with non-negative Ricci curvature.

Odd GKM-manifolds with non-negative curvature split cohomology.

Estimates parameters of a rectified Gaussian distribution using ReLU networks.

The study examines manifolds with specific curvature properties and finds topological and metric constraints.

Let $(M,g)$ be a complete non-compact Riemannian surface. We consider operators of the form $Δ+ aK + W$, where $Δ$ is the non-negative Laplacian, $K$ the Gaussian curvature, $W$ a locally integrable function, and $a$ a positive real number. Assuming that the positive part of $W$ is integrable, we address the question "…

Proves solution uniqueness for biomembrane shape prediction.

In this paper we study non-negatively curved and rationally elliptic GKM$_4$ manifolds and orbifolds. We show that their rational cohomology rings are isomorphic to the rational cohomology of certain model orbifolds. These models are quotients of isometric actions of finite groups on non-negatively curved torus orbifol…

Study optimal execution in financial markets with constraints.

Study Kähler metrics on complex tori with almost non-negative scalar curvature.

We prove the vanishing of the first Betti number on compact manifolds admitting a Weyl structure whose Ricci tensor satisfies certain positivity conditions, thus obtaining a Bochner-type vanishing theorem in Weyl geometry. We also study compact Hermitian-Weyl manifolds with non-negative symmetric part of the Ricci tens…

Sharp inequality for submanifolds in manifolds with non-negative Ricci curvature.

The study examines symmetries in spaces with positive or non-negative curvature.

The paper proves conjectures and classifies metrics on 3D manifolds.

Survey on rigidity and almost rigidity of Green functions in non-negative Ricci curvature spaces.

We study spaces and moduli spaces of Riemannian metrics with non-negative Ricci or non-negative sectional curvature on closed and open manifolds. We construct, in particular, the first classes of manifolds for which these moduli spaces have non-trivial rational homotopy, homology and cohomology groups. We also show tha…

Let $(M,g_0)$ be a compact $n$-dimensional Riemannian manifold with a finite number of singular points, where the metric is asymptotic to a non-negatively curved cone over $(\mathbb{S}^{n-1},g)$. We show that there exists a smooth Ricci flow starting from such a metric with curvature decaying like C/t. The initial metr…

Study on rigidity with non-negative intermediate curvature on low-dimensional manifolds.

The distributional category bounds manifold invariants and imposes constraints.

We introduce and demonstrate the variational autoencoder (VAE) for probabilistic non-negative matrix factorisation (PAE-NMF). We design a network which can perform non-negative matrix factorisation (NMF) and add in aspects of a VAE to make the coefficients of the latent space probabilistic. By restricting the weights i…

Lower bound on minimum vertex degree for non-negative Lin-Lu-Yau curvature on graphs.

A robust algorithm for non-negative matrix factorization (NMF) is presented in this paper with the purpose of dealing with large-scale data, where the separability assumption is satisfied. In particular, we modify the Linear Programming (LP) algorithm of [9] by introducing a reduced set of constraints for exact NMF. In…