arXiv research

State spaces of multifactor approximations of nonnegative Volterra processes are linear transformations of the nonnegative orthant.

Fixed points of nonnegative neural networks are analyzed using fixed point theory.

In this paper, we propose a new fast and robust recursive algorithm for near-separable nonnegative matrix factorization, a particular nonnegative blind source separation problem. This algorithm, which we refer to as the successive nonnegative projection algorithm (SNPA), is closely related to the popular successive pro…

Study Euler characteristic of manifolds with almost nonnegative curvature operator, showing nonnegativity under certain conditions.

Study open Alexandrov spaces with nonnegative curvature, proving structural results.

Sharp inequalities for manifolds with nonnegative curvature.

Study on Kähler manifolds with nonnegative Ricci curvature, focusing on rigidity.

We provide techniques for studying the nonnegatively curved left-invariant metrics on a compact Lie group. For "straight" paths of left-invariant metrics starting at bi-invariant metrics and ending at nonnegatively curved metrics, we deduce a nonnegativity property of the initial derivative of curvature. We apply this …

Survey on open manifolds with nonnegative Ricci curvature and open questions.

We discuss the cobordism type of spin manifolds with nonnegative sectional curvature. We show that in each dimension $4k \geq 12$, there are infinitely many cobordism types of simply connected and nonnegatively curved spin manifolds. Moreover, we raise and analyze a question about possible cobordism obstructions to non…

Normalized nonnegative models assign probability distributions to users and random variables to items; see [Stark, 2015]. Rating an item is regarded as sampling the random variable assigned to the item with respect to the distribution assigned to the user who rates the item. Models of that kind are highly expressive. F…

The exact nonnegative matrix factorization (exact NMF) problem is the following: given an $m$-by-$n$ nonnegative matrix $X$ and a factorization rank $r$, find, if possible, an $m$-by-$r$ nonnegative matrix $W$ and an $r$-by-$n$ nonnegative matrix $H$ such that $X = WH$. In this paper, we propose two heuristics for exac…

Given compact Lie groups H\subset G, we study the space of G-invariant metrics on G/H with nonnegative sectional curvature. For an intermediate subgroup K between H and G, we derive conditions under which enlarging the Lie algebra of K maintains nonnegative curvature on G/H. Such an enlarging is possible if (K,H) is a …

Huisken's isoperimetric mass is always nonnegative.

We study manifolds with almost nonnegative curvature operator (ANCO) and provide first examples of closed simply connected ANCO mannifolds that do not admit nonnegative curvature operator.

New method reduces computational cost for nonnegative low rank matrix approximation.

New proof of splitting theorem and finite ends of minimal hypersurfaces in nonnegative curvature manifolds.

In this paper, we generalize topological results known for noncompact manifolds with nonnegative Ricci curvature to spaces with nonnegative $N$-Bakry Émery Ricci curvature. We study the Splitting Theorem and a property called the geodesic loops to infinity property in relation to spaces with nonnegative $N$-Bakry Émery…

This note is a study of nonnegativity conditions on curvature which are preserved by the Ricci flow. We focus on specific kinds of curvature conditions which we call noncoercive, these are the conditions for which nonnegative curvature and vanishing scalar curvature doesn't imply flatness. We show that, in dimensions g…

New vanishing theorems for genera derived under almost nonnegative Ricci curvature.

Let V be an open manifold with complete nonnegatively curved metric such that the normal sphere bundle to a soul has no section. We prove that the souls of nearby nonnegatively curved metrics on V are smoothly close. Combining this result with some topological properties of pseudoisotopies we show that for many V the s…

A new algorithm solves nonnegative least squares faster with nonnegative data.

The paper classifies solutions to semilinear equations on curved spaces.

We find new obstructions to the existence of complete Riemannian metric of nonnegative sectional curvature on manifolds with infinite fundamental groups. In particular, we construct many examples of vector bundles whose total spaces admit no nonnegatively curved metric.

The paper studies CR Yamabe solutions on Sasakian manifolds with nonnegative curvature.

We establish a link between rational homotopy theory and the problem which vector bundles admit complete Riemannian metric of nonnegative sectional curvature. As an application, we show for a large class of simply-connected nonnegatively curved manifolds that, if C lies in the class and T is a torus of positive dimensi…

Ancient Ricci flows with nonnegative curvature operator have bounded entropy.

Study connects isoperimetric sets, mass concepts, and nonnegative scalar curvature.

Paper proposes a clustering algorithm for nonnegative data.

Nonnegative Boltzmann machines (NNBMs) are recurrent probabilistic neural network models that can describe multi-modal nonnegative data. NNBMs form rectified Gaussian distributions that appear in biological neural network models, positive matrix factorization, nonnegative matrix factorization, and so on. In this paper,…

We describe a construction of Riemannian metrics of nonnegative sectional curvature on a closed smooth nonorientable 4-manifold with fundamental group of order two that realizes a homotopy class that was not previously known to contain nonnegatively curved manifolds. The procedure yields new metrics of nonnegative sect…

We apply various topological methods to distinguish connected components of moduli spaces of complete Riemannian metrics of nonnegative sectional curvature on open manifolds. The new geometric ingredient is that souls of nearby nonnegatively curved metrics are ambiently isotopic.

Uniform bounds on ends for non-branching CD spaces with nonnegative curvature outside a compact set.

Paper studies nonnegative Tucker decomposition identifiability with sparsity conditions.

In this paper, we prove a general maximum principle for the time dependent Lichnerowicz heat equation on symmetric tensors coupled with the Ricci flow on complete Riemannian manifolds. As an application we construct complete manifolds with bounded nonnegative sectional curvature of dimension greater than or equal to fo…

Establishes refined singularity estimate for nonnegative n-superharmonic functions in locally conformally flat manifolds.

Totally geodesic dual leaves on curved manifolds are also curved.

The paper tackles tensor factorization and completion from noisy data.

In this note, we answer positively a question by Belegradek and Kapovitch about the relation between rational homotopy theory and a problem in Riemannian geometry which asks that total spaces of which vector bundles over compact nonnegative curved manifolds admit (complete) metrics with nonnegative curvature.

A new NMF variant tackles underdetermined problems with sparse and separable assumptions.

The study examines 4D steady gradient Ricci solitons with nonnegative curvature away from a compact set.

We construct several infinite families of nonnegatively curved manifolds of low cohomogeneity and small dimension which can be distinguished by their cohomology rings. In particular, we exhibit an infinite family of eight-dimensional cohomogeneity one manifolds of nonnegative curvature with pairwise non-isomorphic comp…

Study ancient Ricci flows with nonnegative Ricci curvature and their asymptotic geometry.

Simplified Obata-Vétois argument for Einstein manifolds with nonnegative scalar curvature.

Study shows unbounded Pontryagin numbers on curved manifolds.

New examples show nonnegatively curved metrics with same soul but different moduli space components.

Smooths metrics with nonnegative scalar curvature near singular sets.

Paper studies convergence of nonnegative scalar curvature metrics to a specific limit space.