DeepMP improves non-negative sparse recovery performance.
problem Recovering non-negative sparse signals with high coherence.
method Reformulated non-negative matching pursuit as a deep neural network.
result DeepMP yields significant improvement in exact recovery performance.
Sharp inequality in spaces with non-negative Ricci curvature.
problem Proving a sharp isoperimetric inequality in metric measure spaces.
method Using volume entropy in non-compact metric measure spaces with non-negative synthetic Ricci curvature.
result Proved a sharp dimension-free isoperimetric inequality.
Non-negative curvature affects Markov chains' mixing and expansion properties.
problem Understanding the behavior of Markov chains with non-negative curvature.
method Analyzing conductance, displacement, and cutoff phenomenon in sparse Markov chains.
result Non-negatively curved Markov chains exhibit specific, non-standard behavior in terms of mixing and expansion.
Formal manifolds with non-negative Ricci curvature have formal covers.
problem Formality of manifolds with non-negative Ricci curvature.
method Study of universal covers and formal properties.
result Closed non-orientable manifolds with non-negative Ricci curvature are formal.
In this paper we study non-negatively curved and rationally elliptic GKM4 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 Kähler metrics on complex tori with almost non-negative scalar curvature.
problem Stability of Kähler metrics on complex tori.
method Proved convergence of non-collapsing subsequence of Kähler metrics to flat torus.
result Kähler metrics with almost non-negative scalar curvature on complex tori converge to flat torus.
Sharp inequality for submanifolds in manifolds with non-negative Ricci curvature.
problem Establishing a Fenchel-Willmore inequality for submanifolds in manifolds with non-negative Ricci curvature.
method Analyzing submanifolds in manifolds with non-negative intermediate Ricci curvature and Euclidean volume growth.
result Sharp Fenchel-Willmore inequality for submanifolds in manifolds with non-negative intermediate Ricci curvature.
The study examines symmetries in spaces with positive or non-negative curvature.
problem Understanding symmetries in spaces with curvature constraints.
method Survey of existing results for Riemannian manifolds with specified curvature properties and symmetries.
result Results on symmetries in spaces with curvature bounds.
The paper proves conjectures and classifies metrics on 3D manifolds.
problem Proving conjectures and classifying metrics on 3D manifolds with specific curvature conditions.
method Analytical proofs and classification theorems.
result Critical metrics on 3D manifolds are isometric to geodesic balls in space forms.
Survey on rigidity and almost rigidity of Green functions in non-negative Ricci curvature spaces.
problem Rigidity and almost rigidity of Green functions in non-negative Ricci curvature spaces.
method Survey and observation on Cheeger-Yau inequality on RCD spaces.
result Observations on the Cheeger-Yau inequality and its applications.
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…
Study on rigidity with non-negative intermediate curvature on low-dimensional manifolds.
problem Extending non-existence theorem of positive scalar curvature to product manifolds.
method Introduced intermediate curvature and studied rigidity conditions.
result Rigidity when intermediate curvature is non-negative in low dimensions.
We prove that if a closed, smooth, simply-connected 4-manifold with a circle action admits an almost non-negatively curved sequence of invariant Riemannian metrics, then it also admits a non-negatively curved Riemannian metric invariant with respect to the same action. The same is shown for torus actions of higher rank…
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.
problem Determining the minimum vertex degree for non-negative Lin-Lu-Yau curvature.
method Investigation of Ollivier-Ricci curvature and Lin-Lu-Yau modification on locally finite graphs.
result Lower bound on minimum vertex degree ensuring non-negative Lin-Lu-Yau curvature.
Upper bounds on Laplacian eigenvalues on manifolds with non-negative curvature.
problem Bounding Laplacian eigenvalues on manifolds with non-negative scalar curvature.
method Investigation of invariant spectrum on compact Riemannian manifolds with large isometry groups.
result Upper bounds for eigenvalues of the invariant spectrum assuming non-negative scalar curvature.
Optimal diameter estimates for 3D spaces with non-negative Ricci curvature.
problem Estimating the diameter of 3D spaces with non-negative Ricci curvature.
method Proving positive scalar curvature passes to Ricci limit spaces of non-negative curvature.
result Optimal Bonnet-Myers upper bound for 3D spaces.
New Bochner technique for foliations with non-negative Ricci curvature.
problem Analyzing foliations with non-negative transverse Ricci curvature.
method Generalizing Bochner technique to foliations with non-negative transverse Ricci curvature.
result Obtained a new vanishing theorem for basic cohomology.
Paper proves edge-connectivity equals minimum degree for graphs with non-negative curvature.
problem Edge-connectivity vs. minimum degree in graphs with non-negative curvature.
method Analyzes finite connected graphs with non-negative Lin-Lu-Yau curvature.
result Edge-connectivity equals minimum degree for graphs with non-negative curvature.
nUDEs use neural networks to model biology without negative values.
problem Unrealistic negative values in hybrid models of biology.
method Developed non-negative UDEs (nUDEs) with regularization techniques.
result nUDEs provide realistic solutions for biological models.
Non-negative L1-approximating polynomials for Gaussian distributions are proven for certain classes of sets.
problem Existence of non-negative L1-approximating polynomials for Gaussian distributions. method Proving the existence of degree-k non-negative polynomials that approximate indicator functions of sets with Gaussian surface area in L1-norm. result Proves the existence of non-negative L1-approximating polynomials for certain classes of sets with Gaussian surface area. NCL improves interpretability of deep features by enforcing non-negativity.
problem Lack of interpretability in deep representations.
method Non-negative Contrastive Learning (NCL) using non-negativity constraints.
result NCL outperforms standard contrastive learning in feature disentanglement and selection.
Compact Kähler orbifolds with non-negative Ricci curvature are simply connected.
problem Understanding the topology of Kähler orbifolds with non-negative Ricci curvature.
method Proved orbifold versions of Kobayashi's theorem.
result Compact Kähler orbifolds with non-negative Ricci curvature are simply connected under certain conditions.
Vanishing theorem on CR manifolds with non-negative curvature.
problem Vanishing theorem for Betti numbers on CR manifolds.
method Application of Bochner technique to CR manifolds with non-negative curvature.
result Proof of vanishing theorem for Betti numbers.
Study on Kähler manifolds with non-negative mixed curvature, proving splitting and structure theorems.
problem Investigating properties of Kähler manifolds with specific curvature conditions.
method Conformal perturbation method.
result Established structure and splitting theorems for Kähler manifolds with non-negative mixed curvature.
Paper generalizes bipolar theorems for non-negative random variables.
problem Problems with existing bipolar theorems under stronger assumptions.
method Generalizes existing theorems in a robust probabilistic framework.
result Provides necessary and sufficient conditions for bipolar representation.
Sharp isoperimetric inequality for Finsler manifolds with non-negative Ricci curvature.
problem Proving an isoperimetric inequality for Finsler manifolds with specific curvature properties.
method Analyzing measured Finsler manifolds with non-negative Ricci curvature and Euclidean volume growth.
result Sharp isoperimetric inequality and rigidity results for the inequality.
In this article, a six-parameter family of highly connected 7-manifolds which admit an SO(3)-invariant metric of non-negative sectional curvature is constructed and the Eells-Kuiper invariant of each is computed. In particular, it follows that all exotic spheres in dimension 7 admit an SO(3)-invariant metric of non-neg…
New rigidity theorems for spin fill-ins with non-negative scalar curvature.
problem Mean curvature rigidity for spin fill-ins with non-negative scalar curvature.
method Two spinorial techniques: extending boundary spinors and comparison using index theory.
result New Witten-type integral inequality for the mass of asymptotically Schwarzschild manifolds.
The paper estimates Betti numbers for graphs with specific curvatures, proving bounds and characterizing rigidity.
problem Estimating Betti numbers for graphs with non-negative curvatures.
method Establishing Betti number estimates for graphs with non-negative Ollivier and Bakry-Émery curvatures.
result Upper bounds on the first Betti number for graphs with non-negative curvatures, with characterizations of rigidity.
New metrics with non-negative scalar curvature are always Ricci-flat on certain surgeries.
problem Understanding metrics with non-negative scalar curvature on surgeries of manifolds.
method Analyzing spin surgeries and their impact on metrics with non-negative scalar curvature.
result Complete metrics with non-negative scalar curvature are Ricci-flat on certain surgeries.
We classify closed, simply-connected, non-negatively curved 6-manifolds of almost maximal symmetry rank up to equivariant diffeomorphism.
Graphs with bounded degrees and non-negative Ollivier-Ricci curvature have subexponential growth and diffusive random walk.
problem Understanding geometric properties of graphs with non-negative Ollivier-Ricci curvature.
method Analyzing the geometric properties of graphs with non-negative Ollivier-Ricci curvature, proving subexponential growth and diffusive random walk.
result For graphs with bounded degrees and non-negative Ollivier-Ricci curvature, the average log-volume growth and random walk displacement are subexponential.
Non-negative blind source separation (non-negative BSS), which is also referred to as non-negative matrix factorization (NMF), is a very active field in domains as different as astrophysics, audio processing or biomedical signal processing. In this context, the efficient retrieval of the sources requires the use of sig…
The study finds infinitely many 7-manifolds with non-negative curvature but not homotopy equivalent to bundles.
problem Constructing and analyzing non-negative curvature 7-manifolds.
method Constructing a family of 7-manifolds with specific properties and computing their linking forms.
result The family contains infinitely many manifolds not homotopy equivalent to S3-bundles over S4. The paper extends Gray's result to quaternion-Kähler manifolds.
problem Understanding quaternion-Kähler manifolds with non-negative quaternionic sectional curvature.
method Introducing quaternionic sectional curvature, proving Wolf spaces have non-negative curvature, and using nearly Kähler twistor spaces.
result Every quaternion-Kähler manifold with non-negative quaternionic sectional curvature is a Wolf space.
New proof shows certain 3D spaces are essentially like infinite space.
problem Characterizing 3D spaces with non-negative Ricci curvature.
method Integrable Ricci curvature, Sobolev inequality, spectral non-negativity.
result Proves complete Riemannian 3-manifolds are diffeomorphic to R3. 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…
We provide an equivariant description/classification of all complete (compact or not) non-negatively curved manifolds M together with a co-compact action by a reflection group W, and moreover, classify such W. In particular, we show that the building blocks consist of the classical constant curvature models and general…
Non-negative blind source separation (BSS) has raised interest in various fields of research, as testified by the wide literature on the topic of non-negative matrix factorization (NMF). In this context, it is fundamental that the sources to be estimated present some diversity in order to be efficiently retrieved. Spar…
In this note, we study the radius of positively curved or non-negatively curved Alexandrov space with strictly convex boundary, with convexity measured by the Base-Angle defined by Alexander and Bishop. We also estimate the volume of the boundary of non-negatively curved spaces as well as the rigidity case, which can b…
New bounds on Bartnik mass for surfaces with non-negative first eigenvalue.
problem Bounding Bartnik mass for surfaces with spectral non-negativity condition.
method Proving upper bound on Bartnik mass using spectral non-negativity condition.
result Bounded above by √(|S²|_g/16π) under spectral non-negativity.
Unified framework for non-negative matrices and tensors using Wasserstein loss.
problem Finding low-dimensional representations of high-dimensional datasets with non-negative constraints.
method Unified mathematical framework with a smoothed Wasserstein loss, convex dual formulation for efficient computation.
result Efficient solution for non-negative matrix and tensor factorisations with Wasserstein loss.
We show that the set SCLrp of stable commutator lengths on recursively presented groups equals the set of non-negative right-computable numbers. Hence all non-negative algebraic or computable numbers are in SCLrp and SCLrp is not closed under subtraction. We also show that every non-negative real number …
In this paper we study the evolution of almost non-negatively curved (possibly singular) three dimensional metric spaces by Ricci flow. The non-negatively curved metric spaces which we consider arise as limits of smooth Riemannian manifolds (M_i,g_i), i \in N, whose Ricci curvature is not less than -c^2(i), where c^2(i…
SOS programming verifies MTW tensor non-negativity for optimal transport maps.
problem Verifying MTW tensor non-negativity for general cost functions is difficult.
method Sum-of-Squares (SOS) programming for verifying and approximating MTW non-negativity.
result SOS programming provides certificates and approximations of MTW non-negativity.
New method for inference on covariates in NMF with random effects.
problem Formal inference for covariate effects in NMF with non-negativity constraints.
method NMF-RE model with random effects, ridge updates, df-based cap, asymptotic linearization, wild bootstrap.
result Valid inference on covariates with non-negativity constraint, avoiding degeneracy.
In contrast to the homogeneous case, we show that there are compact cohomogeneity one manifolds, that do not support invariant metrics of non-negative sectional curvature. In fact we exhibit infinite families of such manifolds including the exotic Kervaire spheres. Such examples exist for any codimension of the singula…