New solutions found with negative mass in general relativity.
problem Finding metrics with negative mass in general relativity.
method Constructing families of metrics with specific properties.
result Obtained new classes of solutions with negative mass.
Uniform negative immersions prove coherence of one-relator groups.
problem Proving coherence of one-relator groups.
method Using uniform negative immersions and linear-programming techniques.
result One-relator groups with uniform negative immersions are coherent.
Proposes a novel method for generating hard negatives near time series data boundaries.
problem Challenges in generating effective negative samples for time series anomaly detection.
method Reconstruction-driven boundary negative generation framework using reinforcement learning.
result Improves anomaly representation learning and achieves competitive detection performance.
The study confirms a conjecture about Kähler manifolds with quasi-negative curvature.
problem Confirming a long-standing conjecture about Kähler manifolds with quasi-negative curvature.
method Introducing (ε,δ)--quasi-negativity and applying gap-type theorems. result Obtained gap-type theorems for ∫Xc1(KX)n>0 in terms of real bisectional curvature and weighted orthogonal Ricci curvature. New mass definition for negative cosmological constant spacetimes.
problem Defining quasilocal mass for spacetimes with negative cosmological constant.
method Spinorial approach based on previous work for vanishing cosmological constant.
result Non-negative mass, equal to Misner-Sharp mass in spherical symmetry, zero for AdS.
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.
The paper extends Heintze-Kobayashi-Wolf theory to negatively curved homogeneous Finsler manifolds.
problem Understanding negatively curved homogeneous Finsler manifolds.
method Generalizing Heintze-Kobayashi-Wolf theory to homogeneous Finsler geometry, proving two main theorems.
result Negatively curved homogeneous Finsler manifolds are isometric to Lie groups with specific properties.
It was asked by J.Birman, Williams, and L.Rudolph whether nontrivial Lorentz knots have always positive signature. Lorentz knots are examples of positive braids (in our convention they have all crossings negative so they are negative links). It was shown by L.Rudolph that positive braids have positive signature (if the…
This paper proves equivalences of portfolio optimization problems with negative expectile and omega ratio. We derive subgradients for the negative expectile as a function of the portfolio from a known dual representation of expectile and general theory about subgradients of risk measures. We also give an elementary der…
New theory shows how learning algorithms can create a bias towards negative outcomes.
problem Negativity bias in adaptive learning algorithms.
method Generalization of the Hot Stove Effect to settings with negative estimates leading to smaller sample sizes.
result Negativity bias persists even when negative estimates do not lead to avoidance.
SANS uses graph structure to find meaningful negatives for entity and relation embeddings.
problem Finding hard negatives for entity and relation embeddings in knowledge graphs.
method Structure Aware Negative Sampling (SANS) that selects negatives from a node's k-hop neighborhood.
result SANS finds semantically meaningful negatives and is competitive with state-of-the-art approaches.
Motivated by the study of Killing forms on compact Riemannian manifolds of negative sectional curvature, we introduce the notion of generalized vector cross products on Rn and give their classification. Using previous results about Killing tensors on negatively curved manifolds and a new characterization of…
Let (M,ω) be a compact Kähler manifold with negative holomorphic sectional curvature. It was proved by Wu-Yau and Tosatti-Yang that M is necessarily projective and has ample canonical bundle. In this paper, we show that any irreducible subvariety of M is of general type. Moreover, we can extend the theorem to the…
Negative step sizes improve second-order methods for neural networks.
problem Second-order methods discard negative curvature, limiting their effectiveness.
method Introduce negative step sizes in second-order methods combined with Wolfe line search.
result Negative step sizes lead to global convergence and improved performance.
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.
We analyze properties of links which have diagrams with a small number of negative crossings. We show that if a nontrivial link has a diagram with all crossings positive except possibly one, then the signature of the link is negative. If a link diagram has two negative crossings, we show that the signature of the link …
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.
A version of the singular Yamabe problem in bounded domains yields complete conformal metrics with negative constant scalar curvatures. In this paper, we study whether these metrics have negative Ricci curvatures. Affirmatively, we prove that these metrics indeed have negative Ricci curvatures in bounded convex domains…
The Wu-Yau theorem is verified for negative curvature, and new examples of Kähler-Einstein metrics are found.
problem The Wu-Yau theorem and its positive analog.
method Examples and conjectures to verify the Wu-Yau theorem and its positive analog.
result New examples of Kähler-Einstein metrics without negative holomorphic sectional curvature.
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 shows regions close to negatively curved metrics are minimal fillings and rigid.
problem Boundary rigidity and minimality of metrics near negatively curved ones.
method Generalizes previous work on filling volume minimality and boundary rigidity for almost hyperbolic metrics.
result Regions with metrics close to a negatively curved symmetric metric are strict minimal fillings and boundary rigid.
The paper counts geodesic loops on surfaces without conjugate points.
problem Counting geodesic loops on surfaces of genus at least 2 without conjugate points.
method Proves asymptotic estimates for closed geodesic loops on compact surfaces with no conjugate points.
result Generalizes classical counting results and sector theorems for surfaces of strictly negative curvature.
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…
Transformer learns to estimate negative binomial parameters efficiently.
problem Parameter estimation for over-dispersed count data in large screens.
method Pre-trained transformer trained on synthetic data generation to invert parameter to count transformation.
result Method of moments provides faster, more efficient, and better-calibrated estimates.
A common challenge in estimating parameters of probability density functions is the intractability of the normalizing constant. While in such cases maximum likelihood estimation may be implemented using numerical integration, the approach becomes computationally intensive. The score matching method of Hyvärinen [2005] …
Proved contractibility of geodesic triangulation space on hyperbolic surfaces.
problem Open problem on contractibility of geodesic triangulations on hyperbolic surfaces.
method Generalized Tutte's embedding theorem for negative curvature surfaces.
result Contractibility of geodesic triangulation space proved.
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…
Two remarks on curvature properties of Kähler manifolds.
problem Curvature properties of Kähler manifolds.
method Analyzing semi-positive holomorphic sectional curvature and quasi-negative k-Ricci curvature. result For semi-positive holomorphic sectional curvature, the rational dimension of the MRC fibration equals the number of non-truly-flat directions. For quasi-negative k-Ricci curvature, the canonical bundle is ample. Two new models improve option valuation for negative or mean reverting futures markets.
problem Valuation of futures contracts with negative underlying prices.
method Proposed two models: Ornstein-Uhlenbeck and continuous time GARCH.
result Improved option values compared to Black 76, especially for negative or mean reverting markets.
Negative dependence improves machine learning performance.
problem Traditional independence limits machine learning capabilities.
method Negative dependence models, including DPPs and perturbed lattice models.
result Negative dependence often surpasses traditional methods in various machine learning tasks.
State-of-the-art approaches for Knowledge Base Completion (KBC) exploit deep neural networks trained with both false and true assertions: positive assertions are explicitly taken from the knowledge base, whereas negative ones are generated by random sampling of entities. In this paper, we argue that random sampling is …
We show that the positive mass theorem holds for continuous Riemannian metrics that lie in the Sobolev space Wloc2,n/2 for manifolds of dimension less than or equal to 7 or spin-manifolds of any dimension. More generally, we give a (negative) lower bound on the ADM mass of metrics for which the scalar curvat…
Negative momentum accelerates convergence in minimax games but at a suboptimal rate.
problem The convergence rate of negative momentum in minimax games is suboptimal.
method Extending variational inequality formulation, connecting momentum method with Chebyshev polynomials.
result Negative momentum accelerates convergence locally but at a suboptimal rate.
The optimal dividend problem by De Finetti (1957) has been recently generalized to the spectrally negative Lévy model where the implementation of optimal strategies draws upon the computation of scale functions and their derivatives. This paper proposes a phase-type fitting approximation of the optimal strategy. We con…
Generative model improves safety in self-driving simulators and human motion generation.
problem Improving generative models for constrained domains like safety-critical applications.
method Developed Gen-neG, a denoising diffusion model that uses oracle-assisted guidance.
result Empirically validated Gen-neG for collision avoidance and safety-guarded human motion generation.
Negative curvature manifolds have vanishing bounded volume class if and only if Cheeger constant is positive.
problem Negative curvature manifolds and their volume classes.
method Integration of volume forms and isoperimetric constants.
result Vanishing of bounded volume class implies positivity of Cheeger constant and vice versa.
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…
The paper introduces negative controls to evaluate causal discovery algorithms, improving their reliability.
problem Lack of a general guideline for evaluating causal discovery algorithms.
method Derive exact distributional results under random guessing for evaluation metrics and propose a pipeline for using negative controls.
result Evaluation metrics can achieve very favorable values under random guessing, highlighting the need for negative control results.
The paper models stock returns using q-Gaussians and negative binomials.
problem Modeling stock return distributions and pricing options.
method Proposes a generalized jump-diffusion model and uses q-Gaussians and negative binomial distributions. result An explicit option pricing formula is derived.
We show that zero is not an eigenvalue of the conformal Laplacian for generic Riemannian metrics. We also discuss non-compactness for sequences of metrics with growing number of negative eigenvalues of the conformal Laplacian.
Every negative amphichiral knot is rationally slice.
problem Proving every negative amphichiral knot is rationally slice.
method Systematic analysis of the action induced by the negative amphichiral map on the JSJ decomposition of the link exterior.
result Every negative amphichiral link is rationally slice.
Proposes a new method for posterior sampling using MMD with negative distance kernel.
problem Posterior sampling and conditional generative modeling.
method Approximates joint distribution using discrete Wasserstein gradient flows of MMD with negative distance kernel.
result Establishes an error bound for posterior distributions and proves the method is a Wasserstein gradient flow.
A theoretical framework for non-negative matrix factorization based on generalized dual Kullback-Leibler divergence, which includes members of the exponential family of models, is proposed. A family of algorithms is developed using this framework and its convergence proven using the Expectation-Maximization algorithm. …
The paper explores the relationship between joint mixability and negative dependence structures.
problem Understanding the connection between joint mixability and various negative dependence concepts.
method Analyzes the properties of joint mixes and their relation to negative dependence structures.
result Derives necessary and sufficient conditions for a joint mix to be negatively dependent.
Extends conformal prediction to contrastive learning for better coverage of positive samples.
problem Lack of principled guarantees on coverage in contrastive learning.
method Introduces minimum-volume covering sets with learnable constraints.
result Improves inclusion-exclusion trade-offs in positive and negative samples.
New theorem shows certain curved surfaces are uniquely identified by their geodesic lengths.
problem Identifying surfaces by their geodesic lengths.
method Analyzes metrics on simple, thick negatively curved two-dimensional P-manifolds.
result Piecewise negatively curved Riemannian metrics on simple, thick two-dimensional P-manifolds are uniquely determined by their geodesic lengths.
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.
This paper shows how optimizing with hard negative examples improves image retrieval.
problem Training with hard negative examples leads to poor training behavior.
method Characterize the space of triplets, derive why hard negatives fail, and offer a fix to the loss function.
result Optimizing with hard negative examples leads to more generalizable features and better image retrieval.