arXiv research

Study classifies static potentials on 3-manifolds, proving one-dimensionality under specific conditions.

We show that if an asymptotically flat manifold with horizon boundary admits a global static potential, then the static potential must be zero on the boundary. We also show that if an asymptotically flat manifold with horizon boundary admits an unbounded static potential in the exterior region, then the manifold must c…

We consider the question whether a static potential on an asymptotically flat 3-manifold can have nonempty zero set which extends to the infinity. We prove that this does not occur if the metric is asymptotically Schwarzschild with nonzero mass. If the asymptotic assumption is relaxed to the usual assumption under whic…

The paper proves a geometric capacitary inequality for sub-static manifolds with harmonic potentials.

The Yamabe invariant is linked to static potentials and eigenvalues.

In this paper we study some global properties of static potentials on asymptotically flat $3$-manifolds $(M,g)$ in the nonvacuum setting. Heuristically, a static potential $f$ represents the (signed) length along $M$ of an irrotational timelike Killing vector field, which can degenerate on surfaces corresponding to the…

The paper studies static manifolds with boundary and their properties.

Study proves a sharp upper bound for the zero set area of a static manifold's potential.

In this paper we present a new approach to the study of asymptotically flat static metrics arising in general relativity. In the case where the static potential is bounded, we introduce new quantities which are proven to be monotone along the level set flow of the potential function. We then show how to use these prope…

The study proves unique static manifolds with positive scalar curvature and boundary.

Paper defines Bartnik mass for hyperbolic extensions and proves staticity.

On the boundary of a compact Riemannian manifold $(Ω, g)$ whose metric $g$ is static, we establish a functional inequality involving the static potential of $(Ω, g)$, the second fundamental form and the mean curvature of the boundary $\partial Ω$ respectively.

Deep brain stimulation (DBS) is a surgical treatment for Parkinson's Disease. Static models based on quasi-static approximation are common approaches for DBS modeling. While this simplification has been validated for bioelectric sources, its application to rapid stimulation pulses, which contain more high-frequency pow…

We compute a Bochner type formula for static three-manifolds and deduce some applications in the case of positive scalar curvature. We also explain in details the known general construction of the (Riemannian) Einstein (n+1)-manifold associated to a maximal domain of a static n-manifold where the static potential is po…

In this paper we study non-singular vacuum static space-times with non-zero cosmological constant. We introduce new integral quantities, and under suitable assumptions we prove their monotonicity along the level set flow of the static potential. We then show how to use these properties to derive a number of sharp geome…

Study on stellar models' topology and mass using minimal surfaces.

Paper proves rigidity of static manifolds and applies to metric extensions.

Probabilistic programming is a powerful abstraction for statistical machine learning. Applying static analysis methods to probabilistic programs could serve to optimize the learning process, automatically verify properties of models, and improve the programming interface for users. This field of static analysis for pro…

We define a parabolic flow of pluriclosed metrics. This flow is of the same family introduced by the authors in \cite{ST}. We study the relationship of the existence of the flow and associated static metrics topological information on the underlying complex manifold. Solutions to the static equation are automatically H…

The paper investigates geometrical aspects of static spacetime with almost gradient Ricci solitons.

Article provides Bernstein gradient estimates for heat equations with potential terms.

In this paper we consider an Einstein-type equation which generalizes important geometric equations, like static and critical point equations. We prove that a complete Einstein-type manifold with fourth-order divergence-free Weyl tensor and zero radial Weyl curvature is locally a warped product with $(n-1)$-dimensional…

Knowledge graphs (KGs) typically contain temporal facts indicating relationships among entities at different times. Due to their incompleteness, several approaches have been proposed to infer new facts for a KG based on the existing ones-a problem known as KG completion. KG embedding approaches have proved effective fo…

In this paper we present an end-to-end deep learning framework to turn images that show dynamic content, such as vehicles or pedestrians, into realistic static frames. This objective encounters two main challenges: detecting all the dynamic objects, and inpainting the static occluded background with plausible imagery. …

New symmetries found in Riemann-Cartan geometries.

In this paper, we study a three-dimensional Ricci-degenerate Riemannian manifold $(M^3,g)$ that admits a smooth nonzero solution $f$ to the equation \begin{align} \label{a1a} \nabla df=ψRc+φg, \end{align} where $ψ,φ$ are given smooth functions of $f$, $Rc$ is the Ricci tensor of $g$. Spaces of this type include various…

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

Proves stability of spacetime Penrose inequality for spherical symmetric initial data.

The paper classifies electrovacuum spaces in higher dimensions, proving several key results.

This paper considers mean-variance optimization under uncertainty, specifically when one desires a sparsified set of optimal portfolio weights. From the standpoint of a Bayesian investor, our approach produces a small portfolio from many potential assets while acknowledging uncertainty in asset returns and parameter es…

We propose the factorized action variational autoencoder (FAVAE), a state-of-the-art generative model for learning disentangled and interpretable representations from sequential data via the information bottleneck without supervision. The purpose of disentangled representation learning is to obtain interpretable and tr…

Introduces electrostatic manifolds with boundary for curvature problems.

Paper develops a new estimator for panel data with endogenous treatments, improving causal inference.

Constellation learns group-level visual relationships for abstract reasoning.

Using the tractor calculus to study smooth metric measure spaces, we adapt results of Gover and Nurowski to give sharp metric obstructions to the existence of quasi-Einstein metrics on suitably generic manifolds. We do this by introducing an analogue of the Weyl tractor $W$ to the setting of smooth metric measure space…

The new field of adaptive data analysis seeks to provide algorithms and provable guarantees for models of machine learning that allow researchers to reuse their data, which normally falls outside of the usual statistical paradigm of static data analysis. In 2014, Dwork, Feldman, Hardt, Pitassi, Reingold and Roth introd…

New static vacuum metrics confirmed for near Euclidean boundary data.

Extends static vacuum metrics with specific boundary conditions.

We classify static manifolds which admit more than one static decomposition whenever a condition on the curvature is fullfilled. For this, we take a standard static vector field and analyze its associated one parameter family of projections onto the base. We show that the base itself is a static manifold and the warpin…

Study of 3D vacuum static spaces with specific curvature properties.

New rigidity theorem on static manifolds with boundary.

Geometric inequalities for static convex domains in hyperbolic space proved.

The paper classifies vacuum static spaces with harmonic curvature.

The moduli space of static finite energy solutions to Ward's integrable chiral model is the space $M_N$ of based rational maps from $\CP^1$ to itself with degree $N$. The Lagrangian of Ward's model gives rise to a Kähler metric and a magnetic vector potential on this space. However, the magnetic field strength vanishes…

The study proves geometric inequalities for static convex domains in static rotationally symmetric spaces.

With online payment platforms being ubiquitous and important, fraud transaction detection has become the key for such platforms, to ensure user account safety and platform security. In this work, we present a novel method for detecting fraud transactions by leveraging patterns from both users' static profiles and users…

Proves equality in Minkowski inequality for static, flat manifolds.

We consider Killing vector fields on standard static space-times and obtain equations for a vector field on a standard static space-time to be Killing. We also provide a characterization of Killing vector fields on standard static space-times with compact Riemannian parts.