arXiv research

Paper defines and proves geometric uniqueness of Einstein field equations.

We introduce a new elliptic operator on null hypersurfaces of four-dimensional Lorentzian manifolds. This operator depends on the first and second fundamental forms of the sections of a foliation of the null hypersurface and its novelty originates from its covariant transformation under change of foliation. It thus pro…

The paper proves asymptotic normality for multinomial logistic regression on null covariates.

Defines constraint tensor for null hypersurfaces, providing explicit geometry.

Proves the Kundt conjecture in arbitrary dimensions, confirming its validity.

Semi-supervised method boosts two-sample testing with covariate data.

Paper develops statistical tests for covariance matrix regression on manifold.

Solves characteristic problem in general relativity for null data.

AdaPT-GMM improves multiple testing power with covariates.

We consider the problem of large-scale inference on the row or column variables of data in the form of a matrix. Often this data is transposable, meaning that both the row variables and column variables are of potential interest. An example of this scenario is detecting significant genes in microarrays when the samples…

In this work we obtain the limit of the Hawking energy of a large class of foliations along general null hypersurfaces $Ω$ satisfying a weak notion of asymptotic flatness. The foliations are not required to be either geodesic or approaching large spheres at infinity. The limit is obtained in terms of a reference backgr…

Let G be a finite connected simple graph. We define the moduli space of conformal structures on G. We propose a definition of conformally covariant operators on graphs, motivated by [25]. We provide examples of conformally covariant operators, which include the edge Laplacian and the adjacency matrix on graphs. In the …

Semi-supervised learning improves prediction using unlabeled data.

We show that any $k$ Osserman Lorentzian algebraic curvature tensor has constant sectional curvature and give an elementary proof that any local 2 point homogeneous Lorentzian manifold has constant sectional curvature. We also show that a Szabó Lorentzian covariant derivative algebraic curvature tensor vanishes.

Study transverse metric expansion on null hypersurfaces, proving uniqueness for Killing horizons.

We develop a monitoring procedure to detect changes in a large approximate factor model. Letting $r$ be the number of common factors, we base our statistics on the fact that the $\left( r+1\right)$-th eigenvalue of the sample covariance matrix is bounded under the null of no change, whereas it becomes spiked under cha…

The paper calibrates shrinkage covariance estimators for spectral functionals in high dimensions.

The paper characterizes ambient metrics using conformal completion and null infinity properties.

Paper proves existence of ambient manifolds for null hypersurfaces solving Einstein equations.

The paper examines extreme value statistics of high-dimensional sample covariances, with applications in finance and image analysis.

The n-dimensional Lorentzian manifolds with vanishing second covariant derivative of the Riemann tensor (2-symmetric spacetimes) are characterized and classified. The main result is that either they are locally symmetric or they have a covariantly constant null vector field, in this case defining a subfamily of Brinkma…

New method tests causal association using noise contrastive backdoor adjustment.

Study on surfaces in neutral space forms with zero mean curvature.

I'll describe a general geometric setup allowing for a generalization of Rehren duality to asymptotically anti-de Sitter spacetimes whose classical matter distribution is sufficiently well-behaved as to prevent the occurence of singularities in the sense of null geodesic incompleteness. I'll also comment on the issues …

We present a family of four-dimensional Lorentzian manifolds whose invariant classification requires the seventh covariant derivative of the curvature tensor. The spacetimes in questions are null radiation, type N solutions on an anti-de Sitter background. The large order of the bound is due to the fact that these spac…

Develops a formalism for studying general horizons and derives a near-horizon equation.

We study risk of the minimum norm linear least squares estimator in when the number of parameters $d$ depends on $n$, and $\frac{d}{n} \rightarrow \infty$. We assume that data has an underlying low rank structure by restricting ourselves to spike covariance matrices, where a fixed finite number of eigenvalues grow with…

Study on overlaps of singular vectors in Gaussian matrix submatrices.

We consider the class of locally boost isotropic spacetimes in arbitrary dimension. For any spacetime with boost isotropy, the corresponding curvature tensor and all of its covariant derivatives must be simultaneously of alignment type ${\bf D}$ relative to some common null frame. Such spacetimes are known as type ${\b…

In this study, we define a family of null curves in Minkowski 3-space and called null similar curves. We obtain some properties of these special curves. We show that two null curves are null similar curves if and only if these curves form a null Bertrand pair. Moreover, we obtain that the family of null geodesics and n…

Identifies null hypersurfaces with constant surface gravity.

Study optimal transport on null hypersurfaces and null energy condition.

In this paper, we define the notion of eikonal helix and eikonal slant helix for null curves in the 4-dimensional Lorentzian manifold M 1 4 and give a characterization for the null curve to be the null eikonal helix. Moreover, we indicate an important relation between the null eikonal helix and null eikonal slant helix…

Study on null helices in semi-Riemannian manifolds with special submanifolds.

Study examines null vector fields on Lorentzian manifolds.

A maximum principle for C^0 null hypersurfaces is obtained and used to derive a splitting theorem for spacetimes which contain null lines. As a consequence of this null splitting theorem, it is proved that an asymptotically simple vacuum (Ricci flat) spacetime which contains a null line is isometric to Minkowski space.

Minimal surfaces in Heisenberg group have null curves and lines.

Network data is prevalent in many contemporary big data applications in which a common interest is to unveil important latent links between different pairs of nodes. Yet a simple fundamental question of how to precisely quantify the statistical uncertainty associated with the identification of latent links still remain…

We clarify the relationship between the null geodesic completeness of an Einstein Lorentz manifold and its conformal Kobayashi pseudodistance. We show that an Einstein manifold has at least one incomplete null geodesic if its pseudodistancfe is nontrivial. If its pseudodistance is nondegenerate, all of its null geodesi…

Study on null hypersurfaces with constant angle in Lorentzian manifolds.

We exploit the link between the transport equation and derivatives of expectations to construct efficient pathwise gradient estimators for multivariate distributions. We focus on two main threads. First, we use null solutions of the transport equation to construct adaptive control variates that can be used to construct…

In this paper, we study inextensible flows of partially null and pseudo null curves in E_1^4. We give neccessary and sufficent conditions for inextensible flows of partially null and pseudo null curves in E_1^4

First, we prove that indefinite Sasakian manifolds do not admit any screen conformal $r$-null submanifolds, tangent to the structure vector field. We, therefore, define a special class of null submanifolds, called; {\it contact screen conformal} $r$-null submanifold of indefinite Sasakian manifolds. Several characteriz…

There are very few general theorems on the kernel of the well-known Lichnerowicz Laplacian. In the present article we consider the geometry of the kernel of this operator restricted to covariant (not necessarily symmetric or skew-symmetric) tensors. Our approach is based on the analytical method, due to Bochner, of pro…

The study finds regular null hypersurfaces in a perturbed Schwarzschild black hole exterior.

The paper shows how null hypersurfaces behave in Lorentz-Minkowski space.

Study of mean curvature flow on null hypersurfaces leading to MOTS.

Let $M^{n+1}_1$ be a light-like geodesically complete Lorentzian $(n+1)$-manifold satisfying the null energy condition. We show that null hypersurfaces properly immersed in $M^{n+1}_1$ are totally geodesic.