arXiv research

Study on null-projectability of Levi-Civita connections in neutral metrics.

4-dimensional spaces equipped with 2-dimensional (complex holomorphic or real smooth) completely integrable distributions are considered. The integral manifolds of such distributions are totally null and totally geodesics 2-dimensional surfaces which are called the null strings. Properties of congruences (foliations) o…

Study on null submanifolds in indefinite complex contact geometry.

Study of optical geometries with intrinsic torsion in general relativity.

In [21], the authors initiated the study of quasi generalized CR (QGCR)-null submanifolds. In this paper, attention is drawn to some distributions on ascreen QGCR-null submanifolds in an indefinite nearly cosymplectic manifold. We characterize totally umbilical and irrotational ascreen QGCR-null submanifolds. We finall…

We study transformations of coordinates on a Lorentzian Einstein manifold with a parallel distribution of null lines and show that the general Walker coordinates can be simplified. In these coordinates, the full Lorentzian Einstein equation is reduced to equations on a family of Einstein Riemannian metrics.

Locally, a screen integrable globally null manifold $M$ splits through a Riemannian leaf $M'$ of its screen distribution and a null curve $\mathcal{C}$ tangent to its radical distribution. The leaf $M'$ carries a lot of geometric information about $M$ and, in fact, forms a basis for the study of expanding and non-expan…

The problem of detecting data anomaly is considered. Under the null hypothesis that models anomaly-free data, measurements are assumed to be from an unknown distribution with some authenticated historical samples. Under the composite alternative hypothesis, measurements are from an unknown distribution positive distanc…

Cluster analysis is an unsupervised learning strategy that can be employed to identify subgroups of observations in data sets of unknown structure. This strategy is particularly useful for analyzing high-dimensional data such as microarray gene expression data. Many clustering methods are available, but it is challengi…

In the present paper, we show that the geometry of a screen integrable null hypersurface can be generated from an isometric immersion of a leaf of its screen distribution into the ambient space. We prove, under certain geometric conditions, that such immersions are contained in semi-Euclidean spheres or hyperbolic spac…

The purpose of the present work is to study (marginally) trapped submanifolds lying in a null hypersurface. Let $(M,g,N)\to\Bm(c)$ be a null hypersurface of a space-time with constant sectional curvature $c$, endowed with a Screen Integrable and Conformal rigging $N$. The (Marginally) Trapped Submanifolds we are intere…

We introduce a class of null hypersurfaces of a semi-Riemannian manifold, namely, screen quasi-conformal hypersurfaces, whose geometry may be studied through the geometry of its screen distribution. In particular, this notion allows us to extend some results of previous works to the case in which the sectional curvatur…

Major internet companies routinely perform tens of thousands of A/B tests each year. Such large-scale sequential experimentation has resulted in a recent spurt of new algorithms that can provably control the false discovery rate (FDR) in a fully online fashion. However, current state-of-the-art adaptive algorithms can …

Testing-by-betting strategies almost surely go bankrupt under null hypotheses.

Markov regime switching models have been used in numerous empirical studies in economics and finance. However, the asymptotic distribution of the likelihood ratio test statistic for testing the number of regimes in Markov regime switching models has been an unresolved problem. This paper derives the asymptotic distribu…

We propose to investigate test statistics for testing homogeneity in reproducing kernel Hilbert spaces. Asymptotic null distributions under null hypothesis are derived, and consistency against fixed and local alternatives is assessed. Finally, experimental evidence of the performance of the proposed approach on both ar…

We consider the goodness-of-fit testing problem of distinguishing whether the data are drawn from a specified distribution, versus a composite alternative separated from the null in the total variation metric. In the discrete case, we consider goodness-of-fit testing when the null distribution has a possibly growing or…

An almost Robinson structure on an $n$-dimensional Lorentzian manifold $(\mcM,g)$, where $n=2m+ε$, $ε\in \{ 0 ,1 \}$, is a complex $m$-plane distribution $\mcN$ that is totally null with respect to the complexified metric, and intersects its complex conjugate in a real null line distribution $\mcK$, say. When $\mcN$ an…

There are many statistical tests that verify the null hypothesis: the variable of interest has the same distribution among k-groups. But once the null hypothesis is rejected, how to present the structure of dissimilarity between groups? In this article, we introduce The Merging Path Plot - a methodology, and factorMerg…

Finite resources limit false discovery rate control in structured hypothesis spaces.

We investigate the problem of semi-parametric maximum likelihood under constraints on summary statistics. Such a procedure results in a discrete probability distribution that maximises the likelihood among all such distributions under the specified constraints (called estimating equations), and is an approximation to t…

Conditional independence testing is a fundamental problem underlying causal discovery and a particularly challenging task in the presence of nonlinear and high-dimensional dependencies. Here a fully non-parametric test for continuous data based on conditional mutual information combined with a local permutation scheme …

Sequential tests for two-sample and independence testing using betting strategies.

The paper sets thresholds for testing correlation in hypergraphs, distinguishing between independent and correlated states.

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…

Study on continuous sequence classification with distribution uncertainty.

Distance correlation has gained much recent attention in the data science community: the sample statistic is straightforward to compute and asymptotically equals zero if and only if independence, making it an ideal choice to discover any type of dependency structure given sufficient sample size. One major bottleneck is…

Study uses topological signatures to quantify financial market complexity.

Identifies null hypersurfaces with constant surface gravity.

Study optimal transport on null hypersurfaces and null energy condition.

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

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.

A family of maximum mean discrepancy (MMD) kernel two-sample tests is introduced. Members of the test family are called Block-tests or B-tests, since the test statistic is an average over MMDs computed on subsets of the samples. The choice of block size allows control over the tradeoff between test power and computatio…

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.

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…

Kernel tests assess equivalence between distributions without assuming specific moments.

Integrates outlier detection into neural networks for improved performance.

Study on null hypersurfaces with constant angle in Lorentzian manifolds.

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

Local classification of 4D Ricci solitons with specific algebra properties.

Study on completeness of foliations and null Killing fields in Lorentzian manifolds.

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…

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

We study the geometry and holonomy of semi-Riemannian, time-like metric cones that are indecomposable, i.e., which do not admit a local decomposition into a semi-Riemannian product. This includes irreducible cones, for which the holonomy can be classified, as well as non irreducible cones. The latter admit a parallel d…

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