Two-sample tests for multivariate data and especially for non-Euclidean data are not well explored. This paper presents a novel test statistic based on a similarity graph constructed on the pooled observations from the two samples. It can be applied to multivariate data and non-Euclidean data as long as a dissimilarity measure on the sample space can be defined, which can usually be provided by...

We introduce the notion of a k-type slant helix in Minkowski space E1. For partially null and pseudo null curves in E1, we express some characterizations in terms of their curvature and torsion functions. AMS subject classifications: 53C40, 53C50

This paper is concerned with the Cauchy problem for relativistic membrane equation (RME) embedded in $${\mathbb {R}}^{1+(1+n)}$$ $$n=2, \, 3$$ . We show that RME a class of large (in energy norm) initial data admits global, smooth solution. The are given by short pulse type, which introduced Christodoulou his work on formation black holes [10]. Due to quasilinear feature RME, we construct two m...

A characteristic value formulation of the Weyl double copy leads to an asymptotic formulation. We find that holds asymptotically in cases where full solution is algebraically general, using rotating STU supergravity black holes as example. The provides clues regarding relation between symmetries follows from copy. Using C-metric example, we show a previous interpretation this gravity superrotat...

In this correspondence we derive the asymptotic distribution of the MUSIC null spectrum, from which an exact expression of the asymptotic variance of the MUSIC null spectrum can be obtained. The result presented in this correspondence is a simpler alternative and a special case of a more general result recently obtained by Lee and Wengrovitz.

A new sufficient condition for photons emitted near future null infinity to reach is derived by studying geodesics in the Bondi coordinates asymptotically flat spacetimes. In our previous works [M. Amo et al., Phys. Rev. D 104, 064025 (2021).; M. 105, 064074 (2022).], such a was established outward or tangential directions constant radial surfaces. This paper improves result including inward di...

The present paper deals with functions acting on the digits of an q-ary expansion. In particular let n be a positive integer, then we call

Tests for regression neglected nonlinearity based on artificial neural networks (ANNs) have so far been studied by separately analyzing the two ways in which the null of regression linearity can hold. This implies that the asymptotic behavior of general ANN-based tests for neglected nonlinearity is still an open question. Here we analyze a convenient ANN-based quasi-likelihood ratio statistic f...