Related papers: Bi-invariant Two-Sample Tests in Lie Groups for Sh…

Any abstract (not necessarily continuous) group automorphism of a simple, compact Lie group must be continuous due to Cartan (1930) and van der Waerden (1933). The purpose of this paper is to study a similar question in nilpotent Lie…

We study the matter bispectrum of large structure by comparing theoretical models (perturbation theories and halo models) to numerical simulations using shape and amplitude correlators. We show that among the perturbation theories at one…

In the context of a connected, simply connected, nilpotent Lie group, whose representations are square-integrable modulo the center, we find characterization results of extra-invariant spaces under the left translations associated with the…

This paper studies the reduction by symmetry of a variational obstacle avoidance problem. We derive the reduced necessary conditions in the case of Lie groups endowed with a left-invariant metric, and for its corresponding Riemannian…

The primary goal of this paper is to study topological invariants in two dimensional twofold rotation and time-reversal symmetric spinful systems. In this paper, firstly we build a new homotopy invariant based on the lifting of the Wilson…

In this note we use techniques in the topology of 2-complexes to recast some tools that have arisen in the study of planar tiling questions. With spherical pictures we show that the tile counting group associated to a set $T$ of tiles and a…

We propose robust two-sample tests for comparing means in time series. The framework accommodates a wide range of applications, including structural breaks, treatment-control comparisons, and group-averaged panel data. We first consider…

We discuss the generalization of the local renormalization group approach to theories in which Weyl symmetry is gauged. These theories naturally correspond to scale invariant - rather than conformal invariant - models in the flat space…

Aimed at geometric applications, we prove the homology cobordism invariance of the $L^2$-betti numbers and $L^2$-signature defects associated to the class of amenable groups lying in Strebel's class $D(R)$, which includes some interesting…

We construct invariant complex product (hyperparacomplex, indefinite quaternion) structures on the manifolds underlying the real noncompact simple Lie groups $SL(2m-1,\RR)$, $SU(m,m-1)$ and $SL(2m-1,\CC)^\RR$. We show that on the last two…

We present a novel approach for nonlinear statistical shape modeling that is invariant under Euclidean motion and thus alignment-free. By analyzing metric distortion and curvature of shapes as elements of Lie groups in a consistent…

This paper reconsiders the problem of testing the equality of two unspecified continuous distributions. The framework, which we propose, allows for readable and insightful data visualisation and helps to understand and quantify how two…

Persistent homology is a vital tool for topological data analysis. Previous work has developed some statistical estimators for characteristics of collections of persistence diagrams. However, tools that provide statistical inference for…

We introduce a kernel-based two-sample test for comparing probability distributions up to group actions. Our construction yields invariant kernels for locally compact $\sigma$-compact groups and extends classical Haar-based approaches…

Applications of harmonic analysis on finite groups were recently introduced to measure partition problems, with a variety of equipartition types by convex fundamental domains obtained as the vanishing of prescribed Fourier transforms.…

Testing equality of two multivariate distributions is a classical problem for which many non-parametric tests have been proposed over the years. Most of the popular two-sample tests, which are asymptotically distribution-free, are based…

In this paper, we propose a new test for testing the equality of two population covariance matrices in the ultra-high dimensional setting that the dimension is much larger than the sizes of both of the two samples. Our proposed methodology…

Hypothesis testing for graphs has been an important tool in applied research fields for more than two decades, and still remains a challenging problem as one often needs to draw inference from few replicates of large graphs. Recent studies…

We present a conceptual model to measure disparity--the target study--where social groups may be similarly situated (i.e., balanced) on allowable covariates. Our model, based on a sampling design, does not intervene to assign social group…

We develop a theory of "quasi"-Hamiltonian G-spaces for which the moment map takes values in the group G itself rather than in the dual of the Lie algebra. The theory includes counterparts of Hamiltonian reductions, the Guillemin-Sternberg…