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Related papers: An overview of uniformity tests on the hypersphere

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We consider linear and time-dependent perturbations of periodic transport equations on the two-dimensional torus. For generic perturbations, we prove the existence of a large class of initial data whose Sobolev norms diverge exponentially…

Analysis of PDEs · Mathematics 2025-10-21 Gabriel Rivière , Maria Teresa Rotolo

A long noted difficulty when assessing the reliability (or calibration) of forecasting systems is that reliability, in general, is a hypothesis not about a finite dimensional parameter but about an entire functional relationship. A…

Data Analysis, Statistics and Probability · Physics 2020-12-09 Jochen Bröcker

Hyperuniform particle arrangements are characterized by a local number variance that grows more slowly than the volume of the observation window. We generalize this concept to describe particle systems in which particles carry weights:…

Statistical Mechanics · Physics 2026-03-04 Salvatore Torquato , Jaeuk Kim , Michael A. Klatt , Roberto Car , Paul J. Steinhardt

Spaces of quasi-invariant measures supplied with different topologies are studied. Their embeddings, projective decompositions, conditions for their metrizability are investigated. Theorems about convergence of nets of quasi-invariant…

Probability · Mathematics 2016-06-08 Sergey Victor Ludkowski

Author developed a uniform model for different spaces where distance and angle measure kinds are parameters. This model is calculus centric, but can also be used in theoretical research. It is useful in the following domains: deduction of…

Metric Geometry · Mathematics 2018-07-30 Alexandru Popa

Shape constraints yield flexible middle grounds between fully nonparametric and fully parametric approaches to modeling distributions of data. The specific assumption of log-concavity is motivated by applications across economics, survival…

Methodology · Statistics 2024-04-16 Robin Dunn , Aditya Gangrade , Larry Wasserman , Aaditya Ramdas

A hypercycle equation with infinitely many types of macromolecules is formulated and studied both analytically and numerically. The resulting model is given by an integro-differential equation of the mixed type. Sufficient conditions for…

Populations and Evolution · Quantitative Biology 2022-07-12 Alexander S. Bratus , Olga S. Chmereva , Ivan Yegorov , Artem S. Novozhilov

We provide an elementary proof of the equivalence of various notions of uniform hyperbolicity for a class of $\mathrm{GL}(2,\mathbb{C})$ cocycles and establish a Johnson-type theorem for extended CMV matrices, relating the spectrum to the…

Spectral Theory · Mathematics 2016-12-15 David Damanik , Jake Fillman , Milivoje Lukic , William Yessen

We study hyperuniform properties in various two-dimensional periodic and quasiperiodic point patterns. Using the histogram of the two-point distances, we develop an efficient method to calculate the hyperuniformity order metric, which…

Statistical Mechanics · Physics 2024-10-01 A. Koga , S. Sakai

The proposed universality of small scale turbulence is investigated for a set of measurements in a cryogenic free jet with a variation of the Reynolds number (Re) from 8500 to 10^6. The traditional analysis of the statistics of velocity…

Fluid Dynamics · Physics 2009-11-07 Ch. Renner , J. Peinke , R. Friedrich , O. Chanal , B. Chabaud

We study the variance in the number of points contained within a window $\Omega$ of arbitrary size, and to further illuminate our understanding of {\it hyperuniform} systems, i.e., point patterns that do not possess long-wavelength…

Statistical Mechanics · Physics 2009-11-10 Salvatore Torquato , Frank H. Stillinger

The paper analyses properties of a large class of "path-based" Data Envelopment Analysis models through a unifying general scheme. The scheme includes the well-known oriented radial models, the hyperbolic distance function model, the…

Optimization and Control · Mathematics 2023-08-22 Margaréta Halická , Mária Trnovská , Aleš Černý

We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…

Statistics Theory · Mathematics 2025-07-29 Karl Oskar Ekvall , Matteo Bottai

Hypothesis testing in singular statistical models is often regarded as inherently problematic due to non-identifiability and degeneracy of the Fisher information. We show that the fundamental obstruction to testing in such models is not…

Statistics Theory · Mathematics 2026-03-02 Sean Plummer

We give a nearly-optimal algorithm for testing uniformity of distributions supported on $\{-1,1\}^n$, which makes $\tilde O (\sqrt{n}/\varepsilon^2)$ queries to a subcube conditional sampling oracle (Bhattacharyya and Chakraborty (2018)).…

Data Structures and Algorithms · Computer Science 2021-02-08 Clément L. Canonne , Xi Chen , Gautam Kamath , Amit Levi , Erik Waingarten

This paper introduces two new families of non-parametric tests of goodness-of-fit on the compact classical groups. One of them is a family of tests for the eigenvalue distribution induced by the uniform distribution, which is consistent…

Statistics Theory · Mathematics 2018-02-27 Amir Sepehri

Given observations from a circular random variable contaminated by an additive measurement error, we consider the problem of minimax optimal goodness-of-fit testing in a non-asymptotic framework. We propose direct and indirect testing…

Statistics Theory · Mathematics 2020-07-14 Sandra Schluttenhofer , Jan Johannes

In this paper, we revisit the classical goodness-of-fit problems for univariate distributions; we propose a new testing procedure based on a characterisation of the uniform distribution. Asymptotic theory for the simple hypothesis case is…

Methodology · Statistics 2021-08-17 Bruno Ebner , Shawn Liebenberg , Jaco Visagie

We prove large deviations principles for spectral measures of perturbed (or spiked) matrix models in the direction of an eigenvector of the perturbation. In each model under study, we provide two approaches, one of which relying on large…

Probability · Mathematics 2021-09-24 Nathan Noiry , Alain Rouault

The effective numerical method is developed performing the test of the hyperbolicity of chaotic dynamics. The method employs ideas of algorithms for covariant Lyapunov vectors but avoids their explicit computation. The outcome is a…

Chaotic Dynamics · Physics 2012-03-28 Pavel V. Kuptsov