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A new hierarchical distribution on arbitrary sparse precision matrices
Gianluca Mastrantonio, Pierfrancesco Alaimo Di Loro, Marco Mingione
https://arxiv.org/abs/2506.09607

A new hierarchical distribution on arbitrary sparse precision matrices
We introduce a general strategy for defining distributions over the space of sparse symmetric positive definite matrices. Our method utilizes the Cholesky factorization of the precision matrix, imposing sparsity through constraints on its elements while preserving their independence and avoiding the numerical evaluation of normalization constants. In particular, we develop the S-Bartlett as a modified Bartlett decomposition, recovering the standard Wishart as a particular case. By incorporating…

This https://arxiv.org/abs/2501.16144 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A Survey of the Holroyd-Talbot Conjecture
A family of sets is intersecting if every pair of its members has an element in common. Such a family of sets is called a star if some element is in every set of the family. Given a graph $G$, let $μ(G)$ denote the size of the smallest maximal independent set of $G$. In 2005, Holroyd and Talbot conjectured the following generalization of the Erdős-Ko-Rado Theorem: for $1\le r\le μ(G)/2$, there is a maximum size intersecting family of independent $r$-sets that is a star. In this paper we pres…

Optimal quantum sampling on distributed databases
Longyun Chen, Jingcheng Liu, Penghui Yao
https://arxiv.org/abs/2506.07724 https://a…

Optimal quantum sampling on distributed databases
Quantum sampling, a fundamental subroutine in numerous quantum algorithms, involves encoding a given probability distribution in the amplitudes of a pure state. Given the hefty cost of large-scale quantum storage, we initiate the study of quantum sampling in a distributed setting. Specifically, we assume that the data is distributed among multiple machines, and each machine solely maintains a basic oracle that counts the multiplicity of individual elements. Given a quantum sampling task, which …

Causality-aware Safety Testing for Autonomous Driving Systems
Wenbing Tang, Mingfei Cheng, Renzhi Wang, Yuan Zhou, Chengwei Liu, Yang Liu, Zuohua Ding
https://arxiv.org/abs/2506.08688

Causality-aware Safety Testing for Autonomous Driving Systems
Simulation-based testing is essential for evaluating the safety of Autonomous Driving Systems (ADSs). Comprehensive evaluation requires testing across diverse scenarios that can trigger various types of violations under different conditions. While existing methods typically focus on individual diversity metrics, such as input scenarios, ADS-generated motion commands, and system violations, they often fail to capture the complex interrelationships among these elements. This oversight leads to ga…

Segregated Runge-Kutta schemes for the time integration of the incompressible Navier-Stokes equations in presence of pressure stabilization
Pavel Bakhvalov
https://arxiv.org/abs/2506.09519

Segregated Runge-Kutta schemes for the time integration of the incompressible Navier-Stokes equations in presence of pressure stabilization
Segregated Runge-Kutta (SRK) schemes are time integration methods for the incompressible Navier-Stokes equations. In this approach, convection and diffusion can be independently treated either explicitly or implicitly, which in particular allows to construct implicit-explicit (IMEX) methods. Original SRK schemes (Colomes, Badia, IJNME, 2015) are designed for finite-element methods that satisfy the inf-sup condition. In this paper, the idea of SRK schemes is generalized to spatial discretization…

This https://arxiv.org/abs/2505.09443 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Variational formulations of transport on combinatorial meshes
We develop analogues of the primal and mixed variational formulations of the conservation laws describing transport of scalar physical properties for topological spaces referred to as cell complexes. The development is restricted to cell complexes with cells having connectivity of simple polytopes. Such spaces are suitable representations of physical systems composed of elements of different apparent topological dimensions, where all elements might have individual properties, and elements of a …

Well, fuck. Had I known ahead of time, I’d have flown to Hawaii for the long weekend.
#scomo #auspol https://aus.social/@maude…

This https://arxiv.org/abs/2407.01101 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Packing Density of Sets With Only Two Nonmixed Gaps
For a finite set of integers such that the first few gaps between its consecutive elements equal $a$, while the remaining gaps equal $b$, we study dense packings of its translates on the line. We obtain an explicit lower bound on the corresponding optimal density, conjecture its tightness, and prove it in case one of the gap lengths, $a$ or $b$, appears only once. This is equivalent to a Motzkin problem on the independence ratio of certain integer distance graphs.

Permutation-Free High-Order Interaction Tests
Zhaolu Liu, Robert L. Peach, Mauricio Barahona
https://arxiv.org/abs/2506.05963 https://

Permutation-Free High-Order Interaction Tests
Kernel-based hypothesis tests offer a flexible, non-parametric tool to detect high-order interactions in multivariate data, beyond pairwise relationships. Yet the scalability of such tests is limited by the computationally demanding permutation schemes used to generate null approximations. Here we introduce a family of permutation-free high-order tests for joint independence and partial factorisations of $d$ variables. Our tests eliminate the need for permutation-based approximations by leverag…