Tootfinder

A Note on Proper Relational Structures
Adam Bjorndahl, Philip Sink
https://arxiv.org/abs/2506.17142 https://arxiv.org/pdf/2506.17142

A Note on Proper Relational Structures
In this note we provide an algorithm for translating relational structures into "proper" relational structures, i.e., those such that there is no pair of worlds w and u such that w is accessible from u for every agent. In particular, our method of translation preserves many classical properties of relational structures, such as transitivity and the Euclidean property. As a result, this method of translation has many applications in the literature on Simplicial Semantics for modal logic, where t…

A note on congruences for the difference between even cranks and odd cranks
Russelle Guadalupe
https://arxiv.org/abs/2506.16267 https://

A note on congruences for the difference between even cranks and odd cranks
Recently, Amdeberhan and Merca proved some arithmetic properties of the difference $C(n)$ between the number of partitions of $n$ with even cranks and those with odd cranks and the sequence $a(n)$ whose generating function is the reciprocal of that of $C(n)$. In this note, we give new elementary proofs of some of their main results and extend them. In particular, we establish Ramanujan-type congruences modulo $5$ and $25$ for certain finite sums involving $C(n)$ and $a(n)$. Our proofs employ th…

A note on twisted, straight, and sheared waveguide
Diana C. S. Bello
https://arxiv.org/abs/2506.15938 https://arxiv.org/pdf/2506.1593…

A note on twisted, straight, and sheared waveguide
In this work, we analyze the Dirichlet Laplacian $-Δ_Ω^D$ in an unbounded waveguide $Ω\subset \mathbb R^3$, where the cross-section is translated in a constant direction and rotated along a spatial line. We focus on the effects of twisting on the spectrum, discussing conditions under which discrete eigenvalues emerge. Our results highlight the interplay between geometry and spectral properties, showing that shearing can induce a richer spectral structure even in straight waveguides.

A note on the properties of the confidence set for the local average treatment effect obtained by inverting the score test
Ezequiel Smucler, Ludovico Lanni, David Masip
https://arxiv.org/abs/2506.10449

A note on the properties of the confidence set for the local average treatment effect obtained by inverting the score test
We study the properties of the score confidence set for the local average treatment effect in non and semiparametric instrumental variable models. This confidence set is constructed by inverting a score test based on an estimate of the nonparametric influence function for the estimand, and is known to be uniformly valid in models that allow for arbitrarily weak instruments; because of this, the confidence set can have infinite diameter at some laws. We characterize the six possible forms the sc…

Correlation functions of von Neumann entropy
Mathew W. Bub, Allic Sivaramakrishnan
https://arxiv.org/abs/2506.10917 https://arxiv.org…

Correlation functions of von Neumann entropy
In this note, we study two-point correlation functions of modular Hamiltonians. We show that in general quantum systems, these correlators obey properties similar to those of von Neumann entropy and capacity of entanglement, both of which are special cases of these correlators. Then we specialize to two spacelike-separated spherical subregions in conformal field theories. We present direct computations of the vacuum two-point function that confirm its equivalence to the stress-tensor conformal …

Short note on phase retrievable weaving fusion frames
Animesh Bhandari
https://arxiv.org/abs/2506.08478 https://arxiv.org/pdf/2506.08…

Short note on phase retrievable weaving fusion frames
Fusion frames are extensively studied due to their effectiveness in recovering signals from large-scale data. They are applicable in distributed processing, wireless sensor networks, and packet encoding systems due to their robustness and redundancy. Motivated by the foundational work of Bemrose et al.\cite{Be16} and Balan\cite{Ba13}, this paper investigates the theoretical properties and characterizations of phase retrievable weaving fusion frames. These frames offer enhanced redundancy and st…

This https://arxiv.org/abs/2412.03857 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

An Excursion with Divergence Properties
In this note, we compare and contrast various selective divergence properties such as the properties of being discretely selective and selectively highly divergent. We identify and incorporate a class of subsemigroups of the semigroup of strictly increasing maps from the naturals to themselves. We investigate certain implications for hyperspaces of finite subsets and characterize the closed discrete selection game on a space in terms of a particular selection game on the Vietoris hyperspace of …

This https://arxiv.org/abs/2502.02274 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Hyperpolygonal arrangements
In 2024, Bellamy, Craw, Rayan, Schedler, and Weiss introduced a particular family of real hyperplane arrangements stemming from hyperpolygonal spaces associated with certain quiver varieties which we thus call hyperpolygonal arrangements $\mathcal H_n$. In this note we study these arrangements and investigate their properties systematically. Remarkably the arrangements $\mathcal H_n$ discriminate between essentially all local properties of arrangements. In addition we show that hyperpolygonal a…

On gauge transforms of autonomous ordinary differential equations
Giuseppe Gaeta, Sebastian Walcher
https://arxiv.org/abs/2506.07189 https://

On gauge transforms of autonomous ordinary differential equations
The notion of gauge transform has its origin in Physics (Field Theory). In the present note we discuss -- from a purely mathematical perspective -- special gauge transforms of autonomous first order ODE's and their special properties. Particular attention is given to the problem of identifying those nonautonomous ODE's which are gauge transforms of autonomous systems.

On the Spherical Dirichlet Distribution: Corrections and Results
Jose H Guardiola
https://arxiv.org/abs/2506.04441 https://arxiv.org/…

On the Spherical Dirichlet Distribution: Corrections and Results
This note corrects a technical error in Guardiola (2020, Journal of Statistical Distributions and Applications), presents updated derivations, and offers an extended discussion of the properties of the spherical Dirichlet distribution. Today, data mining and gene expressions are at the forefront of modern data analysis. Here we introduce a novel probability distribution that is applicable in these fields. This paper develops the proposed Spherical-Dirichlet Distribution designed to fit vectors …

On Chaos in QFT
Jacob Sonnenschein, Nadav Shrayer
https://arxiv.org/abs/2506.10784 https://arxiv.org/pdf/2506.10784

On Chaos in QFT
In this note we explore the chaotic behavior of non-integrable QFTs and compare them to integrable ones. We choose as prototypes the double sine-Gordon and the sine-Gordon models. We analyze their discrete spectrum determined by a truncation method. We examine the map of the corresponding energy eigenvalues to the eigenvalues of the random matrix theory (RMT) Gaussian orthogonal ensemble (GOE). This is done by computing the following properties: (a) The distribution of the adjacent spacings and…

This https://arxiv.org/abs/2303.17191 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the continuity of Følner averages
It is known that if each point $x$ of a dynamical system is generic for some invariant measure $μ_x$, then there is a strong connection between certain ergodic and topological properties of that system. In particular, if the acting group is abelian and the map $x\mapsto μ_x$ is continuous, then every orbit closure is uniquely ergodic. In this note, we show that if the acting group is not abelian, orbit closures may well support more than one ergodic measure even if $x\mapsto μ_x$ is contin…