English
Related papers

Related papers: Exploring Collatz Dynamics with Human-LLM Collabor…

200 papers

Large Language Models (LLMs) have achieved remarkable success in tasks requiring complex reasoning, such as code generation, mathematical problem solving, and algorithmic synthesis -- especially when aided by reasoning tokens and…

Computation and Language · Computer Science 2025-06-13 Jaechul Roh , Varun Gandhi , Shivani Anilkumar , Arin Garg

Let $q$ be an odd prime, and let $T_{q}:\mathbb{Z}\rightarrow\mathbb{Z}$ be the Shortened $qx+1$ map, defined by $T_{q}\left(n\right)=n/2$ if $n$ is even and $T_{q}\left(n\right)=\left(qn+1\right)/2$ if $n$ is odd. The study of the dynamics…

Number Theory · Mathematics 2023-12-18 M. C. Siegel

We study transitions in log-correlated Random Energy Models (logREMs) that are related to the violation of a Seiberg bound in Liouville field theory (LFT): the binding transition and the termination point transition (a.k.a. pre-freezing).…

Statistical Mechanics · Physics 2018-04-18 Xiangyu Cao , Pierre Le Doussal , Alberto Rosso , Raoul Santachiara

Let $\Gamma<\mathrm{SL}_2(\mathbb{Z})$ be a non-elementary finitely generated subgroup and let $\Gamma(q)$ be its congruence subgroup of level $q$ for each $q\in \mathbb{N}$. We obtain an asymptotic formula for the matrix coefficients of…

Dynamical Systems · Mathematics 2015-09-23 Hee Oh , Dale Winter

We give a unified treatment of dispersive sum rules for four-point correlators in conformal field theory. We call a sum rule dispersive if it has double zeros at all double-twist operators above a fixed twist gap. Dispersive sum rules have…

High Energy Physics - Theory · Physics 2023-01-11 Simon Caron-Huot , Dalimil Mazac , Leonardo Rastelli , David Simmons-Duffin

We provide a complete elaboration of the $L^2$-Hilbert space hypocoercivity theorem for the degenerate Langevin dynamics with multiplicative noise, studying the longtime behaviour of the strongly continuous contraction semigroup solving the…

Functional Analysis · Mathematics 2022-05-25 Alexander Bertram , Martin Grothaus

We set up a strategy for studying large families of logarithmic conformal field theories by using the enlarged symmetries and non--semi-simple associative algebras appearing in their lattice regularizations (as discussed in a companion…

High Energy Physics - Theory · Physics 2008-11-26 N. Read , H. Saleur

We prove a compactness theorem for sequences of low-action punctured holomorphic curves of controlled topology, in any dimension, without imposing the typical assumption of uniformly bounded Hofer energy. In the limit, we extract a family…

Symplectic Geometry · Mathematics 2024-07-02 Dan Cristofaro-Gardiner , Rohil Prasad

We investigate the high-temperature dynamical conductivity $\sigma(\omega)$ in two one-dimensional integrable quantum lattice models: the anisotropic XXZ spin chain and the Hubbard chain. The emphasis is on the metallic regime of both…

Strongly Correlated Electrons · Physics 2021-09-29 P. Prelovšek , M. Mierzejewski , J. Herbrych

We investigate a recombination-drift-diffusion model coupled to Poisson's equation modelling the transport of charge within certain types of semiconductors. In more detail, we study a two-level system for electrons and holes endowed with an…

Analysis of PDEs · Mathematics 2021-11-24 Klemens Fellner , Michael Kniely

The Collatz map (or the $3n{+}1$-map) $f$ is defined on positive integers by setting $f(n)$ equal to $3n+1$ when $n$ is odd and $n/2$ when $n$ is even. The Collatz conjecture states that starting from any positive integer $n$, some iterate…

Operator Algebras · Mathematics 2025-02-04 Takehiko Mori

The Landauer approach to diffusive transport is mathematically related to the solution of the Boltzmann transport equation, and expressions for the thermoelectric parameters in both formalisms are presented. Quantum mechanical and…

Mesoscale and Nanoscale Physics · Physics 2015-05-14 Changwook Jeong , Raseong Kim , Mathieu Luisier , Supriyo Datta , Mark Lundstrom

For defining the conductance of single molecule junctions with a redox functionality in an electrochemical cell, two conceptually different electron transport mechanisms, namely coherent tunnelling and vibrationally induced hopping compete…

Mesoscale and Nanoscale Physics · Physics 2015-06-22 Georg Kastlunger , Robert Stadler

State-of-the-art Datalog engines include expressive features such as ADTs (structured heap values), stratified aggregation and negation, various primitive operations, and the opportunity for further extension using FFIs. Current…

Programming Languages · Computer Science 2022-11-22 Thomas Gilray , Arash Sahebolamri , Sidharth Kumar , Kristopher Micinski

We consider the symmetric simple exclusion process in $\mathbb Z^d$ with quenched bounded dynamic random conductances and prove its hydrodynamic limit in path space. The main tool is the connection, due to the self-duality of the process,…

Probability · Mathematics 2021-02-03 Frank Redig , Ellen Saada , Federico Sau

Tracing out a Galilean-invariant Caldeira-Leggett environment breaks Galilean boost covariance of the reduced dynamics, while spatial translations and rotations survive intact. An operator-level analysis of the exact Hu-Paz-Zhang master…

Quantum Physics · Physics 2026-05-01 Leonardo F. Calderón , Esteban Marulanda , Santiago Morales , Leonardo A. Pachón

Generative modeling within constrained sets is essential for scientific and engineering applications involving physical, geometric, or safety requirements (e.g., molecular generation, robotics). We present a unified framework for…

Machine Learning · Computer Science 2026-04-21 Kijung Jeon , Michael Muehlebach , Molei Tao

Let A be a simple, unital, exact, and finite C*-algebra which absorbs the Jiang-Su algebra Z tensorially. We prove that the Cuntz semigroup of A admits a complete order embedding into an ordered semigroup obtained from the Elliott invariant…

Operator Algebras · Mathematics 2007-05-23 Francesc Perera , Andrew S. Toms

In this paper, we consider a few iterative decoding schemes for the joint source-channel coding of correlated sources. Specifically, we consider the joint source-channel coding of two erasure correlated sources with transmission over…

Information Theory · Computer Science 2009-10-08 Arvind Yedla , Henry D. Pfister , Krishna R. Narayanan

In this paper a new conjecture equivalent to Collatz conjecture is presented. In particural, showing that (all) the solution(s) of newly introduced iterative functional equation(s) have a given property is equivalent to prove Collatz…

General Mathematics · Mathematics 2023-05-18 Giulio Masetti