Tootfinder

Information-Theoretical Approach to Relaxation Time Distribution in Rheology: Log-Normal Relaxation Spectrum Model
Takashi Uneyama
https://arxiv.org/abs/2509.02059 https://

Information-Theoretical Approach to Relaxation Time Distribution in Rheology: Log-Normal Relaxation Spectrum Model
The relaxation modulus of a viscoelastic fluid can be decomposed into multiple Maxwell models and characterized by the relaxation spectrum for the relaxation time. It is empirically known that the logarithmic relaxation time is useful to express the relaxation spectrum. We use information geometry to analyze the relaxation modulus and shown that the logarithmic relaxation time is the most natural variable for the relaxation spectrum. Then we use information theory to estimate the most probable …

Bounds for sets of remainders
Omkar Baraskar, Ingrid Vukusic
https://arxiv.org/abs/2508.20853 https://arxiv.org/pdf/2508.20853

Bounds for sets of remainders
Let $s(n)$ be the number of different remainders $n \bmod k$, where $1 \leq k \leq \lfloor n/2 \rfloor$. This rather natural sequence is sequence A283190 in the OEIS and while some basic facts are known, it seems that surprisingly it has barely been studied. First, we prove that $s(n) = c \cdot n + O(n/(\log n \log \log n))$, where $c$ is an explicit constant. Then we focus on differences between consecutive terms $s(n)$ and $s(n+1)$. It turns out that the value can always increase by at most o…

Exponential Lower Bounds on the Size of ResLin Proofs of Nearly Quadratic Depth
Sreejata Kishor Bhattacharya, Arkadev Chattopadhyay
https://arxiv.org/abs/2507.23008 https://

Exponential Lower Bounds on the Size of ResLin Proofs of Nearly Quadratic Depth
Itsykson and Sokolov identified resolution over parities, denoted by $\text{Res}(\oplus)$, as a natural and simple fragment of $\text{AC}^0[2]$-Frege for which no super-polynomial lower bounds on size of proofs are known. Building on a recent line of work, Efremenko and Itsykson proved lower bounds of the form $\text{exp}(N^{Ω(1)})$, on the size of $\text{Res}(\oplus)$ proofs whose depth is upper bounded by $O(N\log N)$, where $N$ is the number of variables of the unsatisfiable CNF formula. Th…

Complexity of Financial Time Series: Multifractal and Multiscale Entropy Analyses
Oday Masoudi, Farhad Shahbazi, Mohammad Sharifi
https://arxiv.org/abs/2507.23414 https://

Complexity of Financial Time Series: Multifractal and Multiscale Entropy Analyses
We employed Multifractal Detrended Fluctuation Analysis (MF-DFA) and Refined Composite Multiscale Sample Entropy (RCMSE) to investigate the complexity of Bitcoin, GBP/USD, gold, and natural gas price log-return time series. This study provides a comparative analysis of these markets and offers insights into their predictability and associated risks. Each tool presents a unique method to quantify time series complexity. The RCMSE and MF-DFA methods demonstrate a higher complexity for the Bitcoin…

Optimal quantum simulation of linear non-unitary dynamics
Guang Hao Low, Rolando D. Somma
https://arxiv.org/abs/2508.19238 https://arxiv.org/pdf/2508.19238…

Optimal quantum simulation of linear non-unitary dynamics
We present a quantum algorithm for simulating the time evolution generated by any bounded, time-dependent operator $-A$ with non-positive logarithmic norm, thereby serving as a natural generalization of the Hamiltonian simulation problem. Our method generalizes the recent Linear-Combination-of-Hamiltonian-Simulation (LCHS) framework. In instances where $A$ is time-independent, we provide a block-encoding of the evolution operator $e^{-At}$ with $\mathcal{O}\big(t\log\frac{1}ε)$ queries to the …

from my link log —
Recto: a truly 2D language.
https://masatohagiwara.net/recto.html
saved 2025-08-18 https://dotat.at/:/PGR…

Recto — a truly 2D language
Recto is a 2D programming language that uses nested rectangles as its core syntax, encoding structure and recursion directly in space instead of a linear stream of text. Recto explores new ways to write, parse, and reason about code—and even natural language—spatially.

A Bouquet of Results on Maximum Range Sum: General Techniques and Hardness Reductions
Rachana Gusain, Saladi Rahul, Aditya Subramanian
https://arxiv.org/abs/2509.16008 https://

A Bouquet of Results on Maximum Range Sum: General Techniques and Hardness Reductions
We revisit the maximum range sum (MaxRS) problem: given a set $P$ of $n$ weighted points in $\mathbb{R}^d$ and a range $Q$ (typically axis-aligned $d$-box or $d$-ball), the goal is to place $Q$ to maximize the total weight of points in $P\cap Q$. We study three natural variations: (1) Dynamic MaxRS: The goal is to update the placement of a $d$-ball under point insertions and deletions. We give a randomized $(\frac{1}{2}-ε)$-approximation with update time $O_ε(\log n)$. The approximation fac…

Automated File-Level Logging Generation for Machine Learning Applications using LLMs: A Case Study using GPT-4o Mini
Mayra Sofia Ruiz Rodriguez, SayedHassan Khatoonabadi, Emad Shihab
https://arxiv.org/abs/2508.04820

Automated File-Level Logging Generation for Machine Learning Applications using LLMs: A Case Study using GPT-4o Mini
Logging is essential in software development, helping developers monitor system behavior and aiding in debugging applications. Given the ability of large language models (LLMs) to generate natural language and code, researchers are exploring their potential to generate log statements. However, prior work focuses on evaluating logs introduced in code functions, leaving file-level log generation underexplored -- especially in machine learning (ML) applications, where comprehensive logging can enh…

Linear independence of periods for the symmetric square $L$-functions
Tianyu Ni, Hui Xue
https://arxiv.org/abs/2507.17608 https://arx…

Linear independence of periods for the symmetric square $L$-functions
For $S_k$, the space of cusp forms of weight $k$ for the full modular group, we first introduce periods on $S_k$ associated to symmetric square $L$-functions. We then prove that for a fixed natural number $n$, if $k$ is sufficiently large relative to $n$, then any $n$ such periods are linearly independent. With some extra assumption, we also prove that for $k\geq e^{12}$, we can always pick up to $\frac{\log k}{4}$ arbitrary linearly independent periods.

Lower bounds for planar Arithmetic Circuits
C. Ramya, Pratik Shastri
https://arxiv.org/abs/2509.11322 https://arxiv.org/pdf/2509.11322

Lower bounds for planar Arithmetic Circuits
Arithmetic circuits are a natural well-studied model for computing multivariate polynomials over a field. In this paper, we study planar arithmetic circuits. These are circuits whose underlying graph is planar. In particular, we prove an $Ω(n\log n)$ lower bound on the size of planar arithmetic circuits computing explicit bilinear forms on $2n$ variables. As a consequence, we get an $Ω(n\log n)$ lower bound on the size of arithmetic formulas and planar algebraic branching programs computing e…

Rough numbers between consecutive primes
Ayla Gafni, Terence Tao
https://arxiv.org/abs/2508.06463 https://arxiv.org/pdf/2508.06463

Rough numbers between consecutive primes
Using a sieve-theoretic argument, we show that almost all gaps $(p_n, p_{n+1})$ between consecutive primes $p_n, p_{n+1}$ contain a natural number $m$ whose least prime factor $p(m)$ is at least the length $p_{n+1} - p_n$ of the gap, confirming a prediction of Erdős. In fact the number $N(X)$ of exceptional gaps with $p_n \in [X,2X]$ is shown to be at most $O(X/\log^2 X)$. Assuming a form of the Hardy--Littlewood prime tuples conjecture, we establish a more precise asymptotic $N(X) \sim c X / …