Tootfinder

Characterizing Equivalence of Logically Constrained Terms via Existentially Constrained Terms (Full Version)
Kanta Takahata, Jonas Sch\"opf, Naoki Nishida, Takahito Aoto
https://arxiv.org/abs/2505.21986

Characterizing Equivalence of Logically Constrained Terms via Existentially Constrained Terms (Full Version)
Logically constrained term rewriting is a rewriting framework that supports built-in data structures such as integers and bit vectors. Recently, constrained terms play a key role in various analyses and applications of logically constrained term rewriting. A fundamental question on constrained terms arising there is how to characterize equivalence between them. However, in the current literature only limited progress has been made on this. In this paper, we provide several sound and complete so…

This https://arxiv.org/abs/2409.03394 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Partitioning 2-edge-coloured bipartite graphs into monochromatic cycles
Given an $r$-edge-colouring of the edges of a graph $G$, we say that it can be partitioned into $p$ monochromatic cycles when there exists a set of $p$ vertex-disjoint monochromatic cycles covering all the vertices of $G$. In the literature of this problem, an edge and a single vertex both count as a cycle. We show that for every $2$-colouring of the edges of a complete balanced bipartite graph, $K_{n,n}$, it can be partitioned into at most 4 monochromatic cycles. This type of question was fi…

Mind the Gap: A Formal Investigation of the Relationship Between Log and Model Complexity -- Extended Version
Patrizia Schalk, Artem Polyvyanyy
https://arxiv.org/abs/2505.23233

Mind the Gap: A Formal Investigation of the Relationship Between Log and Model Complexity -- Extended Version
Simple process models are key for effectively communicating the outcomes of process mining. An important question in this context is whether the complexity of event logs used as inputs to process discovery algorithms can serve as a reliable indicator of the complexity of the resulting process models. Although various complexity measures for both event logs and process models have been proposed in the literature, the relationship between input and output complexity remains largely unexplored. In…

Measurement of the Lund plane for light- and beauty-quark jets
LHCb collaboration, et al.
https://arxiv.org/abs/2505.23530 https://ar…

Measurement of the Lund plane for light- and beauty-quark jets
The substructure of jets in quantum chromodynamics (QCD) has garnered significant attention with the advent of infrared- and collinear-safe clustering algorithms and observables. A key question emerging from these studies is how in-jet emissions at soft and hard energy scales, across collinear and wide angles relative to the emitter, differ with the mass of the emitting parton. The Lund jet plane (LJP) is a perturbatively well-defined substructure observable that maps the radiation pattern of j…

This https://arxiv.org/abs/2306.11965 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qbi…

Symmetry's Edge in Cortical Dynamics: Multiscale Dynamics of Ensemble Excitation and Inhibition
Creating a quantitative theory for the cortex presents challenges and raises questions. What are the significant scales--micro, meso, or macroscopic? What are the interactions--pairwise, higher order, or mean-field? And what control parameters are relevant--noisy, dissipative, or emergent? We suggest an approach inspired by advances in understanding matter. This involves identifying invariances in neuron ensemble dynamics, searching for order parameters connecting key degrees of freedom and d…

Revisiting the Li abundances of Stars with and without Detected Planets from the High Resolution Spectroscopy
Jinxiao Qin, Hong-Liang Yan, Wenyuan Cui, Jian-Rong Shi, Subo Dong, Shuai Liu, Zeming Zhou, Miao Tian, Zhenyan Huo, Xiangsong Fang, Jinghua Zhang, Chunqian Li, Mingyi Ding, Song Wang, Henggeng Han
https://arxiv.org/abs/2…

Revisiting the Li abundances of Stars with and without Detected Planets from the High Resolution Spectroscopy
Whether the presence of planets affects the lithium (Li) abundance of their host stars is still an open question. To investigate the difference of the Li abundance between planet-host stars (HS) and isolated stars (IS) with no detected planets, we analyze a large sample of stars with temperatures ranging from 4600 to 6600 K and metallicity ranging from -0.55 to +0.50. The sample consists of 279 HS whose spectra were taken from the California-Kepler Survey (CKS), which followed up planets detect…

The high precision time nuts, a.k.a. the “Time Lords” had a pretty good demonstration at #Hamvention. They built an LLM that had ingested 10 years of papers and mailing lists and could answer questions reliably

This https://arxiv.org/abs/2505.15707 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

When are syzygies of the residue field self-dual?
Finitely generated reflexive modules over commutative Noetherian rings form a key component of Auslander and Bridger's stable module theory and are likewise essential in the study of Cohen--Macaulay representations. Recently, H. Dao characterized Arf local rings as exactly those one-dimensional Cohen--Macaulay local rings over which every finitely generated reflexive module is self-dual, and raised the general question of characterizing rings over which every finitely generated reflexive module…

This https://arxiv.org/abs/2505.15707 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

When are syzygies of the residue field self-dual?
Finitely generated reflexive modules over commutative Noetherian rings form a key component of Auslander and Bridger's stable module theory and are likewise essential in the study of Cohen--Macaulay representations. Recently, H. Dao characterized Arf local rings as exactly those one-dimensional Cohen--Macaulay local rings over which every finitely generated reflexive module is self-dual, and raised the general question of characterizing rings over which every finitely generated reflexive module…