Tootfinder

Stable first order theories as simplicial profinite sets
Misha Gavrilovich
https://arxiv.org/abs/2510.00854 https://arxiv.org/pdf/2510.00854

Stable first order theories as simplicial profinite sets
We rewrite simplicially the standard definitions of a complete first order theory, a model of it, and various characterisations of stability of a complete first order theory. In our reformulations the simplicial language replaces the standard definitions based on syntax, making them formally unnecessary. We view a complete first-order theory as a symmetric simplicial object in the category of profinite sets and open continuous maps, defined by the functor sending a finite set of variables int…

Uncertainties within Weather Regime definitions for the Euro-Atlantic sector in ERA5 and CMIP6
Lotte Hompes, Swinda K. J. Falkena, Laurens P. Stoop
https://arxiv.org/abs/2508.21701

Uncertainties within Weather Regime definitions for the Euro-Atlantic sector in ERA5 and CMIP6
Certain Weather Regimes (WR) are associated with a higher risk of energy shortages, i.e. Blocking regimes for European winters. However, there are many uncertainties tied to the implementation of WRs and associated risks in the energy sector. Especially the impact of climate change is unknown. We investigate these uncertainties by looking at three methodologically diverse Euro-Atlantic WR definitions. We carry out a thorough validation of these methods and analyse their methodological and spa…

A Practitioner's Guide to Multi-turn Agentic Reinforcement Learning
Ruiyi Wang, Prithviraj Ammanabrolu
https://arxiv.org/abs/2510.01132 https://arxiv.o…

A Practitioner's Guide to Multi-turn Agentic Reinforcement Learning
We study what actually works and what doesn't for training large language models as agents via multi-turn reinforcement learning. Despite rapid progress, existing frameworks and definitions are fragmented, and there is no systematic formulation or analysis of which design choices matter across tasks. We address this gap by first breaking down the design space into three inter-related pillars -- environment, reward, and policy -- and empirically derive a recipe for training LLM agents in situate…

Double Orthogonal Factorization Systems
C. B. Aberl\'e, Elena Caviglia, Matthew Kukla, Rub\'en Maldonado, Luca Mesiti, Dorette Pronk, Tanjona Ralaivaosaona
https://arxiv.org/abs/2509.26343

Double Orthogonal Factorization Systems
We define strict and lax orthogonal factorization systems on double categories. These consist of an orthogonal factorization system on arrows and one on double cells that are compatible with each other. Our definitions are motivated by several explicit examples, including factorization systems on double categories of spans, relations and bimodules. We then prove monadicity results for orthogonal factorization systems on double categories in order to justify our definitions. For fibrant double c…

@… Yeah, I am not opposed to state varying across that level. Across applications, maintained by separate teams or even departments, of course! You don’t want to couple yourself to people who might have drastically different definitions of “success” to you.
But within a single application, serving a single purpose? Only if there’s no better way.…

In Search of Homology for Quasigroups of Bol-Moufang Type
Anthony Christiana, Ben Clingenpeel, Huizheng Guo, Jinseok Oh, Jozef H. Przytycki, Anna Zamojska-Dzienio
https://arxiv.org/abs/2508.21268

In Search of Homology for Quasigroups of Bol-Moufang Type
We initiate (co)homology theory for quasigroups of Bol-Moufang type based on analysis of their extensions by affine quasigroups of the same type. We use these extensions to define second and third boundary operations, $\partial_2(x,y)$ and $\partial_3(x,y,z)$, respectively. We use these definitions to compute the second homology groups for several examples from the work of Phillips and Vojtechovsky. We speculate about the relation between these homology groups and those obtained from a small ca…

The twistor lifts of surfaces in 4-spaces
Naoya Ando
https://arxiv.org/abs/2509.22253 https://arxiv.org/pdf/2509.22253

The twistor lifts of surfaces in 4-spaces
This is a survey of the twistor lifts of surfaces in 4-spaces. In most part of this survey, the space is the Euclidean $4$-space $E^4$. The definitions of the Gauss maps and the twistor lifts of surfaces in $E^4$ are given by complex structures of $E^4$. Based on these definitions, we can understand that the Gauss maps of minimal surfaces are holomorphic and characterize isotropicity of minimal surfaces.

Hey @… I was just listening to the great literary olfactoloy episode with @allylouks.bsky.social€, but I feel that the existence/role of human pheromones has been a bit misrepresented.
I have worked on mammalian pheromones for my PhD, and I have encountered (at least) two major definitions of the term "pheromone", one based on the function of a substance, and the other, which I personally prefer, on the information flow involved in it (https://doi.org/10.1159/000096511).
Based on the Sbarbati & Osculati definition, a pheromone would be a component that conveys information between individuals of the same species.
There is also quite a bit of research that argues for the existence of human pheromones (e.g. https://doi.org/10.1002/ar.a.20125, https://doi.org/10.1002/ar.a.20125, https://doi.org/10.1126/science.1198331)
However, the discussion on the existence of human pheromones is difficult, as it touches on the topic of free will as many reactions to odor are involuntary. During the International Symposium on Olfaction and Taste held in Iceland in 2024, there have been several session on human olfaction touching on sensitive aspects such as olfaction-mediated effects on mate choice and pregnancy, but none of the researchers dared utter the word pheromone, while colleagues working on other mammals where happily talking about pheromonal effects for very similar topics.
Long story short, I feel that saying there is no hard evidence for human pheromones is misrepresenting the current research.

The “you don’t even know what a Nazi is” people are so laughable.
Dude, go fuck yourself, but before you do look up what “Nazi” means in a dictionary and that there’s 3 definitions for the word.

$\chi$ -extending modular lattices
Jesus Adrian Celis-Gonz\'alez, Hugo Alberto Rinc\'on-Mej\'ia
https://arxiv.org/abs/2509.22903 https://arxiv.…

$χ$ -extending modular lattices
This paper investigates the theory of lattices, focusing on extending lattices relative to abstract classes, modular lattices, and torsion lattices. Definitions of type-1 and type-2 extending lattices are provided, along with their weakly extending counterparts. Modular and upper continuous lattices are analyzed, with lemmas establishing relationships between pseudo-complements, complements, and essential elements. Applications to module theory are highlighted.

Do LLMs Adhere to Label Definitions? Examining Their Receptivity to External Label Definitions
Seyedali Mohammadi, Bhaskara Hanuma Vedula, Hemank Lamba, Edward Raff, Ponnurangam Kumaraguru, Francis Ferraro, Manas Gaur
https://arxiv.org/abs/2509.02452

Do LLMs Adhere to Label Definitions? Examining Their Receptivity to External Label Definitions
Do LLMs genuinely incorporate external definitions, or do they primarily rely on their parametric knowledge? To address these questions, we conduct controlled experiments across multiple explanation benchmark datasets (general and domain-specific) and label definition conditions, including expert-curated, LLM-generated, perturbed, and swapped definitions. Our results reveal that while explicit label definitions can enhance accuracy and explainability, their integration into an LLM's task-solvin…

WTMAD-4: A Fair Weighting Scheme for GMTKN55
Kyle R. Bryenton, Erin R. Johnson
https://arxiv.org/abs/2509.23498 https://arxiv.org/pdf/2509.23498

WTMAD-4: A Fair Weighting Scheme for GMTKN55
The GMTKN55 data set is a collection of standard benchmarks used in molecular quantum chemistry that spans small- and large-molecule thermochemistry, reaction barriers, and non-covalent interactions. Herein, we identify a flaw in the weighted mean absolute deviation (WTMAD) definitions commonly used to quantify performance of various electronic-structure methods for the GMTKN55 set, which under-weight some of its component benchmarks by orders of magnitude. A new WTMAD-4 metric is proposed, bas…

Ground Stratification for a Logic of Definitions with Induction
Nathan Guermond (University of Minnesota), Gopalan Nadathur (University of Minnesota)
https://arxiv.org/abs/2510.12297

Ground Stratification for a Logic of Definitions with Induction
The logic underlying the Abella proof assistant includes mechanisms for interpreting atomic predicates through fixed point definitions that can additionally be treated inductively or co-inductively. However, the original formulation of the logic includes a strict stratification condition on definitions that is too restrictive for some applications such as those that use a logical relations based approach to semantic equivalence. Tiu has shown how this restriction can be eased by utilizing a wea…

Local Fractional Calculus currently. A Mosaic of Definitions and the Quest for Unification
Juan E. N\'apoles Vald\'es
https://arxiv.org/abs/2508.19253 https://

Local Fractional Calculus currently. A Mosaic of Definitions and the Quest for Unification
In this paper, we present an overview of the development of one of the most dynamic areas of mathematics today: local differential operators of non-integer order. The underlying question is whether we are witnessing a period of consolidation and are on the way to a general formulation of this fascinating topic.

Lunar Time Ephemeris $\texttt{LTE440}$: definitions, algorithm and performance
Xu Lu, Tian-Ning Yang, Yi Xie
https://arxiv.org/abs/2509.18511 https://arxiv…

Entropy-Bounded Computational Geometry Made Easier and Sensitive to Sortedness
David Eppstein, Michael T. Goodrich, Abraham M. Illickan, Claire A. To
https://arxiv.org/abs/2508.20489

Entropy-Bounded Computational Geometry Made Easier and Sensitive to Sortedness
We study entropy-bounded computational geometry, that is, geometric algorithms whose running times depend on a given measure of the input entropy. Specifically, we introduce a measure that we call range-partition entropy, which unifies and subsumes previous definitions of entropy used for sorting problems and structural entropy used in computational geometry. We provide simple algorithms for several problems, including 2D maxima, 2D and 3D convex hulls, and some visibility problems, and we show…

Multi-Robot Navigation in Social Mini-Games: Definitions, Taxonomy, and Algorithms
Rohan Chandra, Shubham Singh, Abhishek Jha, Dannon Andrade, Hriday Sainathuni, Katia Sycara
https://arxiv.org/abs/2508.13459

Multi-Robot Navigation in Social Mini-Games: Definitions, Taxonomy, and Algorithms
The ``Last Mile Challenge'' has long been considered an important, yet unsolved, challenge for autonomous vehicles, public service robots, and delivery robots. A central issue in this challenge is the ability of robots to navigate constrained and cluttered environments (e.g., doorways, hallways, corridor intersections), often while competing for space with other robots and humans. We refer to these environments as ``Social Mini-Games'' (SMGs). SMGs are tightly coupled, high-agency interactions …

Odd that we think definitions are definitive. :-)
-- Larry Wall in <199702221943.LAA20388@wall.org>

LLM as an Execution Estimator: Recovering Missing Dependency for Practical Time-travelling Debugging
Yunrui Pei, Hongshu Wang, Wenjie Zhang, Yun Lin, Weiyu Kong, Jin song Dong
https://arxiv.org/abs/2508.18721

LLM as an Execution Estimator: Recovering Missing Dependency for Practical Time-travelling Debugging
Dynamic data dependency, answering "why a variable has this value?", is critical for debugging. Given a program step `s` reading a variable `v`, finding the dynamic definition of `v` is challenging. Traditional methods require either (1) exhaustive instrumentation of all possible definitions of `v` in one run or (2) replicating the run to re-examine reads/writes - both costly. If `v` is defined in a library, instrumentation becomes expensive; for non-deterministic programs, replication is infea…

I am having severe issues with LSPs.
Now it is Rust Analyzer.
Before I had OOMs with the Go LSP.
And I am not alone; there are many posts like this.
Regardless of editors.
People report it with VSCode and NeoVim.
I guess I will get back to Zed again for now.
Just the conveniences of auto-complete, going to definitions, keyboard-only use and nice integration with a terminal is what I'm after.
I know that IDEs have terminal panes, but they are cumbe…

Universal perspectives on irredundance for X-set parameters
Bryan Curtis, Mary Flagg, Leslie Hogben
https://arxiv.org/abs/2509.18486 https://arxiv.org/pdf/…

Rao Differential Privacy
Carlos Soto
https://arxiv.org/abs/2508.17135 https://arxiv.org/pdf/2508.17135

Rao Differential Privacy
Differential privacy (DP) has recently emerged as a definition of privacy to release private estimates. DP calibrates noise to be on the order of an individuals contribution. Due to the this calibration a private estimate obscures any individual while preserving the utility of the estimate. Since the original definition, many alternate definitions have been proposed. These alternates have been proposed for various reasons including improvements on composition results, relaxations, and formaliza…

Multi-Instrument Observations and Tracking of a Coronal Mass Ejection Front From Low to Middle Corona
Oleg Stepanyuk, Kamen Kozarev
https://arxiv.org/abs/2508.18867 https://

Multi-Instrument Observations and Tracking of a Coronal Mass Ejection Front From Low to Middle Corona
The shape and dynamics of coronal mass ejections (CMEs) vary significantly based on the instrument and wavelength used. This has led to significant debate about the proper definitions of CME/shock fronts, pile-up/compression regions, and cores observations in projection in optically thin vs. optically thick emission. Here we present an observational analysis of the evolving shape and kinematics of a large-scale CME that occurred on May 7, 2021 on the eastern limb of the Sun as seen from 1 au. T…

Two Decades of Probabilistic Approach to Liouville Conformal Field Theory
R\'emi Rhodes, Vincent Vargas
https://arxiv.org/abs/2509.21053 https://arxiv.…

Two Decades of Probabilistic Approach to Liouville Conformal Field Theory
Over the past twenty years, the probabilistic approach to Liouville Conformal Field Theory (LCFT) has undergone remarkable developments, transforming a collection of ideas at the interface of probability, geometry, complex analysis and physics into a coherent mathematical theory. Building on Gaussian Free Fields and Gaussian Multiplicative Chaos, rigorous definitions of correlation functions and partition functions have been established, culminating in the probabilistic derivation of the DOZZ f…

Structuring Definitions in Mathematical Libraries
Alena Gusakov, Peter Nelson, Stephen Watt
https://arxiv.org/abs/2509.10828 https://arxiv.org/pdf/2509.108…

Structuring Definitions in Mathematical Libraries
Codifying mathematical theories in a proof assistant or computer algebra system is a challenging task, of which the most difficult part is, counterintuitively, structuring definitions. This results in a steep learning curve for new users and slow progress in formalizing even undergraduate level mathematics. There are many considerations one has to make, such as level of generality, readability, and ease of use in the type system, and there are typically multiple equivalent or related definition…

Metrics, KPIs, and Taxonomy for Data Valuation and Monetisation - A Systematic Literature Review
Eduardo Vyhmeister, Bastien Pietropaoli, Alejando Martinez Molina, Montserrat Gonzalez-Ferreiro, Gabriel Gonzalez-Castane, Jordi Arjona Aroca, Andrea Visentin
https://arxiv.org/abs/2508.18331

Metrics, KPIs, and Taxonomy for Data Valuation and Monetisation - A Systematic Literature Review
Data valuation and data monetisation are complex subjects but essential to most organisations today. Unfortunately, they still lack standard procedures and frameworks for organisations to follow. In this survey, we introduce the reader to the concepts by providing the definitions and the background required to better understand data, monetisation strategies, and finally metrics and KPIs used in these strategies. We have conducted a systematic literature review on metrics and KPIs used in data v…

Enabling Drone Detection with SWARM Repeater-Assisted MIMO ISAC
Palatip Jopanya, Diana P. M. Osorio
https://arxiv.org/abs/2509.19119 https://arxiv.org/pdf/…

Algebraic conformal nets, investigation of the locally constant case -- M1 internship supervised by Domenico Fiorenza
Quentin Moreau
https://arxiv.org/abs/2508.18275 https://

Algebraic conformal nets, investigation of the locally constant case -- M1 internship supervised by Domenico Fiorenza
We define the tricategory of algebraic conformal nets, defects, sectors and intertwiners where algebraic refers to the absence of a topology on the relevant algebras and modules. We aim at making these definitions satisfying from a categorical point of view, and in a few cases, e.g., for defects, we propose more general definitions than what can be found in the literature. This allows us in particular to propose an implementation of solitons as defects. Then we focus on the locally constant cas…

A Universal Framework for Offline Serendipity Evaluation in Recommender Systems via Large Language Models
Yu Tokutake, Kazushi Okamoto, Kei Harada, Atsushi Shibata, Koki Karube
https://arxiv.org/abs/2508.17571

A Universal Framework for Offline Serendipity Evaluation in Recommender Systems via Large Language Models
Serendipity in recommender systems (RSs) has attracted increasing attention as a concept that enhances user satisfaction by presenting unexpected and useful items. However, evaluating serendipitous performance remains challenging because its ground truth is generally unobservable. The existing offline metrics often depend on ambiguous definitions or are tailored to specific datasets and RSs, thereby limiting their generalizability. To address this issue, we propose a universally applicable eval…

The AI Literacy Heptagon: A Structured Approach to AI Literacy in Higher Education
Veronika Hackl, Alexandra Mueller, Maximilian Sailer
https://arxiv.org/abs/2509.18900 https://…

The Macavity of Degrowth – Waste, the Empire that isn’t there…
Jon Cloke* “You may seek him in the basement, you may look up in the air But I tell you once and once again, Macavity’s not there!” Growth, Degrowth, Post-Growth There are so many accepted definitions of economic growth that it’s almost a monad, “a most basic substance” that goes without question. In one recent example, Max Roser (2021) defines growth as “an increase in the quantity and quality of the…

The Macavity of Degrowth – Waste, the Empire that isn’t there…
Jon Cloke* “You may seek him in the basement, you may look up in the air But I tell you once and once again, Macavity’s not there!” Growth, Degrowth, Post-Growth There are so many accepted definiti…

The Fair Game: Auditing & Debiasing AI Algorithms Over Time
Debabrota Basu, Udvas Das
https://arxiv.org/abs/2508.06443 https://arxiv.org/pdf/2508.06443…

The Fair Game: Auditing & Debiasing AI Algorithms Over Time
An emerging field of AI, namely Fair Machine Learning (ML), aims to quantify different types of bias (also known as unfairness) exhibited in the predictions of ML algorithms, and to design new algorithms to mitigate them. Often, the definitions of bias used in the literature are observational, i.e. they use the input and output of a pre-trained algorithm to quantify a bias under concern. In reality,these definitions are often conflicting in nature and can only be deployed if either the ground t…

Monotone tail functions: definitions, properties, and application to risk-reducing strategies
Hamza Hanbali, Daniel Linders
https://arxiv.org/abs/2508.12608 https://

Monotone tail functions: definitions, properties, and application to risk-reducing strategies
This paper studies properties of functions having monotone tails. We extend Theorem 1 of Dhaene et al. (2002a) and show how the tail quantiles of a random variable transformed with a monotone tail function can be expressed as the transformed tail quantiles of the original random variable. The main result is intuitive, in that Dhaene et al. (2002a) properties still hold, but only for certain quantile values. However, the proof presents some complications that arise especially when the function i…

A statistical note on extending Christensen's limits of agreement with the mean
Heidi S{\o}gaard Christensen, Martin B{\o}gsted, Jens Borgbjerg
https://arxiv.org/abs/2508.16250

A statistical note on extending Christensen's limits of agreement with the mean
Limits of agreement with the mean (LOAM) can be used for assessing agreement of continuous measurements made by different observers. Definitions of a LOAM for measuring reproducibility has been introduced under a two-way random effects model without interaction between subject and observer. Here we extend that model framework to include a subject-observer interaction, allowing the separation of residual measurement error and systematic variation in how individual observers measure specific obje…

Linear Orders and the Real Line
Trey Smith, Aksel Ozer
https://arxiv.org/abs/2508.15644 https://arxiv.org/pdf/2508.15644

Linear Orders and the Real Line
Definitions of dense linear orders (with/without endpoints), separable linear orders, complete linear orders, the countable chain condition for linear orders, a Suslin line/Suslin tree and Suslin's problem Statement and proof of Cantor's Theorem characterizing (Q,<) as the only countable dense linear order without endpoints, up to isomorphism, the corollary which characterizes (R,<) as the only separable complete dense linear order without endpoints, every countable linear order embeds into (Q,…

Saturated base change of toroidal morphisms
Santai Qu
https://arxiv.org/abs/2509.15590 https://arxiv.org/pdf/2509.15590

Saturated base change of toroidal morphisms
We show that saturated base change of a dominant toroidal morphism is also toroidal. For completeness, we give full details on equivalence between definitions regarding toroidal embeddings and toroidal morphisms in literature. Moreover, we show in detail the equivalence between toroidal embeddings and logarithmically regular log-varieties, respectively, toroidal morphisms and logarithmically smooth morphisms.

Rescaled expansive measures for flows
Yun Yang
https://arxiv.org/abs/2508.16536 https://arxiv.org/pdf/2508.16536 …

Rescaled expansive measures for flows
We introduce the notion of rescaled expansive measures to study a measure-theoretic formulation of rescaled expansiveness for flows, particularly in the presence of singularities. Equivalent definitions are established via reparametrizations of different regularities. Under the assumption of positive entropy, we prove the existence of invariant rescaled expansive measures. In the appendix, we derive a rescaled version of the Brin-Katok local entropy formula for flows, extending [7] from nonsing…

Means of Random Variables in Lie Groups
Shiraz Khan, Jikai Ye, Gregory S. Chirikjian
https://arxiv.org/abs/2508.12030 https://arxiv.org/pdf/2508.12030

Means of Random Variables in Lie Groups
The concepts of mean (i.e., average) and covariance of a random variable are fundamental in statistics, and are used to solve real-world problems such as those that arise in robotics, computer vision, and medical imaging. On matrix Lie groups, multiple competing definitions of the mean arise, including the Euclidean, projected, distance-based (i.e., Fréchet and Karcher), group-theoretic, and parametric means. This article provides a comprehensive review of these definitions, investigates their…

Actually, I do want to come back to masculinity under patriarchy and whiteness under white supremacy because I think it's worth talking more about. The "man" under patriarchy (at least "Western" patriarchy) is represented as power and independence. The man needs nothing and thus owes nothing to anyone. The man controls and is not controlled, which is intimately related to independence as dependence can make someone vulnerable to control. The image of "man" projects power and invulnerability. At the same time "man" is a bumbling fool who can't be held accountable for his inability to control his sexual urges. He must be fed and cared for, as though another child. His worst behaviors must be dismissed with phrases such as "boys will be boys" and "locker room talk." The absurdity of the concept of human "independence" is impossible to understate.
Even if you go all Ted Kaczynski, you have still been raised and taught. This is, perhaps, why it is so much more useful to think in terms of obligations than rights. Rights can be claimed and protected with violence alone, but obligations reveal the true interdependence that sustains us. A "man" may assert his rights. Yet, on some level, we all know that the "man" of patriarchy acts as a child who is not mature enough to recognize his obligations.
White violence and white fragility reflect the same dichotomy. "The master race" somehow always needs brown folks to make all their shit and do all the reproductive labor for them. For those who fully embrace whiteness, the "safe space" is a joke. DEI shows weakness. Yet, when presented with an honest history adults become children who are incapable of differentiating between criticism and simple facts. *They* become the ones who must be kept safe. The expectation to be responsible for one's own words and actions, one of the very core definitions of being an adult, is far too much to expect. Their guilt needs room, needs tending, needs caring. White people cannot simply "grow the fuck up" or, as they may say of slavery, "fucking get over it."
And again, interestingly, it is *rights* that they reference: "Mah Freeze PEACH!" I find it hard to distinguish between such and my own child's assertion that anything she doesn't like is "not fair!" No, these assertions fail to recognize the fundamental fabric of adult society: the obligations we hold to each other.
At the intersection of all privilege is the sovereign, the ultimate god-man-baby. Again, referencing the essay (https://hexmhell.writeas.com/observations-on-domination-and-trump)
> This is where it becomes important to consider the ideology behind the sovereign ritual. Participation within the sovereign ritual denotes to the participants elements of the sovereign. That is, all agents of the sovereign are, essentially, micro dictators. By carrying out the will of the sovereign, these micro dictators can, by extension, act outside of the law.
While law enforcement is the ultimate representative of sovereign violence, privileges allow a gradated approximation of the sovereign. Those who are "closer" in privilege to the sovereign may, for example, be permitted to carry out violence against those who are father away. The gradation of privilege turns the whole society, except for the least privileged, into a cult that protects the privilege system on behalf of the most privileged. (And immediately Malcolm X pops to mind as having already talked about part of this relationship in 1963 https://www.youtube.com/watch?v=jf7rsCAfQCo.)

Computation of Graph Polynomials via Tree Decomposition: Theory, Algorithms, and Python Implementation
Mehul Bafna, Shaghik Amirian
https://arxiv.org/abs/2509.16816 https://

Computation of Graph Polynomials via Tree Decomposition: Theory, Algorithms, and Python Implementation
Graph polynomials encode fundamental combinatorial invariants of graphs. Their computation is investigated using tree and path decomposition frameworks, with formal definitions of treewidth, k-trees, and pathwidth establishing the structural basis for algorithmic efficiency. Explicit algorithms are constructed for each polynomial, leveraging decomposition order and state transformation mappings to enable tractable computation on graphs of bounded treewidth. Python implementations validate the m…

Composition Direction of Seymour's Theorem for Regular Matroids -- Formally Verified
Martin Dvorak, Tristan Figueroa-Reid, Rida Hamadani, Byung-Hak Hwang, Evgenia Karunus, Vladimir Kolmogorov, Alexander Meiburg, Alexander Nelson, Peter Nelson, Mark Sandey, Ivan Sergeev
https://arxiv.org/abs/2509.20539

Composition Direction of Seymour's Theorem for Regular Matroids -- Formally Verified
Seymour's decomposition theorem is a hallmark result in matroid theory presenting a structural characterization of the class of regular matroids. Formalization of matroid theory faces many challenges, most importantly that only a limited number of notions and results have been implemented so far. In this work, we formalize the proof of the forward (composition) direction of Seymour's theorem for regular matroids. To this end, we develop a library in Lean 4 that implements definitions and result…

The Quantum Method of Planes - Local Pressure Definitions for Machine Learning Potentials
E. R. Smith
https://arxiv.org/abs/2509.16257 https://arxiv.org/pd…

The Quantum Method of Planes - Local Pressure Definitions for Machine Learning Potentials
Stress or Pressure is a central quantity in engineering, and remains vital in molecular modelling. However, the commonly used virial stress tensor is not valid away from thermodynamic equilibrium, a common state required in fluid dynamics and non-equilibrium molecular dynamics (NEMD) simulation. This is solved by using the method of planes (MoP), a mechanical form of pressure, simply interpreted as the force divided by area but derived from the firm foundations of statistical mechanics. We pres…

Previously on... Automating Code Review
Robert Heum\"uller, Frank Ortmeier
https://arxiv.org/abs/2508.18003 https://arxiv.org/pdf/2508.18003

Previously on... Automating Code Review
Modern Code Review (MCR) is a standard practice in software engineering, yet it demands substantial time and resource investments. Recent research has increasingly explored automating core review tasks using machine learning (ML) and deep learning (DL). As a result, there is substantial variability in task definitions, datasets, and evaluation procedures. This study provides the first comprehensive analysis of MCR automation research, aiming to characterize the field's evolution, formalize lear…

Jets at electron-positron colliders
Giovanni Stagnitto
https://arxiv.org/abs/2508.14700 https://arxiv.org/pdf/2508.14700

Jets at electron-positron colliders
We provide a pedagogical introduction to the physics of hadronic jets and event shapes at electron-positron colliders. We present some of the main jet definitions and event shape observables studied at lepton colliders and discuss how to produce theoretical predictions in perturbative quantum chromodynamics (QCD), both at fixed order and with resummation or parton showers. We further introduce important topics in jet substructure that have seen developments in a lepton collider environment, suc…

Enriching Object-Centric Event Data with Process Scopes: A Framework for Aggregation and Analysis
Shahrzad Khayatbashi, Majid Rafiei, Jiayuan Chen, Timotheus Kampik, Gregor Berg, Amin Jalali
https://arxiv.org/abs/2508.18830

Enriching Object-Centric Event Data with Process Scopes: A Framework for Aggregation and Analysis
Object-Centric Process Mining enables the analysis of complex operational behavior by capturing interactions among multiple business objects (e.g., orders, items, deliveries). These interactions are recorded using Object-Centric Event Data (OCED) formats, such as the Object-Centric Event Log (OCEL). However, existing formats lack explicit definitions of process scopes, which restricts analysis to individual processes and limits insights to a low level of granularity. In practice, OCED often spa…

Some equivalent definitions for weighted Korenblum and Bloch-type spaces of the upper half-plane
Benoit F. Sehba
https://arxiv.org/abs/2508.07294 https://a…

Some equivalent definitions for weighted Korenblum and Bloch-type spaces of the upper half-plane
In this paper, we prove some equivalent characterizations of weighted Korenblum spaces and Bloch spaces in terms of symbols of bounded Hankel operators.

🤖 Context-Aware Agents
Build agents maintaining context across hundreds of tool calls and multi-step workflows with complete #API documentation, tool definitions, and interaction histories without losing coherence.
💰 Pricing Structure
Standard rates: Prompts ≤200K tokens ($3/MTok input, $15/MTok output)
Extended context: Prompts >200K tokens ($6/MTok input, $22.50/MTok out…

Generating the Spanning Trees of Series-Parallel Graphs up to Graph Automorphism
Mithra Karamchedu, Lucas Bang
https://arxiv.org/abs/2508.13480 https://arx…

Generating the Spanning Trees of Series-Parallel Graphs up to Graph Automorphism
In this paper, we investigate the problem of generating the spanning trees of a graph $G$ up to the automorphisms or "symmetries" of $G$. After introducing and surveying this problem for general input graphs, we present algorithms that fully solve the case of series-parallel graphs, under two standard definitions. We first show how to generate the nonequivalent spanning trees of a oriented series-parallel graph $G$ in output-linear time, where both terminals of $G$ have been individually distin…

Crosslisted article(s) found for physics.atom-ph. https://arxiv.org/list/physics.atom-ph/new
[1/1]:
- The Quantum Method of Planes - Local Pressure Definitions for Machine Learning Potentials
E. R. Smith

Geometric Phase of Stochastic Oscillators
Yangyang Du
https://arxiv.org/abs/2509.10900 https://arxiv.org/pdf/2509.10900

Geometric Phase of Stochastic Oscillators
Several definitions of phase have been proposed for stochastic oscillators, among which the mean-return-time phase and the stochastic asymptotic phase have drawn particular attention. Quantitative comparisons between these two definitions have been done in previous studies, but physical interpretations of such a relation are still missing. In this work, we illustrate this relation using the geometric phase, which is an essential concept in both classical and quantum mechanics. We use properties…

🤔 What exactly is “life?” Astrobiologists still have more questions than answers
https://bigthink.com/hard-science/what-exactly-is-life-astrobiologists-still-have-more-questions-than-answers/

What exactly is “life”? Astrobiologists still have more questions than answers
Our narrow, Earth-bound definitions of life could leave us blind to the Universe’s strangest forms on future space missions.

CrowdQuery: Density-Guided Query Module for Enhanced 2D and 3D Detection in Crowded Scenes
Marius D\"ahling, Sebastian Krebs, J. Marius Z\"ollner
https://arxiv.org/abs/2509.08738

CrowdQuery: Density-Guided Query Module for Enhanced 2D and 3D Detection in Crowded Scenes
This paper introduces a novel method for end-to-end crowd detection that leverages object density information to enhance existing transformer-based detectors. We present CrowdQuery (CQ), whose core component is our CQ module that predicts and subsequently embeds an object density map. The embedded density information is then systematically integrated into the decoder. Existing density map definitions typically depend on head positions or object-based spatial statistics. Our method extends these…

Revisiting Functional Derivatives in Multi-object Tracking
Jan Krej\v{c}\'i, Ond\v{r}ej Straka, Petr Girg, Ji\v{r}\'i Benedikt
https://arxiv.org/abs/2508.12982 https://

Revisiting Functional Derivatives in Multi-object Tracking
Probability generating functionals (PGFLs) are efficient and powerful tools for tracking independent objects in clutter. It was shown that PGFLs could be used for the elegant derivation of practical multi-object tracking algorithms, e.g., the probability hypothesis density (PHD) filter. However, derivations using PGFLs use the so-called functional derivatives whose definitions usually appear too complicated or heuristic, involving Dirac delta ``functions''. This paper begins by comparing differ…

Using nonassociative algebras to classify skew polycyclic codes up to isometry and equivalence
Susanne Pumpluen
https://arxiv.org/abs/2508.10139 https://ar…

Using nonassociative algebras to classify skew polycyclic codes up to isometry and equivalence
We propose new definitions of equivalence and isometry for skew polycyclic codes that will lead to tighter classifications than existing ones. This helps to reduce the number of previously known isometry and equivalence classes, and state precisely when these different notions coincide. In the process, we classify classes of skew $(f,σ,δ)$-polycyclic codes with the same performance parameters, to avoid duplicating already existing codes. We exploit that the generator of a skew polycyclic co…

[OT] What is #AGI? Nobody agrees, and it's tearing Microsoft and OpenAI apart. https://arstechnica.com/ai/2025/07/agi-may-be-impossible-to-define-and…

What is AGI? Nobody agrees, and it’s tearing Microsoft and OpenAI apart.
Several definitions make measuring “human-level” AI an exercise in moving goalposts.

Entropy Measures for Transition Matrices in Random Systems
Zhaohui Chen, Rene Meyer, Zhuo-Yu Xian
https://arxiv.org/abs/2508.09261 https://arxiv.org/pdf/25…

Entropy Measures for Transition Matrices in Random Systems
A transition matrix can be constructed through the partial contraction of two given quantum states. We analyze and compare four different definitions of entropy for transition matrices, including (modified) pseudo entropy, SVD entropy, and ABB entropy. We examine the probabilistic interpretation of each entropy measure and show that only the distillation interpretation of ABB entropy corresponds to the joint success probability of distilling entanglement between the two quantum states used to c…

Day 11: Bee Johnson
As promised, back to printed books, and since I hadn't yet done any authors of picture or board books, here's one. It looks like Johnson is primarily an illustrator and has only written a single kids' book, but it's a magnificent one: "What Can A Mess Make?"
Naturally, the illustrations are rich and evocative, but it's also got one of my favorite formats (just a few lines per page, with consistent meter and rhymes throughout) and has the incredibly charming theme of two sisters who are constantly making messes, except it highlights the fun (and other emotions) they get out of their messy play, reminding parents cleaning up messes that there's a benefit to letting your kids make the mess in the first place, which is an idea that's stuck with me as I clean up my own kids' messes. This book checks *all* of my boxes for a good picture book (which is kinda hard).
#20AuthorsNoMen
P.S. at this point, I think I've exhausted the range of "author" definitions I wanted to include in my list, and I've now got the unenviable task of balancing between genres and trying to hit some of my favorite authors before we get to 20. We'll see how that goes...

From Mimicry to True Intelligence (TI) - A New Paradigm for Artificial General Intelligence
Meltem Subasioglu, Nevzat Subasioglu
https://arxiv.org/abs/2509.14474 https://…

From Mimicry to True Intelligence (TI) - A New Paradigm for Artificial General Intelligence
The debate around Artificial General Intelligence (AGI) remains open due to two fundamentally different goals: replicating human-like performance versus replicating human-like cognitive processes. We argue that current performance-based definitions are inadequate because they provide no clear, mechanism-focused roadmap for research, and they fail to properly define the qualitative nature of genuine intelligence. Drawing inspiration from the human brain, we propose a new paradigm that shifts the…

Less is More: On Copy Complexity in Quantum Cryptography
Prabhanjan Ananth, Eli Goldin
https://arxiv.org/abs/2510.04992 https://arxiv.org/pdf/2510.04992

Less is More: On Copy Complexity in Quantum Cryptography
Quantum cryptographic definitions are often sensitive to the number of copies of the cryptographic states revealed to an adversary. Making definitional changes to the number of copies accessible to an adversary can drastically affect various aspects including the computational hardness, feasibility, and applicability of the resulting cryptographic scheme. This phenomenon appears in many places in quantum cryptography, including quantum pseudorandomness and unclonable cryptography. To address th…

Reachability is Decidable for ATM-Typable Finitary PCF with Effect Handlers
Ryunosuke Endo, Tachio Terauchi
https://arxiv.org/abs/2508.12572 https://arxiv.…

Reachability is Decidable for ATM-Typable Finitary PCF with Effect Handlers
It is well known that the reachability problem for simply-typed lambda calculus with recursive definitions and finite base-type values (finitary PCF) is decidable. A recent paper by Dal Lago and Ghyselen has shown that the same problem becomes undecidable when the language is extended with algebraic effect and handlers (effect handlers). We show that, perhaps surprisingly, the problem becomes decidable even with effect handlers when the type system is extended with answer type modification (ATM…

Lie groups in tangent join restriction categories
Robin Cockett, Florian Schwarz
https://arxiv.org/abs/2509.18410 https://arxiv.org/pdf/2509.18410

Teaching Introductory Functional Programming Using Haskelite
Pedro Vasconcelos (University of Porto)
https://arxiv.org/abs/2508.03640 https://arxiv.org/pdf…

Teaching Introductory Functional Programming Using Haskelite
Learning functional programming requires learning a substitution-based computational model. While substitution should be a familiar concept from high-school algebra, students often have difficulty applying it to new settings, such as recursive definitions, algebraic data types and higher-order functions. Step-by-step interpreters have been shown to help beginners by clarifying misconceptions and improving understanding. This paper reports on the experience of using a step-by-step tracing inte…

Short history of signed exceptional sequences
Kiyoshi Igusa, Gordana Todorov
https://arxiv.org/abs/2509.10910 https://arxiv.org/pdf/2509.10910

Short history of signed exceptional sequences
Whereas exceptional sequences have a long history with many well-known connections to combinatorics, signed exceptional sequences are relatively recent. The authors introduced this concept in 2017 [19], although it was retroactively realized that the category of noncrossing partitions [24] is a special case of this construction. Buan and Marsh [4] have introduced the concept of $τ$-exceptional sequences to generalize the definitions and theorems to all finite dimensional algebras. This short p…

Ergodicity detection algorithms: Scaling of ergodicity in random symbolic dynamics
M. S\"uzen
https://arxiv.org/abs/2508.08319 https://arxiv.org/pdf/2…

Ergodicity detection algorithms: Scaling of ergodicity in random symbolic dynamics
The mathematical definitions of distinct concepts that are needed in building an ergodicity detec- tion algorithm are introduced in a framework. This algorithmic framework is expressed in a discrete setting in an accessible manner for broader quantitative practitioners without loss of generality. At the same time, the common misconceptions of the requirement of visiting all available states in the time-averaged quantities for physical systems and non-existence of an ergodic process are resolved…

Fine-grained CDN Delegation
Ethan Thompson, Ali Sadeghi Jahromi, AbdelRahman Abdou
https://arxiv.org/abs/2510.09983 https://arxiv.org/pdf/2510.09983…

Fine-grained CDN Delegation
The use of Content Delivery Networks (CDNs) has significantly increased over the past decade, with approximately 55 million websites currently relying on CDN services. Emerging solutions, such as Delegated Credentials (RFC 9345), lack fine-grained definitions of many critical aspects of delegation, such as the length of delegation chains, revocation mechanism, permitted operations, and a well-defined scope for said delegation. We present Delegation Certificates (DeCerts), which modify X.509 cer…

Word Error Rate Definitions and Algorithms for Long-Form Multi-talker Speech Recognition
Thilo von Neumann, Christoph Boeddeker, Marc Delcroix, Reinhold Haeb-Umbach
https://arxiv.org/abs/2508.02112

Word Error Rate Definitions and Algorithms for Long-Form Multi-talker Speech Recognition
The predominant metric for evaluating speech recognizers, the Word Error Rate (WER) has been extended in different ways to handle transcripts produced by long-form multi-talker speech recognizers. These systems process long transcripts containing multiple speakers and complex speaking patterns so that the classical WER cannot be applied. There are speaker-attributed approaches that count speaker confusion errors, such as the concatenated minimum-permutation WER cpWER and the time-constrained cp…

Joint reductions and mixed Buchsbaum-Rim multiplicities of modules and a joint-reduction-number-zero theorem
Daniel Katz, Vijay Kodiyalam, J. K. Verma
https://arxiv.org/abs/2508.07437

Joint reductions and mixed Buchsbaum-Rim multiplicities of modules and a joint-reduction-number-zero theorem
We offer new definitions of joint reductions and mixed Buchsbaum-Rim multiplicity for certain collections of modules over a Noetherian local ring and illustrate their application to give two different proofs of a joint-reduction-number-zero theorem for integrally closed modules over two-dimensional regular local rings. We also relate the mixed Buchsbaum-Rim multiplicity of modules to the Euler-Poincaré characteristic of a natural Koszul complex and relate it to the mixed Buchsbaum-Rim multipli…

Combined Approximations for Uniform Operational Consistent Query Answering
Marco Calautti, Ester Livshits, Andreas Pieris, Markus Schneider
https://arxiv.org/abs/2508.15814 http…

Combined Approximations for Uniform Operational Consistent Query Answering
Operational consistent query answering (CQA) is a recent framework for CQA based on revised definitions of repairs, which are built by applying a sequence of operations (e.g., fact deletions) starting from an inconsistent database until we reach a database that is consistent w.r.t. the given set of constraints. It has been recently shown that there is an efficient approximation for computing the percentage of repairs that entail a given query when we focus on primary keys, conjunctive queries, …

Foundational theory for optimal decision tree problems. II. Optimal hypersurface decision tree algorithm
Xi He
https://arxiv.org/abs/2509.12057 https://arx…

Foundational theory for optimal decision tree problems. II. Optimal hypersurface decision tree algorithm
Decision trees are a ubiquitous model for classification and regression tasks due to their interpretability and efficiency. However, solving the optimal decision tree (ODT) problem remains a challenging combinatorial optimization task. Even for the simplest splitting rules--axis-parallel hyperplanes--it is NP-hard to optimize. In Part I of this series, we rigorously defined the proper decision tree model through four axioms and, based on these, introduced four formal definitions of the ODT prob…

@… I’m not really sure what that means.
I find it odd that we are deliberating definitions when it has very little to do with my reply to your original question.

Extropy-Based Generalized Divergence and Similarity Ratios: Theory and Applications
Saranya P., Sunoj S. M
https://arxiv.org/abs/2508.13696 https://arxiv.o…

Extropy-Based Generalized Divergence and Similarity Ratios: Theory and Applications
In this article, we propose two classes of relative information measures based on extropy, viz., the generalized extropy similarity ratio (GESR) and generalized extropy divergence ratio (GEDR), that measure the similarity and discrepancy between two probability distributions, respectively. Definitions of GESR and GEDR are proposed along with their fundamental axioms, properties, and some measures satisfying those axioms are also introduced. The relationship of GESR with the popular cosine simil…

Ontology-Guided Query Expansion for Biomedical Document Retrieval using Large Language Models
Zabir Al Nazi, Vagelis Hristidis, Aaron Lawson McLean, Jannat Ara Meem, Md Taukir Azam Chowdhury
https://arxiv.org/abs/2508.11784

Ontology-Guided Query Expansion for Biomedical Document Retrieval using Large Language Models
Effective Question Answering (QA) on large biomedical document collections requires effective document retrieval techniques. The latter remains a challenging task due to the domain-specific vocabulary and semantic ambiguity in user queries. We propose BMQExpander, a novel ontology-aware query expansion pipeline that combines medical knowledge - definitions and relationships - from the UMLS Metathesaurus with the generative capabilities of large language models (LLMs) to enhance retrieval effect…

On defining Kemeny's constant for non-backtracking random walks
Jane Breen, Mark Kempton, Adam Knudson, Matthew Shumway
https://arxiv.org/abs/2510.06650 https://

On defining Kemeny's constant for non-backtracking random walks
We propose two possible definitions for a version of Kemeny's constant of a graph based on non-backtracking random walks (in place of the usual simple random walk). We show that these two definitions coincide for edge-transitive graphs, and give a condition generalizing edge-transitive for which equality holds, and investigate by how much they can differ in general. We compute our non-backtracking Kemeny's constant for several families of graphs.

Generative Logic: A New Computer Architecture for Deterministic Reasoning and Knowledge Generation
Nikolai Sergeev
https://arxiv.org/abs/2508.00017 https://

Generative Logic: A New Computer Architecture for Deterministic Reasoning and Knowledge Generation
We present Generative Logic (GL), a deterministic architecture that begins from user-supplied axiomatic definitions -- written in a minimalist Mathematical Programming Language (MPL) -- and systematically explores their deductive neighborhood. Definitions are compiled into a distributed grid of simple Logic Blocks (LBs) that exchange messages; any time several expressions unify under an inference rule, a new fact is emitted with full provenance to its sources, yielding replayable, auditable pro…

Overview of Complex System Design
John W. Sheppard
https://arxiv.org/abs/2508.11026 https://arxiv.org/pdf/2508.11026

Overview of Complex System Design
This chapter serves as an introduction to systems engineering focused on the broad issues surrounding realizing complex integrated systems. What is a system? We pose a number of possible definitions and perspectives, but leave open the opportunity to consider the system from the target context where it will be used. Once we have a system in mind, we acknowledge the fact that this system needs to integrate a variety of pieces, components, subsystems, in order for it to accomplish its task. There…

Perspectives, Needs and Challenges for Sustainable Software Engineering Teams: A FinServ Case Study
Satwik Ghanta, Peggy Gregory, Gul Calikli
https://arxiv.org/abs/2509.12466 ht…

Perspectives, Needs and Challenges for Sustainable Software Engineering Teams: A FinServ Case Study
Sustainable Software Engineering (SSE) is slowly becoming an industry need for reasons including reputation enhancement, improved profits and more efficient practices. However, SSE has many definitions, and this is a challenge for organisations trying to build a common and broadly agreed understanding of the term. Although much research effort has gone into identifying general SSE practices, there is a gap in understanding the sustainability needs of specific organisational contexts, such as fi…

GenOM: Ontology Matching with Description Generation and Large Language Model
Yiping Song, Jiaoyan Chen, Renate A. Schmidt
https://arxiv.org/abs/2508.10703 https://

GenOM: Ontology Matching with Description Generation and Large Language Model
Ontology matching (OM) plays an essential role in enabling semantic interoperability and integration across heterogeneous knowledge sources, particularly in the biomedical domain which contains numerous complex concepts related to diseases and pharmaceuticals. This paper introduces GenOM, a large language model (LLM)-based ontology alignment framework, which enriches the semantic representations of ontology concepts via generating textual definitions, retrieves alignment candidates with an embe…

Atiyah Classes in the Context of Generalized Complex Geometry
Dadi Ni
https://arxiv.org/abs/2508.10723 https://arxiv.org/pdf/2508.10723

Atiyah Classes in the Context of Generalized Complex Geometry
In analogy to the classical holomorphic setting, Lang, Jia and Liu introduced the notion of the Atiyah class for a generalized holomorphic vector bundle using three different approaches: leveraging $\rm{\check{C}}$ech cohomology, employing the first jet short exact sequence, and adopting the perspective of Lie algebroid pairs. The purpose of this note is to establish the equivalence among these diverse definitions of the Atiyah class.

Disclosure and Evaluation as Fairness Interventions for General-Purpose AI
Vyoma Raman, Judy Hanwen Shen, Andy K. Zhang, Lindsey Gailmard, Rishi Bommasani, Daniel E. Ho, Angelina Wang
https://arxiv.org/abs/2510.05292

Disclosure and Evaluation as Fairness Interventions for General-Purpose AI
Despite conflicting definitions and conceptions of fairness, AI fairness researchers broadly agree that fairness is context-specific. However, when faced with general-purpose AI, which by definition serves a range of contexts, how should we think about fairness? We argue that while we cannot be prescriptive about what constitutes fair outcomes, we can specify the processes that different stakeholders should follow in service of fairness. Specifically, we consider the obligations of two major gr…

CHUCKLE -- When Humans Teach AI To Learn Emotions The Easy Way
Ankush Pratap Singh, Houwei Cao, Yong Liu
https://arxiv.org/abs/2510.09382 https://arxiv.org…

CHUCKLE -- When Humans Teach AI To Learn Emotions The Easy Way
Curriculum learning (CL) structures training from simple to complex samples, facilitating progressive learning. However, existing CL approaches for emotion recognition often rely on heuristic, data-driven, or model-based definitions of sample difficulty, neglecting the difficulty for human perception, a critical factor in subjective tasks like emotion recognition. We propose CHUCKLE (Crowdsourced Human Understanding Curriculum for Knowledge Led Emotion Recognition), a perception-driven CL frame…

Topological weak containment
Riley Thornton
https://arxiv.org/abs/2510.10882 https://arxiv.org/pdf/2510.10882

Topological weak containment
We build on work of Elek and Zucker and develop a topological analogue of the theory of weak containment. We show that definitions in terms of local patterns, containment in ultra(co)products, and continuous model theory are all equivalent, just as in ergodic theory. And, for actions on Cantor space, we show these are all equivalent to approximate conjugacy. Restricting our attention to Cantor space, we connect this theory to questions about generic actions. We show how the shape of the space…

When isometry and equivalence for skew constacyclic codes coincide
Monica Nevins, Susanne Pumpluen
https://arxiv.org/abs/2508.06695 https://arxiv.org/pdf/2…

When isometry and equivalence for skew constacyclic codes coincide
We show that the notions of $(n,σ)$-isometry and $(n,σ)$-equivalence introduced by Ou-azzou et al coincide for most skew $(σ,a)$-constacyclic codes of length $n$. To prove this, we show that all Hamming-weight-preserving homomorphisms between their ambient algebras must have degree one when those algebras are nonassociative. We work in the general setting of commutative base rings $S$. As a consequence, we propose new definitions of equivalence and isometry of skew constacyclic codes that ex…

Null reduction and dynamical realization of Carrollian conformal symmetries
Ashis Saha, Rabin Banerjee, Sunandan Gangopadhyay
https://arxiv.org/abs/2510.06896 https://

Null reduction and dynamical realization of Carrollian conformal symmetries
We start from a Lorentzian action in a deformed light-cone background and applying the method of null reduction leads to a Carrollian action in one lower spacetime dimensions. We also identify the correct light-cone definitions of the symmetry generators and their dynamical forms in terms of the fields and take the $c\rightarrow0$ limit. It is observed that these generators produces the known kinematic Carrollian conformal algebraic commutation relations.

Cyclic and alternating $U$-statistics
Svante Janson
https://arxiv.org/abs/2510.12480 https://arxiv.org/pdf/2510.12480…

Cyclic and alternating $U$-statistics
We define cyclic $U$-statistics as a variant of $U$-statistics based on variables $X_1,\dots,X_n$ that are assumed to be cyclically ordered. We also define alternating $U$-statistics where in the definition terms are summed with alternating sings (in three different ways). Only $U$-statistics of order 2 are considered. The definitions are inspired by special cases studied by Chebikin (2008) and Even-Zohar (2017) for random permutations. We show limit theorems similar to well-known results for…

Parametric General Fractional Calculus: Nonlocal Operators Acting on Function with Respect to Another Function
Vasily E. Tarasov
https://arxiv.org/abs/2509.12218 https://…

Parametric General Fractional Calculus: Nonlocal Operators Acting on Function with Respect to Another Function
In this paper, we present the definitions and some properties of the general fractional integrals (GFIs) and general fractional derivatives (GFDs) of a function f(x) with respect to another function g(x). Examples of special cases of parametric GF operators are described. Some properties of the parametric GFIs and the parametric GFDs are proved. Representation of the parametric GFIs and parametric GFDs via the GF integrals on the finite interval (a,b). Fundamental theorems of parametric GFC are…

Entropy and multiplicity of hadrons in the high energy limit within dipole cascade models
Krzysztof Kutak, S\'andor L\"ok\"os
https://arxiv.org/abs/2509.07898 http…

Entropy and multiplicity of hadrons in the high energy limit within dipole cascade models
We investigate and compare QCD dipole cascade models, the 1D Mueller dipole model, its high energy limit and its generalization that follows from studies of 1D systems with conformal symmetry. To address the ambiguity stemming from different definitions of the rapidity ranges in experimental measurements, we propose the entropy as the function of the logarithm of the average multiplicity, $S(\ln\langle n \rangle)$, as a universal observable. From the solutions of the models, we calculate both t…

Nucleation-free independent graphs with implied nonedges
Jialong Cheng, Meera Sitharam, Ileana Streinu, William Sims
https://arxiv.org/abs/2508.12417 https://

Nucleation-free independent graphs with implied nonedges
We give inductive constructions of independent graphs that contain implied nonedges but do not contain any non-trivial rigid subgraphs, or \emph{nucleations}: some of the constructions and proofs apply to 3-dimensional abstract rigidity matroids with their respective definitions of nucleations and implied nonedges. The first motivation for the inductive constructions of this paper, which generate an especially intractable class of flexible circuits, is to illuminate further obstacles to settlin…

Type Theory with Single Substitutions
Ambrus Kaposi (E\"otv\"os Lor\'and University), Szumi Xie (E\"otv\"os Lor\'and University)
https://arxiv.org/abs/2510.12303

Type Theory with Single Substitutions
Type theory can be described as a generalised algebraic theory. This automatically gives a notion of model and the existence of the syntax as the initial model, which is a quotient inductive-inductive type. Algebraic definitions of type theory include Ehrhard's definition of model, categories with families (CwFs), contextual categories, Awodey's natural models, C-systems, B-systems. With the exception of B-systems, these notions are based on a parallel substitution calculus where substitutions …

Towards Ontology-Based Descriptions of Conversations with Qualitatively-Defined Concepts
Barbara Gendron (LORIA, UL), Ga\"el Guibon (LIPN, LORIA), Mathieu D'aquin (LORIA, UL)
https://arxiv.org/abs/2509.04926

Towards Ontology-Based Descriptions of Conversations with Qualitatively-Defined Concepts
The controllability of Large Language Models (LLMs) when used as conversational agents is a key challenge, particularly to ensure predictable and user-personalized responses. This work proposes an ontology-based approach to formally define conversational features that are typically qualitative in nature. By leveraging a set of linguistic descriptors, we derive quantitative definitions for qualitatively-defined concepts, enabling their integration into an ontology for reasoning and consistency c…

Exploring Formal Math on the Blockchain: An Explorer for Proofgold
Chad E. Brown, Cezary Kaliszyk, Josef Urban
https://arxiv.org/abs/2509.08267 https://arx…

Exploring Formal Math on the Blockchain: An Explorer for Proofgold
Proofgold is a blockchain that supports formalized mathematics alongside standard cryptocurrency functionality. It incorporates logical constructs into the blockchain, including declarations of formal theories, definitions, propositions and proofs. It also supports placing and collecting bounties on proving these propositions, incentivizing the development of the formal libraries contained in Proofgold. In this paper, we present a web-based blockchain explorer for Proofgold. The system exposes …

A Rapid Review Regarding the Concept of Legal Requirements in Requirements Engineering
Jukka Ruohonen
https://arxiv.org/abs/2509.06012 https://arxiv.org/pd…

A Rapid Review Regarding the Concept of Legal Requirements in Requirements Engineering
Out of a personal puzzlement, recent peer review comments, and demonstrable confusion in the existing literature, the paper presents a rapid review of the concept of legal requirements (LRs) in requirements engineering (RE) research. According to reviewing results, a normative understanding of LRs has often been present, although proper definitions and conceptual operationalizations are lacking. Some papers also see LRs as functional and others as non-functional requirements. Legal requirements…

DriftBench: Defining and Generating Data and Query Workload Drift for Benchmarking
Guanli Liu, Renata Borovica-Gajic
https://arxiv.org/abs/2510.10858 https://

DriftBench: Defining and Generating Data and Query Workload Drift for Benchmarking
Data and workload drift are key to evaluating database components such as caching, cardinality estimation, indexing, and query optimization. Yet, existing benchmarks are static, offering little to no support for modeling drift. This limitation stems from the lack of clear definitions and tools for generating data and workload drift. Motivated by this gap, we propose a unified taxonomy for data and workload drift, grounded in observations from both academia and industry. Building on this foundat…

A recursive definition for the polymatroid Tutte polynomial
Xiaxia Guan, Xian'an Jin, Weiling Yang
https://arxiv.org/abs/2510.11046 https://arxiv.org/p…

A recursive definition for the polymatroid Tutte polynomial
The Tutte polynomial is a significant invariant of graphs and matroids. It is well-known that it has three equivalent definitions: bases expansion, rank generating function, and deletion-contraction formula. The polymatroid Tutte polynomial $\mathscr{T}_{P}$ generalizes the Tutte polynomial from matroids to polymatroids $P$. In \emph{[Adv. Math. 402 (2022) 108355.]} and \emph{[J. Combin. Theory Ser. A 188 (2022) 105584]}, the authors provided bases expansion and rank generating function constru…

GenAI-based test case generation and execution in SDV platform
Denesa Zyberaj, Lukasz Mazur, Nenad Petrovic, Pankhuri Verma, Pascal Hirmer, Dirk Slama, Xiangwei Cheng, Alois Knoll
https://arxiv.org/abs/2509.05112

GenAI-based test case generation and execution in SDV platform
This paper introduces a GenAI-driven approach for automated test case generation, leveraging Large Language Models and Vision-Language Models to translate natural language requirements and system diagrams into structured Gherkin test cases. The methodology integrates Vehicle Signal Specification modeling to standardize vehicle signal definitions, improve compatibility across automotive subsystems, and streamline integration with third-party testing tools. Generated test cases are executed withi…

Efficient Mining of Low-Utility Sequential Patterns
Jian Zhu, Zhidong Lin, Wensheng Gan, Ruichu Cai, Zhifeng Hao, Philip S. Yu
https://arxiv.org/abs/2510.10243 https://

Efficient Mining of Low-Utility Sequential Patterns
Discovering valuable insights from rich data is a crucial task for exploratory data analysis. Sequential pattern mining (SPM) has found widespread applications across various domains. In recent years, low-utility sequential pattern mining (LUSPM) has shown strong potential in applications such as intrusion detection and genomic sequence analysis. However, existing research in utility-based SPM focuses on high-utility sequential patterns, and the definitions and strategies used in high-utility S…

Higher order differential calculus in mathlib
S\'ebastien Gou\"ezel (IRMAR)
https://arxiv.org/abs/2509.04922 https://arxiv.org/pdf/2509.04922

Higher order differential calculus in mathlib
We report on the higher-order differential calculus library developed inside the Lean mathematical library mathlib. To support a broad range of applications, we depart in several ways from standard textbook definitions: we allow arbitrary fields of scalars, we work with functions defined on domains rather than full spaces, and we integrate analytic functions in the broader scale of smooth functions. These generalizations introduce significant challenges, which we address from both the mathemati…

Colored Petri Nets are Lax Double Functors
Jade Master, Joe Moeller
https://arxiv.org/abs/2510.01946 https://arxiv.org/pdf/2510.01946

Colored Petri Nets are Lax Double Functors
We give a characterization of colored Petri nets as lax double functors. Framing colored Petri nets in terms of category theory allows for canonical definitions of various well-known constructions on colored Petri nets. In particular, we show how morphisms of colored Petri nets may be understood as natural transformations. A result from folklore, which we sketch in the appendix, shows that lax double functors are equivalent to functors with codomain their former domain. We use this result to ch…

Replaced article(s) found for cs.LO. https://arxiv.org/list/cs.LO/new
[1/1]:
- Deciding the Existence of Interpolants and Definitions in First-Order Modal Logic
Agi Kurucz, Frank Wolter, Michael Zakharyaschev