Tootfinder

"#Serendipity is generally defined as the accidental discovery of something valuable while searching for something else. It’s also a hotly contested component of the library research process: is it a failure of #library systems or facilitated by the physical design of libraries, the cat…

How Well Do LLMs Predict Prerequisite Skills? Zero-Shot Comparison to Expert-Defined Concepts
Ngoc Luyen Le, Marie-H\'el\`ene Abel
https://arxiv.org/abs/2507.18479 https://

How Well Do LLMs Predict Prerequisite Skills? Zero-Shot Comparison to Expert-Defined Concepts
Prerequisite skills - foundational competencies required before mastering more advanced concepts - are important for supporting effective learning, assessment, and skill-gap analysis. Traditionally curated by domain experts, these relationships are costly to maintain and difficult to scale. This paper investigates whether large language models (LLMs) can predict prerequisite skills in a zero-shot setting, using only natural language descriptions and without task-specific fine-tuning. We introdu…

Guessing sequences of eigenvectors for LMPs defining spectrahedral relaxations of Eulerian rigidly convex sets
Alejandro Gonz\'alez Nevado
https://arxiv.org/abs/2507.18434 h…

Guessing sequences of eigenvectors for LMPs defining spectrahedral relaxations of Eulerian rigidly convex sets
Stable multivariate Eulerian polynomials were introduced by Brändén. Particularizing some variables, it is possible to extract real zero multivariate Eulerian polynomials from them. These real zero multivariate Eulerian polynomials can be fed into constructions of spectrahedral relaxations providing therefore approximations to the (Eulerian) rigidly convex sets defined by these polynomials. The accuracy of these approximations is measured through the behaviour in the diagonal, where the usual…

$H$-based Quivers with potentials and their representations
Xiaoyue Lin
https://arxiv.org/abs/2509.19782 https://arxiv.org/pdf/2509.19782

$H$-based Quivers with potentials and their representations
We generalize Derksen-Weyman-Zelevinsky's theory of quivers with potentials (QPs) to an $H$-based setting by considering quivers with exactly one loop at each vertex, asking the loops to be nilpotent and so attaching a truncated polynomial ring $H_i$ to each vertex. The algebra is then defined by taking the quotient of the complete path algebra by relations arising from analogs of the Jacobian ideals of a given potential. We develop the mutation theory for such $H$-based QPs and their decorated…

Counting the number of $2$-periodic $\mathcal{O}_{K}$-points of a discrete dynamical system with applications from arithmetic statistics, V
Brian Kintu
https://arxiv.org/abs/2508.16393

Counting the number of $2$-periodic $\mathcal{O}_{K}$-points of a discrete dynamical system with applications from arithmetic statistics, V
In this follow-up paper, we again inspect a surprising relationship between the set of $2$-periodic points of a polynomial map $φ_{d, c}$ defined by $φ_{d, c}(z) = z^d + c$ for all $c, z \in \mathcal{O}_{K}$ and the coefficient $c$, where $K$ is any number field of degree $n\geq 2$ and $d>2$ is an integer. As before, we again study here counting problems that are inspired by the exciting advances on $2$-torsion point-counting in arithmetic statistics and on $2$-periodic point-counting in arit…

Intersections of the Ekedahl-Oort and Newton Polygon Stratifications of $\mathcal{A}_{5}$
Elvira Lupoian, Mychelle Parker
https://arxiv.org/abs/2509.19878 https://

Intersections of the Ekedahl-Oort and Newton Polygon Stratifications of $\mathcal{A}_{5}$
The moduli space $\mathcal{A}_g$ of principally polarised abelian varieties of dimension $g$, defined over an algebraically closed field of characteristic $p >0$, is studied through various stratifications. The two most prominent ones are the Newton polygon stratification, based on the isogeny class of the $p$-divisible group of an abelian variety, and the Ekedahl-Oort stratification, defined by the isomorphism class of its $p$-torsion group scheme. In general, it is not known how the strata of…

"Syndicalism is a method of industrial organization which goes away from all the traditional conceptions of authority and government, of capitalism and the State. While communism, in abolishing individual capitalism, creates a worse monster in its place in the form of the economic state, syndicalism leaves all the patterns of administration which in the past have resulted only in the oppression and exploitation of man by man, and sets out to build an organizational form based on the nat…

Data-Free Knowledge Distillation for LiDAR-Aided Beam Tracking in MmWave Systems
Abolfazl Zakeri, Nhan Thanh Nguyen, Ahmed Alkhateeb, Markku Juntti
https://arxiv.org/abs/2509.19092

Data-Free Knowledge Distillation for LiDAR-Aided Beam Tracking in MmWave Systems
Multimodal sensing reduces beam training overhead but is constrained by machine learning complexity and dataset demands. To address this, we propose a data-free (DF) knowledge distillation (KD) framework for efficient LiDAR-aided mmWave beam tracking, i.e., predicting the best current and future beams. Specifically, we propose a knowledge inversion framework, where a generator synthesizes LiDAR input data from random noise, guided by a loss function defined on the features and outputs of a pre-…

Reduced coaction Lie algebra, double shuffle Lie algebra and noncommutative krv2 equation
Megan Howarth, Muze Ren
https://arxiv.org/abs/2509.20275 https://…

Reduced coaction Lie algebra, double shuffle Lie algebra and noncommutative krv2 equation
We study the reduced coaction Lie algebra $\mathfrak{rc}_0$, which is defined by an algebraic equation satisfied by the reduced coaction (an upgraded version of the necklace cobracket) and the skew-symmetric condition. We prove that the double shuffle Lie algebra $\mathfrak{dmr}_0$ together with the skew-symmetric condition injects to $\mathfrak{rc}_0$, and that $\mathfrak{rc}_0$ together with the krv1 equation injects to the Kashiwara-Vergne Lie algebra $\mathfrak{krv}_2$.

Paraconsistent Constructive Modal Logic
Han Gao, Daniil Kozhemiachenko, Nicola Olivetti
https://arxiv.org/abs/2508.17758 https://arxiv.org/pdf/2508.17758…

Paraconsistent Constructive Modal Logic
We present a family of paraconsistent counterparts of the constructive modal logic CK. These logics aim to formalise reasoning about contradictory but non-trivial propositional attitudes like beliefs or obligations. We define their Kripke-style semantics based on intuitionistic frames with two valuations which provide independent support for truth and falsity; they are connected by strong negation as defined in Nelson's logic. A family of systems is obtained depending on whether both modal oper…

A Variant Of Chaitin's Omega function
Yuxuan Li, Shuheng Zhang, Xiaoyan Zhang, Xuanheng Zhao
https://arxiv.org/abs/2508.16892 https://arxiv.org/pdf/250…

A Variant Of Chaitin's Omega function
We investigate the continuous function $f$ defined by $$x\mapsto \sum_{σ\le_L x }2^{-K(σ)}$$ as a variant of Chaitin's Omega from the perspective of analysis, computability, and algorithmic randomness. Among other results, we obtain that: (i) $f$ is differentiable precisely at density random points; (ii) $f(x)$ is $x$-random if and only if $x$ is weakly low for $K$ (low for $Ω$); (iii) the range of $f$ is a null, nowhere dense, perfect $Π^0_1(\emptyset')$ class with Hausdorff dimension $1$;…

Unified trajectory criterion for quantum and classical non-Markovianity
Le Hu, Archana Kamal
https://arxiv.org/abs/2508.16064 https://arxiv.org/pdf/2508.16…

Unified trajectory criterion for quantum and classical non-Markovianity
We propose a simple criterion for non-Markovianity: a quantum master equation is non-Markovian if and only if its \textit{trajectory set} contains a \textit{self-intersecting trajectory} (defined in the main text). Since self-intersection is invariant under time reversal, our criterion implies that Markovianity itself is time-reversal invariant: This property is not possessed by many existing criteria based on information flow or complete positivity. For a given quantum master equation, the set…

FUNCanon: Learning Pose-Aware Action Primitives via Functional Object Canonicalization for Generalizable Robotic Manipulation
Hongli Xu, Lei Zhang, Xiaoyue Hu, Boyang Zhong, Kaixin Bai, Zolt\'an-Csaba M\'arton, Zhenshan Bing, Zhaopeng Chen, Alois Christian Knoll, Jianwei Zhang
https://arxiv.org/abs/2509.19102

How Soft is Too Soft? Tuning Order and Disorder in Dimeric Core-Soft Colloids with Bond Flexibility
Leandro B. Krott, Davi Felipe Kray Silva, A. de J. R\'ios-Roldan, Victor M. Trejos, J. Antonio Moreno-Razo, Jos\'e Rafael Bordin
https://arxiv.org/abs/2507.18377

How Soft is Too Soft? Tuning Order and Disorder in Dimeric Core-Soft Colloids with Bond Flexibility
We employ molecular dynamics simulations to explore how internal flexibility affects phase transitions in soft-matter systems composed of dimers interacting via a core-softened potential with two characteristic length scales. Monomers are connected by harmonic springs with varying stiffness, allowing us to tune the dimer rigidity from highly flexible to nearly rigid. Flexible dimers reproduce the behavior of monomeric systems, displaying well-defined BCC and HCP crystalline phases separated by …

On the problem of filling by a Poincar\'e-Einstein metric in dimension 4
Sun-Yung Alice Chang, Yuxin Ge
https://arxiv.org/abs/2509.18430 https://arxiv.…

Source-Condition Analysis of Kernel Adversarial Estimators
Antonio Olivas-Martinez, Andrea Rotnitzky
https://arxiv.org/abs/2508.17181 https://arxiv.org/pdf…

Source-Condition Analysis of Kernel Adversarial Estimators
In many applications, the target parameter depends on a nuisance function defined by a conditional moment restriction, whose estimation often leads to an ill-posed inverse problem. Classical approaches, such as sieve-based GMM, approximate the restriction using a fixed set of test functions and may fail to capture important aspects of the solution. Adversarial estimators address this limitation by framing estimation as a game between an estimator and an adaptive critic. We study the class of Re…

Schwarzian Norm Estimates for Analytic Functions Associated with Convex Functions
Molla Basir Ahamed, Rajesh Hossain, Sabir Ahammed
https://arxiv.org/abs/2506.19873

Schwarzian Norm Estimates for Analytic Functions Associated with Convex Functions
Let $\mathcal{A}$ denote the class of analytic functions $f$ on the unit disc $\mathbb{D}=\{z\in\mathbb{C}:\;|z|<1\}$ normalized by $f(0)=0$ and $f^{\prime}(0)=1$. In the present article, we consider and $\mathcal{F}(c)$ the subclasses of $\mathcal{A}$ are defined by \begin{align*} \mathcal{F}(c)=\bigg\{f\in\mathcal{A}:\;{\rm Re}\;\bigg(1+\frac{zf^{\prime\prime}(z)}{f^{\prime}(z)}\bigg)>1-\frac{c}{2},\;\;\mbox{for some}\;c\in(0,3]\bigg\}, \end{align*} and derive sharp bounds f…

Shape Theorem for the Contact Process in a Dynamical Random Environment
Michel Reitmeier, Marco Seiler
https://arxiv.org/abs/2508.16330 https://arxiv.org/p…

Shape Theorem for the Contact Process in a Dynamical Random Environment
We study the contact process in a dynamical random environment defined on the vertices and edges of a graph. For a broad class of processes, we establish an asymptotic shape theorem for the set H_t, which represents the vertices that have been infected up to time t. More precisely, we show that this asymptotic shape is characterized -- similar to the basic contact process -- by a cone spanned by a convex set U, provided certain growth conditions are satisfied. Notably, we find that the asymptot…

Quasi-Contact Forces with Resonant Range Control in Rydberg Atoms
Mohammadsadegh Khazali
https://arxiv.org/abs/2507.17361 https://arxiv.org/pdf/2507.17361 https://arxiv.org/html/2507.17361
arXiv:2507.17361v1 Announce Type: new
Abstract: We introduce a novel method to engineer sharply peaked, distance-selective interactions between neutral atoms by exploiting interaction-induced resonances within a resonantly driven Rydberg ladder system. By tuning laser parameters, a subsystem eigenstate twist rapidly and brought into degeneracy with the atomic ground state at precisely defined interatomic separations, resulting in an effective potential sharply localized around this resonance distance. Unlike previous off-resonant macrodimer-based schemes, our approach significantly enhances interaction sharpness and strength, reaching MHz scales, and provides straightforward experimental tunability without requiring sub-wavelength positional control. Analytic expressions, validated through comprehensive master-equation simulations, detail the interaction profile's amplitude, width, and resonant distance. This precise control facilitates parallel entangling gates crucial for measurement-based quantum computing and enables simulation of complex lattice Hamiltonians with customizable connectivity. Additionally, our scheme opens possibilities for novel studies in molecular physics through micrometer-scale bond-length diatomic molecules.
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$\mathbb{Z}_2$ topological invariant in three-dimensional PT- and PC-symmetric class CI band structures
Ken Shiozaki
https://arxiv.org/abs/2509.19825 https://

$\mathbb{Z}_2$ topological invariant in three-dimensional PT- and PC-symmetric class CI band structures
We construct a previously missing $\mathbb{Z}_2$ topological invariant for three-dimensional band structures in symmetry class CI defined by parity-time (PT) and parity-particle-hole (PC) symmetries. PT symmetry allows one to define a real Berry connection and, based on the $η$-invariant, a spin-Chern--Simons (spin-CS) action. We show that PC symmetry quantizes the spin-CS action to $\{0,2π\}$ with $4π$ periodicity, thereby yielding a well-defined $\mathbb{Z}_2$ invariant. This invariant is …

A Family of Berndt-Type Integrals and Associated Barnes Multiple Zeta Functions
Xinyue Gu Ce Xu, Jianing Zhou
https://arxiv.org/abs/2506.20074 https://

A Family of Berndt-Type Integrals and Associated Barnes Multiple Zeta Functions
In this paper, we focus on calculating a specific class of Berndt integrals, which exclusively involves (hyperbolic) cosine functions. Initially, this integral is transformed into a Ramanujan-type hyperbolic (infinite) sum via contour integration. Subsequently, a function incorporating theta is defined. By employing the residue theorem, the mixed Ramanujan-type hyperbolic (infinite) sum with both hyperbolic cosine and hyperbolic sine in the denominator is converted into a simpler Ramanujan-type…

Chiseling: Powerful and Valid Subgroup Selection via Interactive Machine Learning
Nathan Cheng, Asher Spector, Lucas Janson
https://arxiv.org/abs/2509.19490 https://

Chiseling: Powerful and Valid Subgroup Selection via Interactive Machine Learning
In regression and causal inference, controlled subgroup selection aims to identify, with inferential guarantees, a subgroup (defined as a subset of the covariate space) on which the average response or treatment effect is above a given threshold. E.g., in a clinical trial, it may be of interest to find a subgroup with a positive average treatment effect. However, existing methods either lack inferential guarantees, heavily restrict the search for the subgroup, or sacrifice efficiency by naive d…

Effective Pressure of the FRW Universe
Shi-Bei Kong
https://arxiv.org/abs/2507.17789 https://arxiv.org/pdf/2507.17789…

Effective Pressure of the FRW Universe
In this paper, we study the effective pressure of the $N$-dimensional FRW(Friedmann-Robertson-Walker) universe in Einstein gravity, Gauss-Bonnet gravity, and Lovelock gravity. The effective pressure is defined by $P_{eff}:=-dE/dV$, where $E=ρV$ is the effective energy and $V$ is the volume of the FRW universe inside the apparent horizon. The effective pressure in Einstein gravity is always negative and its absolute value decreases with the horizon radius $R_A$. The effective pressure in Gauss-…

Federated Aggregation of Demand Flexibility
Yifan Dong, Ge Chen, Junjie Qin
https://arxiv.org/abs/2509.19612 https://arxiv.org/pdf/2509.19612

Federated Aggregation of Demand Flexibility
This paper proposes a federated framework for demand flexibility aggregation to support grid operations. Unlike existing geometric methods that rely on a static, pre-defined base set as the geometric template for aggregation, our framework establishes a true federated process by enabling the collaborative optimization of this base set without requiring the participants sharing sensitive data with the aggregator. Specifically, we first formulate the base set optimization problem as a bilevel pro…

DefElement: an encyclopedia of finite element definitions
Matthew W. Scroggs, Pablo D. Brubeck, Joseph P. Dean, J{\o}rgen S. Dokken, India Marsden
https://arxiv.org/abs/2506.20188

DefElement: an encyclopedia of finite element definitions
DefElement is an online encyclopedia of finite element definitions that was created and is maintained by the authors of this paper. DefElement aims to make information about elements defined in the literature easily available in a standard format. There are a number of open-source finite element libraries available, and it can be difficult to check that an implementation of an element in a library matches the element's definition in the literature or implementation in another library, especiall…

On the Stability of the Euler Characteristic Transform for a Perturbed Embedding
Jasmine George, Oscar Lledo Osborn, Elizabeth Munch, Messiah Ridgley II, Elena Xinyi Wang
https://arxiv.org/abs/2506.19991

On the Stability of the Euler Characteristic Transform for a Perturbed Embedding
The Euler Characteristic Transform (ECT) is a robust method for shape classification. It takes an embedded shape and, for each direction, computes a piecewise constant function representing the Euler Characteristic of the shape's sublevel sets, which are defined by the height function in that direction. It has applications in TDA inverse problems, such as shape reconstruction, and is also employed with machine learning methodologies. In this paper, we define a distance between the ECTs of two d…

In Reverie Together: Ten Years of Mathematical Discovery with a Machine Collaborator
Randy Davila, Boris Brimkov, Ryan Pepper
https://arxiv.org/abs/2507.17780 https://

In Reverie Together: Ten Years of Mathematical Discovery with a Machine Collaborator
We present four open conjectures in graph theory generated by the automated conjecturing system \texttt{TxGraffiti}. Each conjecture is concise, grounded in natural graph invariants, and empirically validated across hundreds of graphs. Despite extensive effort, these statements remain unresolved--defying both proof and counterexample. They are not only mathematical challenges but creative expressions--born of symbolic pattern recognition and mathematician-defined heuristics, refined through yea…

Homogenization and 3D-2D dimension reduction of a functional on manifold valued BV space
Luca Lussardi, Andrea Torricelli, Elvira Zappale
https://arxiv.org/abs/2507.18390 https:…

Homogenization and 3D-2D dimension reduction of a functional on manifold valued BV space
We study the simultaneous homogenization and dimension reduction of an energy functional with linear growth defined on the space of manifold valued Sobolev functions. The study is carried out by $Γ$-convergence, providing an integral representation result in the space of manifold constrained functions with bounded variation

Thermodynamics of rotating fermions
Victor E. Ambrus, Aleksandar Geci\'c
https://arxiv.org/abs/2509.17640 https://arxiv.org/pdf/2509.17640

Thermodynamics of rotating fermions
We consider the thermodynamic properties of a rotating gas of fermions. We begin by constructing the thermodynamic potential $Φ$ and its associated current $ϕ^μ$ within the grand canonical ensemble of a macroscopic rigidly rotating body, where the ensemble parameters are the temperature $T_0$ and chemical potential $μ_0$ on the rotation axis, as well as the rotation angular velocity $Ω_0$. We then consider the problem of local thermodynamics, where the thermodynamic state is defined by the…

I'm at best a combat C programmer so this latest zmap fix may be perfectly reasonable.
https://github.com/zmap/zmap/pull/944
Is it common, and is it a best practice to not free memory allocated in some use cases? That may be two separation questions.
I have always freed memory allo…

Context Steering: A New Paradigm for Compression-based Embeddings by Synthesizing Relevant Information Features
Guillermo Sarasa Dur\'an, Ana Granados Fontecha, Francisco de Borja Rodr\'iguez Ort\'iz
https://arxiv.org/abs/2508.14780

Context Steering: A New Paradigm for Compression-based Embeddings by Synthesizing Relevant Information Features
Compression-based distances (CD) offer a flexible and domain-agnostic means of measuring similarity by identifying implicit information through redundancies between data objects. However, as similarity features are derived from the data, rather than defined as an input, it often proves difficult to align with the task at hand, particularly in complex clustering or classification settings. To address this issue, we introduce "context steering," a novel methodology that actively guides the featur…

Chimera games emerging from coevolutionary dynamics with endogenous feedbacks
Federico Maria Quetti, Andrea Civilini, Giacomo Frigerio, Silvia Figini, Giacomo Livan, Vito Latora
https://arxiv.org/abs/2506.20603

Chimera games emerging from coevolutionary dynamics with endogenous feedbacks
From climate change to financial bubbles and wars, the rapid pace of change in our world clearly shows that the commonly adopted assumption of a static environment in evolutionary game-theoretic models is often unrealistic. In this work, we introduce a coevolutionary game model where the game environment and the strategy dynamics are mutually coupled. In particular, the game played at each time is endogenously defined as a convex combination of two social dilemmas, weighted by the current abund…

An improved nonlocal electron heat transport model for magnetized plasmas
Z. H. Chen, Z. Q. Zhao, X. H. Yang, L. R. Li, B. Zeng, Z. Li, B. H. Xu, G. B. Zhang, H. H. Ma, M. Tang, Y. Y. Ma, H. Xu, F. Q. Shao, J. Zhang
https://arxiv.org/abs/2508.17309

An improved nonlocal electron heat transport model for magnetized plasmas
Distortions in the electron distribution function driven by intense temperature gradients critically influence the generation and evolution of heat flux and magnetic fields in plasmas under the condition of inertial confinement fusion. Describing such kinetic behaviors at large spatiotemporal scales typically requires multigroup models based on simplified Vlasov-Fokker-Planck equations. However, the accuracy of existing multigroup models remains uncertain, without a well-defined methodology for…

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

Homomorphism Calculus for User-Defined Aggregations
Ziteng Wang, Ruijie Fang, Linus Zheng, Dixin Tang, Isil Dillig
https://arxiv.org/abs/2508.15109 https://

Homomorphism Calculus for User-Defined Aggregations
Data processing frameworks like Apache Spark and Flink provide built-in support for user-defined aggregation functions (UDAFs), enabling the integration of domain-specific logic. However, for these frameworks to support \emph{efficient} UDAF execution, the function needs to satisfy a \emph{homomorphism property}, which ensures that partial results from independent computations can be merged correctly. Motivated by this problem, this paper introduces a novel \emph{homomorphism calculus} that can…

On exploration of an interior mirror descent flow for stochastic nonconvex constrained problem
Kuangyu Ding, Kim-Chuan Toh
https://arxiv.org/abs/2507.15264

On exploration of an interior mirror descent flow for stochastic nonconvex constrained problem
We study a nonsmooth nonconvex optimization problem defined over nonconvex constraints, where the feasible set is given by the intersection of the closure of an open set and a smooth manifold. By endowing the open set with a Riemannian metric induced by a barrier function, we obtain a Riemannian subgradient flow formulated as a differential inclusion, which remains strictly within the interior of the feasible set. This continuous dynamical system unifies two classes of iterative optimization me…

On the dimension-free control of higher order truncated Riesz transforms by higher order Riesz transforms
Maciej Kucharski, Mateusz Kwa\'snicki, B{\l}a\.zej Wr\'obel
https://arxiv.org/abs/2507.17510

On the dimension-free control of higher order truncated Riesz transforms by higher order Riesz transforms
Fix a positive integer $k$. Let $R_k$ be a higher order Riesz transform of order $k$ on $\mathbb{R}^d$ and let $R_k^t,$ $t>0,$ be the corresponding truncated Riesz transform. We study the relation between $\|R_k f\|_{L^p(\mathbb{R}^d)}$ and $\|R_k^t f\|_{L^p(\mathbb{R}^d)}$ for $p=1$, $p=\infty,$ and $p=2.$ This is performed via analysis of the factorization operator $M_k^t$ defined by the relation $R_k^t=M_k^t R_k.$ The operator $M_k^t$ is a convolution operator associated …

Exploring shell effects in fission yields of neutron-deficient Th, Ac, and Ra isotopes near N=126
J. L. Rodr\'iguez-S\'anchez, J. Ta\"ieb
https://arxiv.org/abs/2508.17024

Exploring shell effects in fission yields of neutron-deficient Th, Ac, and Ra isotopes near N=126
Studies of nuclear fission over recent decades have led to a well-defined mapping of neutron and proton shell effects across the nuclear chart, particularly within the valley of stability. These shell effects play a crucial role in driving the asymmetric splitting of fissioning nuclei, as reflected in fission yields that are strongly influenced by spherical and deformed shell closures. In the actinide region, the existence of two primary fission modes, standard I and standard II, has been well-…

Cyclic Operators, Linear Functionals and RKHS
Yi Wang
https://arxiv.org/abs/2507.17358 https://arxiv.org/pdf/2507.17358

Cyclic Operators, Linear Functionals and RKHS
Given a commuting $n$-tuple of bounded linear operators on a Hilbert space, together with a distinguished cyclic vector, Jim Agler defined a linear functional $Λ_{\mathbf{T},h}$ on the polynomial ring $\mathbb{C}[\mathbf{z},\bar{\mathbf{z}}]$. ``Near subnormality properties'' of an operator $T$ are translated into positivity properties of $Λ_{T,h}$. In this paper, we approach ``near subnormality properties'' in a different way by answering the following question: when is $Λ_{\mathbf{T},h}$ g…

SpinAdaptedSecondQuantization.jl 1.0 -- A Simple and Pedagogical Approach to Symbolic Quantum Chemistry
Marcus T. Lexander, Tor S. Haugland, Federico Rossi, Henrik Koch
https://arxiv.org/abs/2508.16342

SpinAdaptedSecondQuantization.jl 1.0 -- A Simple and Pedagogical Approach to Symbolic Quantum Chemistry
The development of new electronic structure methods is a very time consuming and error prone process when done by hand. SpinAdaptedSecondQuantization.jl is an open-source Julia package we have developed for working with automated electronic structure theory development. The code focuses on being user-friendly and extensible, allowing for easy use of both user- and pre-defined fermionic and/or bosonic operators, tensors, and orbital spaces. This allows the code to be used to efficiently investig…

On a multivariate extension for Copula-based Conditional Value at Risk
Andres Mauricio Molina Barreto
https://arxiv.org/abs/2508.16132 https://arxiv.org/pd…

On a multivariate extension for Copula-based Conditional Value at Risk
Copula-based Conditional Value at Risk (CCVaR) is defined as an alternative version of the classical Conditional Value at Risk (CVaR) for multivariate random vectors intended to be real-valued. We aim to generalize CCVaR to several dimensions (d>=2) when the dependence structure is given by an Archimedean copula. While previous research focused on the bivariate case, leaving the multivariate version unexplored, an almost closed-form expression for CCVaR under an Archimedean copula is derived. T…

A q-Supercongruence Motivated by Higher-Order Generalized Lehmer-Euler Numbers
Wei-Wei Qi
https://arxiv.org/abs/2507.16825 https://ar…

A q-Supercongruence Motivated by Higher-Order Generalized Lehmer-Euler Numbers
Certain generalization of Euler numbers was defined in 1935 by Lehmer using cubic roots of unity, as a natural generalization of Bernoulli and Euler numbers. In this paper, we define a new polynomial related to the higher-order generalized Lehmer-Euler numbers and determine its a q-supercongruence.

Analytic two-loop amplitudes for di-jet and $\gamma $jet production mediated by a heavy-quark loop
Federico Coro, Christoph Nega, Lorenzo Tancredi, Fabian J. Wagner
https://arxiv.org/abs/2509.15315

Analytic two-loop amplitudes for di-jet and $γ+$jet production mediated by a heavy-quark loop
In this paper, we present analytical results for the two-loop QCD corrections to the production of two partons or a photon and a parton in hadronic collisions, mediated by loops of massive quarks. These amplitudes involve Feynman integrals defined on an elliptic curve. We compute them by generalizing our recent results for the production of two photons to include additional crossings of the corresponding master integrals, which we compute in terms of the same basis of independent iterated integ…

Statistics-encoded tensor network approach in disordered quantum many-body spin chains
Hao Zhu, Ding-Zu Wang, Shi-Ju Ran, Guo-Feng Zhang
https://arxiv.org/abs/2508.16286 https:/…

Statistics-encoded tensor network approach in disordered quantum many-body spin chains
Simulating the dynamics of quantum many-body systems with disorder is a fundamental challenge. In this work, we propose a general approach -- the statistics-encoded tensor network (SeTN) -- to study such systems. By encoding disorder into an auxiliary layer and averaging separately, SeTN restores translational invariance, enabling a well-defined transfer matrix formulation. We derive a universal criterion, $n \gg α^2 t^2$, linking discretization $n$, disorder strength $α$, and evolution durat…

The block decomposition of the principal representation category of reductive algebraic groups with Frobenius maps
Xiaoyu Chen, Junbin Dong
https://arxiv.org/abs/2506.20378

The block decomposition of the principal representation category of reductive algebraic groups with Frobenius maps
Let ${\bf G}$ be a connected reductive algebraic group defined over the finite field $\mathbb{F}_q$ with $q$ elements. Let $\Bbbk$ be a field such that $\op{char} \Bbbk \ne \op{char} \mathbb{F}_q$. In this paper, we study the extensions of simple modules (over $\Bbbk$) in the principal representation category $\mathscr{O}(\bf G)$ which is defined in \cite{D1}. In particular, we get the block decomposition of $\mathscr{O}(\bf G)$, which is parameterized by the central characters of ${\bf G}$.

Computability of Separation Axioms in Countable Second Countable Spaces
Andrew DeLapo, David Gonzalez
https://arxiv.org/abs/2507.18564 https://arxiv.org/pd…

Computability of Separation Axioms in Countable Second Countable Spaces
We analyze the effective content of countable, second countable topological spaces by directly calculating the complexity of several topologically defined index sets. We focus on the separation principles, calibrating an arithmetic completeness result for each of the Tychonoff separation axioms. Beyond this, we prove completeness results for various other topological properties, such as being Polish and having a particular Cantor-Bendixson rank, using tools from computable structure theory. Thi…

A cluster criterion for potential degeneracy of superelliptic curves
Jeffrey Yelton
https://arxiv.org/abs/2508.15974 https://arxiv.org/pdf/2508.15974

A cluster criterion for potential degeneracy of superelliptic curves
Let $K$ be a field with a discrete valuation; let $p$ be a prime; and let $C$ be the curve defined by an equation of the form $y^p = f(x)$. We show that the curve $C$ has a model over an algebraic extension of $K$ whose special fiber consists of genus-$0$ components and has at worst nodal singularities if and only if the cluster data of the roots of $f$ satisfies a certain criterion, and when these hold, we show explicitly how to build the minimal regular model of $C$. We develop an interpretat…

Universal Scaling Functions of the Gr{\"u}neisen Ratio near Quantum Critical Points
Xuan Zhou, Enze Lv, Wei Li, Yang Qi
https://arxiv.org/abs/2509.17362 https://

Universal Scaling Functions of the Gr{ü}neisen Ratio near Quantum Critical Points
The Grüneisen ratio, defined as $Γ_g \equiv (1/T) (\partial T/\partial g)_S$, serves as a highly sensitive probe for detecting quantum critical points (QCPs) driven by an external feild $g$ and for characterizing the magnetocaloric effect (MCE). Near a QCP, the Grüneisen ratio displays a universal divergence which is governed by a universality-class-dependent scaling function stemming from the scale invariance. In this work, we systematically investigate the universal scaling functions of Gr…

Population-Dependent r-process Scatter in the Globular Cluster M15
Lauren E. Henderson, Roman Gerasimov, Evan N. Kirby
https://arxiv.org/abs/2509.16840 https://

Population-Dependent r-process Scatter in the Globular Cluster M15
Multiple populations, defined by correlations between light element abundances, are an almost ubiquitous property of globular clusters. On the other hand, dispersions among the heavy elements are limited to a few rare clusters. In this letter, we present Mg, Y, Ba, La, and Eu measurements for 89 stars in M15 with errors < 0.4 dex from Keck/DEIMOS medium-resolution spectra. We find higher Ba, La, and Eu dispersions in the first generation of stars than in the second generation at a significance …

Synchronization of Dirac-Bianconi driven oscillators
Riccardo Muolo, Iv\'an Le\'on, Yuzuru Kato, Hiroya Nakao
https://arxiv.org/abs/2506.20163 http…

Synchronization of Dirac-Bianconi driven oscillators
In dynamical systems on networks, one assigns the dynamics to nodes, which are then coupled via links. This approach does not account for group interactions and dynamics on links and other higher dimensional structures. Higher-order network theory addresses this by considering variables defined on nodes, links, triangles, and higher-order simplices, called topological signals (or cochains). Moreover, topological signals of different dimensions can interact through the Dirac-Bianconi operator, w…

Stable Invariants of Words from Random Matrices II: Formulas and Extensions
Doron Puder, Yotam Shomroni
https://arxiv.org/abs/2509.17271 https://arxiv.org/…

Stable Invariants of Words from Random Matrices II: Formulas and Extensions
Let $w$ be a word in a free group. As was revealed by Magee and Puder in [arXiv:1802.04862], the stable commutator length (scl) of $w$, a well-known topological invariant, can also be defined in terms of certain stable Fourier coefficients of $w$-random unitary matrices. In the first part of the current work [arXiv:2311.17733], we demonstrated how this phenomenon is much broader: we proved more instances of such results and conjectured others. These new results and conjectures involved other to…

Cuckoo Attack: Stealthy and Persistent Attacks Against AI-IDE
Xinpeng Liu, Junming Liu, Peiyu Liu, Han Zheng, Qinying Wang, Mathias Payer, Shouling Ji, Wenhai Wang
https://arxiv.org/abs/2509.15572

Cuckoo Attack: Stealthy and Persistent Attacks Against AI-IDE
Modern AI-powered Integrated Development Environments (AI-IDEs) are increasingly defined by an Agent-centric architecture, where an LLM-powered Agent is deeply integrated to autonomously execute complex tasks. This tight integration, however, also introduces a new and critical attack surface. Attackers can exploit these components by injecting malicious instructions into untrusted external sources, effectively hijacking the Agent to perform harmful operations beyond the user's intention or awar…

Heterogeneous Quantile Treatment Effect Estimation for Longitudinal Data with High-Dimensional Confounding
Zhixin Qiu, Huichen Zhu, Wenjie Wang, Yanlin Tang
https://arxiv.org/abs/2508.16326

Heterogeneous Quantile Treatment Effect Estimation for Longitudinal Data with High-Dimensional Confounding
Causal inference plays a fundamental role in various real-world applications. However, in the motivating non-small cell lung cancer (NSCLC) study, it is challenging to estimate the treatment effect of chemotherapy on circulating tumor DNA (ctDNA). First, the heterogeneous treatment effects vary across patient subgroups defined by baseline characteristics. Second, there exists a broad set of demographic, clinical and molecular variables act as potential confounders. Third, ctDNA trajectories ove…

The Flight of the Bumblebee in a Non-Commutative Geometry: A New Black Hole Solution
A. A. Ara\'ujo Filho, N. Heidari, Iarley P. Lobo, Yuxuan Shi, Francisco S. N. Lobo
https://arxiv.org/abs/2509.17867

The Flight of the Bumblebee in a Non-Commutative Geometry: A New Black Hole Solution
This paper investigates a new black hole solution within the framework of bumblebee gravity, incorporating non-commutative corrections parameterized by $Θ$ and implemented through the Moyal twist $\partial_r \wedge \partial_θ$. Notably, the event horizon remains unaffected by $Θ$, while the surface gravity becomes ill-defined, in agreement with the behavior previously reported for the non-commutative Schwarzschild black hole [1]. The propagation of light is examined by analyzing null geodesi…

Quarterback Mystery: Who's Really the Better Star? https://insidethestar.com/quarterback-mystery-whos-really-the-better-star

Line Aspect Ratio
Arash Vaezi
https://arxiv.org/abs/2506.20508 https://arxiv.org/pdf/2506.20508…

Line Aspect Ratio
We address the problem of covering a target segment $\overline{uv}$ using a finite set of guards $\mathcal{S}$ placed on a source segment $\overline{xy}$ within a simple polygon $\mathcal{P}$, assuming weak visibility between the target and source. Without geometric constraints, $\mathcal{S}$ may be infinite, as shown by prior hardness results. To overcome this, we introduce the {\it line aspect ratio} (AR), defined as the ratio of the \emph{long width} (LW) to the \emph{short width} (SW) of $\…

Hypergeometric Motives from Toric Hypersurfaces
Asem Abdelraouf
https://arxiv.org/abs/2509.17624 https://arxiv.org/pdf/2509.17624

Hypergeometric Motives from Toric Hypersurfaces
In this paper, we study two compactifications of general hypersurfaces defined by the vanishing of linear combinations of $d+2$ monomials in $d$-dimensional algebraic tori. We prove that the number of their $\mathbb{F}_q$-points is given by finite hypergeometric sums under certain general conditions. In the process, we introduce the notion of a gamma triple, which allows us to extend the classical definition of finite hypergeometric sums to prime powers corresponding to the cyclotomic field of …

Extremal Lyapunov exponents in random dynamics
Thirupathi Perumal, Shrihari Sridharan
https://arxiv.org/abs/2507.16764 https://arxiv.…

Extremal Lyapunov exponents in random dynamics
In this manuscript, we consider finitely many maps, all of which are defined on a smooth compact measure space, with at least one map in the collection having degree strictly bigger than 1. Working with random dynamics generated by this setting, we obtain an expression for the extremal Lyapunov exponents, that characterise the instability of typical orbits, as the limit of the averages of the logarithm of the operator norm of linear cocycles of generic orbits. We obtain this as a consequence to…

Low-Rank Adaptation of Evolutionary Deep Neural Networks for Efficient Learning of Time-Dependent PDEs
Jiahao Zhang, Shiheng Zhang, Guang Lin
https://arxiv.org/abs/2509.16395 ht…

Low-Rank Adaptation of Evolutionary Deep Neural Networks for Efficient Learning of Time-Dependent PDEs
We study the Evolutionary Deep Neural Network (EDNN) framework for accelerating numerical solvers of time-dependent partial differential equations (PDEs). We introduce a Low-Rank Evolutionary Deep Neural Network (LR-EDNN), which constrains parameter evolution to a low-rank subspace, thereby reducing the effective dimensionality of training while preserving solution accuracy. The low-rank tangent subspace is defined layer-wise by the singular value decomposition (SVD) of the current network weig…

Distance Distribution Functions and Probabilistic Metric Spaces on C*-algebras
Rasoul Abazari
https://arxiv.org/abs/2509.16498 https://arxiv.org/pdf/2509.1…

Distance Distribution Functions and Probabilistic Metric Spaces on C*-algebras
In this paper, by using the concept of positive elements of $C^*$-algebras instead of the real numbers $\mathbb{R}$, a generalization of distribution functions, with a particular focus on distance distribution functions has been introduced as a novel approach in statistical mathematics. Also, by applying this concept, probabilistic metric space on $C^*$-algebras is defined and some properties such as topology and fixed point theorems have been investigated. Finally, some examples and applicatio…

Differential Equations for Wilson Loops in ABJM Theory
Takao Suyama
https://arxiv.org/abs/2509.16545 https://arxiv.org/pdf/2509.16545

Differential Equations for Wilson Loops in ABJM Theory
We derive a system of differential equations which are satisfied by the vevs of BPS Wilson loops and 't Hooft coupling of ABJM theory. They are Picard-Fuchs equations of an algebraic curve defined by the derivative of the planar resolvent of the corresponding matrix model. The weak and strong coupling behaviors can be reproduced by their local solutions around regular singularities. We also obtain a recursion relation which can be used to determine the planar vevs of BPS Wilson loops in arbitra…

Excellent article by Ibrahim Diallo that serves as a quick overview of image formats for the web! ^^
What Learning React Won't Teach You: Image Formats
https://idiallo.com/blog/react-and-image-format?utm_source=tldrwebdev

Advancing Lunar Communication through Inter-domain Space Networks and Dynamic Orchestration
Selen Gecgel Cetin, Baris Donmez, Gunes Karabulut Kurt
https://arxiv.org/abs/2507.15483

Advancing Lunar Communication through Inter-domain Space Networks and Dynamic Orchestration
The reawakened era of lunar exploration is defined by a strategic shift from temporary visits to a sustained international and commercial presence, resulting in an unprecedented demand for a robust and continuously available communication infrastructure. The conventional direct-to-Earth communication architecture relies on limited and oversubscribed deep space networks, which are further challenged by the radiative environment and insufficient visibility in certain areas of the cislunar domain.…

G\"odel Mirror: A Formal System For Contradiction-Driven Recursion
Jhet Chan
https://arxiv.org/abs/2509.16239 https://arxiv.org/pdf/2509.16239

Gödel Mirror: A Formal System For Contradiction-Driven Recursion
We introduce the Gödel Mirror, a formal system defined in Lean 4 that treats contradiction as a control signal for recursive structural evolution. Inspired by Gödelian self-reference, our system's operational semantics encode symbolic paradoxes as deterministic transitions. Unlike systems designed to guarantee normalization, the Gödel Mirror is a minimal and verifiable architecture that leverages a controlled, non-terminating loop as a productive feature. Our Lean 4 mechanization proves …

Good Morning #Canada
July 24th, 1534, the original Cross of Gaspé was erected overlooking the bay of Gaspé, by the crew of Jacques Cartier on his first trip exploration in the Gulf of St. Lawrence. Planting the cross symbolized the ownership of the territory on behalf of the King of France. Today, a granite Cross of Gaspé, erected in 1934, has replaced the original. Amazing that the installation of a religious artifact defined clear ownership of a continent you didn't know existed just days prior.
I have a small Easter Island statue in my garden that I'm going to install in the middle of my neighbour's yard. Wish me luck.
#CanadaIsAwesome #History #Colonization
https://youtu.be/aXZkwrI3V10?si=8abMJ6iEnSgGLUCr

Quantum dot energy levels in bilayer graphene: Exact and approximate study
G. Giavaras
https://arxiv.org/abs/2506.20162 https://arxiv…

Quantum dot energy levels in bilayer graphene: Exact and approximate study
In bilayer graphene the exact energy levels of quantum dots can be derived from the four-component continuum Hamiltonian. Here, we study the quantum dot energy levels with approximate equations and compare them with the exact levels. The starting point of our approach is the four-component continuum model and the quantum dot is defined by a continuous potential well in a uniform magnetic field. Using some simple arguments we demonstrate realistic regimes where approximate quantum dot equations …

Defining a phylogenetic tree with the minimum number of small-state characters
Yangjing Long, Tong Wang
https://arxiv.org/abs/2508.15533 https://arxiv.org/…

Defining a phylogenetic tree with the minimum number of small-state characters
Phylogenetic trees represent evolutionary relationships and can be uniquely defined by sets of finite-state biological characteristics. Despite prior work showing that sufficiently large trees can be determined by $r$-state character sets, the minimal leaf thresholds $n_r$ remain largely unknown. In this work, we establish the 3-state case as $n_3 = 8$, providing a concrete base for higher-state analyses. We then resolve the 5-state problem by constructing a counterexample for $n=15$ and provin…

An adaptive Hermite spectral method for the Boltzmann equation
Sihong Shao, Yanli Wang, Jie Wu
https://arxiv.org/abs/2509.17981 https://arxiv.org/pdf/2509.…

An adaptive Hermite spectral method for the Boltzmann equation
We propose an adaptive Hermite spectral method for the three-dimensional velocity space of the Boltzmann equation guided by a newly developed frequency indicator. For the homogeneous problem, the indicator is defined by the contribution of high-order coefficients in the spectral expansion. For the non-homogeneous problem, a Fourier-Hermite scheme is employed, with the corresponding frequency indicator formulated based on distributions across the entire spatial domain. The adaptive Hermite metho…

Two combinatorial puzzles arising from the theory of Kohnert polynomials
Theo Koss, Nicholas Mayers, Alex Moon
https://arxiv.org/abs/2509.17170 https://arx…

Two combinatorial puzzles arising from the theory of Kohnert polynomials
Motivated by recent work of Hanser and Mayers, we study two combinatorial puzzles arising from the theory of Kohnert polynomials. Such polynomials are defined as generating polynomials for certain collections of diagrams consisting of unit cells arranged in the first quadrant generated from an initial "seed diagram" by applying what are called "Kohnert moves". Each Kohnert move affects the position of at most cell of a diagram, attempting to move the rightmost cell of a given row to the first a…

Some subsets of set F in the diluted Hofstadter problem
Jonathan H. B. Deane, Guido Gentile
https://arxiv.org/abs/2509.17764 https://arxiv.org/pdf/2509.177…

Some subsets of set F in the diluted Hofstadter problem
We continue work started in [1] concerning integer sequences q(n), n in N, defined by q(n) = q(n-q(n-1)) + f(n), with q(1) = 1. Here, f(n), with f(1) = 0, is a given sequence. We define F as the set of semi-infinite sequence f such that the resulting sequence q exists. This requires that the term q(n-q(n-1)) be defined for all n, that is, 0 < q(n) < n+1 applies for all n in N.

Spectral Methods for Polynomial Optimization
Elvira Moreno, Venkat Chandrasekaran
https://arxiv.org/abs/2507.16272 https://arxiv.org/…

Spectral Methods for Polynomial Optimization
We present a hierarchy of tractable relaxations to obtain lower bounds on the minimum value of a polynomial over a constraint set defined by polynomial equations. In contrast to previous convex relaxation techniques for this problem, our method is based on computing the smallest generalized eigenvalue of a pair of matrices derived from the problem data, which can be accomplished for large problem instances using off-the-shelf software. We characterize the algebraic structure in a problem that f…

Connecting Early Dark Energy to Late Dark Energy by the Diluting Matter Potential
Eduardo I. Guendelman, Ramon Herrera, Pedro Labrana
https://arxiv.org/abs/2507.17095 https://…

Connecting Early Dark Energy to Late Dark Energy by the Diluting Matter Potential
In this work we study a scale invariant gravity theory containing two scalar fields, dust particles and a measure defined from degrees of freedom independent of the metric. The integration of the degrees of freedom that define the measure spontaneously break the scale symmetry, leaving us in the Einstein frame with an effective potential that is dependent on the density of the particles. The potential contains three flat regions, one for inflation, another for early dark energy and the third fo…

Spurion Analysis for Non-Invertible Selection Rules from Near-Group Fusions
Motoo Suzuki, Ling-Xiao Xu, Hao Y. Zhang
https://arxiv.org/abs/2508.14970 https://

Spurion Analysis for Non-Invertible Selection Rules from Near-Group Fusions
We generalize the framework of spurion analysis to a class of selection rules arising from non-invertible fusion algebras in perturbation theory. As a first step toward systematic applications to particle physics, we analyze the near-group fusion algebras, defined by fusion rules built from a finite Abelian group $G$ extended by a single non-invertible element. Notable examples include the Fibonacci and Ising fusion rules. We introduce a systematic scheme for labeling coupling constants at the …

Monodromy representation of graphs
Kai Yuan, Yan Wang
https://arxiv.org/abs/2509.17910 https://arxiv.org/pdf/2509.17910

Monodromy representation of graphs
It is well-known that every vertex-transitive graph admits a representation as a coset graph. In this paper, we extend this construction by introducing monodromy graphs defined through double cosets. Our main result establishes that every graph is isomorphic to a monodromy graph, providing a new combinatorial framework for graph representation. Moreover, we show that every graph gives rise to an arc-transitive graph through its monodromy representation. Inspired by the monodromy representation …

Multidimensional contracted rotations
Jose Pedro Gaivao, Benito Pires
https://arxiv.org/abs/2509.17639 https://arxiv.org/pdf/2509.17639

Multidimensional contracted rotations
We study the dynamics of multidimensional contracted rotations and address a problem posed by Y. Bugeaud and J-P. Conze in \textit{Acta Arithmetica} in 1999. More precisely, we show that if $A$ is an invertible linear contraction of $\mathbb{R}^d$, then the map $f: [0,1)^d\to [0,1)^d$ defined by $f(x) = Ax +b\,\,(\textrm{mod}\,\mathbb{Z}^d)$ is asymptotically periodic for Lebesgue almost all $b\in\mathbb{R}^d$.

On the Differential Topology of Expressivity of Parameterized Quantum Circuits
Johanna Barzen, Frank Leymann
https://arxiv.org/abs/2507.16401 https://

On the Differential Topology of Expressivity of Parameterized Quantum Circuits
Parameterized quantum circuits play a key role in quantum computing. Measuring the suitability of such a circuit for solving a class of problems is needed. One such promising measure is the expressivity of a circuit, which is defined in two main variants. The variant in focus of this contribution is the so-called dimensional expressivity which measures the dimension of the submanifold of states produced by the circuit. Understanding this measure needs a lot of background from differential topol…

Weights for $\mathrm{K}$-motives on stacks
Thiago Landim
https://arxiv.org/abs/2509.18281 https://arxiv.org/pdf/2509.18281…

Neural Brownian Motion
Qian Qi
https://arxiv.org/abs/2507.14499 https://arxiv.org/pdf/2507.14499

Neural Brownian Motion
This paper introduces the Neural-Brownian Motion (NBM), a new class of stochastic processes for modeling dynamics under learned uncertainty. The NBM is defined axiomatically by replacing the classical martingale property with respect to linear expectation with one relative to a non-linear Neural Expectation Operator, $\varepsilon^θ$, generated by a Backward Stochastic Differential Equation (BSDE) whose driver $f_θ$ is parameterized by a neural network. Our main result is a representation theo…

Source-Guided Flow Matching
Zifan Wang, Alice Harting, Matthieu Barreau, Michael M. Zavlanos, Karl H. Johansson
https://arxiv.org/abs/2508.14807 https://ar…

Source-Guided Flow Matching
Guidance of generative models is typically achieved by modifying the probability flow vector field through the addition of a guidance field. In this paper, we instead propose the Source-Guided Flow Matching (SGFM) framework, which modifies the source distribution directly while keeping the pre-trained vector field intact. This reduces the guidance problem to a well-defined problem of sampling from the source distribution. We theoretically show that SGFM recovers the desired target distribution …

Finite Entropy Implies Finite Dimension in Quantum Gravity
T. Banks
https://arxiv.org/abs/2509.17856 https://arxiv.org/pdf/2509.17856

Finite Entropy Implies Finite Dimension in Quantum Gravity
Quantum Field Theory (QFT) introduced us to the notion that a causal diamond in space-time corresponded to a subsystem of a quantum mechanical system defined on the global space-time. Work by Jacobson\cite{ted95}, Fischler and Susskind\cite{fs} and particularly Bousso\cite{bousso} suggested that in the quantum theory of gravity this subsystem should have a density matrix of finite entropy. These authors formalized older intuitive arguments based on black hole physics. Although mathematically, T…

Cluster Expansion and Decay of Correlations for Multidimensional Long-Range Ising Models
Lucas Affonso, Rodrigo Bissacot, Jo\~ao Maia, Jo\~ao F. Rodrigues, Kelvyn Welsch
https://arxiv.org/abs/2508.15666

Cluster Expansion and Decay of Correlations for Multidimensional Long-Range Ising Models
We develop the cluster expansion for the multidimensional multiscaled contours defined by three of us. These contours are suitable for long-range Ising models with interaction $J_{xy}=J(|x-y|)= J/|x-y|^α$, $J>0$, and $α>d$. As an application of the convergence of the cluster expansion at low temperatures, we study the decay of the truncated two-point correlation functions, showing that the decay is algebraic with coefficient $α$.

NPUEval: Optimizing NPU Kernels with LLMs and Open Source Compilers
Sarunas Kalade, Graham Schelle
https://arxiv.org/abs/2507.14403 https://

NPUEval: Optimizing NPU Kernels with LLMs and Open Source Compilers
Neural processing units (NPUs) are gaining prominence in power-sensitive devices like client devices, with AI PCs being defined by their inclusion of these specialized processors. Running AI workloads efficiently on these devices requires libraries of optimized kernels. Creating efficient kernels demands expertise in domain-specific C++ with vector intrinsics and in-depth knowledge of the target architecture. Unlike GPU programming, which has had years to mature, NPU programming is new, with sm…

Eccentric Connectivity Index of Strongly Connected Digraphs
Vysakh Chakooth, Prasanth G. Narasimha-Shenoi, Prakash G. Narasimha-Shenoi
https://arxiv.org/abs/2509.17019 https://

Eccentric Connectivity Index of Strongly Connected Digraphs
Let $G = (V, E)$ be a graph with non-empty set of vertices $V$ and set of edges $E$. The \emph{eccentric connectivity index} of the graph $G$ is defined as $$\displaystyle{ξ^C(G) = \sum_{u \in V} d_u \;ecc(u)}$$ where $d_u$ is the degree and $ecc(u)$ is the eccentricity of the vertex $u \in V$. This article is an attempt to find the \emph{eccentric connectivity index} of strongly connected digraph $D$ with respect to the metric, \textit{maximum distance} defined by $md(u,v)=\max\{\vec{d}(u,v),…

Chern classes of the multilayer fractional quantum Hall bundle on Riemann surfaces
Mar\'ia Abad Aldonza (UVSQ), Florent Dupont (IRMA)
https://arxiv.org/abs/2509.17515 https:…

Chern classes of the multilayer fractional quantum Hall bundle on Riemann surfaces
The so-called multilayer wave functions were introduced in the study of the fractional Quantum Hall effect by Halperin and others. They are defined with the help of a symmetric matrix $K$ in $M^k(\mathbb{N})$, which encodes the couplings between the $k$ layers where particles live. We study the multilayer quantum states in the case where each layer is a Riemann surface of genus $g$. These states form a vector bundle over the Jacobian variety of the Riemann surface, or the space of Aharonov-Bohm…

Multipartite Markov Gaps and Entanglement Wedge Multiway Cuts
Norihiro Iizuka, Akihiro Miyata, Mitsuhiro Nishida
https://arxiv.org/abs/2507.15262 https://

Multipartite Markov Gaps and Entanglement Wedge Multiway Cuts
The Markov gap, defined as the difference between reflected entropy and mutual information, serves as a diagnostic for quantum recoverability and multipartite entanglement. In holographic settings, it admits a geometric interpretation as the deviation between entanglement wedge cross-sections and RT surfaces. Motivated by this holographic perspective, we propose a generalization of the Markov gap to multipartite systems by using a reflected multi-entropy. The resulting Multipartite Markov gap c…

Exact alternative optima for nonlinear optimization problems defined with maximum component objective function constrained by the Sugeno-Weber fuzzy relational inequalities
Amin Ghodousian, Sara Zal, Minoo Ahmadi
https://arxiv.org/abs/2509.12669

Exact alternative optima for nonlinear optimization problems defined with maximum component objective function constrained by the Sugeno-Weber fuzzy relational inequalities
In this paper, we study a latticized optimization problem with fuzzy relational inequality constraints where the feasible region is formed as the intersection of two inequality fuzzy systems and Sugeno-Weber family of t-norms is considered as fuzzy composition. Sugeno-Weber family of t-norms and t-conorms is one of the most applied one in various fuzzy modelling problems. This family of t-norms and t-conorms was suggested by Weber for modeling intersection and union of fuzzy sets. Also, the t-c…

Characterizing NC1 with Typed Monoids
Anuj Dawar, Aidan T. Evans
https://arxiv.org/abs/2508.11019 https://arxiv.org/pdf/2508.11019

Characterizing NC1 with Typed Monoids
Krebs et al. (2007) gave a characterization of the complexity class TC0 as the class of languages recognized by a certain class of typed monoids. The notion of typed monoid was introduced to extend methods of algebraic automata theory to infinite monoids and hence characterize classes beyond the regular languages. We advance this line of work beyond TC0 by giving a characterization of NC1. This is obtained by first showing that NC1 can be defined as the languages expressible in an extension of …

A Weight Structure on Rigid Analytic Motives over a Field
Kaixing Cao
https://arxiv.org/abs/2509.16683 https://arxiv.org/pdf/2509.16683

A Weight Structure on Rigid Analytic Motives over a Field
In this paper, we construct a monoidal weight structure on the stable $\infty$-category of rigid analytic motives over a local field $K$ via Galois descent. This extends the weight structure on the full subcategory of rigid analytic motives with good reduction, which is defined by Binda-Gallauer-Vezzani. As an application, we show that the Hyodo-Kato realization factors through the weight complex functor studied by Bondarko and Sosnilo. In particular, the weight complex yields a spectral sequen…

Exact Relation Between Wehrl-R\'enyi Entropy and Many-Body Entanglement
Pengfei Zhang, Chen Xu, Peng Zhang
https://arxiv.org/abs/2509.16036 https://arx…

Exact Relation Between Wehrl-Rényi Entropy and Many-Body Entanglement
Quantum entanglement is key to understanding correlations and emergent phenomena in quantum many-body systems. For $N$ qubits (distinguishable spin-$1/2$ particles) in a pure quantum state, many-body entanglement can be characterized by the purity of the reduced density matrix of a subsystem, defined as the trace of the square of this reduced density matrix. Nevertheless, this approach depends on the choice of subsystem. In this letter, we establish an exact relation between the Wehrl-Rényi en…

On asymptotic formula of the partition function $p_A(n)$
David Christopher, Davamani Christober
https://arxiv.org/abs/2509.17193 https://arxiv.org/pdf/2509…

On asymptotic formula of the partition function $p_A(n)$
The partition function, $p_A(n)$, is defined to be the number of partitions of $n$ with parts in the set A, where $n$ is a positive integer and $A$ is a set of positive integers. It is well documented that: if A is a finite set with $\gcd(A)=1$ and $|A|=k$, then \[p_A(n)\sim \frac{n^{k-1}}{(\prod_{a\in A}a)(k-1)!}. \] Number of proofs have been obtained for this estimate. In this article, we give a new proof for the above estimate by making use of the fact that: $p_A(n)$ is a $quasi\ …

Poor man's transcendence for Frobenius traces of elliptic curves
Florian Luca, Wadim Zudilin
https://arxiv.org/abs/2507.14773 https://

Poor man's transcendence for Frobenius traces of elliptic curves
Let $E$ be an elliptic curve without complex multiplication defined over $\mathbb Q$. Viewing the sequence of its Frobenius traces $(a_p(E))_p$ indexed by primes $p$ as an element in the "poor man's adèle ring", we prove its transcendence over $\mathbb Q$.

Rigorous dense graph limit of a model for biological transportation networks
Nuno J. Alves, Jan Haskovec
https://arxiv.org/abs/2507.15829 https://

Rigorous dense graph limit of a model for biological transportation networks
We rigorously derive the dense graph limit of a discrete model describing the formation of biological transportation networks. The discrete model, defined on undirected graphs with pressure-driven flows, incorporates a convex energy functional combining pumping and metabolic costs. It is constrained by a Kirchhoff law reflecting the local mass conservation. We first rescale and reformulate the discrete energy functional as an integral `semi-discrete' functional, where the Kirchhoff law transfor…

A result on spanning trees with bounded total excess
Sizhong Zhou
https://arxiv.org/abs/2507.15139 https://arxiv.org/pdf/2507.15139…

A result on spanning trees with bounded total excess
Let $G$ be a connected graph and $T$ a spanning tree of $G$. Let $ρ(G)$ denote the adjacency spectral radius of $G$. The $k$-excess of a vertex $v$ in $T$ is defined as $\max\{0,d_T(v)-k\}$. The total $k$-excess $\mbox{te}(T,k)$ is defined by $\mbox{te}(T,k)=\sum\limits_{v\in V(T)}{\max\{0,d_T(v)-k\}}$. A tree $T$ is said to be a $k$-tree if $d_T(v)\leq k$ for any $v\in V(T)$, that is to say, the maximum degree of a $k$-tree is at most $k$. In fact, $T$ is a spanning $k$-tree if and only if $\…

All-mechanical coherence protection and fast control of a spin qubit
Eliza Cornell, Zhujing Xu, Zhaoyou Wang, Hana K. Warner, Eliana Mann, Michael Haas, Smarak Maity, Graham Joe, Liang Jiang, Peter Rabl, Benjamin Pingault, Marko Lon\v{c}ar
https://arxiv.org/abs/2508.13356

All-mechanical coherence protection and fast control of a spin qubit
In a phononic quantum network, quantum information is stored and processed within stationary nodes defined by solid-state spins, and the information is routed between nodes by phonons. The phonon holds distinct advantages over its electromagnetic counterpart the photon, including smaller device footprints, reduced crosstalk, long coherence times at low temperatures, and strong interactions with both solid-state spins and electromagnetic waves. Enhanced interactions between a phononic cavity and…

Emergent classical gravity as stress-tensor deformed field theories
Yun-Ze Li, Yunfei Xie, Song He
https://arxiv.org/abs/2508.15461 https://arxiv.org/pdf/2…

Emergent classical gravity as stress-tensor deformed field theories
We introduce a framework in which classical gravity arises from stress-tensor deformations of quantum field theories (QFTs). By expressing the deformed partition function as a gravitational path integral, we propose an equivalent description between a seed QFT coupled to gravity and an effective field theory defined on a deformation-induced metric. This approach, which does not rely on holography or extra dimensions, applies to a variety of gravitational models, including Einstein and Palatini …

Brauer groups of conic bundles over elliptic curves
Abdulmuhsin Alfaraj
https://arxiv.org/abs/2509.16051 https://arxiv.org/pdf/2509.16051

Brauer groups of conic bundles over elliptic curves
We study the Brauer groups of regular conic bundles over elliptic curves defined over a number field $k$. We explicitly compute the Brauer group of the conic bundle when the singular fibres lie above $k$-points that are divisible by $2$ in $E(k)$, and the corresponding ramification fields are isomorphic. We apply the result to compute the Brauer group of a class of surfaces analogous to that of Châtelet surfaces. We investigate Brauer-Manin obstructions to weak approximation coming from the re…

On the edge reconstruction of the second immanantal polynomials of undirected graph and digraph
Tingzeng Wu
https://arxiv.org/abs/2507.14607 https://

On the edge reconstruction of the second immanantal polynomials of undirected graph and digraph
Let $M=(m_{ij})$ be an $n\times n$ matrix. The second immanant of matrix $M$ is defined by \begin{eqnarray*} d_{2}(M)=\sum_{σ\in S_{n}}χ_{2}(σ)\prod_{s=1}^{n}m_{sσ(s)}, \end{eqnarray*} where $χ_{2}$ is the irreducible character of $S_{n}$ corresponding to the partition $(2^{1},1^{n-2})$. The polynomial $d_{2}(xI-M)$ is called the second immanantal polynomial of matrix $M$. Denote by $D(G)$ (resp. $D(\overrightarrow{G})$) and $A(G)$ (resp. $A(\overrightarrow{G})$) the diagonal matrix of ver…

A story of webs: the webs by conics on del Pezzo quartic surfaces and Gelfand-MacPherson's web of the spinor tenfold
Luc Pirio
https://arxiv.org/abs/2507.12180

A story of webs: the webs by conics on del Pezzo quartic surfaces and Gelfand-MacPherson's web of the spinor tenfold
In a previous paper, we studied the web by conics $\boldsymbol{\mathcal W}_{{\rm dP}_4}$ on a del Pezzo quartic surface ${\rm dP}_4$ and proved that it enjoys suitable versions of most of the remarkable properties satisfied by Bol's web $\boldsymbol{\mathcal B}$. In particular, Bol's web can be seen as the toric quotient of the Gelfand-MacPherson web naturally defined on the $A_4$-grassmannian variety $G_2(\mathbf C^5)$ and we have shown that $\boldsymbol{\mathcal W}_{{\rm dP}_4}$ can be obtain…

Stoimenow matchings avoiding multiple Catalan patterns simultaneously
Shuzhen Lv, Sergey Kitaev
https://arxiv.org/abs/2509.12726 https://arxiv.org/pdf/2509…

Stoimenow matchings avoiding multiple Catalan patterns simultaneously
Motivated by Vassiliev's knot invariants, Stoimenow introduced a special class of matchings, now known as Stoimenow matchings. These matchings have since been linked to various combinatorial structures enumerated by the Fishburn numbers. In a recent paper, a problem posed by Bevan et al. was addressed concerning the identification of subsets of Stoimenow matchings counted by the Catalan numbers. Five such subsets were presented, each defined by the avoidance of a single pattern, referred to as …

Dimensions of toggleability spaces
Ben Adenbaum, Spencer Daugherty, Nicholas Mayers
https://arxiv.org/abs/2508.14974 https://arxiv.org/pdf/2508.14974

Dimensions of toggleability spaces
We establish a conjecture of Defant, Hopkins, Poznanović, and Propp concerning the dimensions of toggleability spaces for products of chains, shifted staircases, type-A root posets, and type-B posets. Generalizing this result, we show that for a larger family of posets defined by restricted diagrams, the dimensions of toggleability spaces are equal to the rank of the poset plus one. As part of our approach, we build upon the technique of rook statistics introduced by Chan, Haddadan, Hopkins, a…