Tootfinder

Quantum and Simulated Annealing-Based Iterative Algorithms for QUBO Relaxations of the Sparsest $k$-Subgraph Problem
Omkar Bihani, Roman Ku\v{z}el, Janez Povh, Dunja Pucher
https://arxiv.org/abs/2509.08544

Quantum and Simulated Annealing-Based Iterative Algorithms for QUBO Relaxations of the Sparsest $k$-Subgraph Problem
In this paper, we introduce three QUBO (Quadratic Unconstrained Binary Optimization) relaxations for the sparsest $k$-subgraph (SkS) problem: a quadratic penalty relaxation, a Lagrangian relaxation, and an augmented Lagrangian relaxation. The effectiveness of these approaches strongly depends on the choice of penalty parameters. We establish theoretical results characterizing the parameter values for which the QUBO relaxations are exact. For practical implementation, we propose three iterative …

Deep opacity and AI: A threat to XAI and to privacy protection mechanisms
Vincent C. M\"uller
https://arxiv.org/abs/2509.08835 https://arxiv.org/pdf/2…

Deep opacity and AI: A threat to XAI and to privacy protection mechanisms
It is known that big data analytics and AI pose a threat to privacy, and that some of this is due to some kind of "black box problem" in AI. I explain how this becomes a problem in the context of justification for judgments and actions. Furthermore, I suggest distinguishing three kinds of opacity: 1) the subjects do not know what the system does ("shallow opacity"), 2) the analysts do not know what the system does ("standard black box opacity"), or 3) the analysts cannot possibly know what the …

Optimal Control of a Hemivariational Inequality of Stationary Convective Brinkman-Forchheimer Extended Darcy equations with Numerical Approximation
Wasim Akram, Manil T. Mohan
https://arxiv.org/abs/2509.09287

Optimal Control of a Hemivariational Inequality of Stationary Convective Brinkman-Forchheimer Extended Darcy equations with Numerical Approximation
This paper studies an optimal control problem for a stationary convective Brinkman-Forchheimer extended Darcy (CBFeD) hemivariational inequality in two and three dimensions, subject to control constraints, and develops its numerical approximation. The hemivariational inequality provides the weak formulation of a stationary incompressible fluid flow through a porous medium, governed by the CBFeD equations, which account for convection, damping, and nonlinear resistance effects. The problem incor…

Performance enhancement in Josephson traveling wave parametric amplifiers by tailoring the relative distance between junctions
M. A. Gali Labarias, T. Yamada, Y. Nakashima, Y. Urade, J. Claramunt, K. Inomata
https://arxiv.org/abs/2509.07292

Performance enhancement in Josephson traveling wave parametric amplifiers by tailoring the relative distance between junctions
Josephson traveling wave parametric amplifiers with heterogeneously spaced junctions are theoretically investigated. We consider unit cells with three junctions and characterize their interaction by spatially displaced fields defined by node fluxes. To solve this problem we define the system action and apply the variational principle to obtain the static action, which determines the equations of motion. This work shows that gain and bandwidth can be increased by modifying the relative distance …

A recursive approach for the determination of the nice sections of width three having a 4-crown stack as retract
Frank a Campo
https://arxiv.org/abs/2510.05640 https://

A recursive approach for the determination of the nice sections of width three having a 4-crown stack as retract
The characterization of the finite minimal automorphic posets of width three is still an open problem. Niederle has shown that this task can be reduced to the characterization of the nice sections of width three having a non-trivial tower of nice sections as retract. In our article, we characterize those of them which have a 4-crown stack as retract and we develop a recursive approach for their determination. We apply the approach on a sub-class $\mathfrak{N}_2$ of nice sections of width three …

Series C, Episode 04 - Dawn of the Gods
DAYNA: Orac with delusions of grandeur, Zen unable to control the ship. I'd say we've a lot of little problems on our hands.
AVON: Course deflection is zero zero five. Speed Standard by five and increasing. I'd say we have one large problem on our hands.
https://blake.torpidit…

Solvability of Infinite Systems of Nonlinear Caputo Fractional Differential equations in generalized Hahn Sequence Space
Khurshida Parvin, Bipan Hazarika, Awad A. Bakery
https://arxiv.org/abs/2509.06959

Solvability of Infinite Systems of Nonlinear Caputo Fractional Differential equations in generalized Hahn Sequence Space
This paper presents the Hausdorff measure of noncompactness (MNC) within the framework of the generalized Hahn sequence space. By applying the MNC, we explore the existence of solutions for nonlinear Caputo fractional differential equations subject to three-point integral boundary conditions in the generalized Hahn sequence space. We apply certain sufficient conditions to ensure the uniqueness of solutions to the aforementioned problem, utilizing the Banach fixed-point theorem, and discuss the …

Optimal Multi-Mode Propulsion Mission Design Using Direct Collocation
George V. Haman III, Anil V. Rao
https://arxiv.org/abs/2509.07336 https://arxiv.org/p…

Optimal Multi-Mode Propulsion Mission Design Using Direct Collocation
The problem of minimizing the transfer time between periodic orbits in the Earth-Moon elliptic restricted three-body problem using a multi-mode propulsion system is considered. By employing the true anomaly on the primary orbit as the independent variable and introducing normalized time as an additional state, the need to repeatedly solve Kepler's equation at arbitrary epochs is eliminated. Furthermore, a propellant constraint is imposed on the high-thrust mode to activate the multi-mode capabi…

Comparing Normal Form Representations for Station-Keeping near Cislunar Libration Points
Carson Hunsberger, David Schwab, Roshan Eapen, Puneet Singla
https://arxiv.org/abs/2510.06368

Comparing Normal Form Representations for Station-Keeping near Cislunar Libration Points
The normal forms provide useful approximations for many trajectories of interest within the circular restricted three-body problem. This paper aims to thoroughly compare two of these forms: the Birkhoff normal form and the resonant normal form, highlighting the strengths of each for the representation of center manifold trajectories. A method of station-keeping is introduced, analogous to Floquet modes, in which the unstable component is minimized at specific points along a trajectory through i…

The Three-Body Limit Cycle: Universal Form for General Regulators
Langxuan Chen, Feng Wu, Xincheng Lin, Sebastian K\"onig, Ubirajara van Kolck, Pengfei Zhang
https://arxiv.org/abs/2509.04746

The Three-Body Limit Cycle: Universal Form for General Regulators
The Efimov effect, a remarkable realization of discrete scale invariance, emerges in the three-body problem with short-range interactions and is understood as a renormalization group (RG) limit cycle within Short-Range Effective Field Theory (SREFT). While the analytic form of the three-body renormalization relation has been established for a sharp cutoff regulator, its universality for other regulators remains underexplored. In this letter, we derive the universal functional form of the three-…

Cowboys Could Run Into George Pickens Problem After Quiet Week 1, Per Writer https://heavy.com/sports/nfl/dallas-cowboys/george-pickens-week1-issue/?adt_ei=[email]

From KP-I Lump Solution to Travelling wave of 3D Gravity Capillary Water wave problem
Changfeng Gui, Shanfa Lai, Yong Liu, Juncheng Wei, Wen Yang
https://arxiv.org/abs/2509.06084

From KP-I Lump Solution to Travelling wave of 3D Gravity Capillary Water wave problem
In this paper, we study the three-dimensional gravity-capillary water wave problem involving an irrotational, perfect fluid with gravity and surface tension. We focus on steady waves propagating uniformly in one direction. Assuming constant wave speed and water depth, we analyze the fluid's velocity potential and boundary conditions. Using the Kadomtsev-Petviashvili (KP)-I equation as a simplified model, we show that, within a specific parameter range, the problem admits a fully localized solit…

Spectral Graph Clustering under Differential Privacy: Balancing Privacy, Accuracy, and Efficiency
Mohamed Seif, Antti Koskela, H. Vincent Poor, Andrea J. Goldsmith
https://arxiv.org/abs/2510.07136

Spectral Graph Clustering under Differential Privacy: Balancing Privacy, Accuracy, and Efficiency
We study the problem of spectral graph clustering under edge differential privacy (DP). Specifically, we develop three mechanisms: (i) graph perturbation via randomized edge flipping combined with adjacency matrix shuffling, which enforces edge privacy while preserving key spectral properties of the graph. Importantly, shuffling considerably amplifies the guarantees: whereas flipping edges with a fixed probability alone provides only a constant epsilon edge DP guarantee as the number of nodes g…

A Practical Guide to Rigorously Locate Periodic Orbits in Discrete Dynamics
Luc\'ia Alonso Mozo, Olivier H\'enot, Phillipo Lappicy
https://arxiv.org/abs/2510.06373 https…

A Practical Guide to Rigorously Locate Periodic Orbits in Discrete Dynamics
Periodic orbits are important objects of discrete dynamical systems, but finding them is not always easy. We present a self-contained introductory account, aimed at non-experts, to prove their existence and study their stability using the aid of the computer. The method consists in three main steps. First, we reformulate the problem of identifying a $p$-periodic orbit as a root-finding problem. Second, we find a numerical approximation of the root (i.e. a periodic orbit candidate). Third, we ve…

ReasonEmbed: Enhanced Text Embeddings for Reasoning-Intensive Document Retrieval
Jianlyu Chen, Junwei Lan, Chaofan Li, Defu Lian, Zheng Liu
https://arxiv.org/abs/2510.08252 http…

ReasonEmbed: Enhanced Text Embeddings for Reasoning-Intensive Document Retrieval
In this paper, we introduce ReasonEmbed, a novel text embedding model developed for reasoning-intensive document retrieval. Our work includes three key technical contributions. First, we propose ReMixer, a new data synthesis method that overcomes the triviality problem prevalent in previous synthetic datasets, enabling large-scale production of 82K high-quality training samples. Second, we design Redapter, a self-adaptive learning algorithm that dynamically adjusts training each sample's weight…

Three-point connectivity constant for $q$-state Potts spin clusters
Gefei Cai, Haoyu Liu, Baojun Wu, Zijie Zhuang
https://arxiv.org/abs/2510.05850 https://…

Three-point connectivity constant for $q$-state Potts spin clusters
Recently, Ang--Cai--Sun--Wu (2024) determined the three-point connectivity constant for two-dimensional critical percolation, confirming a prediction of Delfino and Viti (2010). In this paper, we address the analogous problem for planar critical $q$-state Potts spin clusters. We introduce a continuum three-point connectivity constant and compute it explicitly. Under the scaling-limit conjecture for Potts spin clusters, this quantity coincides with the scaling limit of the properly normalized pr…

On Equivalent Characterizations of NP in Abstract Models of Computation
Jeremy C. Kirn, Lucas Meijer, Tillmann Miltzow, Hans L. Bodlaender
https://arxiv.org/abs/2510.05894 https…

On Equivalent Characterizations of NP in Abstract Models of Computation
We investigate machine models similar to Turing machines that are augmented by the operations of a first-order structure $\mathcal{R}$, and we show that under weak conditions on $\mathcal{R}$, the complexity class $\text{NP}(\mathcal{R})$ may be characterized in three equivalent ways: (1) by polynomial-time verification algorithms implemented on $\mathcal{R}$-machines, (2) by the $\text{NP}(\mathcal{R})$-complete problem $\text{SAT}(\mathcal{R})$, and (3) by existential second-order metafinite …

On the inverse problem of the earthquake source and the three-phase relaxation mode of the source after the formation of a main rupture in it
A. V. Guglielmi
https://arxiv.org/abs/2510.01679

On the inverse problem of the earthquake source and the three-phase relaxation mode of the source after the formation of a main rupture in it
The fundamentals of the phenomenological theory of aftershocks are presented. The theory contains an original concept of the proper time of the earthquake source, the course of which, generally speaking, differs from the course of world time. Within the framework of the theory, a new method for processing and analyzing earthquakes has been developed. Analysis of the Tohoku earthquake demonstrated the effectiveness of the method. Three phases of relaxation of the source were discovered. In the i…

Inverse problem for the Navier-Stokes equations and identification of immersed obstacles in the Mediterranean Sea
Mourad Hrizi, Marwa Ouni, Maatoug Hassine
https://arxiv.org/abs/2509.05287

Inverse problem for the Navier-Stokes equations and identification of immersed obstacles in the Mediterranean Sea
This paper presents a theoretical and numerical investigation of object detection in a fluid governed by the three-dimensional evolutionary Navier--Stokes equations. To solve this inverse problem, we assume that interior velocity measurements are available only within a localized subregion of the fluid domain. First, we present an identifiability result. We then formulate the problem as a shape optimization task: to identify the obstacle, we minimize a nonlinear least-squares criterion with a r…

Energy Transition Domain and Its Application in Constructing Gravity-Assist Escape Trajectories
Shuyue Fu, Xiaowen Liu, Di Wu, Peng Shi, Shengping Gong
https://arxiv.org/abs/2509.00518

Energy Transition Domain and Its Application in Constructing Gravity-Assist Escape Trajectories
This Note proposes the concept and theory of energy transition domain (ETD) defined by the mechanical energy of spacecraft in the Earth-Moon planar circular restricted three-body problem (PCR3BP) inspired by the pioneering work from Ano{è} et al. (2024) on the ETD defined by the two-body energy with respect to the secordary body in the PCR3BP. An effective construction method of gravity-assist escape trajectories is then proposed. Firstly, the concept of the ETD defined by the mechanical energ…

September was a great month. I finally have a desk, and changed something in my daily routine. I read another two books of the Dungeon Crawler Carl series, watched High and Low and The Phantom of the Opera, and tell you about "I Love My Computer" by Ninajirachi.
https://www.davideaversa.it/blog/change…

The Changelog – September 2025
September was a great month. I finally have a desk, and I finally changed something in my daily routine. I read another two books of the Dungeon Crawler Carl series and finished the Three-Body Problem trilogy. I watched High and Low and The Phantom of the Opera, and I will share my connection I Love My Computer by Ninajirachi. Finally, my two cents about Silksong.

from my link log —
Tiling with three polygons is undecidable.
https://arxiv.org/abs/2409.11582
saved 2024-11-21 https://dotat.at/…

Tiling with Three Polygons is Undecidable
We prove that the following problem is co-RE-complete and thus undecidable: given three simple polygons, is there a tiling of the plane where every tile is an isometry of one of the three polygons (either allowing or forbidding reflections)? This result improves on the best previous construction which requires five polygons.

Topological Regularization for Force Prediction in Active Particle Suspension with EGNN and Persistent Homology
Sadra Saremi, Amirhossein Ahmadkhan Kordbacheh
https://arxiv.org/abs/2509.06574

Topological Regularization for Force Prediction in Active Particle Suspension with EGNN and Persistent Homology
Capturing the dynamics of active particles, i.e., small self-propelled agents that both deform and are deformed by a fluid in which they move is a formidable problem as it requires coupling fine scale hydrodynamics with large scale collective effects. So we present a multi-scale framework that combines the three learning-driven tools to learn in concert within one pipeline. We use high-resolution Lattice Boltzmann snapshots of fluid velocity and particle stresses in a periodic box as input to t…

Exploration-Exploitation-Evaluation (EEE): A Framework for Metaheuristic Algorithms in Combinatorial Optimization
Ethan Davis
https://arxiv.org/abs/2510.05027 https://

Exploration-Exploitation-Evaluation (EEE): A Framework for Metaheuristic Algorithms in Combinatorial Optimization
We introduce a framework for applying metaheuristic algorithms, such as ant colony optimization (ACO), to combinatorial optimization problems (COPs) like the traveling salesman problem (TSP). The framework consists of three sequential stages: broad exploration of the parameter space, exploitation of top-performing parameters, and uncertainty quantification (UQ) to assess the reliability of results. As a case study, we apply ACO to the TSPLIB berlin52 dataset, which has a known optimal tour leng…

Global well-posedness and large time behavior of 3D incompressible inhomogeneous magnetohydrodynamic equations in the exterior of a cylinder
Jitao Liu, Min Liu
https://arxiv.org/abs/2509.06293

Global well-posedness and large time behavior of 3D incompressible inhomogeneous magnetohydrodynamic equations in the exterior of a cylinder
When the vaccum is allowed, if the global existence and uniqueness of strong solutions to three dimensional incompressible inhomogeneous magnetohydrodynamic equations holds true or not has always been a challenging open problem, even for the magnetofluids with special structures. In this paper, through deeply exploring the internal structure and characteristic of axisymmetric flows, we obtain some new discoveries and give a partial answer to above issue. More precisely, we prove that the axisym…

"Electric bicycles are under increasing scrutiny, often for the wrong reasons. In this three-part series, PeopleForBikes separates fact from fiction to protect the future of e-bikes in America, clarify what qualifies as a legal electric bicycle, and call out bad actors mislabeling high-powered motor vehicles as e-bikes."

The E-Bike Problem is an E-Moto Problem | PeopleForBikes

An approach using geometric diagrams to generic Bell inequalities with multiple observables
Junghee Ryu, Jinhyoung Lee, Hoon Ryu
https://arxiv.org/abs/2510.05622 https://…

An approach using geometric diagrams to generic Bell inequalities with multiple observables
We extend the generic Bell inequalities suggested by Son, Lee, and Kim [Phys. Rev. Lett. 96, 060406 (2006)] to incorporate multiple observables for tripartite systems and introduce a geometric methodology for calculating classical upper bounds of the inequalities. Our method transforms the problem of finding the classical upper bounds into identifying constraints in linear congruence relations. Using this approach, we derive the upper bounds for scenarios with three and four observables per par…

Observing Without Doing: Pseudo-Apprenticeship Patterns in Student LLM Use
Jade Hak, Nathaniel Lam Johnson, Matin Amoozadeh, Amin Alipour, Souti Chattopadhyay
https://arxiv.org/abs/2510.04986

Observing Without Doing: Pseudo-Apprenticeship Patterns in Student LLM Use
Large Language Models (LLMs) such as ChatGPT have quickly become part of student programmers' toolkits, whether allowed by instructors or not. This paper examines how introductory programming (CS1) students integrate LLMs into their problem-solving processes. We conducted a mixed-methods study with 14 undergraduates completing three programming tasks while thinking aloud and permitted to access any resources they choose. The tasks varied in open-endedness and familiarity to the participants and…

Maximum Biclique for Star 1,2,3 -free and Bounded Bimodularwidth Twin-free Bipartite Graphs $\star$
Fabien de Montgolfier (IRIF), Renaud Torfs (IRIF)
https://arxiv.org/abs/2510.04621

Maximum Biclique for Star 1,2,3 -free and Bounded Bimodularwidth Twin-free Bipartite Graphs $\star$
There are three usual definitions of a maximum bipartite clique (biclique) in a bipartite graph\,: either maximizing the number of vertices, or of edges, or finding a maximum balanced biclique. The first problem can be solved in polynomial time, the last ones are NP-complete. Here we show how these three problems may be efficiently solved for two classes of bipartite graphs: Star123-free twin-free graphs, and bounded bimodularwidth twin-free graphs, a class that may be defined using bimodular d…

Description of Non-Spherical Black Holes in 5D Einstein Gravity via the Riemann-Hilbert Problem
Jun-ichi Sakamoto, Shinya Tomizawa
https://arxiv.org/abs/2510.02093 https://

Description of Non-Spherical Black Holes in 5D Einstein Gravity via the Riemann-Hilbert Problem
We investigate the solution-generating technique based on the Breitenlohner-Maison (BM) linear system, for asymptotically flat, stationary, bi-axisymmetric black hole solutions with various horizon topologies in five-dimensional vacuum Einstein theory. We construct the monodromy matrix associated with the BM linear system, which provides a unified framework for describing three distinct asymptotically flat, vacuum black hole solutions with a single angular momentum in five dimensions, each with…

Encoding Numeric Computations and Infusing Heuristic Knowledge Using Integrity Constraints in stableKanren
Xiangyu Guo, Ajay Bansal
https://arxiv.org/abs/2510.04049 https://

Encoding Numeric Computations and Infusing Heuristic Knowledge Using Integrity Constraints in stableKanren
This paper presents examples of using integrity constraints in stableKanren to encode numeric computations for problem solving. Then, we use one of the examples to introduce multiple ways to infuse heuristic knowledge and reduce solving time. stableKanren is an extension of miniKanren that supports normal logic programs under stable model semantics. stableKanren further supports numeric computation by constructing a constraint store for integrity constraints. There are three ways to extend a re…

The Popular Dimension of Matchings
Frank Connor, Louis-Roy Langevin, Ndiam\'e Ndiaye, Agn\`es Totschnig, Rohit Vasishta, Adrian Vetta
https://arxiv.org/abs/2509.25150 https:…

The Popular Dimension of Matchings
We study popular matchings in three classical settings: the house allocation problem, the marriage problem, and the roommates problem. In the popular matching problem, (a subset of) the vertices in a graph have preference orderings over their potential matches. A matching is popular if it gets a plurality of votes in a pairwise election against any other matching. Unfortunately, popular matchings typically do not exist. So we study a natural relaxation, namely popular winning sets which are a s…

Cubic incompleteness: Hilbert's tenth problem begins at degree three
Milan Rosko
https://arxiv.org/abs/2510.00759 https://arxiv.org/pdf/2510.00759

Cubic incompleteness: Hilbert's tenth problem begins at degree three
We present a preliminary result addressing a long-standing open question: Are cubic Diophantine equations undecidable?} We answer in the affirmative. By encoding Gödel's first incompleteness theorem via a Fibonacc-based Göodel numbering and the Zeckendorf representation, we reduce the arithmetic complexity sufficiently to construct an explicit \emph{cubic Diophantine equation} whose solvability is independent of a model provided by \emph{Peano axioms}. We present three results. First, a commo…

On the uniqueness of the discrete Calderon problem on multi-dimensional lattices
Maolin Deng, Bangti Jin
https://arxiv.org/abs/2509.18203 https://arxiv.org…

The Subset Sum Matching Problem
Yufei Wu, Manuel R. Torres, Parisa Zehtabi, Alberto Pozanco Lancho, Michael Cashmore, Daniel Borrajo, Manuela Veloso
https://arxiv.org/abs/2508.19218

The Subset Sum Matching Problem
This paper presents a new combinatorial optimisation task, the Subset Sum Matching Problem (SSMP), which is an abstraction of common financial applications such as trades reconciliation. We present three algorithms, two suboptimal and one optimal, to solve this problem. We also generate a benchmark to cover different instances of SSMP varying in complexity, and carry out an experimental evaluation to assess the performance of the approaches.

Classical Heisenberg and XY models on zigzag ladder lattices with nearest-neighbor bilinear-biquadratic exchange: Exact solution for the ground-state problem
Yuriy Dublenych
https://arxiv.org/abs/2509.26318

Classical Heisenberg and XY models on zigzag ladder lattices with nearest-neighbor bilinear-biquadratic exchange: Exact solution for the ground-state problem
An exact and complete solution of the ground-state problem for the classical Heisenberg and XY models with nearest-neighbor bilinear-biquadratic exchange on two- and three-dimensional lattices composed of isosceles triangles is determined with the use of a cluster method. It is shown how the geometric frustration due to the presence of triangles as structural units leads to the emergence of a rich phase diagram with incommensurate spiral orderings and their collinear limits, as well as canted a…

Alleviating Cosmological Tensions with the Hadrosymmetric Twin Higgs
Mohammad Soroori Sotudeh, Zahra Davari, Sara Khatibi, Nima Khosravi
https://arxiv.org/abs/2510.00852 https:/…

Alleviating Cosmological Tensions with the Hadrosymmetric Twin Higgs
The Hadrosymmetric Twin Higgs (HTH) model provides a natural solution to the little hierarchy problem by incorporating all three generations of quarks in a twin sector. Unlike other Twin Higgs scenarios, such as the Mirror Twin Higgs (MTH), the HTH framework avoids introducing additional light states or radiation and thus remains consistent with stringent bounds on the effective number of relativistic species, $ΔN_{\rm eff}$. Its particle content and interactions also make it difficult to prob…

Let's do a deep dive into this paper: "Why Language Models Hallucinate."
When this came out, many people's summary was "even OpenAI admits that hallucinations are a fundamental problem of transformers/autoregressive models/LLMs."
I've seen many people conclude that this means OpenAI is grifting, knows they're building on a wrong paradigm, knows they won't get to AGI etc.

Incorporating Pre-trained Diffusion Models in Solving the Schr\"odinger Bridge Problem
Zhicong Tang, Tiankai Hang, Shuyang Gu, Dong Chen, Baining Guo
https://arxiv.org/abs/2508.18095

Incorporating Pre-trained Diffusion Models in Solving the Schrödinger Bridge Problem
This paper aims to unify Score-based Generative Models (SGMs), also known as Diffusion models, and the Schrödinger Bridge (SB) problem through three reparameterization techniques: Iterative Proportional Mean-Matching (IPMM), Iterative Proportional Terminus-Matching (IPTM), and Iterative Proportional Flow-Matching (IPFM). These techniques significantly accelerate and stabilize the training of SB-based models. Furthermore, the paper introduces novel initialization strategies that use pre-trained…

The hereditariness problem for the \v{C}ern\'y conjecture
Emanuele Rodaro, Riccardo Venturi
https://arxiv.org/abs/2509.17992 https://arxiv.org/pdf/2509…

The hereditariness problem for the Černý conjecture
This paper addresses the lifting problem for the Černý conjecture: namely, whether the validity of the conjecture for a quotient automaton can always be transferred (or "lifted") to the original automaton. Although a complete solution remains open, we show that it is sufficient to verify the Černý conjecture for three specific subclasses of reset automata: radical, simple, and quasi-simple. Our approach relies on establishing a Galois connection between the lattices of congruences and ideal…

Local divers pick away at Lake Malawi’s underwater garbage problem https://news.mongabay.com/2025/10/local-divers-pick-away-at-lake-malawis-underwater-garbage-problem/

Local divers pick away at Lake Malawi’s underwater garbage problem
CAPE MACLEAR, Malawi — On a clear August morning, three scuba divers disappeared under the waters of Lake Malawi. Above them, serenity: The clear water rippled gently, spick-and-span Cape Maclear Beach was empty of tourists and the shoreline trees stood calm. Half an hour later, having covered an area just 30 meters (100 feet) from […]

Maxx Crosby Doesn’t Hold Back After Raiders Lose to Bears https://heavy.com/sports/nfl/las-vegas-raiders/maxx-crosby-reacts-loss-bears/?adt_ei=[email]

Finite element analysis of an eigenvalue problem arising from neutron transport
Nicol\'as A. Barnafi, Felipe Lepe, Francisca Mu\~noz Riquelme
https://arxiv.org/abs/2510.05368

Finite element analysis of an eigenvalue problem arising from neutron transport
In two and three dimensions, we analyze a finite element method to approximate the solutions of an eigenvalue problem arising from neutron transport. We derive the eigenvalue problem of interest, which results to be non-symmetric. Under a standard finite element approximation based on piecewise polynomials of degree $k \geq 1$, and under the framework of the compact operators theory, we prove convergence and error estimates of the proposed method. We report a series of numerical tests in order …

On the Parameterized Complexity of Grundy Domination and Zero Forcing Problems
Robert Scheffler
https://arxiv.org/abs/2508.18104 https://arxiv.org/pdf/2508…

On the Parameterized Complexity of Grundy Domination and Zero Forcing Problems
We consider two different problem families that deal with domination in graphs. On the one hand, we focus on dominating sequences. In such a sequence, every vertex dominates some vertex of the graph that was not dominated by any earlier vertex in the sequence. The problem of finding the longest dominating sequence is known as $\mathsf{Grundy~Domination}$. Depending on whether the closed or the open neighborhoods are used for domination, there are three other versions of this problem. We show th…

Limits to the Hall effect and other nonreciprocal effects in three-dimensional metamaterials
Christian Kern, Graeme W. Milton
https://arxiv.org/abs/2509.01593 https://

Limits to the Hall effect and other nonreciprocal effects in three-dimensional metamaterials
Metamaterials can exhibit exotic nonreciprocal properties, yet corresponding fundamental limits and design blueprints achieving them are largely unexplored. Here, we derive comprehensive bounds on the effective nonreciprocal properties of three-dimensional metamaterials and identify microstructures achieving or approaching these bounds. We assume that the underlying equations are equivalent to the conductivity problem in a weak applied magnetic field. While we focus on the Hall effect, our resu…

The Price of Connectivity Augmentation on Planar Graphs
Hugo A. Akitaya, Justin Dallant, Erik D. Demaine, Michael Kaufmann, Linda Kleist, Frederick Stock, Csaba D. T\'oth, Torsten Ueckerdt
https://arxiv.org/abs/2509.01096

The Price of Connectivity Augmentation on Planar Graphs
Given two classes of graphs, $\mathcal{G}_1\subseteq \mathcal{G}_2$, and a $c$-connected graph $G\in \mathcal{G}_1$, we wish to augment $G$ with a smallest cardinality set of new edges $F$ to obtain a $k$-connected graph $G'=(V,E\cup F) \in \mathcal{G}_2$. In general, this is the $c\to k$ connectivity augmentation problem. Previous research considered variants where $\mathcal{G}_1=\mathcal{G}_2$ is the class of planar graphs, plane graphs, or planar straight-line graphs. In all three settings, …

Learn2Reg 2024: New Benchmark Datasets Driving Progress on New Challenges
Lasse Hansen, Wiebke Heyer, Christoph Gro{\ss}br\"ohmer, Frederic Madesta, Thilo Sentker, Wang Jiazheng, Yuxi Zhang, Hang Zhang, Min Liu, Junyi Wang, Xi Zhu, Yuhua Li, Liwen Wang, Daniil Morozov, Nazim Haouchine, Joel Honkamaa, Pekka Marttinen, Yichao Zhou, Zuopeng Tan, Zhuoyuan Wang, Yi Wang, Hongchao Zhou, Shunbo Hu, Yi Zhang, Qian Tao, Lukas F\"orner, Thomas Wendler, Bailiang Jian, Christian Wachinge…

Learn2Reg 2024: New Benchmark Datasets Driving Progress on New Challenges
Medical image registration is critical for clinical applications, and fair benchmarking of different methods is essential for monitoring ongoing progress. To date, the Learn2Reg 2020-2023 challenges have released several complementary datasets and established metrics for evaluations. However, these editions did not capture all aspects of the registration problem, particularly in terms of modality diversity and task complexity. To address these limitations, the 2024 edition introduces three new …

Mitigating the barren plateau problem in linear optics
Matthew D. Horner
https://arxiv.org/abs/2510.02430 https://arxiv.org/pdf/2510.02430

Mitigating the barren plateau problem in linear optics
We demonstrate a significant speedup of variational quantum algorithms that use discrete variable boson sampling when the parametrised phase shifters are constrained to have two distinct eigenvalues. This results in a cost landscape with less local minima and barren plateaus regardless of the problem, ansatz or circuit layout. This works without reliance on any classical pre-processing and allows for the fast gradient-free Rotosolve algorithm to be used. We propose three ways to achieve this by…

The uniqueness of inverse scattering problems, reciprocity principles, and nonradiating sources related to low-signature structures
Johan Helsing, Anders Karlsson
https://arxiv.org/abs/2509.26304

The uniqueness of inverse scattering problems, reciprocity principles, and nonradiating sources related to low-signature structures
This paper is about perfectly electrically conducting structures designed to produce negligible scattered power when exposed to a time-harmonic plane electromagnetic wave. The structures feature cavities capable of concealing objects. Theoretical investigations of the properties of the structures combined with accurate numerical computations lead to three key findings: the first concerns the uniqueness of the solution to an inverse scattering problem, the second establishes a reciprocity relati…

Robust Cislunar Navigation via LFT-Based $\mathcal{H}_\infty$ Filtering with Bearing-Only Measurements
Raktim Bhattacharya
https://arxiv.org/abs/2510.04942 https://

Robust Cislunar Navigation via LFT-Based $\mathcal{H}_\infty$ Filtering with Bearing-Only Measurements
This paper develops a robust estimation framework for cislunar navigation that embeds the Circular Restricted Three-Body Problem (CR3BP) dynamics and bearing-only optical measurements within a Linear Fractional Transformation (LFT) representation. A full-order $\mathcal{H}_\infty$ observer is synthesized with explicit $\mathcal{L}_2$ performance bounds. The formulation yields a nonlinear estimator that operates directly on the governing equations and avoids reliance on local linearizations. Dom…

Hearing the Order: Investigating Selection Bias in Large Audio-Language Models
Yu-Xiang Lin, Chen-An Li, Sheng-Lun Wei, Po-Chun Chen, Hsin-Hsi Chen, Hung-yi Lee
https://arxiv.org/abs/2510.00628

Hearing the Order: Investigating Selection Bias in Large Audio-Language Models
Large audio-language models (LALMs) are often used in tasks that involve reasoning over ordered options. An open question is whether their predictions are influenced by the order of answer choices, which would indicate a form of selection bias and undermine their reliability. In this paper, we identify and analyze this problem in LALMs. We demonstrate that no model is immune to this bias through extensive experiments on six LALMs across three widely used benchmarks and their spoken counterparts…

WFC/WFD: Web Fuzzing Commons, Dataset and Guidelines to Support Experimentation in REST API Fuzzing
Omur Sahin, Man Zhang, Andrea Arcuri
https://arxiv.org/abs/2509.01612 https:/…

WFC/WFD: Web Fuzzing Commons, Dataset and Guidelines to Support Experimentation in REST API Fuzzing
Fuzzing REST APIs is an important research problem, with practical applications and impact in industry. As such, a lot of research work has been carried out on this topic in the last few years. However, there are three major issues that hinder further progress: how to deal with API authentication; how to catalog and compare different fault types found by different fuzzers; and what to use as case study to facilitate fair comparisons among fuzzers. To address these important challenges, we prese…

Vector Trifference
Siddharth Bhandari, Abhishek Khetan
https://arxiv.org/abs/2510.04079 https://arxiv.org/pdf/2510.04079

Vector Trifference
We investigate a geometric generalization of trifference, a concept introduced by Elias in 1988 in the study of zero-error channel capacity. In the discrete setting, a code C \subseteq {0,1,2}^n is trifferent if for any three distinct codewords x, y, z in C, there exists a coordinate i in [n] where x_i, y_i, z_i are all distinct. Determining the maximum size of such codes remains a central open problem; the classical upper bound |C| \leq 2 * (3/2)^n, proved via a simple pruning argume…

Separation of Three or More Autonomous Mobile Models under Hierarchical Schedulers
Shota Naito, Tsukasa Ninomiya, Koichi Wada
https://arxiv.org/abs/2508.19805 https://

Separation of Three or More Autonomous Mobile Models under Hierarchical Schedulers
Understanding the computational power of mobile robot systems is a fundamental challenge in distributed computing. While prior work has focused on pairwise separations between models, we explore how robot capabilities, light observability, and scheduler synchrony interact in more complex ways. We first show that the Exponential Times Expansion (ETE) problem is solvable only in the strongest model -- fully-synchronous robots with full mutual lights ($\mathcal{LUMT}^F$). We then introduce the H…

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.…

Projective Plane Subdivision Method For Initial Orbit Determination
Ruiqi Huang, Anton Leykin, Michela Mancini
https://arxiv.org/abs/2509.14397 https://arx…

Projective Plane Subdivision Method For Initial Orbit Determination
Initial Orbit Determination (IOD) is the classical problem of estimating the orbit of a body in space without any presumed information about the orbit. The geometric formulation of the ''angles-only'' IOD in three-dimensional space: find a conic curve with a given focal point meeting the given lines of sight (LOS). We provide an algebraic reformulation of this problem and confirm that five is the minimal number of lines necessary to have a finite number of solutions in a non-special case, and t…

The problem of finding three numbers such that the sum or difference of any two of them is a square number
Seiji Tomita
https://arxiv.org/abs/2508.15781 https://

The problem of finding three numbers such that the sum or difference of any two of them is a square number
Euler explored the problem of finding three numbers such that the sum or difference of any two of them is a perfect square. He discovered a parametric solution represented by polynomials of degree 18 and identified the smallest of these solutions. Additionally, we derive two parametric solutions using the elliptic curve method and find all solutions within the range of $10^8$.

Goldman-Turaev formality from the Kontsevitch integral
Dror Bar-Natan, Zsuzsanna Dancso, Tamara Hogan, Jessica Liu, Nancy Scherich
https://arxiv.org/abs/2509.20983 https://

Goldman-Turaev formality from the Kontsevitch integral
We present a new solution to the formality problem for the framed Goldman--Turaev Lie bialgebra, constructing Goldman-Turaev homomorphic expansions (formality isomorphisms) from the Kontsevich integral. Our proof uses a three dimensional derivation of the Goldman-Turaev Lie biaglebra arising from a low-degree Vassiliev quotient -- the {\em emergent} quotient -- of tangles in a thickened punctured disk, modulo a Conway skein relation. This is in contrast to Massuyeau's 2018 proof using braids. A…

At least he understood the location and extent of our problem. Not great on the solution side, but we will be workshopping that... https://bird.makeup/users/macfarlanenews/statuses/1969117630578540785

Scott MacFarlane
ALERT: Justice Dept will seek minimum 30-year prison term for Nicholas Roske, the California man who pleaded guilty in attempt to assassinate Justice Brett Kavanugh Feds argue Roske was targeting UP TO THREE justices for assassination COURT FILING: https://storage.courtlistener.com/recap/gov.uscourts.mdd.514255/gov.uscourts.mdd.514255.98.0.pdf

Precoloring extension with demands on paths
Arun Kumar Das, Michal Opler, Tom\'a\v{s} Valla
https://arxiv.org/abs/2509.18936 https://arxiv.org/pdf/2509…

Precoloring extension with demands on paths
Let $G$ be a graph with a set of precolored vertices, and let us be given an integer distance parameter $d$ and a set of integer demands $d_1,\dots,d_c$. The Distance Precoloring Extension with Demands (DPED) problem is to compute a vertex $c$-coloring of $G$ such that the following three conditions hold: (i) the resulting coloring respects the colors of the precolored vertices, (ii) the distance of two vertices of the same color is at least $d$, and (iii) the number of vertices colored by colo…

Fermion mass ratios from the exceptional Jordan algebra
Tejinder P. Singh
https://arxiv.org/abs/2508.10131 https://arxiv.org/pdf/2508.10131

Fermion mass ratios from the exceptional Jordan algebra
We revisit the "three generations" problem and the pattern of charged-fermion masses from the vantage of octonionic and Clifford algebra structures. Working with the exceptional Jordan algebra J3(OC) (right-handed flavor) and the symmetric cube of SU(3) (left-handed charge frame), we show that a single minimal ladder in the symmetric cube, together with the Dynkin Z2 swap (the A2 diagram flip), leads to closed-form expressions for the square-root mass ratios of all three charged families. The u…

Oof, fuck microsoft.
But also, there's no reason to use permissive licenses any more. "Open source" has taken over the world. We no longer have to work with billion-dollar companies in order to get our stuff used. Now we need to protect ourselves from being taken advantage of by them.
https://

Trion polaron problem in bulk and two-dimensional materials
V. Shahnazaryan, A. Kudlis, K. Varga, I. A. Shelykh, I. V. Tokatly
https://arxiv.org/abs/2508.14756 https://

Trion polaron problem in bulk and two-dimensional materials
We develop a microscopic theoryof the trion polaron: a bound state of two electrons and one hole, dressed by longitudinal optical (LO) phonons. Starting from the Frohlich Hamiltonian, which describes the interaction of charged particles with LO phonons in three-dimensional (bulk) and two-dimensional (monolayer) polar crystals, we adopt the intermediate coupling variational approximation of Lee, Low, and Pines, and generalize it for the three-body problem. This yields an effective three-particle…

Broncos' Payton backs QB Nix: 'Just keep firing' https://www.espn.com/nfl/story/_/id/46381627/broncos-payton-backs-bo-nix-amid-struggles-just-keep-firing

Signal-to-noise and spatial resolution in in-line imaging. 3. Optimization using a simple model
T. E. Gureyev, D. M. Paganin, H. M. Quiney
https://arxiv.org/abs/2510.01892 https…

Signal-to-noise and spatial resolution in in-line imaging. 3. Optimization using a simple model
The problem of optimization of propagation-based phase-contrast imaging setups is considered in the case of projection X-ray imaging and three-dimensional tomography with phase retrieval. For two-dimensional imaging, a simple model for a homogeneous edge feature embedded in a bulk sample is used to obtain analytical expressions for the image intensity. This model allows for explicit optimization of the geometrical parameters of the imaging setup and the choice of X-ray energy that maximizes the…

rStar2-Agent: Agentic Reasoning Technical Report
Ning Shang, Yifei Liu, Yi Zhu, Li Lyna Zhang, Weijiang Xu, Xinyu Guan, Buze Zhang, Bingcheng Dong, Xudong Zhou, Bowen Zhang, Ying Xin, Ziming Miao, Scarlett Li, Fan Yang, Mao Yang
https://arxiv.org/abs/2508.20722

rStar2-Agent: Agentic Reasoning Technical Report
We introduce rStar2-Agent, a 14B math reasoning model trained with agentic reinforcement learning to achieve frontier-level performance. Beyond current long CoT, the model demonstrates advanced cognitive behaviors, such as thinking carefully before using Python coding tools and reflecting on code execution feedback to autonomously explore, verify, and refine intermediate steps in complex problem-solving. This capability is enabled through three key innovations that makes agentic RL effective at…

On the $PGL_2(q)$-orbits of lines of $PG(3,q)$ and binary quartic forms in characteristic three
Krishna Kaipa, Puspendu Pradhan
https://arxiv.org/abs/2508.11229 https://

On the $PGL_2(q)$-orbits of lines of $PG(3,q)$ and binary quartic forms in characteristic three
We consider the problem of classifying the lines of the projective $3$-space $PG(3,q)$ over a finite field $\mathbb{F}_q$ into orbits of the group $PGL_2(q)$ of linear symmetries of the twisted cubic $C$. The problem has been solved in literature in characteristic different from $3$, and in this work, we solve the problem in characteristic $3$. We reduce this problem to another problem, which is the classification of binary quartic forms into $PGL_2(q)$-orbits. We first solve the latter problem…

ECHO: Ego-Centric modeling of Human-Object interactions
Ilya A. Petrov, Vladimir Guzov, Riccardo Marin, Emre Aksan, Xu Chen, Daniel Cremers, Thabo Beeler, Gerard Pons-Moll
https://arxiv.org/abs/2508.21556

ECHO: Ego-Centric modeling of Human-Object interactions
Modeling human-object interactions (HOI) from an egocentric perspective is a largely unexplored yet important problem due to the increasing adoption of wearable devices, such as smart glasses and watches. We investigate how much information about interaction can be recovered from only head and wrists tracking. Our answer is ECHO (Ego-Centric modeling of Human-Object interactions), which, for the first time, proposes a unified framework to recover three modalities: human pose, object motion, and…

A note on the Davis-Yin three-operator splitting method
Maoran Wang, Xingju Cai
https://arxiv.org/abs/2509.22032 https://arxiv.org/pdf/2509.22032

A note on the Davis-Yin three-operator splitting method
This paper addresses the monotone inclusion problem in a real Hilbert space, with the objective of identifying a point \( x \in \mathcal{H} \) such that \( 0 \in Ax + Bx + Cx \), where \( A \) and \(C\) are maximal monotone operators and \( B \) is a \(β\)-cocoercive operator. The Davis-Yin three-operator splitting method constitutes a widely used algorithm for solving this problem. This method consists of two subproblems: the first entails a backward step, whereas the second comprises a backw…

Raiders’ Geno Smith Gives Blunt Words After Loss to Chargers https://heavy.com/sports/nfl/las-vegas-raiders/geno-smith-blunt-loss-chargers/?adt_ei=[email]

Identifying Fixed Points in the Three-Body Problem Using a High-Order Transfer Map
Xingyu Zhou, Lorenzo Ano`e, Roberto Armellin, Dong Qiao, Xiangyu Li
https://arxiv.org/abs/2509.12671

Identifying Fixed Points in the Three-Body Problem Using a High-Order Transfer Map
Periodic orbits (POs) play a central role in the circular restricted three-body problem (CRTBP). This paper introduces a method to search for POs by identifying single- and multiple-revolution fixed points in chosen Poincare maps that describe the CRTBP dynamics, with a theoretical capability to detect all fixed points across arbitrary revolution counts exhaustively.First, high-order transfer maps (HOTMs), represented as polynomials, are constructed within the differential algebra (DA) framewor…

LAPIS: A Performance Portable, High Productivity Compiler Framework
Brian Kelley, Sivasankaran Rajamanickam
https://arxiv.org/abs/2509.25605 https://arxiv.…

LAPIS: A Performance Portable, High Productivity Compiler Framework
Portability, performance, and productivity are three critical dimensions for evaluating a programming model or compiler infrastructure. Several modern programming models for computational science focus on performance and portability. On the other end, several machine learning focused programming models focus on portability and productivity. A clear solution that is strong in all three dimensions has yet to emerge. A second related problem arises when use cases from computational science converg…

from my link log —
Rendezvous hashing explained.
https://randorithms.com/2020/12/26/rendezvous-hashing.html
saved 2025-09-16 https://

Recognizing Penny and Marble Graphs is Hard for Existential Theory of the Reals
Anna Lubiw, Marcus Schaefer
https://arxiv.org/abs/2508.10136 https://arxiv.…

Recognizing Penny and Marble Graphs is Hard for Existential Theory of the Reals
We show that the recognition problem for penny graphs (contact graphs of unit disks in the plane) is $\exists\mathbb{R}$-complete, that is, computationally as hard as the existential theory of the reals, even if a combinatorial plane embedding of the graph is given. The exact complexity of the penny graph recognition problem has been a long-standing open problem. We lift the penny graph result to three dimensions and show that the recognition problem for marble graphs (contact graphs of unit …

Weighted First Order Model Counting for Two-variable Logic with Axioms on Two Relations
Qipeng Kuang, V\'aclav K\r{u}la, Ond\v{r}ej Ku\v{z}elka, Yuanhong Wang, Yuyi Wang
https://arxiv.org/abs/2508.11515

Weighted First Order Model Counting for Two-variable Logic with Axioms on Two Relations
The Weighted First-Order Model Counting Problem (WFOMC) asks to compute the weighted sum of models of a given first-order logic sentence over a given domain. The boundary between fragments for which WFOMC can be computed in polynomial time relative to the domain size lies between the two-variable fragment ($\text{FO}^2$) and the three-variable fragment ($\text{FO}^3$). It is known that WFOMC for \FOthree{} is $\mathsf{\#P_1}$-hard while polynomial-time algorithms exist for computing WFOMC for $…

Super-resolution of 4D flow MRI through inverse problem explicit solving
Aur\'elien de Turenne, R\'emi Cart-Lamy, Denis Kouam\'e
https://arxiv.org/abs/2509.21071 htt…

Super-resolution of 4D flow MRI through inverse problem explicit solving
Four-dimensional Flow MRI (4D Flow MRI) enables non-invasive, time-resolved imaging of blood flow in three spatial dimensions, offering valuable insights into complex hemodynamics. However, its clinical utility is limited by low spatial resolution and poor signal-to-noise ratio (SNR), imposed by acquisition time constraints. In this work, we propose a novel method for super-resolution and denoising of 4D Flow MRI based on the explicit solution of an inverse problem formulated in the complex dom…

A Survey of Reasoning and Agentic Systems in Time Series with Large Language Models
Ching Chang, Yidan Shi, Defu Cao, Wei Yang, Jeehyun Hwang, Haixin Wang, Jiacheng Pang, Wei Wang, Yan Liu, Wen-Chih Peng, Tien-Fu Chen
https://arxiv.org/abs/2509.11575

A Survey of Reasoning and Agentic Systems in Time Series with Large Language Models
Time series reasoning treats time as a first-class axis and incorporates intermediate evidence directly into the answer. This survey defines the problem and organizes the literature by reasoning topology with three families: direct reasoning in one step, linear chain reasoning with explicit intermediates, and branch-structured reasoning that explores, revises, and aggregates. The topology is crossed with the main objectives of the field, including traditional time series analysis, explanation a…

Chiefs in danger zone with impotent offense, while Steelers disappoint on defense; plus, 3 NFL closers https://www.nfl.com/news/chiefs-in-danger-zone-with-impotent-offense-while-steelers-disappoint-on-defense-plus-3-nfl-c…

Non-invertible Symmetry as a Solution to the Strong CP Problem in a GUT-inspired Standard Model
Tatsuo Kobayashi, Hajime Otsuka, Tsutomu T. Yanagida
https://arxiv.org/abs/2508.12287

Non-invertible Symmetry as a Solution to the Strong CP Problem in a GUT-inspired Standard Model
We propose a three-zero texture for the down-quark mass matrix within a $SU(5)$ GUT-inspired Standard Model, enforced by a non-invertible selection rule originating from $\mathbb{Z}_2$ gauging of $\mathbb{Z}_N$ symmetries. Assuming CP invariance at the high-energy scale, our framework solves the strong CP problem while reproducing a realistic quark mass matrix. The CP symmetry is spontaneously broken down at an intermediate scale via complex vacuum expectation values of new scalar fields $η_i$…

Further fundamental bounds on the Hall effect in three-dimensional metamaterials
Christian Kern, Graeme W. Milton
https://arxiv.org/abs/2509.19513 https://…

Further fundamental bounds on the Hall effect in three-dimensional metamaterials
We consider the problem of bounding the effective nonreciprocal properties of metamaterials. Recently, significant progress was made by showing that this problem can be reduced to bounding an equivalent reciprocal one and applying a monotonicity argument. Here, we build upon this result and provide bounds incorporating additional information about the metamaterial. Specifically, in the two-phase case, we provide bounds for isotropic metamaterials. In the multiphase case, we provide bounds for u…

Understanding Distribution Structure on Calibrated Recommendation Systems
Diego Correa da Silva, Denis Robson Dantas Boaventura, Mayki dos Santos Oliveira, Eduardo Ferreira da Silva, Joel Machado Pires, Frederico Ara\'ujo Dur\~ao
https://arxiv.org/abs/2508.13568

Understanding Distribution Structure on Calibrated Recommendation Systems
Traditional recommender systems aim to generate a recommendation list comprising the most relevant or similar items to the user's profile. These approaches can create recommendation lists that omit item genres from the less prominent areas of a user's profile, thereby undermining the user's experience. To solve this problem, the calibrated recommendation system provides a guarantee of including less representative areas in the recommended list. The calibrated context works with three distributi…

Hybrid Quantum-Classical Branch-and-Price Method for the Vertex Coloring Problem
Chiara Vercellino, M. Yassine Naghmouchi, Wesley Coelho, Giacomo Vitali, Alberto Scionti, Paolo Viviani, Olivier Terzo, Bartolomeo Montrucchio
https://arxiv.org/abs/2508.18887

Hybrid Quantum-Classical Branch-and-Price Method for the Vertex Coloring Problem
This paper introduces Quantum Classical Branch-and-Price (QCBP), a hybrid quantum-classical algorithm for the Vertex Coloring problem on neutral-atom Quantum Processing Units (QPUs). QCBP embeds quantum computation within the classical Branch-and-Price (BP) framework to address three bottlenecks in classical BP algorithms: the computational cost of Pricing Subproblems (PSPs), branching efficiency, and the quality of primal heuristics. It uses quantum-assisted Column Generation (CG) based on Qua…

Quantitative periodic homogenization of parabolic equations with large drift and potential
Kshitij Sinha (IIT Bombay)
https://arxiv.org/abs/2509.22003 https://

Quantitative periodic homogenization of parabolic equations with large drift and potential
This work aims to study the rates in the context of periodic homogenization of parabolic problems with large lower order terms (both drift and potential). We demonstrate that the solution is a product of three terms: (i) a function of time, (ii) the ground-state of an exponential cell eigenvalue problem and (iii) the solution to a parabolic equation with zero effective drift. For the latter, we derive $\mathrm L^2$ rates in the homogenization limit.

On the Shape of the Symmetric Solution Set of a Linear Complementarity Problem with Interval Data
Uwe Sch\"afer
https://arxiv.org/abs/2508.16824 https://

On the Shape of the Symmetric Solution Set of a Linear Complementarity Problem with Interval Data
In this paper we give some two-dimensional and some three-dimensional examples for the shape of the symmetric solution set of a linear complementarity problem where the given data are not explicitly known but can only be enclosed in intervals.

The coupling of mixed and primal finite element methods for the coupled body-plate problem
Jun Hu, Zhen Liu, Rui Ma
https://arxiv.org/abs/2509.10827 https://

The coupling of mixed and primal finite element methods for the coupled body-plate problem
This paper considers the coupled problem of a three-dimensional elastic body and a two-dimensional plate, which are rigidly connected at their interface. The plate consists of a plane elasticity model along the longitudinal direction and a plate bending model with Kirchhoff assumptions along the transverse direction. The Hellinger-Reissner formulation is adopted for the body by introducing the stress as an auxiliary variable, while the primal formulation is employed for the plate. The well-pose…

The impact of modeling approaches on controlling safety-critical, highly perturbed systems: the case for data-driven models
Piotr {\L}aszkiewicz, Maria Carvalho, Cl\'audia Soares, Pedro Louren\c{c}o
https://arxiv.org/abs/2509.13531

The impact of modeling approaches on controlling safety-critical, highly perturbed systems: the case for data-driven models
This paper evaluates the impact of three system models on the reference trajectory tracking error of the LQR optimal controller, in the challenging problem of guidance and control of the state of a system under strong perturbations and reconfiguration. We compared a smooth Linear Time Variant system learned from data (DD-LTV) with state of the art Linear Time Variant (LTV) system identification methods, showing its superiority in the task of state propagation. Moreover, we have found that DD-LT…

2 abysmal stats show Ashton Jeanty isn't the problem with Raiders' rushing attack https://www.sportingnews.com/us/nfl/las-vegas-raiders/news/2-abysmal-stats-ashton-jeanty-isnt-problem-raid…

Three-Neighbour Bootstrap Percolation in Thin Three-Dimensional Grids
Will Dolphin, Peter J. Dukes
https://arxiv.org/abs/2509.13589 https://arxiv.org/pdf/2…

Three-Neighbour Bootstrap Percolation in Thin Three-Dimensional Grids
We improve the status of the problem of determining minimum-sized percolating sets in $a \times b \times c$ grids under the $3$-neighbour process. Using several new constructions, we show that optimal percolating sets exist whenever $\min(a,b,c) \ge 7$. As an important step toward this, we also show that all grids with $\min(a,b,c) \ge 4$ have a percolating set whose size exactly achieves the lower bound $(ab+ac+bc)/3$ whenever this value is an integer.

Disjunctions of Two Dependence Atoms
Nicolas Fr\"ohlich, Phokion G. Kolaitis, Arne Meier
https://arxiv.org/abs/2508.16146 https://arxiv.org/pdf/2508.1…

Disjunctions of Two Dependence Atoms
Dependence logic is a formalism that augments the syntax of first-order logic with dependence atoms asserting that the value of a variable is determined by the values of some other variables, i.e., dependence atoms express functional dependencies in relational databases. On finite structures, dependence logic captures NP, hence there are sentences of dependence logic whose model-checking problem is NP-complete. In fact, it is known that there are disjunctions of three dependence atoms whose mod…

A posteriori existence of strong solutions to the Navier-Stokes equations in 3D
Aaron Brunk, Jan Giesselmann, Tabea Tscherpel
https://arxiv.org/abs/2509.25105 https://

A posteriori existence of strong solutions to the Navier-Stokes equations in 3D
Global existence of strong solutions to the three-dimensional incompressible Navier-Stokes equations remains an open problem. A posteriori existence results offer a way to rigorously verify the existence of strong solutions by ruling out blow-up on a certain time interval, using only numerical solutions. In this work we present such a result for the Navier-Stokes equations subject to periodic boundary conditions, which makes use of a version of the celebrated blow-up criterion in the critical s…

On Lattice Diameter Segments and A Discrete Borsuk Partition Problem
Anouk E. Brose, Jes\'us A. De Loera, Gyivan Lopez-Campos, Antonio J. Torres
https://arxiv.org/abs/2508.20009

On Lattice Diameter Segments and A Discrete Borsuk Partition Problem
The lattice diameter of a bounded set $S \subset \mathbb{R}^d$ measures the maximal number of lattice points in a segment whose endpoints are lattice points in $S$. Such a segment is called a lattice diameter segment of $S$. This simple invariant yields interesting applications and challenges. We describe a polynomial-time algorithm that computes lattice diameter segments of lattice polygons and show that computing lattice diameters of semi-algebraic sets in dimensions three and higher is NP-ha…

Global well-posedness of the inviscid resistive isentropic compressible MHD system
Jinkai Li, Liening Qiao
https://arxiv.org/abs/2508.13627 https://arxiv.o…

Global well-posedness of the inviscid resistive isentropic compressible MHD system
Due to the absence of dissipation mechanism to the inviscid compressible systems, it is a challenging problem to prove their global solvability. In this paper, we are concerned with the initial-boundary value problem to the inviscid and resistive isentropic compressible magnetohydrodynamic (MHD) system on three dimensional torus $\mathbb T^3$. Global well-posedness and large time behavior of solutions are established in the first time for the isentropic setting, under the condition that the ini…

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…

Requirements for Early Quantum Advantage and Quantum Utility in the Capacitated Vehicle Routing Problem
Chinonso Onah, Kristel Michielsen
https://arxiv.org/abs/2509.11469 https:…

Requirements for Early Quantum Advantage and Quantum Utility in the Capacitated Vehicle Routing Problem
We introduce a transparent, encoding-agnostic framework for determining when the Capacitated Vehicle Routing Problem (CVRP) can achieve early quantum advantage. Our analysis shows this is unlikely on noisy intermediate scale quantum (NISQ) hardware even in best case scenarios that use the most qubit-efficient direct encodings. Closed-form resource counts, combined with recent device benchmarks, yield three decisive go/no-go figures of merit: the quantum feasibility point and the qubit- and gate…

On three dimensional steady super-Alfv\'{e}nic magnetohydrodynamics shocks with aligned fields
Shangkun Weng, Wengang Yang
https://arxiv.org/abs/2510.12068 https://

On three dimensional steady super-Alfvénic magnetohydrodynamics shocks with aligned fields
The coupled motion between the hydrodynamic flow and magnetic field introduces significant complexity into the structure of the magnetohydrodynamic (MHD) equations. A key factor contributing to this complexity is the presence of Alfvén waves, which critically influences the character of the flow and makes the problem considerably more challenging. Within the framework where the magnetic field is everywhere parallel to the flow velocity, we give an effective decomposition of the steady MHD equa…

Finite element discretizations of bending plates with prestrained microstructure
Klaus B\"ohnlein, Stefan Neukamm, Oliver Sander
https://arxiv.org/abs/2509.26438 https://…

Finite element discretizations of bending plates with prestrained microstructure
We investigate a finite element discretization of an elastic bending-plate model with an effective prestrain. The model has been obtained via homogenization and dimension reduction by Bönlein at al. (2023). Its energy functional is the $Γ$-limit of a three-dimensional nonlinear microstructured elasticity functional. In the derived effective model, the microstructure is incorporated as a local corrector problem, a system of linear elliptic partial differential equations posed on a three-dimens…

Learning with errors may remain hard against quantum holographic attacks
Yunfei Wang, Xin Jin, Junyu Liu
https://arxiv.org/abs/2509.22833 https://arxiv.org…

Learning with errors may remain hard against quantum holographic attacks
The Learning with Errors (LWE) problem underlies modern lattice-based cryptography and is assumed to be quantum hard. Recent results show that estimating entanglement entropy is as hard as LWE, creating tension with quantum gravity and AdS/CFT, where entropies are computed by extremal surface areas. This suggests a paradoxical route to solving LWE by building holographic duals and measuring extremal surfaces, seemingly an easy task. Three possible resolutions arise: that AdS/CFT duality is intr…

Well-balanced high-order method for non-conservative hyperbolic PDEs with source terms: application to one-dimensional blood flow equations with gravity
Chiara Colombo, Caterina Dalmaso, Lucas O. M\"uller, Annunziato Siviglia
https://arxiv.org/abs/2509.22190

Well-balanced high-order method for non-conservative hyperbolic PDEs with source terms: application to one-dimensional blood flow equations with gravity
The present work proposes a well-balanced finite volume-type numerical method for the solution of non-conservative hyperbolic partial differential equations (PDEs) with source terms. The method is characterized, first, by the use of a recently introduced high-order spatial reconstruction, based on generalized Riemann problem information from the previous time level. Such reconstruction is well-balanced up to order three, compact, efficient and easy to implement. Second, the method incorporates …

A comparative study of finite element methods for a class of harmonic map heat flow problems
Nam Anh Nguyen, Arnold Reusken
https://arxiv.org/abs/2508.20590 https://

A comparative study of finite element methods for a class of harmonic map heat flow problems
In this paper, we review and systematically compare three finite element discretization methods for a harmonic map heat flow problem from the unit disk in $\mathbb{R}^2$ to the unit sphere in $\mathbb{R}^3$ in an unified framework. Numerical tests validate the convergence rates in a regime of smooth solutions and are used to compare the methods in terms of computational efficiency. For one of the methods a discrete inf-sup stability result is derived.