Tootfinder

Henry Blodget is launching Solutions, an interview podcast in partnership with Vox Media, on August 18, focusing on challenges in science, business, and society (Max Tani/Semafor)
https://www.semafor.com/article/08/10/2025/with-new-podcas…

With new podcast, Blodget turns to ‘Solutions’ journalism
Henry Blodget talks to Semafor about getting back to the basics: writing and talking about what excites him in business and tech.

🌡️ Fabric8Labs ECAM Enabled Thermal Solutions at Hot Chips 2025
https://www.servethehome.com/fabric8labs-ecam-enabled-thermal-solutions-at-hot-chips-2025/

Fabric8Labs ECAM Enabled Thermal Solutions at Hot Chips 2025
Fabric8Labs ECAM uses the electrical current from an OLED display to manufacture copper liquid cooling 3D coldplates with pixel precision

Transgressive Harmonic Maps and SU(1,1) Self-Duality Solutions
Sebastian Heller, Lothar Schiemanowski, Hartmut Weiss
https://arxiv.org/abs/2509.09497 https://

Transgressive Harmonic Maps and SU(1,1) Self-Duality Solutions
We establish a duality between harmonic maps from Riemann surfaces to hyperbolic 3-space $\mathbb{H}^3$ and harmonic maps from Riemann surfaces to de Sitter three-space $\operatorname{dS}_3$, best viewed as a generalized Gauss map. On the gauge theoretic side, it matches SU(2) and SU(1,1) solutions of Hitchin's self-duality equations via a signature flip along an eigenline of the Higgs field. Reversing this operation typically produces singular solutions, occurring where the eigenline becomes l…

Analytical solutions of CPT-odd Maxwell equations in Schwarzschild spacetime
Hao Wang, Zhi Xiao, Bing Sun
https://arxiv.org/abs/2506.10409 https://

Analytical solutions of CPT-odd Maxwell equations in Schwarzschild spacetime
In this work, we present the CPT-violating (CPTV) Maxwell equations in curved spacetime using the Newman-Penrose (NP) formalism. We obtain a semi-analytical solution to the Maxwell equations in Schwarzschild spacetime under the assumption that the CPT-odd $\left(k_{AF}\right)^μ$ term exhibits spherical symmetry in the Schwarzschild background. Retaining only terms up to linear order in the $\left(k_{AF}\right)^μ$ coefficient, we obtain perturbative solutions by treating the solutions of the L…

New class of time-periodic solutions to the 1D cubic wave equation
Filip Ficek, Maciej Maliborski
https://arxiv.org/abs/2506.10839 https://

New class of time-periodic solutions to the 1D cubic wave equation
In recent papers (arXiv:2407.16507, arXiv:2408.05158) we presented results suggesting the existence of a new class of time-periodic solutions to the defocusing cubic wave equation on a one-dimensional interval with Dirichlet boundary conditions. Here we confirm these findings by rigorously constructing solutions from this class. The proof uses rational arithmetic computations to verify essential operator bounds.

Explaining Tournament Solutions with Minimal Supports
Cl\'ement Contet, Umberto Grandi, J\'er\^ome Mengin
https://arxiv.org/abs/2509.09312 https://…

Explaining Tournament Solutions with Minimal Supports
Tournaments are widely used models to represent pairwise dominance between candidates, alternatives, or teams. We study the problem of providing certified explanations for why a candidate appears among the winners under various tournament rules. To this end, we identify minimal supports, minimal sub-tournaments in which the candidate is guaranteed to win regardless of how the rest of the tournament is completed (that is, the candidate is a necessary winner of the sub-tournament). This notion co…

Toward Quantum Enabled Solutions for Real-Time Currency Arbitrage in Financial Markets
Suman Kumar Roy, Rahul Rana, M Girish Chandra, Nishant Kumar, Manoj Nambiar
https://arxiv.org/abs/2509.09289

Toward Quantum Enabled Solutions for Real-Time Currency Arbitrage in Financial Markets
Currency arbitrage leverages price discrepancies in currency exchange rates across different currency pairs to gain risk-free profits. It involves multiple trading, where short-lived price discrepancies require real-time, high-speed processing of vast solution space, posing challenges for classical computing. In this work, we formulate an enhanced mathematical model for the currency arbitrage problem by adding simple cycle preservation constraints, which guarantee trading cycle validity and eli…

An abstract criterion on the existence and global stability of stationary solutions for random dynamical systems and its applications
Xiang Lv
https://arxiv.org/abs/2508.08497 h…

An abstract criterion on the existence and global stability of stationary solutions for random dynamical systems and its applications
We prove a concise and easily verifiable criterion on the existence and global stability of stationary solutions for random dynamical systems (RDSs). As a consequence, we can show that the $ω$-limit sets of all pullback trajectories of semilnear/nonlinear stochastic differential equations (SDEs) with additive/multiplicative white noise are composed of nontrivial random equilibria. The proof is different from the classical RDS scheme, which was established in \cite{CKS}. Furthermore, in the app…

France-based Scintil Photonics, which is developing integrated photonic system-on-chips for AI infrastructure, raised a $58M Series B led by Yotta and NGP (Tamara Djurickovic/Tech.eu)
https://tech.eu/2025/09/09/scintil-photonics-secure…

Scintil Photonics secured $58M to scale integrated photonics for AI factories
Grenoble-based Scintil Photonics, a company developing integrated Photonic System-on-Chip (PSoC) solutions for AI infrastructure, has closed a $58 million Series B round. The funding will drive global hiring, accelerate production, and expand its international footprint as it launches the industry’s first single-chip DWDM light engine. Built on its proprietary SHIP™ (Scintil Heterogeneous Integration Photonics) process, Scintil’s technology integrates lasers, photodiodes, and modula…

Supposedly, focusing on solutions when listening to someone share a problem instead of simply listening is a “male trait.” I don’t think it’s down to gender differences; I think it’s just about differences between humans, but it is something I do. I wish it weren’t. I just upset my son doing it, & I feel terrible.
Fuck. 😢

Demonstrating Multi-Suction Item Picking at Scale via Multi-Modal Learning of Pick Success
Che Wang, Jeroen van Baar, Chaitanya Mitash, Shuai Li, Dylan Randle, Weiyao Wang, Sumedh Sontakke, Kostas E. Bekris, Kapil Katyal
https://arxiv.org/abs/2506.10359

Demonstrating Multi-Suction Item Picking at Scale via Multi-Modal Learning of Pick Success
This work demonstrates how autonomously learning aspects of robotic operation from sparsely-labeled, real-world data of deployed, engineered solutions at industrial scale can provide with solutions that achieve improved performance. Specifically, it focuses on multi-suction robot picking and performs a comprehensive study on the application of multi-modal visual encoders for predicting the success of candidate robotic picks. Picking diverse items from unstructured piles is an important and chal…

Sensitivity of Optimal Control Solutions and Quantities of Interest with Respect to Component Functions
Jonathan R. Cangelosi, Matthias Heinkenschloss
https://arxiv.org/abs/2506.10804

Sensitivity of Optimal Control Solutions and Quantities of Interest with Respect to Component Functions
This work establishes sensitivities of the solution of an optimal control problem (OCP) and a corresponding quantity of interest (QoI) to perturbations in a state/control-dependent component function that appears in the governing ODEs and the objective function. This extends existing OCP sensitivity results, which consider the sensitivity of the OCP solution with respect to state/control-independent parameters. It is shown that with Carathéodory-type assumptions, the Implicit Function Theorem …

From $n$-Leibniz algebras and linear $n$-racks to the solutions of the (higher analogue of) Yang-Baxter equation
Apurba Das, Suman Majhi
https://arxiv.org/abs/2508.07005 https:/…

From $n$-Leibniz algebras and linear $n$-racks to the solutions of the (higher analogue of) Yang-Baxter equation
In this paper, we first demonstrate that a finite-dimensional $n$-Leibniz algebra naturally gives rise to an $n$-rack structure on the underlying vector space. Given any $n$-Leibniz algebra, we also construct two Yang-Baxter operators on suitable vector spaces and connect them by a homomorphism. Next, we introduce linear $n$-racks as the coalgebraic version of $n$-racks and show that a cocommutative linear $n$-rack yields a linear rack structure and hence a Yang-Baxter operator. An $n$-Leibniz …

Equivariant localization for $D=5$ gauged supergravity
Pietro Benetti Genolini, Jerome P. Gauntlett, Yusheng Jiao, Jaeha Park, James Sparks
https://arxiv.org/abs/2508.08207 http…

Equivariant localization for $D=5$ gauged supergravity
We consider supersymmetric solutions of $D=5$ Euclidean gauged supergravity coupled to an arbitrary number of vector multiplets. We consider solutions that admit both the R-symmetry Killing vector, $\mathcal{K}$, constructed as a bilinear in the Killing spinor, as well as an additional Killing vector $\ell$. Using $\ell$ to perform a dimensional reduction to $D=4$, $\mathcal{N}=2$ gauged supergravity, we show how the $D=5$ on-shell action can be computed using equivariant localization. We illus…

“Terracotta’s porous surface
allows water to slowly evaporate,
carrying heat away and cooling the space around it,”
says Adithya Pradyumna,
an environmental health researcher at Azim Premji University in Bengaluru.
Drawing on this principle, architects in India’s sprawling metro areas
are turning to terracotta for new passive cooling solutions
that range from clay refrigerators to perforated tiles,
ventilated screens, and facades
that al…

Terracotta Is a 3,000-Year-Old Solution to Fighting Extreme Heat
Companies are adapting this humble clay-based ceramic to keep people cool—without electricity

Almost a Complete Proof of the Generalized Erd\H{o}s-Straus Conjecture: ${5}/{a} = {1}/{b} {1}/{c} {1}/{d}$
Bilal Ghermoul
https://arxiv.org/abs/2508.07367 https://

Almost a Complete Proof of the Generalized Erdős-Straus Conjecture: ${5}/{a} = {1}/{b} + {1}/{c} + {1}/{d}$
The generalized Erdős-Straus conjecture, proposed by Wacław Sierpiński in 1956, asks whether the Diophantine equation \[ \frac{5}{a} = \frac{1}{b} + \frac{1}{c} + \frac{1}{d} \] admits positive integer solutions $b,c,d \in \mathbb{N}$ for every integer $a \ge 2$. In this work we present explicit solutions for all integers $a \ge 2$. We begin with the simplest known cases where $a \equiv i \pmod{5}$ for $i \in \{0,2,3,4\}$, providing direct decompositions. The remaining open case, $a \equiv 1…

#European #Cloud Modules
https://berthub.eu/articles/posts/european-cloud-modules/…

Deployment of Containerized Simulations in an API-Driven Distributed Infrastructure
Tim Kraus, Axel Sauer, Ingo Feldner
https://arxiv.org/abs/2506.10642 ht…

Deployment of Containerized Simulations in an API-Driven Distributed Infrastructure
The increasingly dynamic market for embedded systems makes virtual prototypes an indispensable tool for hardware/software codesign. The broad acceptance of the methodology has led to a diverse range of solutions: from open-source, pure console-based simulators to highly capable commercial simulation tools. In this work we present SUNRISE, an infrastructure to provide users a unified approach to utilizing virtual prototyping solutions, facilitate access to various simulation technologies and boo…

From David Suzuki
We need real solutions for affordability, energy security and responding to the threats from the United States.
Canada’s electricity demands are set to triple in the coming decades. We have an opportunity to build shovel-ready, made-in-Canada projects by upgrading Canada’s power grid with renewable power, not fossil fuels.
Did you know Canada’s provincial electricity grids are more connected to the United States than with each other?
1/n

Parallelized computation of quasi-periodic solutions for finite element problems: A Fourier series expansion-based shooting method
Junqing Wu, Ling Hong, Mingwu Li, Jun Jiang
https://arxiv.org/abs/2508.06302

Parallelized computation of quasi-periodic solutions for finite element problems: A Fourier series expansion-based shooting method
High-dimensional nonlinear mechanical systems admit quasi-periodic solutions that are essential for the understanding of the dynamical systems. These quasi-periodic solutions stay on some invariant tori governed by complex PDEs in hyper-time. Here, we propose a Fourier series expansion-based shooting method (FSE-Shooting) for the parallelized computation of quasi-periodic solution with $d$ base frequencies ($d \ge 2$). We represent the associated $d$-torus as a collection of trajectories initia…

Orbits and Masses for 156 Companions from Combined Astrometry and Radial Velocities, and A Validation of Gaia Non-Single Star Solutions
Qier An, Timothy D. Brandt, G. Mirek Brandt, Alexander Venner
https://arxiv.org/abs/2508.08374

Orbits and Masses for 156 Companions from Combined Astrometry and Radial Velocities, and A Validation of Gaia Non-Single Star Solutions
We combine absolute astrometry from Hipparcos and Gaia with archival radial velocities from the Keck/HIRES and ESO/HARPS spectrographs, as well as relative astrometry (when available), to derive masses and orbits for 156 companions around main-sequence stars, including 111 stellar companions, 12 brown dwarfs, and 33 planets. Although this sample is not compiled for occurrence-rate statistics due to systematic biases in non-uniform target selection and varied observing strategies, we nonetheless…

Regularity of Solutions of Mean-Field $G$-SDEs
Karl-Wilhelm Georg Bollweg, Thilo Meyer-Brandis
https://arxiv.org/abs/2508.07867 https://arxiv.org/pdf/2508.…

Regularity of Solutions of Mean-Field $G$-SDEs
We study regularity properties of the unique solution of a mean-field $G$-SDE. More precisely, we consider a mean-field $G$-SDE with square-integrable random initial condition and establish its first and second order Fréchet differentiability in the random initial condition and specify the $G$-SDEs of the respective Fréchet derivatives.

Conservation laws, a new class of group invariant solutions, and its applications for the Whitham Broer Kaup model
Sougata Mandal, Sukhendu Ghosh
https://arxiv.org/abs/2508.06369

Conservation laws, a new class of group invariant solutions, and its applications for the Whitham Broer Kaup model
The Whitham Broer Kaup (WBK) equations provide a fundamental framework for modeling shallow water wave dynamics, effectively capturing both nonlinear and dispersive effects. In this study, we construct a new class of analytical and numerical solutions for the WBK system using Lie symmetry analysis. By determining an optimal system of one-dimensional subalgebras, we obtain symmetry reductions that lead to new kinds of exact wave solutions expressed in hyperbolic, trigonometric, and rational form…

Enhancing Decision Space Diversity in Multi-Objective Evolutionary Optimization for the Diet Problem
Gustavo V. Nascimento, Ivan R. Meneghini, Val\'eria Santos, Eduardo Luz, Gladston Moreira
https://arxiv.org/abs/2508.07077

Enhancing Decision Space Diversity in Multi-Objective Evolutionary Optimization for the Diet Problem
Multi-objective evolutionary algorithms (MOEAs) are essential for solving complex optimization problems, such as the diet problem, where balancing conflicting objectives, like cost and nutritional content, is crucial. However, most MOEAs focus on optimizing solutions in the objective space, often neglecting the diversity of solutions in the decision space, which is critical for providing decision-makers with a wide range of choices. This paper introduces an approach that directly integrates a H…

To ChatGPT: Write a pitch against the use of visual-to-auditory sensory substitution for the blind. https://chatgpt.com/share/684c2ab3-2c68-8004-bf53-c3b401c10064 "Let's stop romanticizing sensory substitution and start prioritizing solutions that actu…

Phone Flooding Protest

PIPES: A Meta-dataset of Machine Learning Pipelines
Cynthia Moreira Maia, Lucas B. V. de Amorim, George D. C. Cavalcanti, Rafael M. O. Cruz
https://arxiv.org/abs/2509.09512 http…

PIPES: A Meta-dataset of Machine Learning Pipelines
Solutions to the Algorithm Selection Problem (ASP) in machine learning face the challenge of high computational costs associated with evaluating various algorithms' performances on a given dataset. To mitigate this cost, the meta-learning field can leverage previously executed experiments shared in online repositories such as OpenML. OpenML provides an extensive collection of machine learning experiments. However, an analysis of OpenML's records reveals limitations. It lacks diversity in pipeli…

Homotopy Iterators
Paul Breiding, Taylor Brysiewicz, Hannah Friedman
https://arxiv.org/abs/2509.08084 https://arxiv.org/pdf/2509.08084

Homotopy Iterators
We introduce the concept of homotopy iterators for performing polynomial homotopy continuation tasks in a memory efficient manner. The main idea is to push forward an iterator for the start solutions of a homotopy via the function which tracks them along the homotopy. Doing so produces a representation of the target solutions, bypassing the need to hold all solutions in memory. We discuss several applications of this datatype ranging from solution counting to data compression.

A Structured Review of Underwater Object Detection Challenges and Solutions: From Traditional to Large Vision Language Models
Edwine Nabahirwa, Wei Song, Minghua Zhang, Yi Fang, Zhou Ni
https://arxiv.org/abs/2509.08490

A Structured Review of Underwater Object Detection Challenges and Solutions: From Traditional to Large Vision Language Models
Underwater object detection (UOD) is vital to diverse marine applications, including oceanographic research, underwater robotics, and marine conservation. However, UOD faces numerous challenges that compromise its performance. Over the years, various methods have been proposed to address these issues, but they often fail to fully capture the complexities of underwater environments. This review systematically categorizes UOD challenges into five key areas: Image quality degradation, target-relat…

I share this irk. Telling folks “climate change already has all the solutions it needs” discourages solvers from working on climate! Clearly climate change is a problem that is not yet resolved, therefore we don’t actually have all the solutions we need. https://mastodon.social/@JeffC1956/114

Enabling Regulatory Multi-Agent Collaboration: Architecture, Challenges, and Solutions
Qinnan Hu, Yuntao Wang, Yuan Gao, Zhou Su, Linkang Du
https://arxiv.org/abs/2509.09215 htt…

Enabling Regulatory Multi-Agent Collaboration: Architecture, Challenges, and Solutions
Large language models (LLMs)-empowered autonomous agents are transforming both digital and physical environments by enabling adaptive, multi-agent collaboration. While these agents offer significant opportunities across domains such as finance, healthcare, and smart manufacturing, their unpredictable behaviors and heterogeneous capabilities pose substantial governance and accountability challenges. In this paper, we propose a blockchain-enabled layered architecture for regulatory agent collabor…

Simulation of Charge Stability Diagrams for Automated Tuning Solutions (SimCATS)
Fabian Hader, Sarah Fleitmann, Jan Vogelbruch, Lotte Geck, Stefan van Waasen
https://arxiv.org/abs/2508.08032

Simulation of Charge Stability Diagrams for Automated Tuning Solutions (SimCATS)
Quantum dots must be tuned precisely to provide a suitable basis for quantum computation. A scalable platform for quantum computing can only be achieved by fully automating the tuning process. One crucial step is to trap the appropriate number of electrons in the quantum dots, typically accomplished by analyzing charge stability diagrams (CSDs). Training and testing automation algorithms require large amounts of data, which can be either measured and manually labeled in an experiment or simulat…

Whereas the fans would call it the affluence of open source I see a shitload of Linux distros that are either solutions looking for a problem or totally irrelevant. Very often both.

On the Convergence of Solutions for the Ginzburg-Landau Equation and System
Rejeb Hadiji, Jongmin Han
https://arxiv.org/abs/2509.09231 https://arxiv.org/pd…

On the Convergence of Solutions for the Ginzburg-Landau Equation and System
Let $(u_\varepsilon)$ be a family of solutions of the Ginzburg--Landau equation with boundary condition $u_\varepsilon = g$ on $\partial Ω$ and of degree $0$. Let $u_0$ denote the harmonic map satisfying $u_0 = g$ on $\partial Ω$. We show that, if there exists a constant $C_1 > 0$ such that for $\varepsilon$ sufficiently small we have $\frac{1}{2} \int_Ω|\nabla u_\ve|^2 dx \leq C_1 \leq \frac{1}{2} \int_Ω|\nabla u_0|^2 dx,$ then $C_1 = \frac{1}{2} \int_Ω|\nabla u_0…

US Health and Human Services centralized medical database – Uh oh
 
This week the Health and Human Services (HHS) agency and the Centers for Medicare and Medicaid Services (CMS) are announcing an initiative to create a centralized database of individual’s health information. The stated rationale for this effort is to improve access to innovative health solutions and improve user access and security. A part of this initiative will include updates to the HIPAA regulations. The effort…

How Well Can Reasoning Models Identify and Recover from Unhelpful Thoughts?
Sohee Yang, Sang-Woo Lee, Nora Kassner, Daniela Gottesman, Sebastian Riedel, Mor Geva
https://arxiv.org/abs/2506.10979

How Well Can Reasoning Models Identify and Recover from Unhelpful Thoughts?
Recent reasoning models show the ability to reflect, backtrack, and self-validate their reasoning, which is crucial in spotting mistakes and arriving at accurate solutions. A natural question that arises is how effectively models can perform such self-reevaluation. We tackle this question by investigating how well reasoning models identify and recover from four types of unhelpful thoughts: uninformative rambling thoughts, thoughts irrelevant to the question, thoughts misdirecting the question a…

Epsilon-Minimax Solutions of Statistical Decision Problems
Andr\'es Aradillas Fern\'andez, Jos\'e Blanchet, Jos\'e Luis Montiel Olea, Chen Qiu, J\"org Stoye, Lezhi Tan
https://arxiv.org/abs/2509.08107

Epsilon-Minimax Solutions of Statistical Decision Problems
A decision rule is epsilon-minimax if it is minimax up to an additive factor epsilon. We present an algorithm for provably obtaining epsilon-minimax solutions of statistical decision problems. We are interested in problems where the statistician chooses randomly among I decision rules. The minimax solution of these problems admits a convex programming representation over the (I-1)-simplex. Our suggested algorithm is a well-known mirror subgradient descent routine, designed to approximately solv…

Cross-Domain Evaluation of Transformer-Based Vulnerability Detection on Open & Industry Data
Moritz Mock, Thomas Forrer, Barbara Russo
https://arxiv.org/abs/2509.09313 https…

Cross-Domain Evaluation of Transformer-Based Vulnerability Detection on Open & Industry Data
Deep learning solutions for vulnerability detection proposed in academic research are not always accessible to developers, and their applicability in industrial settings is rarely addressed. Transferring such technologies from academia to industry presents challenges related to trustworthiness, legacy systems, limited digital literacy, and the gap between academic and industrial expertise. For deep learning in particular, performance and integration into existing workflows are additional concer…

On-the-Fly Machine Learning of Interatomic Potentials for Elastic Property Modeling in Al-Mg-Zr Solid Solutions
Lukas Volkmer, Leonardo Medrano Sandonas, Philip Grimm, Julia Kristin Hufenbach, Gianaurelio Cuniberti
https://arxiv.org/abs/2508.06311

On-the-Fly Machine Learning of Interatomic Potentials for Elastic Property Modeling in Al-Mg-Zr Solid Solutions
The development of resilient and lightweight Aluminum alloys is central to advancing structural materials for energy-efficient engineering applications. To address this challenge, in this study, we explore the elastic properties of Al-Mg-Zr solid solutions by integrating advanced machine learning (ML) techniques with quantum-mechanical (QM) atomistic simulations. For this purpose, we develop accurate and transferable machine-learned interatomic potentials (MLIPs) using two complementary approac…

Poly-liquid behaviors of self-associating fluids and mesoscopic aggregation in liquid solutions
Ilya Davydov, Vassiliy Lubchenko
https://arxiv.org/abs/2509.08123 https://…

Poly-liquid behaviors of self-associating fluids and mesoscopic aggregation in liquid solutions
In conflict with standard notions of thermodynamics, mesoscopically-sized inclusions (``clusters'') of a solute-rich liquid have been observed in equilibrated solutions of proteins and other molecules. According to a complexation scenario proposed earlier, a steady-state ensemble of finite-sized droplets of a metastable solute-rich liquid can emerge in a solution, if the solute molecules can form transient complexes with each other and/or solute. Here we solve for the thermodynamics of an expli…

Bridging the Gap in Phishing Detection: A Comprehensive Phishing Dataset Collector
Aditya Kulkarni, Shahil Manishbhai Patel, Shivam Pradip Tirmare, Vivek Balachandran, Tamal Das
https://arxiv.org/abs/2509.09592

Bridging the Gap in Phishing Detection: A Comprehensive Phishing Dataset Collector
To combat phishing attacks -- aimed at luring web users to divulge their sensitive information -- various phishing detection approaches have been proposed. As attackers focus on devising new tactics to bypass existing detection solutions, researchers have adapted by integrating machine learning and deep learning into phishing detection. Phishing dataset collection is vital to developing effective phishing detection approaches, which highly depend on the diversity of the gathered datasets. The l…

IDEA: Augmenting Design Intelligence through Design Space Exploration
Chuer Chen, Xiaoke Yan, Xiaoyu Qi, Nan Cao
https://arxiv.org/abs/2506.10587 https://

IDEA: Augmenting Design Intelligence through Design Space Exploration
Design spaces serve as a conceptual framework that enables designers to explore feasible solutions through the selection and combination of design elements. However, effective decision-making remains heavily dependent on the designer's experience, and the absence of mathematical formalization prevents computational support for automated design processes. To bridge this gap, we introduce a structured representation that models design spaces with orthogonal dimensions and discrete selectable elem…

A Score-based Diffusion Model Approach for Adaptive Learning of Stochastic Partial Differential Equation Solutions
Toan Huynh, Ruth Lopez Fajardo, Guannan Zhang, Lili Ju, Feng Bao
https://arxiv.org/abs/2508.06834

A Score-based Diffusion Model Approach for Adaptive Learning of Stochastic Partial Differential Equation Solutions
We propose a novel framework for adaptively learning the time-evolving solutions of stochastic partial differential equations (SPDEs) using score-based diffusion models within a recursive Bayesian inference setting. SPDEs play a central role in modeling complex physical systems under uncertainty, but their numerical solutions often suffer from model errors and reduced accuracy due to incomplete physical knowledge and environmental variability. To address these challenges, we encode the governin…

Neural quantum states for emitter dynamics in waveguide QED
Tatiana Vovk, Anka Van de Walle, Hannes Pichler, Annabelle Bohrdt
https://arxiv.org/abs/2508.08964 https://

Neural quantum states for emitter dynamics in waveguide QED
Quantum emitters coupled to one-dimensional waveguides constitute a paradigmatic quantum-optical platform for exploring collective phenomena in open quantum many-body systems. For appropriately spaced emitters, they realize the Dicke model, whose characteristic permutation symmetry allows for efficient exact solutions featuring superradiance. When the emitters are arbitrarily spaced, however, this symmetry is lost and general analytical solutions are no longer available. In this work, we introd…

Ukraine, EU launch $117 million military innovation partnership: https://benborges.xyz/2025/07/11/ukraine-eu-launch-million-military.html

Global Solutions to the Discrete Nonlinear Breakage Equations without Mass Transfer
Mashkoor Ali (LAMA), Philippe Lauren\c{c}ot (LAMA)
https://arxiv.org/abs/2507.06685

Global Solutions to the Discrete Nonlinear Breakage Equations without Mass Transfer
Global existence of mild solutions to the discrete collisional breakage equations is established for a broad class of collision kernels, without imposing any growth assumptions. In addition, classical solutions are constructed, and uniqueness is proved for an appropriate class of kinetic coefficients and initial data. The large time behavior of solutions is also discussed, and numerical simulations are presented to support the theoretical results.

Special restricted partition functions for the stable sheaf cohomology on flag varieties
Mircea Cimpoeas
https://arxiv.org/abs/2509.09418 https://arxiv.org…

Special restricted partition functions for the stable sheaf cohomology on flag varieties
Let $\mathbf a:=(a_1,\ldots,a_r)$ be a sequence of positive integers, $d\geq 2$ and $j\geq 1$, some integers. We study the functions $p_{\mathbf a,d}(n):=$ the number of integer solutions $(x_1,\dots,x_r)$ of $\sum_{i=1}^r a_ix_i=n$, with $x_i\geq 0$ and $x_i \equiv 0,1(\bmod\;d)$, for all $1\leq i\leq r$, and $p_{\mathbf a,d}(n;j):=$ the number of $(x_1,\ldots,x_r)$ as above which satisfy also the condition $\sum_{i=1}^r \left(x_i-(d-2)\left\lfloor \frac{x_i}{d} \right\rfloor\right) =j$. We …

People CEO Neil Vogel calls Google a "bad actor" for refusing to pay publishers for AI content and says Google Search drives 25%-30% of visits to People sites (Jeff John Roberts/Fortune)
https://fortune.com/2025/09/11/media-in…

Google’s AI is the ‘worst’ for stealing content, says People CEO
But Google-owned YouTube could provide a model for media and AI to coexist and thrive, says internet industry pioneer Bill Gross.

Two types of boson stars in $U(1)$ gauged $3 1$-dimensional $O(3)$ sigma-model
Jutta Kunz, Aliaksei Mikhaliuk, Yakov Shnir
https://arxiv.org/abs/2508.07425 https://

Two types of boson stars in $U(1)$ gauged $3+1$-dimensional $O(3)$ sigma-model
We investigate boson stars in an $O(3)$ scalar field theory with a symmetry-breaking potential. By constructing numerically spherically symmetric solutions, we demonstrate that the model gives rise to a rich set of field configurations. The negative coupling constant of the scalar self-interactions allows for two types of boson stars: Type I solutions represent the usual boson stars, that emerge from the vacuum as the boson frequency is decreased below the boson mass, whereas type II boson star…

Neglected solutions in quadratic gravity
Breno L. Giacchini, Ivan Kol\'a\v{r}
https://arxiv.org/abs/2509.07317 https://arxiv.org/pdf/2509.07317

Neglected solutions in quadratic gravity
We report on several previously overlooked families of static spherically symmetric solutions in quadratic gravity. Our main result concerns the existence of solutions whose leading exponents depend on the ratio ${ω=α/(3β)}$ of the four-derivative couplings. We demonstrate that the space of models with ${ω>1}$ contains a dense set that admits non-Frobenius solutions ${(s_*, 2 - 3 s_*)_0}$ (in standard Schwarzschild coordinates), with certain rational numbers $s_*(ω)$. These solutions corre…

An Efficient Application of Goal Programming to Tackle Multiobjective Problems with Recurring Fitness Landscapes
Rodrigo Lankaites Pinheiro, Dario Landa-Silva, Wasakorn Laesanklang, Ademir Aparecido Constantino
https://arxiv.org/abs/2508.08297

An Efficient Application of Goal Programming to Tackle Multiobjective Problems with Recurring Fitness Landscapes
Many real-world applications require decision-makers to assess the quality of solutions while considering multiple conflicting objectives. Obtaining good approximation sets for highly constrained many-objective problems is often a difficult task even for modern multiobjective algorithms. In some cases, multiple instances of the problem scenario present similarities in their fitness landscapes. That is, there are recurring features in the fitness landscapes when searching for solutions to differ…

Nondegeneracy of positive solutions for critical Hartree equation on Heisenberg group and it's applications
Minbo Yang, Shuijin Zhang
https://arxiv.org/abs/2508.07719 https:…

Nondegeneracy of positive solutions for critical Hartree equation on Heisenberg group and it's applications
We study the uniqueness and nondegeneracy of positive bubble solutions for the generalized energy-critical Hartree equation on the Heisenberg group $\mathbb{H}^{n}$, \begin{equation}\label{0.1} -Δ_{\mathbb{H}}u=\left(\int_{\mathbb{H}^{n}}\frac{|u(η)|^{Q^{\ast}_μ}}{|η^{-1}ξ|^μ}\mathrm{d}η\right)|u|^{Q^{\ast}_μ-2}u,~~~ξ,η\in\mathbb{H}^{n}, \end{equation} where $Δ_{\mathbb{H}}$ represents the Kohn Laplacian, $u(η)$ is a real-valued function, $Q=2n+2$ is …

Uniqueness of $S_2$-isotropic solutions to the isotropic $L_p$ Minkowski problem
Yao Wan
https://arxiv.org/abs/2509.08588 https://arxiv.org/pdf/2509.08588

Uniqueness of $S_2$-isotropic solutions to the isotropic $L_p$ Minkowski problem
This paper investigates the spectral properties of the Hilbert-Brunn-Minkowski operator $L_K$ to derive stability estimates for geometric inequalities, including the local Brunn-Minkowski inequality. By analyzing the eigenvalues of $L_K$, we establish the uniqueness of $S_2$-isotropic solutions to the isotropic $L_p$ Minkowski problem in $\mathbb{R}^{n}$ for $\frac{1-3n^2}{2n}\leq p<-n$ with $λ_2(-L_K)\geq \frac{n-1}{2n-1+p}$. Furthermore, we extend this uniqueness result to the range $-2n-1 \…

RedDino: A foundation model for red blood cell analysis
Luca Zedda, Andrea Loddo, Cecilia Di Ruberto, Carsten Marr
https://arxiv.org/abs/2508.08180 https://

RedDino: A foundation model for red blood cell analysis
Red blood cells (RBCs) are essential to human health, and their precise morphological analysis is important for diagnosing hematological disorders. Despite the promise of foundation models in medical diagnostics, comprehensive AI solutions for RBC analysis remain scarce. We present RedDino, a self-supervised foundation model designed for RBC image analysis. RedDino uses an RBC-specific adaptation of the DINOv2 self-supervised learning framework and is trained on a curated dataset of 1.25 millio…

Symmetry and monotonicity of singular solutions for the Hartree equation
Ying Cai, Guangze Gu, Aleks Jevnikar
https://arxiv.org/abs/2508.07893 https://arxi…

Symmetry and monotonicity of singular solutions for the Hartree equation
In this paper we are concerned with positive singular solutions of the following nonlocal Hartree equation $$-Δu\!=\Big( \int_{\mathbb{R}^N\setminus Γ}\frac{F(u(y))}{|x-y|^μ}dy \Big)f (u(x)), \quad x\in \mathbb{R}^N\setminusΓ,$$ where $F$ is the primitive of $f$ and $Γ$ is the singular set. Under suitable assumptions, we prove that $u$ is symmetric and monotone with respect to the singular set by using moving plane methods. Furthermore, we complement this study by showing the exi…

Constructing a Question-Answering Simulator through the Distillation of LLMs
Haipeng Liu, Ting Long, Jing Fu
https://arxiv.org/abs/2509.09226 https://arxiv…

Constructing a Question-Answering Simulator through the Distillation of LLMs
The question-answering (QA) simulator is a model that mimics real student learning behaviors and predicts their correctness of their responses to questions. QA simulators enable educational recommender systems (ERS) to collect large amounts of training data without interacting with real students, thereby preventing harmful recommendations made by an undertrained ERS from undermining actual student learning. Given the QA history, there are two categories of solutions to predict the correctness, …

Link Prediction for Event Logs in the Process Industry
Anastasia Zhukova, Thomas Walton, Christian E. Matt, Bela Gipp
https://arxiv.org/abs/2508.09096 https://

Link Prediction for Event Logs in the Process Industry
Knowledge management (KM) is vital in the process industry for optimizing operations, ensuring safety, and enabling continuous improvement through effective use of operational data and past insights. A key challenge in this domain is the fragmented nature of event logs in shift books, where related records, e.g., entries documenting issues related to equipment or processes and the corresponding solutions, may remain disconnected. This fragmentation hinders the recommendation of previous solutio…

Interior instability of naked singularities of a scalar field
Junbin Li
https://arxiv.org/abs/2508.07655 https://arxiv.org/pdf/2508.07655

Interior instability of naked singularities of a scalar field
We show that the $k$-self-similar naked singularity solutions of the spherically symmetric Einstein--Scalar field system are unstable to black hole formation under perturbations that are totally supported in the interior region, in all regularities strictly below the threshold. The instability below the threshold is also established for exterior perturbations. We also show that general naked singularity solutions are unstable under interior BV perturbations, which provides a new insight into un…

Forecast-Driven MPC for Decentralized Multi-Robot Collision Avoidance
Hadush Hailu, Bruk Gebregziabher, Prudhvi Raj
https://arxiv.org/abs/2508.08264 https://

Forecast-Driven MPC for Decentralized Multi-Robot Collision Avoidance
The Iterative Forecast Planner (IFP) is a geometric planning approach that offers lightweight computations, scal- able, and reactive solutions for multi-robot path planning in decentralized, communication-free settings. However, it struggles in symmetric configurations, where mirrored interactions often lead to collisions and deadlocks. We introduce eIFP-MPC, an optimized and extended version of IFP that improves robustness and path consistency in dense, dynamic environments. The method refines…

The problem of infinite Spin for parabolic and collision solutions in the planar $n$-body problem
Zhe Wang, Guowei Yu
https://arxiv.org/abs/2507.05801 http…

The problem of infinite Spin for parabolic and collision solutions in the planar $n$-body problem
In the planar $n$-body problem, the problem of infinite spin occurs for both parabolic and collision solutions. Recently Moeckel and Montgomery \cite{MM25} showed that there is no infinite spin for total collision solutions. Following their approach, we show it can not happen for both complete and partially parabolic solutions. Our approach also allows us to generalize Moeckel and Montgomery's result to partial collision solutions.

There is a well known bug with Wayland & SDDM on FreeBSD KDE: Ctrl C by keypress abruptly throws you out of your Wayland session. Two things to add to that:
First: KDE and FreeBSD devs are actively looking for FreeBSD help in this, bcs the regular systemd type of logs are obviously not available here for bug tracing. If you can help, please do!
Second: Found a great solutions in the FreeBSD forums. It's a bit hidden in the threads so for clarity's sake:
I disab…

😮‍💨 Carbon 'offsets' aren't working: Researchers offer a 'roadmap' to improve nature-based climate solutions
https://phys.org/news/2025-07-carbon-offsets-roadmap-nature-based.html

Carbon 'offsets' aren't working: Researchers offer a 'roadmap' to improve nature-based climate solutions
A lot of the climate-altering carbon pollution humans release into the atmosphere by burning fossil fuels gets drawn into the Earth's oceans and landscapes through natural processes, mostly through photosynthesis, as plants turn atmospheric carbon dioxide into biomass.

When AIOps Become "AI Oops": Subverting LLM-driven IT Operations via Telemetry Manipulation
Dario Pasquini, Evgenios M. Kornaropoulos, Giuseppe Ateniese, Omer Akgul, Athanasios Theocharis, Petros Efstathopoulos
https://arxiv.org/abs/2508.06394

When AIOps Become "AI Oops": Subverting LLM-driven IT Operations via Telemetry Manipulation
AI for IT Operations (AIOps) is transforming how organizations manage complex software systems by automating anomaly detection, incident diagnosis, and remediation. Modern AIOps solutions increasingly rely on autonomous LLM-based agents to interpret telemetry data and take corrective actions with minimal human intervention, promising faster response times and operational cost savings. In this work, we perform the first security analysis of AIOps solutions, showing that, once again, AI-driven …

SHIELDA: Structured Handling of Exceptions in LLM-Driven Agentic Workflows
Jingwen Zhou, Jieshan Chen, Qinghua Lu, Dehai Zhao, Liming Zhu
https://arxiv.org/abs/2508.07935 https:…

SHIELDA: Structured Handling of Exceptions in LLM-Driven Agentic Workflows
Large Language Model (LLM) agentic systems are software systems powered by LLMs that autonomously reason, plan, and execute multi-step workflows to achieve human goals, rather than merely executing predefined steps. During execution, these workflows frequently encounter exceptions. Existing exception handling solutions often treat exceptions superficially, failing to trace execution-phase exceptions to their reasoning-phase root causes. Furthermore, their recovery logic is brittle, lacking stru…

The Generalized Fermat Equation $x^2 y^3 = z^{25}$
Nuno Freitas, Michael Stoll
https://arxiv.org/abs/2506.10667 https://arxiv.org/p…

The Generalized Fermat Equation $x^2 + y^3 = z^{25}$
We consider the generalized Fermat equation (*) $x^2 + y^3 = z^{25}$. Using the known parameterization of the primitive integral solutions to $x^2 + y^3 = z^5$ (due to Edwards), we reduce the solution of (*) to the solution of five specific equations of the form $H(u,v) = w^5$, where $H$ is homogeneous of degree $10$ with coefficients in a sextic number field $K$, $u$ and $v$ are coprime (rational) integers, and $w \in K$.

Challenges in Mixed Reality in Assisting Adults with ADHD Symptoms
Valerie Tan, Jens Gerken
https://arxiv.org/abs/2508.07854 https://arxiv.org/pdf/2508.078…

Challenges in Mixed Reality in Assisting Adults with ADHD Symptoms
In this position paper, we discuss symptoms of attention deficit hyperactivity disorder (ADHD) in adults, as well as available forms of treatment or assistance in the context of mixed reality. Mixed reality offers many potentials for assisting adults with symptoms commonly found in (but not limited to) ADHD, but the availability of mixed reality solutions is not only limited commercially, but also limited in terms of proof-of-concept prototypes. We discuss two major challenges with attention as…

Stability and asymptotic behaviour of one-dimensional solutions in cylinders
Francesca De Marchis, Lisa Mazzuoli, Filomena Pacella
https://arxiv.org/abs/2509.09648 https://

Stability and asymptotic behaviour of one-dimensional solutions in cylinders
We consider positive one-dimensional solutions of a Lane-Emden relative Dirichlet problem in a cylinder and study their stability/instability properties as the energy varies with respect to domain perturbations. This depends on the exponent $p >1$ of the nonlinearity and we obtain results for $p$ close to 1 and for $p$ large. This is achieved by a careful asymptotic analysis of the one-dimensional solution as $p \to 1$ or $p \to \infty$, which is of independent interest. It allows to detect the…

3-dimensional charged black holes in $f({Q})$ gravity
G. G. L. Nashed, Emmanuel N. Saridakis
https://arxiv.org/abs/2506.10046 https://

3-dimensional charged black holes in $f({Q})$ gravity
We present new exact charged black hole solutions in (2+1) dimensions within the framework of $f({Q})$ gravity, where ${Q}$ denotes the non-metricity scalar. By considering a cubic $f({Q})$ form we derive classes of charged and uncharged spherically symmetric solutions, and we identify conditions under which these reduce to the well-known Banados-Teitelboim-Zanelli (BTZ) black hole. Notably, our analysis reveals a novel charged solution that is asymptotically Anti-de Sitter (AdS) but cannot be …

Weak solutions and incompressible limit of a quasi-incompressible Navier--Stokes/Cahn--Hilliard model for viscous two-phase flows
Mingwen Fei, Xiang Fei, Daozhi Han, Yadong Liu
https://arxiv.org/abs/2508.08090

Weak solutions and incompressible limit of a quasi-incompressible Navier--Stokes/Cahn--Hilliard model for viscous two-phase flows
We study a quasi-incompressible Navier--Stokes/Cahn--Hilliard coupled system which describes the motion of two macroscopically immiscible incompressible viscous fluids with partial mixing in a small interfacial region and long-range interactions. The case of unmatched densities with mass-averaged velocity is considered so that the velocity field is no longer divergence-free, and the pressure enters the equation of the chemical potential. We first prove the existence of global weak solutions to …

"A 6 or a 9?": Ensemble Learning Through the Multiplicity of Performant Models and Explanations
Gianlucca Zuin, Adriano Veloso
https://arxiv.org/abs/2509.09073 https:/…

"A 6 or a 9?": Ensemble Learning Through the Multiplicity of Performant Models and Explanations
Creating models from past observations and ensuring their effectiveness on new data is the essence of machine learning. However, selecting models that generalize well remains a challenging task. Related to this topic, the Rashomon Effect refers to cases where multiple models perform similarly well for a given learning problem. This often occurs in real-world scenarios, like the manufacturing process or medical diagnosis, where diverse patterns in data lead to multiple high-performing solutions.…

Exact WKB of solutions by Borel summation and open TBA
Qianyu Hao
https://arxiv.org/abs/2507.06922 https://arxiv.org/pdf/2507.06922…

Exact WKB of solutions by Borel summation and open TBA
In this paper, we study the exact WKB methods for solutions of the Schrödinger equations corresponding to quantum Seiberg-Witten curves in 4d $\mathcal{N}=2$ theories with surface defects. The tools are Borel summation and Gaiotto-Moore-Neitzke (GMN) open TBA, which is a conjecture that has largely stayed unexplored so far. We study the Borel plane of the solution regularized by a BPS soliton charge and find that its poles on the Borel plane have the physical meaning of BPS soliton central cha…

Innovative Adaptive Imaged Based Visual Servoing Control of 6 DoFs Industrial Robot Manipulators
Rongfei Li, Francis Assadian
https://arxiv.org/abs/2506.10240

Innovative Adaptive Imaged Based Visual Servoing Control of 6 DoFs Industrial Robot Manipulators
Image-based visual servoing (IBVS) methods have been well developed and used in many applications, especially in pose (position and orientation) alignment. However, most research papers focused on developing control solutions when 3D point features can be detected inside the field of view. This work proposes an innovative feedforward-feedback adaptive control algorithm structure with the Youla Parameterization method. A designed feature estimation loop ensures stable and fast motion control whe…

Quantum Annealing for the Set Splitting Problem
Sean Borneman
https://arxiv.org/abs/2508.06410 https://arxiv.org/pdf/2508.06410

Quantum Annealing for the Set Splitting Problem
I present a novel use of quantum annealing to solve the Set Splitting Problem using (QUBO) problem formulation. The contribution of the work is in formulating penalty functions that ensure the ground state of the QUBO Hamiltonian corresponds to valid solutions that split the input subsets. This approach scales linearly in terms of the number of logical qubits relative to problem size. Empirical tests of the proposed solution show convergence to globally optimal solutions, with high accuracy rat…

Normalized solutions for a Sobolev critical quasilinear Schr\"odinger equation
Yuxin Li, Meijie Yang, Xiaojun Chang
https://arxiv.org/abs/2506.10870 h…

Normalized solutions for a Sobolev critical quasilinear Schrödinger equation
In this paper, we study the existence of normalized solutions for the following quasilinear Schrödinger equation with critical exponent: \begin{equation*} -Δu-uΔ(u^2)+λu=τ|u|^{q-2}u+|u|^{2\cdot2^*-2}u,~~~~x\in\R^N, \end{equation*} under the mass constraint $\int_{\R^N}|u|^2dx=c$ for some prescribed $c>0$. Here $τ\in \mathbb{R}$ is a parameter, $λ\in\R$ appears as a Lagrange multiplier, $N\ge3$, $2^*:=\frac{2N}{N-2}$ and $2

Jupiter: Enhancing LLM Data Analysis Capabilities via Notebook and Inference-Time Value-Guided Search
Shuocheng Li, Yihao Liu, Silin Du, Wenxuan Zeng, Zhe Xu, Mengyu Zhou, Yeye He, Haoyu Dong, Shi Han, Dongmei Zhang
https://arxiv.org/abs/2509.09245

Jupiter: Enhancing LLM Data Analysis Capabilities via Notebook and Inference-Time Value-Guided Search
Large language models (LLMs) have shown great promise in automating data science workflows, but existing models still struggle with multi-step reasoning and tool use, which limits their effectiveness on complex data analysis tasks. To address this, we propose a scalable pipeline that extracts high-quality, tool-based data analysis tasks and their executable multi-step solutions from real-world Jupyter notebooks and associated data files. Using this pipeline, we introduce NbQA, a large-scale dat…

New Homogeneous Solutions for the One-Phase Free Boundary Problem
Coleman Hines, James Kolesar, Peter McGrath
https://arxiv.org/abs/2509.09409 https://arxi…

New Homogeneous Solutions for the One-Phase Free Boundary Problem
For each sufficiently large integer $k$, we construct a domain in the round $2$-sphere with $k$ boundary components which is the link of a cone in $\mathbb{R}^3$ admitting a homogeneous solution to the one-phase free boundary problem. This answers a question of Jerison-Kamburov, and also disproves a conjecture of Souam left open in earlier work. The method exploits a new connection with minimal surfaces, which we also use to construct an infinite family of homogeneous solutions in dimension fou…

General relativistic solutions with finite self-energy for a point charge under Bopp-Podolsky electromagnetism
Erik Amorim
https://arxiv.org/abs/2508.06270 https://

General relativistic solutions with finite self-energy for a point charge under Bopp-Podolsky electromagnetism
We establish the existence of a family of static, spherically symmetric spacetimes that are solutions of the Einstein Field Equations of General Relativity coupled to the electric field of a static point charge obeying the equations of electromagnetism of Maxwell-Bopp-Landé-Thomas-Podolsky. The point charge is modeled as a naked singularity with non-positive bare mass. The singularity at the location of the charge is milder than that of the Reissner-Weyl-Nordström solution to the conventional…

Error-Resilient Fast Entangling Gates for Scalable Ion-Trap Quantum Processors
Isabelle Savill-Brown, Zain Mehdi, Alexander K. Ratcliffe, Varun D. Vaidya, Haonan Liu, Simon A. Haine, C. Ricardo Viteri, Joseph J. Hope
https://arxiv.org/abs/2508.07593

Error-Resilient Fast Entangling Gates for Scalable Ion-Trap Quantum Processors
Non-adiabatic two-qubit gate proposals for trapped-ion systems offer superior performance and flexibility over adiabatic schemes at the cost of increased laser control requirements. Existing fast gate schemes are limited by single-qubit transition errors, which constrain the total number of pulses in high-fidelity solutions. We introduce an improved gate search scheme that enables both local and non-local two-qubit gates in chains containing tens of ions. These protocols use a multi-objective m…

HyPINO: Multi-Physics Neural Operators via HyperPINNs and the Method of Manufactured Solutions
Rafael Bischof, Michal Piovar\v{c}i, Michael A. Kraus, Siddhartha Mishra, Bernd Bickel
https://arxiv.org/abs/2509.05117

HyPINO: Multi-Physics Neural Operators via HyperPINNs and the Method of Manufactured Solutions
We present HyPINO, a multi-physics neural operator designed for zero-shot generalization across a broad class of parametric PDEs without requiring task-specific fine-tuning. Our approach combines a Swin Transformer-based hypernetwork with mixed supervision: (i) labeled data from analytical solutions generated via the Method of Manufactured Solutions (MMS), and (ii) unlabeled samples optimized using physics-informed objectives. The model maps PDE parametrizations to target Physics-Informed Neura…

Unconditional alignment of solutions to the Fokker-Planck-Navier-Stokes system with locally averaged Brinkman force
Roman Shvydkoy, Trevor Teolis
https://arxiv.org/abs/2508.07415

Unconditional alignment of solutions to the Fokker-Planck-Navier-Stokes system with locally averaged Brinkman force
We study a coupled Fokker-Planck--Navier-Stokes (FPNS) system modeling the dynamics of interacting particles suspended in a viscous incompressible fluid, where the coupling occurs through a locally averaged Brinkman drag force. Our main result is the unconditional alignment and synchronization of particle and fluid velocities for all weak solutions, in any dimension, on the periodic domain. The proof leverages a new entropy method and a hypocoercivity framework, which together yield quantitativ…

Exact Analytical Traversable Wormhole Solutions in Teleparallel $F(T)$ Gravity with the de Rham-Gabadadze-Tolley Massive Graviton Sector
Alexandre Landry, Yassine Sekhmani, Emmanuel N. Saridakis, Sunil K Maurya, Akram Ali
https://arxiv.org/abs/2508.06290

Exact Analytical Traversable Wormhole Solutions in Teleparallel $F(T)$ Gravity with the de Rham-Gabadadze-Tolley Massive Graviton Sector
In this paper, we derive a novel class of exact, static, spherically symmetric traversable wormhole solutions in teleparallel $F(T)$ gravity augmented by the non-linear de Rham-Gabadadze-Tolley (dRGT) graviton mass term. By using the Morris-Thorne ansatz with a generalized redshift function including constant, logarithmic, and power-law profiles, we rigorously integrate the dRGT-modified conservation laws together with the teleparallel field equations to reconstruct both the shape function $b(r…

Monotonicity in half-spaces for singular quasilinear elliptic problems involving the gradient
Phuong Le
https://arxiv.org/abs/2508.08859 https://arxiv.org/…

Monotonicity in half-spaces for singular quasilinear elliptic problems involving the gradient
We study positive solutions to the problem $-Δ_p u + \vartheta |\nabla u|^q = \frac{1}{u^γ} + f(u)$ in $\mathbb{R}^N_+$ with the zero Dirichlet boundary condition, where $p>1$, $γ>0$, $0

Global weak solutions to a doubly degenerate nutrient taxis system on the whole real line
Federico Herrero-Herv\'as
https://arxiv.org/abs/2508.07503 https://

Global weak solutions to a doubly degenerate nutrient taxis system on the whole real line
This work addresses the one-dimensional Cauchy problem for the doubly degenerate nutrient taxis model \begin{equation*} \begin{cases} \displaystyle \frac{\partial u}{\partial t} = \frac{\partial}{\partial x}(u v u_x) - \frac{\partial}{\partial x}(u^2 v v_x) + u v, & x\in \mathbb{R}, ~t>0, \\ \displaystyle \frac{\partial v}{\partial t} = \frac{\partial^2 v}{\partial x^2} - u v, & x\in \mathbb{R}, ~t>0, \\ u(x,0) = u_0(x) \geq 0, \quad v(x,0) = v_0(x)>0, ~ & x\in \mathbb{R}, \end{cases}…

Optimal decay of global strong solutions to nematic liquid crystal flows in the half-space
Haokun Chen, Yong Wang
https://arxiv.org/abs/2506.10255 https://…

Optimal decay of global strong solutions to nematic liquid crystal flows in the half-space
We study asymptotic behaviors of the higher-order spatial derivatives and the first-order time derivatives for the strong solution to nematic liquid crystal flows in the half-space $\mathbb{R}_+^3$. Furthermore, when the initial data lie in an appropriately weighted Sobolev space, we obtain the decay rates that are faster than the heat kernel. The main tools employed in this paper are the $L^p-L^q$ estimates of the Stokes semigroup, the a priori estimates of the steady Stokes system in $\mathbb…

Global solutions in $L^{p}_{v}L^{\infty}_{x}$ for the Boltzmann equation in bounded domains
Dingqun Deng, Jong-in Kim, Donghyun Lee
https://arxiv.org/abs/2508.05985 https://

Global solutions in $L^{p}_{v}L^{\infty}_{x}$ for the Boltzmann equation in bounded domains
The existence theory for solutions to the Boltzmann equation in bounded domains has primarily been developed within uniformly bounded function classes, such as $L^{\infty}_{x,v}$, as in [Duan-Huang-Wang-Yang,2017], [Duan-Wang,2019], [Guo,2010]. In this paper, we investigate solutions in relaxed function spaces $L^{p}_{v}L^\infty_{x}$ for the initial-boundary value problem of the Boltzmann equation in bounded domains. We consider the case of hard potential under diffuse reflection boundary condi…

Quasilinear elliptic equations with singular quadratic growth terms
Lucio Boccardo, Tommaso Leonori, Luigi Orsina, Francesco Petitta
https://arxiv.org/abs/2508.07695 https://

Quasilinear elliptic equations with singular quadratic growth terms
In this paper we deal with positive solutions for singular quasilinear problems whose model is $$ \begin{cases} -Δu + \frac{|\nabla u|^2}{(1-u)^γ}=g & \mbox{in $Ω$,}\newline \hfill u=0 \hfill & \mbox{on $\partialΩ$,} \end{cases} $$ where $Ω$ is a bounded open set of $\mathbb{R}^N$, $g\geq 0 $ is a function in some Lebesgue space, and $γ>0$. We prove both existence and nonexistence of solutions depending on the value of $γ$ and on the size of $g$.

Boundary estimates for singular elliptic problems involving a gradient term
Phuong Le
https://arxiv.org/abs/2508.07360 https://arxiv.org/pdf/2508.07360

Boundary estimates for singular elliptic problems involving a gradient term
We study the behavior of weak solutions to the singular quasilinear elliptic problem $-Δ_p u + \vartheta |\nabla u|^q = \frac{1}{u^γ} + f(u)$, in a bounded domain with the Dirichlet boundary condition, where $p>1$, $γ>0$, $0

Electroconvection in a Magnetic Field
Elie Abdo, Peter Constantin, Mihaela Ignatova, Quyuan Lin
https://arxiv.org/abs/2508.07439 https://arxiv.org/pdf/2508…

Electroconvection in a Magnetic Field
Electroconvection in a porous medium under a strong transversal magnetic field is described by an active scalar equation for the charge density. The equation has global weak solutions with $L^{\infty}$ data. We show that for strong enough magnetic fields, $L^{\infty}$-small solutions are smooth globally in time and they obey surface quasigeostrophic equations in the limit of infinite magnetic field strength.

Stability and bifurcation of Navier-Stokes equations in an annular domain with mixed boundary conditions
Zhibo Hou, Liang Li, Quan Wang
https://arxiv.org/abs/2508.07694 https://…

Stability and bifurcation of Navier-Stokes equations in an annular domain with mixed boundary conditions
We study the existence and stability of non-trivial steady-state solutions to the two-dimensional incompressible Navier-Stokes equations in an annular domain $Ω= B(0,b) \setminus \overline{B(0,a)}$ with radii $b>a>0$.The outer boundary $\partial B(0, b)$ is subject to the free condition, while the inner boundary $\partial B(0, a)$ obeys a Navier-slip condition with effective slip length $α> 0$. Our main results are fourfold. First, we establish global-in-time strong solutions and derive a sha…

A dynamical system approach to the Chandrasekhar-Hamilton-Jacobi equation
Marie-Fran\c{c}oise Bidaut-V\'eron, Laurent V\'eron
https://arxiv.org/abs/2507.07110

A dynamical system approach to the Chandrasekhar-Hamilton-Jacobi equation
We study the local properties of positive solutions of the equation -Delta u= exp(u) in a punctured domain Omega of RN in the range of parameters q > 1 and M > 0. We prove a series of a priori estimates near a singular point. In the case of radial solutions we use various techniques inherited from the dynamical systems theory to obtain the precise behaviour of singular solutions. We prove also the existence of singular solutions with these precise behaviours.

A new critical exponent for semi-linear damped wave equations with the initial data from Sobolev spaces of negative order
Dinh Van Duong, Tuan Anh Dao
https://arxiv.org/abs/2508.07802

A new critical exponent for semi-linear damped wave equations with the initial data from Sobolev spaces of negative order
In this paper, we would like to study critical exponent for semi-linear damped wave equations with power nonlinearity and initial data belonging to Sobolev spaces of negative order $\dot{H}_m^{-γ}$. Precisely, we obtain a new critical exponent $p_c(m,γ) := 1 + \frac{2m}{n+mγ}$ for $m \in (1, 2], \,γ\in \left[0, \frac{n(m-1)}{m} \right)$ by proving global (in time) existence of small data Sobolev solutions when $p \geq p_c(m,γ)$ and blow-up of weak solutions in finite time even for small da…

On local well-posedness for the nonlinear Schr\"odinger equation with general power nonlinearity
Lucia Arens, Marius Gritl
https://arxiv.org/abs/2506.10595

On local well-posedness for the nonlinear Schrödinger equation with general power nonlinearity
The nonlinear Schrödinger equation plays a fundamental role in mathematical physics, particularly in the study of quantum mechanics and Bose-Einstein condensation. This paper explores two distinct approaches to establishing the local well-posedness of solutions: the semigroup theory ansatz and the Strichartz estimates ansatz. Semigroup theory provides a general and elegant framework rooted in functional analysis, allowing for the interpretation of the time evolution of solutions as operator se…

Pathological solutions of Navier-Stokes equations on $\mathbb{T}^2$ with gradients in Hardy spaces
Jan Burczak, Antonio Hidalgo-Torn\'e
https://arxiv.org/abs/2509.08168 http…

Pathological solutions of Navier-Stokes equations on $\mathbb{T}^2$ with gradients in Hardy spaces
For an arbitrary smooth initial datum, we construct multiple nonzero solutions to the $2$d Navier-Stokes equations, with their gradients in the Hardy space $\mathcal{H}^p$ with any $p \in (0,1)$. Thus, in terms of the path space $C(\mathcal{H}^p)$ for vorticity, $p=1$ is the threshold value distinguishing between non-uniqueness and uniqueness regimes. In order to obtain our result, we develop the needed theory of Hardy spaces on periodic domains.

Existence and nonexistence of solutions for singular quadratic quasilinear equations
David Arcoya, Jos\'e Carmona, Tommaso Leonori, Pedro J. Mart\'inez-Aparicio, Luigi Orsina, Francesco Petitta
https://arxiv.org/abs/2508.06375

Existence and nonexistence of solutions for singular quadratic quasilinear equations
We study both existence and nonexistence of nonnegative solutions for nonlinear elliptic problems with singular lower order terms that have natural growth with respect to the gradient, whose model is $$ \begin{cases} -Δu + \frac{|\nabla u|^2}{u^γ} = f & \mbox{in } Ω,\newline \hfill u=0 \hfill & \mbox{on } \partial Ω, \end{cases} $$ where $Ω$ is an open bounded subset of $\mathbb{R}^N $, $γ> 0$ and $f$ is a function which is strictly positive on every compactly contained subs…

Nonexistence of positive radial solutions for semipositone $\phi$-Laplacian problems with superlinear reaction term
Sigifredo Herr\'on, Emer Lopera, Diana S\'anchez
https://arxiv.org/abs/2508.05930

Nonexistence of positive radial solutions for semipositone $ϕ$-Laplacian problems with superlinear reaction term
The aim of this paper is to prove the nonexistence of positive radial solutions to the problem $-Δ_ϕu=λf(u)$, $x\in B_1(0)$, $u(x)=0$ on $|x|=1$, for $λ>0$ sufficiently large. Here, $ϕ$ is a continuous function, $Δ_ϕ$ denotes the $ϕ$-Laplacian operator which is defined by $Δ_ϕ(u):=div (ϕ(|\nabla u|) \nabla u)$, and $B_1(0)$ is the unit ball in $\mathbb{R}^N$, with $N>1$. Furthermore, $f$ is a continuous, nondecreasing function such that $f(0)<0$, and its behavior …

Minimizing solutions of degenerate Allen-Cahn equations with three wells in $\mathbb{R}^2$
Lia Bronsard, \'Etienne Sandier, Peter Sternberg
https://arxiv.org/abs/2509.08111 …

Minimizing solutions of degenerate Allen-Cahn equations with three wells in $\mathbb{R}^2$
We characterize all minimizers of the vector-valued Allen-Cahn equation in $\mathbb{R}^2$ under the assumption that the potential $W$ has three wells and that the associated degenerate metric does not satisfy the usual strict triangle inequality. These minimizers depend on one variable only in a suitable coordinate system. In particular, we show that no minimizing solutions to $ Δu=\nabla W(u)$ on $\mathbb{R}^2$ can approach the three distinct values of the potential wells.

Global strong solutions to the frame hydrodynamics for biaxial nematic phases
Minjiang Feng, Sirui Li, Qi Zeng
https://arxiv.org/abs/2508.06376 https://arx…

Global strong solutions to the frame hydrodynamics for biaxial nematic phases
In this article, we consider the frame hydrodynamics of biaxial nematic phases, a coupled system between the evolution of the orthonormal frame and the Navier--Stokes equation, which is derived from a molecular-theory-based dynamical tensor model about two second-order tensors. In two and three dimensions, we establish global well-posedness of strong solutions to the Cauchy problem of frame hydrodynamics for small initial data. The key ingredient of the proof relies on estimates of nonlinear te…

$C^{\infty}$-structures approach to travelling wave solutions to the gKdV equation
Antonio J. Pan-Collantes
https://arxiv.org/abs/2507.07112 https://

$C^{\infty}$-structures approach to travelling wave solutions to the gKdV equation
We present a geometric method for finding travelling wave solutions to the generalized Korteweg--de Vries (gKdV) equation $$ u_t + u_{xxx} + a(u)u_x = 0, $$ where $a(u)$ is a smooth function characterizing the nonlinearity. Using the travelling wave ansatz, the gKdV equation reduces to an ordinary differential equation (ODE), which we analyze via the $\mathcal{C}^\infty$-structure-based method, a geometric framework involving sequences of involutive distributions and Pfaffian equations. Startin…

Hunter-type Implosion Profiles for Energy-supercritical Polytropic Equations of State
Ely Sandine
https://arxiv.org/abs/2508.05817 https://arxiv.org/pdf/25…

Hunter-type Implosion Profiles for Energy-supercritical Polytropic Equations of State
We rigorously construct a family of smooth self-similar solutions to the isentropic gravitational Euler-Poisson system with a polytropic equation of state for polytropic indices lying in the full energy-supercritical range, $1<γ<\frac{6}{5}$. The result is an extension of the author's previous construction of Hunter solutions in the isothermal case, $γ=1$, and complements a construction of Larson-Penston-type solutions by Guo-Hadžić-Jang-Schrecker for the same system in the full mass-superc…

Recent research on $(-1)$-homogeneous solutions of stationary Navier-Stokes equations
Li Li, Xukai Yan
https://arxiv.org/abs/2509.07243 https://arxiv.org/p…

Recent research on $(-1)$-homogeneous solutions of stationary Navier-Stokes equations
We make an exposition of recent research on $(-1)$-homogeneous solutions of the three-dimensional incompressible stationary Navier-Stokes equations with singular rays. We also discuss properties of such solutions that are axisymmetric with no swirl, and present graphs illustrating examples that exhibit various typical types of singular behavior.