Tootfinder

🌴 Scientists identify potential climate solutions in 'grassy trees'
#trees

Scientists identify potential climate solutions in 'grassy trees'
Bamboo, palm, and banana trees look and act like trees, but are actually closer to grasses in how they grow because—unlike trees—their stems do not grow wider over time. However, due to their towering structure, scientists struggled with how to both classify them and to fully understand their biology—and benefits.

Copenhagen-based Formalize, whose compliance software serves organizations in 80 countries, raised a €30M Series B co-led by Acton Capital and Blackfin Tech (Tamara Djurickovic/Tech.eu)
https://tech.eu/2025/10/28/formalize-raises-eur30m-to-a…

Formalize raises €30M to advance compliance solutions across Europe
Copenhagen-based Formalize has raised €30 million in a Series B co-led by Acton Capital and Blackfin Tech, with participation from West Hill Capital and CIBC Innovation Banking. The company has raised €50 million to date.Across Europe, organisations face an increasingly complex, interconnected regulatory landscape, with evolving rules reshaping expectations for information security, resilience, and reporting across industries and regions. Formalize, addresses this with a single platform…

BloomAPR: A Bloom's Taxonomy-based Framework for Assessing the Capabilities of LLM-Powered APR Solutions
Yinghang Ma (Jack), Jiho Shin (Jack), Leuson Da Silva (Jack), Zhen Ming (Jack), Jiang, Song Wang, Foutse Khomh, Shin Hwei Tan
https://arxiv.org/abs/2509.25465

BloomAPR: A Bloom's Taxonomy-based Framework for Assessing the Capabilities of LLM-Powered APR Solutions
Recent advances in large language models (LLMs) have accelerated the development of AI-driven automated program repair (APR) solutions. However, these solutions are typically evaluated using static benchmarks such as Defects4J and SWE-bench, which suffer from two key limitations: (1) the risk of data contamination, potentially inflating evaluation results due to overlap with LLM training data, and (2) limited ability to assess the APR capabilities in dynamic and diverse contexts. In this paper,…

Global mild solutions in a critical setting for a forced fractional Boussinesq system
Diego Chamorro (LaMME), Maxence Mansais (LaMME)
https://arxiv.org/abs/2509.26098 https://…

Global mild solutions in a critical setting for a forced fractional Boussinesq system
We study here mild solutions for the forced, incompressible fractional Boussinesq system. Under suitable estimates for the terms involved (in an adapted functional framework) we can invoque a fixed point argument in order to obtain mild solutions. Although many functional spaces can be considered, we are interested here in a critical setting which ensures the existence of global solutions and we will work in particular with parabolic Morrey spaces which provide one of the largest critical funct…

Asymptotic Schwarzschild solutions in $f(R)$ gravity and their observable effects on the photon sphere of black holes
Miguel Aparicio Resco
https://arxiv.org/abs/2510.00702 http…

Asymptotic Schwarzschild solutions in $f(R)$ gravity and their observable effects on the photon sphere of black holes
We investigate asymptotic Schwarzschild exterior solutions in the context of modified gravity theories, specifically within the framework of $f(R)$ gravity, where the asymptotic behavior recovers the standard Schwarzschild solution of General Relativity. Unlike previous studies that rely mainly on analytical approximations, our approach combines asymptotic analysis with numerical integration of the underlying differential equations. Using these solutions, we analyze strong lensing effects to ob…

Horowitz-Polchinski Solutions at Large $k$
Jinwei Chu, David Kutasov
https://arxiv.org/abs/2509.25561 https://arxiv.org/pdf/2509.25561

Horowitz-Polchinski Solutions at Large $k$
In arXiv:2509.02905 [hep-th], we introduced an approximation that allows one to study Horowitz-Polchinski backgrounds beyond the weak coupling regime. In this paper we describe the resulting solutions, and discuss a few related issues.

The Hadamard parametrix on half-Minkowski with Robin boundary conditions: Fundamental solutions and Hadamard states
B. Costeri, C. Dappiaggi, B. A. Ju\'arez-Aubry, R. D. Singh
https://arxiv.org/abs/2509.26035

The Hadamard parametrix on half-Minkowski with Robin boundary conditions: Fundamental solutions and Hadamard states
We address the problem of constructing fundamental solutions and Hadamard states for a Klein-Gordon field in half-Minkowski spacetime with Robin boundary conditions in $d \geq 2$ spacetime dimensions. First, using a generalisation of the Robin-to-Dirichlet map exploited by Bondurant and Fulling [J. Phys. A: Math. Theor. {\bf 38} 7 (2005)] in dimension $2$, we obtain a representation for the advanced and retarded Green operators in terms of a convolution with the kernel of the inverse Robin-to-D…

Some thoughtful stuff about passkeys and the identity ecosystem, includes a few angles I hadn’t thought of: #identity

Passkeys and Modern Authentication
Some thoughts in support of simple solutions.

Call for Nominations: 16th Annual Privacy Papers for Policymakers Awards
https://fpf.org/blog/call-for-nominations-16th-annual-privacy-papers-for-policymakers-awards/
@…

Quantitative evaluations of stability and convergence for solutions of semilinear Klein--Gordon equation
Takuya Tsuchiya, Makoto Nakamura
https://arxiv.org/abs/2508.21659 https:…

Quantitative evaluations of stability and convergence for solutions of semilinear Klein--Gordon equation
We perform some simulations of the semilinear Klein--Gordon equation with a power-law nonlinear term and propose each of the quantitative evaluation methods for the stability and convergence of numerical solutions. We also investigate each of the thresholds in the methods by varying the amplitude of the initial value and the mass, and propose appropriate values.

RARR : Robust Real-World Activity Recognition with Vibration by Scavenging Near-Surface Audio Online
Dong Yoon Lee, Alyssa Weakley, Hui Wei, Blake Brown, Keyana Carrion, Shijia Pan
https://arxiv.org/abs/2508.21167

RARR : Robust Real-World Activity Recognition with Vibration by Scavenging Near-Surface Audio Online
One in four people dementia live alone, leading family members to take on caregiving roles from a distance. Many researchers have developed remote monitoring solutions to lessen caregiving needs; however, limitations remain including privacy preserving solutions, activity recognition, and model generalizability to new users and environments. Structural vibration sensor systems are unobtrusive solutions that have been proven to accurately monitor human information, such as identification and act…

Remotely Almost Periodic Solutions of Scalar Differential Equations
David Cheban
https://arxiv.org/abs/2510.00474 https://arxiv.org/pdf/2510.00474

Remotely Almost Periodic Solutions of Scalar Differential Equations
The aim of this paper is to study the problem of existence of remotely almost periodic solutions for the scalar differential equation $x'=f(t,x),$ where $f:\mathbb R\times \mathbb R\to \mathbb R$ is a continuous, monotone in $x$ and remotely almost periodic in $t$ function. We prove that every solution $φ$ of this equation bounded on the semi-axis $\mathbb R_{+}$ is remotely almost periodic. This statement is a generalization of the well-known Opial's theorem for remotely almost periodic scala…

Thermal Transport Anomalies of Electrolyte Solutions in the Water Supercooled Regime: Signatures of the Liquid-Liquid Water Phase Transition
Guansen Zhao, Fernando Bresme
https://arxiv.org/abs/2508.21751

Thermal Transport Anomalies of Electrolyte Solutions in the Water Supercooled Regime: Signatures of the Liquid-Liquid Water Phase Transition
Water exhibits remarkable anomalies when supercooled, attributed to a hypothesized liquid-liquid phase transition (LLPT) between low-density (LDL) and high-density (HDL) liquid phases. Using non-equilibrium molecular dynamics simulations, we explore thermal transport and coupled effects in supercooled NaCl and LiCl solutions (1-4 m, 200-300 K). At 1 m, thermal conductivity exhibits a pronounced minimum near 220 K, coinciding with maxima in isothermal compressibility and minima in the speed of s…

Weak Martingale Solutions of the Stochastic Schr\"{o}dinger-Poisson-Landau-Lifshitz-Gilbert System
Yurong Wei, Huaqiao Wang
https://arxiv.org/abs/2509.25993 https://…

Weak Martingale Solutions of the Stochastic Schrödinger-Poisson-Landau-Lifshitz-Gilbert System
The Schrödinger-Poisson-Landau-Lifshitz-Gilbert (SPLLG) system can characterize the spin transfer torque mechanism transferring the spin angular momentum to the magnetization dynamics through spin-magnetization coupling. We study the three-dimensional stochastic SPLLG system driven by a multiplicative stochastic force containing a continuous noise and a small jump noise. We establish the existence of weak martingale solutions based on the penalized functional technique, the Faedo-Galerkin appr…

Hill-Type Stability Analysis of Periodic Solutions of Fractional-Order Differential Equations
Paul-Erik Haacker, Remco I. Leine, Renu Chaudhary, Kai Diethelm, Andr\'e Schmidt, Safoura Hashemishahraki
https://arxiv.org/abs/2509.24639

Hill-Type Stability Analysis of Periodic Solutions of Fractional-Order Differential Equations
This paper explores stability properties of periodic solutions of (nonlinear) fractional-order differential equations (FODEs). As classical Caputo-type FODEs do not admit exactly periodic solutions, we propose a framework of Liouville-Weyl-type FODEs, which do admit exactly periodic solutions and are an extension of Caputo-type FODEs. Local linearization around a periodic solution results in perturbation dynamics governed by a linear time-periodic differential equation. In the classical integer…

Challenges and Solutions in Selecting Optimal Lossless Data Compression Algorithms
Md. Atiqur Rahman, MM Fazle Rabbi
https://arxiv.org/abs/2509.25219 https://

Challenges and Solutions in Selecting Optimal Lossless Data Compression Algorithms
The rapid growth of digital data has heightened the demand for efficient lossless compression methods. However, existing algorithms exhibit trade-offs: some achieve high compression ratios, others excel in encoding or decoding speed, and none consistently perform best across all dimensions. This mismatch complicates algorithm selection for applications where multiple performance metrics are simultaneously critical, such as medical imaging, which requires both compact storage and fast retrieval.…

In a move that has left anti-abortion advocates reeling,
the US Food and Drug Administration (FDA) quietly approved a request to manufacture a new abortion pill earlier this week.
Thanks to the approval,
Evita Solutions will be able to manufacture its generic version of mifepristone,
one of two drugs typically used in most US medication abortions.
A generic version of mifepristone, which was first approved as a brand-name drug in 2000, is already available on t…

I'm getting nerdsniped by Holographic Radiance Cascades (it's so jargon-heavy it basically has its own lore, but it's a bag of tricks for real-time raytraced lights/shadows)
https://arxiv.org/abs/2505.02041

Holographic Radiance Cascades for 2D Global Illumination
Efficiently calculating global illumination has always been one of the greatest challenges in computer graphics. Algorithms for approximating global illumination have always struggled to run in realtime for fully dynamic scenes, and have had to rely heavily on stochastic raytracing, spatialtemporal denoising, or undersampled representations, resulting in much lower quality of lighting compared to reference solutions. Even though the problem of calculating global illumination in 2D is significan…

Why?
Certainly Apple must have some of these infected iPhones. And Apple certainly has the tools to dig deep into the phones' systems to figure out how they are being compromised. And Apple has the source code and can do updates.
So why has Apple not blocked this? Same for Google/Android?
"Ice obtains access to Israeli-made spyware that can hack phones and encrypted apps"

A note on general isolation result in Diophantine Approximation
Sergei Pitcyn, Nikolay Moshchevitin
https://arxiv.org/abs/2509.25628 https://arxiv.org/pdf/…

A note on general isolation result in Diophantine Approximation
In the present paper we give very simple general statements which deal with approximation of a real number by rationals and are related to isolation phenomenon. In particular we study functions $ f(x)>f_1(x)>0$ such that existence of solutions $\frac{p}{q}$ of Diophantine inequality $ \left| α-\frac{p}{q}\right|< \frac{f(q)}{q^2} $ leads to the existence of solutions of inequality $ \left| α-\frac{p}{q}\right|< \frac{f_1(q)}{q^2} $.

Cement manufacturers want to go green. Trump is blocking them. - The Washington Post
https://www.washingtonpost.com/climate-solutions/2025/09/02/climate-trump-cement-carbon-capture/

climate solutions digest #7!
https://www.forpeopleandpla.net/weekly-climate-solutions-digest-7/

Weekly Climate Solutions Digest
Welcome Late October arrives with a thin silver light. In the north, the first frosts etch the edges of leaves, while far south, jacarandas toss purple confetti over warm sidewalks. Along the Yangtze’s wetlands, early cranes circle and settle with a hush. The world feels both quiet and in

Site-Specific Beam Learning for Full-Duplex Massive MIMO Wireless Systems
Samuel Li, Ian P. Roberts
https://arxiv.org/abs/2510.00342 https://arxiv.org/pdf/…

Site-Specific Beam Learning for Full-Duplex Massive MIMO Wireless Systems
Existing beamforming-based full-duplex solutions for multi-antenna wireless systems often rely on explicit estimation of the self-interference channel. The pilot overhead of such estimation, however, can be prohibitively high in millimeter-wave and massive MIMO systems, thus limiting the practicality of existing solutions, especially in fast-fading conditions. In this work, we present a novel beam learning framework that bypasses explicit self-interference channel estimation by designing beam c…

ORACLE: A rigorous metric and method to explore all near-optimal designs for energy systems
E. M. Turan, S. Moret, A. Bardow
https://arxiv.org/abs/2509.26452 https://

ORACLE: A rigorous metric and method to explore all near-optimal designs for energy systems
Optimization models are fundamental tools for providing quantitative insights to decision-makers. However, models, objectives, and constraints do not capture all real-world factors accurately. Thus, instead of the single optimal solution, real-world stakeholders are often interested in the near-optimal space -- solutions that lie within a specified margin of the optimal objective value. Solutions in the near-optimal space can then be assessed regarding desirable non-modeled or qualitative aspec…

Architecturally Constrained Solutions to Ill-Conditioned Problems in QUBIC
Leonora Kardum
https://arxiv.org/abs/2510.00090 https://arxiv.org/pdf/2510.00090…

Architecturally Constrained Solutions to Ill-Conditioned Problems in QUBIC
This article introduces a new physics-guided Machine Learning framework, with which we solve the generally non-invertible, ill-conditioned problems through an analytical approach and constrain the solution to the approximate inverse with the architecture of Neural Networks. By informing the networks of the underlying physical processes, the method optimizes data usage and enables interpretability of the model while simultaneously allowing estimation of detector properties and the propagation of…

Blow-up phenomena for the constant scalar curvature and constant boundary mean curvature equation (after Chen and Wu)
Pak Tung Ho, Jinwoo Shin
https://arxiv.org/abs/2508.21343 h…

Blow-up phenomena for the constant scalar curvature and constant boundary mean curvature equation (after Chen and Wu)
In this paper, the compactness of the solutions to the constant scalar curvature and constant boundary mean curvature equation is considered. Chen and Wu constructed a smooth counterexample showing that the compactness of the set of ``lower energy" solutions to the above equation fails when the dimension of the manifold is not less than 62. We prove that a smooth counterexample still exists when the dimension of the manifold is not less than 35.

Very Weak Solutions and Asymptotic Behavior of Leray Solutions to the Stationary Navier-Stokes Equations
Giovanni Paolo Galdi
https://arxiv.org/abs/2510.00265 https://

Very Weak Solutions and Asymptotic Behavior of Leray Solutions to the Stationary Navier-Stokes Equations
Let $\bfu$ be a Leray solution to the Navier-Stokes boundary-value problem in an exterior domain, vanishing at infinity and satisfying the generalized energy inequality. We show that if there exist $R>0$ and ${\sf s}\ge \frac23 q$, $q>6$, such that the $L^{\sf s}-$norm of $\bfu$ on the spherical surface of radius $R$ divided by $R$ is less than a constant depending only on {\sf s} and $q$, then $\bfu(x)$ must decay as $|x|^{-1}$ for $|x|\to\infty$. This result is proved with…

ICE obtains access to Israeli-made spyware that can hack phones and encrypted apps
https://www.theguardian.com/us-news/2025/sep/02/trump-immigration-ice-israeli-spyware

8 coax lanes, DC - 70 GHz, solderless compression fit... *drool*
https://www.hubersuhner.com/en/newsroom/blog-and-literature/blog/introducing-mxpd70-the-next-step-in-multicoax-test-solut…

Wireless Laser Power Transfer for Low-altitude Uncrewed Aerial Vehicle-assisted Internet of Things: Paradigms, Challenges, and Solutions
Chengzhen Li, Likun Zhang, Chuang Zhang, Jiahui Li, Changyuan Zhao, Ruichen Zhang, Geng Sun
https://arxiv.org/abs/2510.00477

Wireless Laser Power Transfer for Low-altitude Uncrewed Aerial Vehicle-assisted Internet of Things: Paradigms, Challenges, and Solutions
Low-altitude uncrewed aerial vehicles (UAVs) have become integral enablers for the Internet of Things (IoT) by offering enhanced coverage, improved connectivity and access to remote areas. A critical challenge limiting their operational capacity lies in the energy constraints of both aerial platforms and ground-based sensors. This paper explores WLPT as a transformative solution for sustainable energy provisioning in UAV-assisted IoT networks. We first systematically investigate the fundamental…

This is a minor annoyance and I’m interested in identifying it as well as exploring solutions.
I frequently mistype (or write) double letters by doubling an adjacent letter & singularizing the should be double letter.
examples:
Booby for Bobby (my pal Bob HATES this)
noddle for noodle
felling for feeling
Could be Dysgraphia or related to Dyslexia.
I'd appreciate pointers to articles / tests, and any other help.
cc/ @…

Complete Classification of Domain Wall Solutions in the $\mathbb{Z}_2$-symmetric 2HDM
Richard A. Battye, Steven J. Cotterill, Adam K. Thomasson
https://arxiv.org/abs/2509.23332 …

Complete Classification of Domain Wall Solutions in the $\mathbb{Z}_2$-symmetric 2HDM
We present a complete classification of domain wall solutions in the two-Higgs Doublet Model (2HDM) with a global $\mathbb{Z}_2$ symmetry, categorised as superconducting, CP-violating, or neither, depending on the scalar particle masses and the ratio of the two Higgs doublets' vacuum expectation values. We demonstrate that any domain wall solution can be reduced to depend on only six of the eight general field components, with further field reductions possible within different regions of the pa…

Cauchy matrix structures and solutions to the nonisospectral three-component mKdV equations
Mengli Tian, Chunxia Li, Yue Li, Fei Li, Yuqin Yao
https://arxiv.org/abs/2508.21434 h…

Cauchy matrix structures and solutions to the nonisospectral three-component mKdV equations
Nonisospectral integrable systems can describe solitary waves in nonuniform media. In this paper, we apply the Cauchy matrix approach to construct three types of nonisospectral matrix modified Korteweg-de Vries (mKdV) eqautions and present their Cauchy matrix structures and solutions. Further, through complex reduction, we further obtain three nonisospectral three-component mKdV (NTCmKdV) equations, which can be regarded as novel members of the nonisospectral Ablowitz-Kaup-Newell-Segur (AKNS) h…

Equivariant Splitting: Self-supervised learning from incomplete data
Victor Sechaud, J\'er\'emy Scanvic, Quentin Barth\'elemy, Patrice Abry, Juli\'an Tachella
https://arxiv.org/abs/2510.00929

Equivariant Splitting: Self-supervised learning from incomplete data
Self-supervised learning for inverse problems allows to train a reconstruction network from noise and/or incomplete data alone. These methods have the potential of enabling learning-based solutions when obtaining ground-truth references for training is expensive or even impossible. In this paper, we propose a new self-supervised learning strategy devised for the challenging setting where measurements are observed via a single incomplete observation model. We introduce a new definition of equiva…

Recursive Self-Aggregation Unlocks Deep Thinking in Large Language Models
Siddarth Venkatraman, Vineet Jain, Sarthak Mittal, Vedant Shah, Johan Obando-Ceron, Yoshua Bengio, Brian R. Bartoldson, Bhavya Kailkhura, Guillaume Lajoie, Glen Berseth, Nikolay Malkin, Moksh Jain
https://arxiv.org/abs/2509.26626…

Recursive Self-Aggregation Unlocks Deep Thinking in Large Language Models
Test-time scaling methods improve the capabilities of large language models (LLMs) by increasing the amount of compute used during inference to make a prediction. Inference-time compute can be scaled in parallel by choosing among multiple independent solutions or sequentially through self-refinement. We propose Recursive Self-Aggregation (RSA), a test-time scaling method inspired by evolutionary methods that combines the benefits of both parallel and sequential scaling. Each step of RSA refines…

PiCSAR: Probabilistic Confidence Selection And Ranking
Joshua Ong Jun Leang, Zheng Zhao, Aryo Pradipta Gema, Sohee Yang, Wai-Chung Kwan, Xuanli He, Wenda Li, Pasquale Minervini, Eleonora Giunchiglia, Shay B. Cohen
https://arxiv.org/abs/2508.21787

PiCSAR: Probabilistic Confidence Selection And Ranking
Best-of-n sampling improves the accuracy of large language models (LLMs) and large reasoning models (LRMs) by generating multiple candidate solutions and selecting the one with the highest reward. The key challenge for reasoning tasks is designing a scoring function that can identify correct reasoning chains without access to ground-truth answers. We propose Probabilistic Confidence Selection And Ranking (PiCSAR): a simple, training-free method that scores each candidate generation using the jo…

Security Issues on the OpenPLC project and corresponding solutions
Chaerin Kim
https://arxiv.org/abs/2509.22664 https://arxiv.org/pdf/2509.22664

Security Issues on the OpenPLC project and corresponding solutions
As Programmable Logic Controller (PLC) became a useful device and rose as an interesting research topic but remained expensive, multiple PLC simulators/emulators were introduced for various purposes. Open-source Programmable Logic Controller (OpenPLC) software, one of the most popular PLC simulators, is designed to be vendor-neutral and run on almost any computer or low-cost embedded devices, e.g., Raspberry Pi, Arduino, and other controllers. The project succeeded in introducing itself as an a…

Interactive Learning for LLM Reasoning
Hehai Lin, Shilei Cao, Minzhi Li, Sudong Wang, Haotian Wu, Linyi Yang, Juepeng Zheng, Chengwei Qin
https://arxiv.org/abs/2509.26306 https:…

Interactive Learning for LLM Reasoning
Existing multi-agent learning approaches have developed interactive training environments to explicitly promote collaboration among multiple Large Language Models (LLMs), thereby constructing stronger multi-agent systems (MAS). However, during inference, they require re-executing the MAS to obtain final solutions, which diverges from human cognition that individuals can enhance their reasoning capabilities through interactions with others and resolve questions independently in the future. To in…

Uber acquihires Belgian data labeling startup Segments.ai to expand its lidar data labeling capabilities; its founders and staff will join Uber AI Solutions (Natalie Lung/Bloomberg)
https://www.bloomberg.com/news/articles/2025-10…

Exact solutions of open quantum Brownian motions on the real line for two-level systems
Manuel D. de la Iglesia, Carlos F. Lardizabal
https://arxiv.org/abs/2509.22604 https://…

Exact solutions of open quantum Brownian motions on the real line for two-level systems
We investigate open quantum Brownian motions as quantum analogues of classical diffusion processes under interaction with an external enviroment. Building upon the microscopic derivation by Sinayskiy and Petruccione [20], we revisit the associated master equation and study its formulation as a generalized parabolic system. Employing Fourier transform methods, we derive exact analytical solutions for one-dimensional evolutions of particles with two-level internal degree of freedom.

Bifurcation Curve Diagrams for a Diffusive Generalized Logistic Problem with Minkowski Curvature Operator and Constant-Yield Harvesting
Shao-Yuan Huang
https://arxiv.org/abs/2510.00362

Bifurcation Curve Diagrams for a Diffusive Generalized Logistic Problem with Minkowski Curvature Operator and Constant-Yield Harvesting
This paper investigates the bifurcation diagrams of positive solutions for a one-dimensional diffusive generalized logistic boundary-value problem with the Minkowski curvature operator and constant yield harvesting. We prove that the corresponding bifurcation curves on both the (lambda, sup-norm of u)-plane and the (mu, sup-norm of u)-plane are C-shaped. Furthermore, by characterizing the bifurcation set on the (mu, lambda)-plane, we determine the exact multiplicity of positive solutions.

Multi-Modal Model Predictive Path Integral Control for Collision Avoidance
Alberto Bertipaglia, Dariu M. Gavrila, Barys Shyrokau
https://arxiv.org/abs/2508.21364 https://…

Multi-Modal Model Predictive Path Integral Control for Collision Avoidance
This paper proposes a novel approach to motion planning and decision-making for automated vehicles, using a multi-modal Model Predictive Path Integral control algorithm. The method samples with Sobol sequences around the prior input and incorporates analytical solutions for collision avoidance. By leveraging multiple modes, the multi-modal control algorithm explores diverse trajectories, such as manoeuvring around obstacles or stopping safely before them, mitigating the risk of sub-optimal solu…

Global weak solutions and incompressible limit of two-dimensional isentropic compressible magnetohydrodynamic equations with ripped density and large initial data
Shuai Wang, Guochun Wu, Xin Zhong
https://arxiv.org/abs/2510.00812

Global weak solutions and incompressible limit of two-dimensional isentropic compressible magnetohydrodynamic equations with ripped density and large initial data
We establish the global existence of weak solutions to isentropic compressible magnetohydrodynamic equations with ripped density in the whole plane provided the bulk viscosity coefficient is properly large. Moreover, we show that such solutions converge globally in time to a weak solution of the inhomogeneous incompressible magnetohydrodynamic equations when the bulk viscosity coefficient tends to infinity. In particular, the initial data can be arbitrarily large and vacuum states are allowed i…

Ouch, very familiar:
> I maintain the project alone, as over the years the community has not expressed a need for more active participation. This is typical for infrastructure-level solutions that users don’t interact with directly.
From https://www.theregister.com/2025/08/27/pop

Putin on the code: DoD reportedly relies on utility written by Russian dev
updated: Fast-glob is widely used in government, security lab says

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…

What a world.
Artificial Intelligence (AI) for Canadian Energy Innovation Call for Proposals
https://natural-resources.canada.ca/funding-partnerships/artificial-intelligence-canadian-energy-innovation

Jetzt wird es total Gaga: Nachdem schon Meta in den USA riesige Datacenter ohne Stromanschluss nur mit Dieselgeneratoren baut, passiert das jetzt auch in GB. Dort sollen zunächst 4 Anlagen gebaut werden, die angeblich CCS abscheiden. Das alles ist ein energiepolitischer und klima- und umwelttechnischer Wahnsinn.

New wave of UK data centres to run on gas engine and CCS microgrid
Deal marks collaboration between AVK, Landmark Power Holdings and Rolls Royce.

An interesting development to make the use of a cable duct easier and more accessible.
These types of safe cross-pavement EV charging solutions are becoming increasingly popular in the UK.
https://www.kerbocharge.com/store/p/kerbo-glide

Easy cable insertion tool — Kerbo Charge
Insert your charging cable into the Kerbo Charge channel without bending down.

Lattica: A Decentralized Cross-NAT Communication Framework for Scalable AI Inference and Training
Ween Yang, Jason Liu, Suli Wang, Xinyuan Song, Lynn Ai, Eric Yang, Tianyu Shi
https://arxiv.org/abs/2510.00183

Lattica: A Decentralized Cross-NAT Communication Framework for Scalable AI Inference and Training
The rapid expansion of distributed Artificial Intelligence (AI) workloads beyond centralized data centers creates a demand for new communication substrates. These substrates must operate reliably in heterogeneous and permissionless environments, where Network Address Translators (NATs) and firewalls impose significant constraints. Existing solutions, however, are either designed for controlled data center deployments or implemented as monolithic systems that tightly couple machine learning logi…

MHINDR - a DSM5 based mental health diagnosis and recommendation framework using LLM
Vaishali Agarwal, Sachin Thukral, Arnab Chatterjee
https://arxiv.org/abs/2509.25992 https://…

MHINDR - a DSM5 based mental health diagnosis and recommendation framework using LLM
Mental health forums offer valuable insights into psychological issues, stressors, and potential solutions. We propose MHINDR, a large language model (LLM) based framework integrated with DSM-5 criteria to analyze user-generated text, dignose mental health conditions, and generate personalized interventions and insights for mental health practitioners. Our approach emphasizes on the extraction of temporal information for accurate diagnosis and symptom progression tracking, together with psychol…

Infinite-Dimensional Stochastic Differential Equations and Diffusion Dynamics of Coulomb Random Point Fields
Hirofumi Osada, Shota Osada
https://arxiv.org/abs/2508.21658 https:/…

Infinite-Dimensional Stochastic Differential Equations and Diffusion Dynamics of Coulomb Random Point Fields
We consider the stochastic dynamics of infinite particle systems in $\mathbb{R}^d$ interacting through the $d$-dimensional Coulomb potential. For arbitrary inverse temperature $β>0$ and all dimensions $d\ge2$, we construct solutions to the associated infinite-dimensional stochastic differential equations (ISDEs). Our main results establish the existence of strong solutions and their pathwise uniqueness. The resulting labeled process is an $(\mathbb{R}^d)^N$-valued diffusion with no invariant m…

Replaced article(s) found for cs.LG. https://arxiv.org/list/cs.LG/new
[2/9]:
- Towards Convexity in Anomaly Detection: A New Formulation of SSLM with Unique Optimal Solutions
Hongying Liu, Hao Wang, Haoran Chu, Yibo Wu

Existence of multiple normalized solutions to a critical growth Choquard equation involving mixed operator
Nidhi Nidhi, K. Sreenadh
https://arxiv.org/abs/2510.00893 https://

Existence of multiple normalized solutions to a critical growth Choquard equation involving mixed operator
In this paper we study the normalized solutions of the following critical growth Choquard equation with mixed local and non-local operators: \begin{equation*} \begin{array}{rcl} -Δu +(-Δ)^s u & = & λu +μ|u|^{p-2}u +(I_α*|u|^{2^*_α})|u|^{2^*_α-2}u \text{ in } \mathbb{R}^N;\;\; \left\| u \right\|_2 & = & τ, \end{array} \end{equation*} here $N\geq 3$, $τ>0$, $I_α$ is the Riesz potential of order $α\in (0,N)$, $2^*_α=\frac{N+α}{N-2}…

Replaced article(s) found for cs.CL. https://arxiv.org/list/cs.CL/new
[4/5]:
- Composing Global Solutions to Reasoning Tasks via Algebraic Objects in Neural Nets
Yuandong Tian

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods
Ferdinand Thein, Hendrik Ranocha
https://arxiv.org/abs/2508.21427

Computing Radially-Symmetric Solutions of the Ultra-Relativistic Euler Equations with Entropy-Stable Discontinuous Galerkin Methods
The ultra--relativistic Euler equations describe gases in the relativistic case when the thermal energy dominates. These equations for an ideal gas are given in terms of the pressure, the spatial part of the dimensionless four-velocity, and the particle density. Kunik et al.\ (2024, https://doi.org/10.1016/j.jcp.2024.113330) proposed genuine multi--dimensional benchmark problems for the ultra--relativistic Euler equations. In particular, they compared full two-dimensional discontinuous Galerkin…

SlimPack: Fine-Grained Asymmetric Packing for Balanced and Efficient Variable-Length LLM Training
Yuliang Liu, Guohao Wu, Shenglong Zhang, Wei Zhang, Qianchao Zhu, Zhouyang Li, Chenyu Wang
https://arxiv.org/abs/2509.26246

SlimPack: Fine-Grained Asymmetric Packing for Balanced and Efficient Variable-Length LLM Training
The efficient distributed training of Large Language Models (LLMs) is severely hampered by the extreme variance in context lengths. This data heterogeneity, amplified by conventional packing strategies and asymmetric forward-backward costs, leads to critical inefficiencies such as cascading workload imbalances and severe hardware underutilization. Existing solutions attempt to mitigate these challenges, but often at the expense of memory or communication efficiency. To address these challenge…

Calyx: Privacy-Preserving Multi-Token Optimistic-Rollup Protocol
Dominik Apel, Zeta Avarikioti, Matteo Maffei, Yuheng Wang
https://arxiv.org/abs/2510.00164 https://

Calyx: Privacy-Preserving Multi-Token Optimistic-Rollup Protocol
Rollup protocols have recently received significant attention as a promising class of Layer 2 (L2) scalability solutions. By utilizing the Layer 1 (L1) blockchain solely as a bulletin board for a summary of the executed transactions and state changes, rollups enable secure off-chain execution while avoiding the complexity of other L2 mechanisms. However, to ensure data availability, current rollup protocols require the plaintext of executed transactions to be published on-chain, resulting in in…

AiDE-Q: Synthetic Labeled Datasets Can Enhance Learning Models for Quantum Property Estimation
Xinbiao Wang, Yuxuan Du, Zihan Lou, Yang Qian, Kaining Zhang, Yong Luo, Bo Du, Dacheng Tao
https://arxiv.org/abs/2509.26109

AiDE-Q: Synthetic Labeled Datasets Can Enhance Learning Models for Quantum Property Estimation
Quantum many-body problems are central to various scientific disciplines, yet their ground-state properties are intrinsically challenging to estimate. Recent advances in deep learning (DL) offer potential solutions in this field, complementing prior purely classical and quantum approaches. However, existing DL-based models typically assume access to a large-scale and noiseless labeled dataset collected by infinite sampling. This idealization raises fundamental concerns about their practical uti…

Retracts of degenerate solutions of the Yang-Baxter equation
P\v{r}emysl Jedli\v{c}ka, Agata Pilitowska
https://arxiv.org/abs/2508.17987 https://arxiv.org/…

Retracts of degenerate solutions of the Yang-Baxter equation
Most of the set-theoretical solutions of the Yang-Baxter equation studied in the past years were non-degenerate multipermutation solutions. For degenerate solutions, a correct definition of multipermutation solutions has not been established so far. We fill here this gap providing a definition of multipermutation solutions that generalizes the one for non-degenerate solutions and we find an axiomatic description of this class by a set of equations that generalizes the equations describing non-d…

GenIA-E2ETest: A Generative AI-Based Approach for End-to-End Test Automation
Elvis J\'unior, Alan Valejo, Jorge Valverde-Rebaza, V\^ania de Oliveira Neves
https://arxiv.org/abs/2510.01024

GenIA-E2ETest: A Generative AI-Based Approach for End-to-End Test Automation
Software testing is essential to ensure system quality, but it remains time-consuming and error-prone when performed manually. Although recent advances in Large Language Models (LLMs) have enabled automated test generation, most existing solutions focus on unit testing and do not address the challenges of end-to-end (E2E) testing, which validates complete application workflows from user input to final system response. This paper introduces GenIA-E2ETest, which leverages generative AI to generat…

this week's climate solutions digest! 🌱💖🌈
https://www.forpeopleandpla.net/weekly-climate-solutions-digest-6/

Weekly Climate Solutions Digest
Welcome Late October light sits lower on the day, turning sidewalks to amber and orchard leaves to copper. Across marshes, geese draw their careful V, a moving stitch that makes the sky feel hand sewn. This week carries the same feeling of stitching things together. Power systems link up across

Splitting Alternating Algorithms for Sparse Solutions of Linear Systems with Concatenated Orthogonal Matrices
Yun-Bin Zhao, Zhong-Feng Sun
https://arxiv.org/abs/2509.24558 https…

Splitting Alternating Algorithms for Sparse Solutions of Linear Systems with Concatenated Orthogonal Matrices
A class of splitting alternating algorithms is proposed for finding the sparse solution of linear systems with concatenated orthogonal matrices. Depending on the number of matrices concatenated, the proposed algorithms are classified into the two-block splitting alternating algorithm (TSAA) and the multi-block splitting alternating algorithm (MSAA). These algorithms aim to decompose a large-scale linear system into two or more coupled subsystems, each significantly smaller than the original sys…

Even before Microsoft Azure had a global failure this week,
Austria's Ministry of Economy had taken a decisive step toward digital sovereignty.
The Ministry is migrating 1,200 employees to a Nextcloud-based cloud and collaboration platform hosted on Austrian-based infrastructure
It's the latest move in a European trend to shift away from Big Tech.

European governments and agencies want to control sensitive data.

Another European agency shifts off Big Tech, as digital sovereignty movement gains steam
European Union states are increasingly shifting toward European-based companies that offer open-source solutions. Here's why.

Splitting and Merging of Stagnation Points of Solutions to the 2D Navier-Stokes Equations
Isidro Benaroya, Alberto Enciso, Daniel Peralta-Salas
https://arxiv.org/abs/2510.00784 …

Splitting and Merging of Stagnation Points of Solutions to the 2D Navier-Stokes Equations
We construct solutions to the Navier-Stokes equations on $\mathbf{R}^2$ with an arbitrary number of stagnation points which merge and split along trajectories that can be prescribed freely, up to a small deformation.

Decentralized and Self-adaptive Core Maintenance on Temporal Graphs
Davide Rucci, Emanuele Carlini, Patrizio Dazzi, Hanna Kavalionak, Matteo Mordacchini
https://arxiv.org/abs/2510.00758

Decentralized and Self-adaptive Core Maintenance on Temporal Graphs
Key graph-based problems play a central role in understanding network topology and uncovering patterns of similarity in homogeneous and temporal data. Such patterns can be revealed by analyzing communities formed by nodes, which in turn can be effectively modeled through temporal $k$-cores. This paper introduces a novel decentralized and incremental algorithm for computing the core decomposition of temporal networks. Decentralized solutions leverage the ability of network nodes to communicate a…

Networked Control and Mean Field Problems Under Diagonal Dominance: Decentralized and Social Optimality
Vivek Khatana, Duo Wang, Petros Voulgaris, Nicola Elia, Naira Hovakimyan
https://arxiv.org/abs/2510.01067

Networked Control and Mean Field Problems Under Diagonal Dominance: Decentralized and Social Optimality
In this article, we employ an input-output approach to expand the study of cooperative multi-agent control and optimization problems characterized by mean-field interactions that admit decentralized and selfish solutions. The setting involves $n$ independent agents that interact solely through a shared cost function, which penalizes deviations of each agent from the group's average collective behavior. Building on our earlier results established for homogeneous agents, we extend the framework t…

Residual Symmetries and Algebraic Structures in the Kerr-Schild Double Copy II
Brandon Holton
https://arxiv.org/abs/2509.25801 https://arxiv.org/pdf/2509.2…

Residual Symmetries and Algebraic Structures in the Kerr-Schild Double Copy II
We complete our investigation into the residual symmetries of the Kerr-Schild double copy for the Schwarzschild solution. In Part I, we showed that the infinite-dimensional residual gauge algebra collapses to the finite-dimensional global isometries when restricted to Killing vectors. Here, we extend the analysis to proper conformal Killing vectors (CKVs), solving the field equations via the method of characteristics to obtain explicit conformal solutions. While asymptotic flatness and horizon …

Symbolic and High-Accuracy Solutions to Differential and Integral Problems via a Novel Recursive Inverse Laplace Method
Mohamed Mostafa
https://arxiv.org/abs/2510.00719 https://…

Symbolic and High-Accuracy Solutions to Differential and Integral Problems via a Novel Recursive Inverse Laplace Method
In this paper, we introduce a novel semi-analytical method for solving a broad class of initial value problems involving differential, integro-differential, and delay equations, including those with fractional and variable-order derivatives. The proposed approach is based on the inverse Laplace transform, applied initially - unlike traditional Laplace-based techniques which begin with a forward transformation. By assuming the unknown solution is the Laplace transform of an auxiliary function, t…

Graph Neural Networks in Large Scale Wireless Communication Networks: Scalability Across Random Geometric Graphs
Romina Garcia Camargo, Zhiyang Wang, Alejandro Ribeiro
https://arxiv.org/abs/2510.00896 …

Graph Neural Networks in Large Scale Wireless Communication Networks: Scalability Across Random Geometric Graphs
The growing complexity of wireless systems has accelerated the move from traditional methods to learning-based solutions. Graph Neural Networks (GNNs) are especially well-suited here, since wireless networks can be naturally represented as graphs. A key property of GNNs is transferability: models trained on one graph often generalize to much larger graphs with little performance loss. While empirical studies have shown that GNN-based wireless policies transfer effectively, existing theoretical …

Chaplygin and Polytropic gases Teleparallel Robertson-Walker $F(T)$ gravity solutions
Alexandre Landry
https://arxiv.org/abs/2508.19912 https://arxiv.org/p…

Chaplygin and Polytropic gases Teleparallel Robertson-Walker $F(T)$ gravity solutions
This paper investigates the Teleparallel Robertson-Walker (TRW) $F(T)$ gravity solutions for a Chaplygin gas, and then for any polytropic gas cosmological source. We use the TRW $F(T)$ gravity field equations (FEs) for each $k$-parameter value case and the relevant gas equation of state (EoS) to find the new teleparallel $F(T)$ solutions. For flat $k=0$ cosmological case, we find analytical solutions valid for any cosmological scale factor. For curved $k=\pm 1$ cosmological cases, we find new a…

Removing cutoff artifacts in the NJL model by a Renormalization Group consistent treatment
Hosein Gholami, Marco Hofmann, Michael Buballa
https://arxiv.org/abs/2508.21735 https:…

Removing cutoff artifacts in the NJL model by a Renormalization Group consistent treatment
We summarize how a renormalization-group (RG)-consistent treatment removes well-known artifacts in NJL-model descriptions of color-superconducting quark matter. We introduce two RG-consistent schemes, "minimal" and "massless", and present analytic solutions for the diquark gap at $T=0$ and for the phase boundary $T_c(μ)$ in symmetric massless matter, representing the high-density limit of the model. We compare the pairing gaps, phase diagram, and speed of sound with results obtained using conv…

On a group of normalized solutions of the higher-dimensional Prouhet--Tarry--Escott problem
Munenori Inagaki, Hideki Matsumura, Masanori Sawa, Yukihiro Uchida
https://arxiv.org/abs/2508.20733

On a group of normalized solutions of the higher-dimensional Prouhet--Tarry--Escott problem
We elucidate, for the first time, a novel group-theoretic structure that arises from certain solutions of the $n$-dimensional Prouhet--Tarry--Escott problem of degree $2$ and size $n$. We prove that the group is isomorphic to the orthogonal group for a certain quadratic form.

Iterative Inference in a Chess-Playing Neural Network
Elias Sandmann, Sebastian Lapuschkin, Wojciech Samek
https://arxiv.org/abs/2508.21380 https://arxiv.o…

Iterative Inference in a Chess-Playing Neural Network
Do neural networks build their representations through smooth, gradual refinement, or via more complex computational processes? We investigate this by extending the logit lens to analyze the policy network of Leela Chess Zero, a superhuman chess engine. We find strong monotonic trends in playing strength and puzzle-solving ability across layers, yet policy distributions frequently follow non-smooth trajectories. Evidence for this includes correct puzzle solutions that are discovered early but s…

Existence, Nonexistence, and Symmetry of Positive Solutions for Fractional Laplacian Problems
Haipeng Lu, Mei Yu
https://arxiv.org/abs/2509.24454 https://a…

Existence, Nonexistence, and Symmetry of Positive Solutions for Fractional Laplacian Problems
This paper studies the properties of solutions to a class of elliptic and parabolic problems involving the fractional Laplacian. By applying the mountain pass theorem, we prove the existence of bounded classical positive solutions in the subcritical regime. Moreover, using the method of moving planes, we establish that these solutions are symmetric or monotone in the first variable. In contrast, we show that no such solutions exist in the supercritical or negative exponent cases. An analysis of…

Cambridge, UK-based Paragraf, which makes graphene-based electronics using standard semiconductor processes, raised a $55M Series C to scale its manufacturing (Tamara Djurickovic/Tech.eu)
https://tech.eu/2025/08/25/paragraf-closes-55m-series-c-funding-round/…

Paragraf closes $55M Series C funding round
Paragraf, the UK-based company leading the way in mass-producing graphene-based electronics using industry-standard semiconductor processes, has completed a $55 million Series C funding round. The funding will speed up the scaling of Paragraf’s manufacturing capabilities and increase production capacity, paving the way for graphene electronics to enter mass markets.Paragraf’s technology fits smoothly into the existing semiconductor ecosystem, offering customers ready-to-use solutions…

Provably Optimal Quantum Circuits with Mixed-Integer Programming
Harsha Nagarajan, Zsolt Szab\'o
https://arxiv.org/abs/2510.00649 https://arxiv.org/pdf…

Provably Optimal Quantum Circuits with Mixed-Integer Programming
We present a depth-aware optimization framework for quantum circuit compilation that unifies provable optimality with scalable heuristics. For exact synthesis of a target unitary, we formulate a mixed-integer linear program (MILP) that linearly handles global-phase equivalence and uses explicit parallel scheduling variables to certify depth-optimal solutions for small-to-medium circuits. Domain-specific valid constraints, including identity ordering, commuting-gate pruning, short-sequence redun…

Automatically Generating Web Applications from Requirements Via Multi-Agent Test-Driven Development
Yuxuan Wan, Tingshuo Liang, Jiakai Xu, Jingyu Xiao, Yintong Huo, Michael R. Lyu
https://arxiv.org/abs/2509.25297

Automatically Generating Web Applications from Requirements Via Multi-Agent Test-Driven Development
Developing full-stack web applications is complex and time-intensive, demanding proficiency across diverse technologies and frameworks. Although recent advances in multimodal large language models (MLLMs) enable automated webpage generation from visual inputs, current solutions remain limited to front-end tasks and fail to deliver fully functional applications. In this work, we introduce TDDev, the first test-driven development (TDD)-enabled LLM-agent framework for end-to-end full-stack web app…

Sentry: Authenticating Machine Learning Artifacts on the Fly
Andrew Gan, Zahra Ghodsi
https://arxiv.org/abs/2510.00554 https://arxiv.org/pdf/2510.00554

Sentry: Authenticating Machine Learning Artifacts on the Fly
Machine learning systems increasingly rely on open-source artifacts such as datasets and models that are created or hosted by other parties. The reliance on external datasets and pre-trained models exposes the system to supply chain attacks where an artifact can be poisoned before it is delivered to the end-user. Such attacks are possible due to the lack of any authenticity verification in existing machine learning systems. Incorporating cryptographic solutions such as hashing and signing can m…

MIT Provost
Anantha P. Chandrakasan told an audience of about 300 undergraduates from the Class of 2029:
“The goal is for MIT to become one of the world’s most prolific, collaborative, and interdisciplinary sources of technological, behavioral, and policy solutions for the global climate challenge over the next decade...
It is something we need to do urgently, and today is your opportunity to play a role in that bold mission.”

Over 1,000 MIT students inspired to work toward climate solutions
New MIT students recently stepped into the shoes of global decision-makers, using the En-ROADS climate solutions simulator to test climate policies, explore solutions, and envision the future they want to create.

Initial traces and solvability of the fast diffusion equation with power-type nonlinearity
Kazuhiro Ishige, Nobuhito Miyake
https://arxiv.org/abs/2509.26054 https://

Initial traces and solvability of the fast diffusion equation with power-type nonlinearity
We investigate the qualitative behavior of the initial traces of nonnegative solutions to the fast diffusion equation with power-type nonlinearity. Necessary conditions for the existence of solutions to the corresponding Cauchy problem are identified. Moreover, sharp sufficient conditions for the existence of solutions are established by employing uniform local Morrey spaces and their generalizations.

Hamilton--Jacobi--Bellman equation for optimal control of stochastic Wasserstein--Hamiltonian system on graphs
Jianbo Cui, Tonghe Dang
https://arxiv.org/abs/2509.25965 https://

Hamilton--Jacobi--Bellman equation for optimal control of stochastic Wasserstein--Hamiltonian system on graphs
Stochastic optimal control problems for Hamiltonian dynamics on graphs have wide-ranging applications in mechanics and quantum field theory, particularly in systems with graph-based structures. In this paper, we establish the existence and uniqueness of viscosity solutions for a new class of Hamilton--Jacobi--Bellman (HJB) equations arising from the optimal control of stochastic Wasserstein--Hamiltonian systems (SWHSs) on graphs. One distinctive feature of these HJB equations is the simultaneou…

The Influence of Uniform Magnetic Fields on Strong Field Gravitational Lensing by Kerr Black Holes
Amnish Vachher, Arun Kumar, Sushant G. Ghosh
https://arxiv.org/abs/2508.21100 …

The Influence of Uniform Magnetic Fields on Strong Field Gravitational Lensing by Kerr Black Holes
We investigate strong gravitational lensing using magnetized Kerr black holes (MKBHs), which are accurate Kerr-Bertotti-Robinson solutions for Kerr black holes in a uniform magnetic field with additional magnetic field strength $B$ apart from mass $M$ and spin $a$. Unlike previous magnetized spacetimes, the MKBH geometry is Petrov type D, devoid of conical singularities, allowing photons to reach asymptotic infinity and making the concept astrophysically feasible. We use the strong deflection l…

Travelling-wave solutions and solitons of KdV, mKdV and NLS equations
Supriya Chatterjee, Pranab Sarkar, Benoy Talukdar
https://arxiv.org/abs/2508.18994 https://

Travelling-wave solutions and solitons of KdV, mKdV and NLS equations
We introduce the concept of soliton solutions of integrable nonlinear partial differential equations and point out that the inverse spectral method represents the rigorous mathematical formalism to construct such solutions. We work with the travelling waves of the KdV, mKdV and nonlinear Schrödinger (NLS) equations and derive a pedagogic method to find their soliton solutions. The travelling wave of the KdV equation leads directly to the well known bell type KdV soliton while the mKdV equation…

Microsoft launches Microsoft Marketplace, combining Azure Marketplace and Microsoft AppSource in a single destination for cloud tools and AI apps and agents (Frederic Lardinois/The New Stack)
https://thenewstack.io/microsoft-launches-a…

Microsoft Launches a Combined Marketplace for Cloud Solutions, AI Apps and Agents
Starting today, the company is combining both Azure Marketplace and Microsoft AppSource under the aptly named "Microsoft Marketplace" banner.

WARP -- Web-Augmented Real-time Program Repairer: A Real-Time Compilation Error Resolution using LLMs and Web-Augmented Synthesis
Anderson de Lima Luiz
https://arxiv.org/abs/2509.25192

WARP -- Web-Augmented Real-time Program Repairer: A Real-Time Compilation Error Resolution using LLMs and Web-Augmented Synthesis
Compilation errors represent a significant bottleneck in software development productivity. This paper introduces WARP (Web-Augmented Real-time Program Repairer), a novel system that leverages Large Language Models (LLMs) and dynamic web-augmented synthesis for real-time resolution of these errors. WARP actively monitors developer terminals, intelligently detects compilation errors, and synergistically combines the understanding of a fine-tuned Code-LLM with relevant solutions, explanations, an…

Infinite-peakon solutions of the Camassa-Holm equation
Xiang-Ke Chang, Jonathan Eckhardt, Aleksey Kostenko
https://arxiv.org/abs/2509.23826 https://arxiv.o…

Infinite-peakon solutions of the Camassa-Holm equation
We study a class of (conservative) low regularity solutions to the Camassa-Holm equation on the line by exploiting the classical moment problem (in the framework of generalized indefinite strings) to develop the inverse spectral transform method. In particular, we identify explicitly the solutions that are amenable to this approach, which include solutions made up of infinitely many peaked solitons (peakons). We determine which part of the solution can be recovered from the moments of the under…

Analytical and Numerical Approaches for Finding Functional Iterates and Roots
Sanay Nesargi, Gregory Roudenko
https://arxiv.org/abs/2509.24049 https://arxi…

Analytical and Numerical Approaches for Finding Functional Iterates and Roots
We investigate solutions to the functional equation $f(f(x)) = e^x$, which can be interpreted as the problem of finding a half iterate of the exponential map. While no elementary solution exists, we construct and analyze non-elementary solutions using methods based on the Lambert W function, tetration, and Abel's functional equation. We examine structural properties of possible solutions, including monotonicity, injectivity, and behavior across different intervals, and provide a piecewise-defin…

A semi-Lagrangian method for solving state constraint Mean Field Games in Macroeconomics
Fabio Camilli, Qing Tang, Yong-shen Zhou
https://arxiv.org/abs/2510.00768 https://

A semi-Lagrangian method for solving state constraint Mean Field Games in Macroeconomics
We study continuous-time heterogeneous agent models cast as Mean Field Games, in the Aiyagari-Bewley-Huggett framework. The model couples a Hamilton-Jacobi-Bellman equation for individual optimization with a Fokker-Planck-Kolmogorov equation for the wealth distribution. We establish a comparison principle for constrained viscosity solutions of the HJB equation and propose a semi-Lagrangian (SL) scheme for its numerical solution, proving convergence via the Barles-Souganidis method. A policy ite…

Gravitational entropy of fluids with energy flux
Roberto A. Sussman, Sebasti\'an N\'ajera, Fernando A. Piza\~na, Juan Carlos Hidalgo
https://arxiv.org/abs/2509.25007 htt…

Gravitational entropy of fluids with energy flux
We examine gravitational entropy growth within the formalism of Clifton, Ellis and Tavakol (CET) applied to a class of spherically symmetric exact solutions whose source is a shear-free fluid with energy flux in a comoving frame. By considering these solutions as potential cosmological models, we update previous literature that considered them only as restricted toy models of radiating spheres collapsing in a Vaidya background. In the present paper we examine the integrability of the CET entrop…

Multiple solutions to the nonlinear Schr\"odinger equation with a partial confinement
Liying Shan, Wei Shuai, Leyun Wu
https://arxiv.org/abs/2509.21806 https://

Multiple solutions to the nonlinear Schrödinger equation with a partial confinement
We consider multiple solutions to the nonlinear Schrödinger equation (NLS) with a partial confinement, which is physically relevant to dynamics of the Bose-Einstein condensate. Our study not only verifies the existence of positive ground state solutions and the nonexistence of least energy sign-changing solutions but also sheds light on the symmetry associated with these solutions. A novel finding is the existence of saddle type nodal solutions with their nodal domains intersecting at the orig…

Blow-up of solutions for discrete semilinear wave equation with the scale-invariant damping
Koji Wada, Kyouhei Wakasa
https://arxiv.org/abs/2510.00439 https://

Blow-up of solutions for discrete semilinear wave equation with the scale-invariant damping
We consider the blow-up problem for discretized scale-invariant nonlinear dissipative wave equations. It is known that the critical exponents for undiscretized equations (continuous equations) are given by Fujita and Strauss exponents depending on the space dimensions. Our purpose is to obtain results for the discretized equations that correspond to those shown for the continuous one. The proof is based on Matsuya [6], who showed the blow-up problem for discrete semilinear wave equations withou…

Radiative and Jet Signatures of Regular Black Holes in Quantum-Corrected Gravity
Chirantana Bhattacharjee, Subhadip Sau, Avijit Mukherjee
https://arxiv.org/abs/2509.26366 https:…

Radiative and Jet Signatures of Regular Black Holes in Quantum-Corrected Gravity
We investigate regular rotating black holes predicted by asymptotically safe gravity, where the Newton constant varies with energy scale and modifies the near horizon geometry. These solutions remain asymptotically flat and avoid central singularities while differing from the classical Kerr spacetime in the strong field region. We compute the radiative efficiency of thin accretion disks and the jet power from the Blandford Znajek mechanism, both of which depend on the deformation parameter of t…

Classification of solutions of an elliptic Hamilton-Jacobi equation
Alessio Porretta, Philippe Souplet
https://arxiv.org/abs/2510.00146 https://arxiv.org/p…

Classification of solutions of an elliptic Hamilton-Jacobi equation
We show that any classical solution of the diffusive Hamilton-Jacobi (DHJ) equation $-Δu= |\nabla u|^p$ in a half-space with zero boundary conditions for $12$, our result completes the full classification picture of the Dirichlet problem for equation (DHJ) in a half-space.

Complexity hierarchies in Euclidean stars
L. Herrera, A. Di Prisco, J. Ospino
https://arxiv.org/abs/2509.26384 https://arxiv.org/pdf/2509.26384

Complexity hierarchies in Euclidean stars
We establish a hierarchy of Euclidean stars according to their degree of complexity, as measured by the complexity factor and the complexity of the pattern of evolution. We consider both, nondissipative and dissipative systems. Solutions are ranged from the simplest one, in order of increasing complexity. Some specific models are found and analyzed in detail.

Weak-strong uniqueness for general cross-diffusion systems with volume filling
Maria Heitzinger, Ansgar J\"ungel
https://arxiv.org/abs/2509.25978 https://

Weak-strong uniqueness for general cross-diffusion systems with volume filling
The weak-strong uniqueness of solutions to a broad class of cross-diffusion systems with volume filling is established. In general, the diffusion matrices are neither symmetric nor positive definite. This issue is overcome by supposing that the equations possess a Boltzmann-type entropy structure, which ensures the existence of bounded weak solutions. In this framework, general conditions on the mobility matrix are identified that allow for the proof of the weak-strong uniqueness property by me…

Exponential Dichotomies in Higher-Dimensional Spatial Dynamics for Elliptic Partial Differential Equations
Margaret Beck, Ryan Goh, Alanna Haslam-Hyde
https://arxiv.org/abs/2510.00917

Exponential Dichotomies in Higher-Dimensional Spatial Dynamics for Elliptic Partial Differential Equations
Exponential dichotomies, when they exist, provide powerful information about the structure of bounded solutions even in the case of an ill-posed evolutionary equation. The method of spatial dynamics, in which one views a spatial variable as a time-like evolutionary variable, allows for the use of classical dynamical systems techniques, such as exponential dichotomies, in broader contexts. This has been utilized to study stationary, traveling wave, time-periodic, and spiral wave solutions of PDE…

Traveling wave solutions for the generalized Burgers-Fisher equation
Razvan Gabriel Iagar, Ariel S\'anchez
https://arxiv.org/abs/2509.24909 https://arx…

Traveling wave solutions for the generalized Burgers-Fisher equation
Traveling wave solutions, in the form $u(x,t)=f(x+ct)$, to the generalized Burgers-Fisher equation $$ \partial_tu=u_{xx}+k(u^n)_x+u^p-u^q, \quad (x,t)\in\mathbb{R}\times(0,\infty), $$ with $n\geq2$, $p>q\geq1$ and $k>0$, are classified with respect to their speed $c\in(-\infty,\infty)$ and the behavior at $\pm\infty$. The existence and uniqueness of traveling waves with any speed $c\in\mathbb{R}$ is established and their behavior as $x\to\pm\infty$ is described. In particular, it is shown that …

Nonuniqueness of Leray-Hopf solutions to the unforced incompressible 3D Navier-Stokes Equation
Thomas Hou, Yixuan Wang, Changhe Yang
https://arxiv.org/abs/2509.25116 https://

Nonuniqueness of Leray-Hopf solutions to the unforced incompressible 3D Navier-Stokes Equation
The nonuniqueness of Leray-Hopf solutions to the unforced incompressible 3D Navier-Stokes equations is one of the central open problems in mathematical fluid dynamics. In this paper, we provide, to our knowledge, the first rigorous computer-assisted proof demonstrating such nonuniqueness. Inspired by earlier works in this area, we construct a Leray-Hopf solution in the self-similar setting and then establish the existence of a second solution by analyzing the stability of the linearized operato…

Global boundedness of solutions of degenerate and non-uniform parabolic equations
Thuyen Dang, Duong Minh Duc
https://arxiv.org/abs/2509.23064 https://arxi…

Global boundedness of solutions of degenerate and non-uniform parabolic equations
Let $2 \le N\in\mathbb{N}$, $Ω$ be a bounded open in $\mathbb{R}^{N}$, $T\in (0,\infty)$, $Q=Ω\times (0,T)$, $u$ be a weak solution of parabolic equation $\displaystyle \frac{\partial u}{\partial t} -Lu= f$, where $L$ is an elliptic operator on a space of functions on $Q$. The coefficients of $L$ may not be bounded, not strictly nor uniformly elliptic, and not of Muckenhoupt type. We obtain global boundedness of $u$. Our result can be applied to $u$, which may vanish on $(A\times (0,T))\cup (…

Existence and numerical approximation of solutions of a Schr\"odinger equation with derivative in the nonlinear term
Juan Carlos Mu\~noz Grajales, Deissy Marcela Pizo
https://arxiv.org/abs/2509.23414

Existence and numerical approximation of solutions of a Schrödinger equation with derivative in the nonlinear term
In this paper, we study a Schrödinger-type equation featuring a derivative in the nonlinear term and incorporating diffusion effects. This type of equation arises in various physical applications, such as modeling low-order magnetization in ferromagnetic nanocables and describing the collision of ferromagnetic solitons in weakly ferromagnetic media. We establish a local well-posedness result for the Cauchy problem associated with this model and analyze the convergence and error order of a Four…