Tootfinder

Schr\"odingerization for quantum linear systems problems
Yin Yang, Yue Yu, Long Zhang
https://arxiv.org/abs/2508.13510 https://arxiv.org/pdf/2508.1351…

Schrödingerization for quantum linear systems problems
We develop a quantum algorithm for linear algebraic equations Ax=b from the perspective of Schrödingerization-form problems, which are characterized by a system of linear convection equations in one higher dimension. When A is positive definite, the solution x can be interpreted as the steady-state solution of linear ODEs. This ODE can be solved by using the LCHS method in [1], which serves as the continuous implementation of the Fourier transform in the Schrödingerization method from [2,3] S…

On the extension of a class of Hermite bivariate interpolation problems
Hakop Hakopian, Anush Khachatryan
https://arxiv.org/abs/2509.14359 https://arxiv.or…

On the extension of a class of Hermite bivariate interpolation problems
We characterize the sets of solvability for Hermite bivariate interpolation problems when the sum of multiplicities is at most $2n + 2$, with $n$ the degree of the polynomial space. This result extends an earlier theorem (2000) by one of the authors concerning the case $2n+1$. The latter theorem, in turn, can be regarded as a natural generalization of a classical theorem of Severi (1921).

Galois module structures and the Hasse principle in twist families via the distribution of Selmer groups
Alex Bartel, Adam Morgan
https://arxiv.org/abs/2508.14026 https://

Galois module structures and the Hasse principle in twist families via the distribution of Selmer groups
We address several seemingly disparate problems in arithmetic geometry: the statistical behaviour of the Galois module structure of Mordell--Weil groups of a fixed elliptic curve over varying quadratic extensions; the frequency of failure of the Hasse principle in quadratic twist families of genus $1$ hyperelliptic curves; and the Hasse principle for Kummer varieties. The common technical ingredient for all of these is a result on the distribution of $2$-Selmer ranks in certain sparse families …

An inexact variable metric proximal linearization method for composite optimization over embedded submanifolds
Hao He, Ruyu Liu, Yitian Qian, Shaohua Pan
https://arxiv.org/abs/2508.12003

An inexact variable metric proximal linearization method for composite optimization over embedded submanifolds
This paper concerns the minimization of the composition of a nonsmooth convex function and a $\mathcal{C}^{1,1}$ mapping over a $\mathcal{C}^2$-smooth embedded closed submanifold $\mathcal{M}$. For this class of nonconvex and nonsmooth problems, we propose an inexact variable metric proximal linearization method by leveraging its composite structure and the retraction and first-order information of $\mathcal{M}$, which at each iteration seeks an inexact solution to a subspace constrained strong…

Replaced article(s) found for math.AP. https://arxiv.org/list/math.AP/new
[1/1]:
- Strong relaxation limit and uniform time asymptotics of the Jin-Xin model in the $L^{p}$ framework
Timoth\'ee Crin-Barat, Ling-Yun Shou, Jianzhong Zhang
https://arxiv.org/abs/2311.04105 https://mastoxiv.page/@arXiv_mathAP_bot/111373086323167893
- Long time regularity for 3d gravity waves with vorticity
Daniel Ginsberg, Fabio Pusateri
https://arxiv.org/abs/2401.10096 https://mastoxiv.page/@arXiv_mathAP_bot/111780770295022186
- Wasserstein Gradient Flows of MMD Functionals with Distance Kernel and Cauchy Problems on Quantil...
Richard Duong, Viktor Stein, Robert Beinert, Johannes Hertrich, Gabriele Steidl
https://arxiv.org/abs/2408.07498 https://mastoxiv.page/@arXiv_mathAP_bot/112964949403866709
- Regularity of solutions for degenerate or singular fully nonlinear integro-differential equations
Jiangwen Wang, Feida Jiang
https://arxiv.org/abs/2408.14779 https://mastoxiv.page/@arXiv_mathAP_bot/113038547448492855
- An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds
Francesco Nobili
https://arxiv.org/abs/2412.05935 https://mastoxiv.page/@arXiv_mathAP_bot/113627373212995916
- The $\mathcal{M}$-Operator and Uniqueness of Nonlinear Kinetic Equations
Ricardo Alonso, Maria Pia Gualdani, Weiran Sun
https://arxiv.org/abs/2506.20775 https://mastoxiv.page/@arXiv_mathAP_bot/114754297465809405
- Magnetic Stabilization of Compressible Flows: Global Existence in 3D Inviscid Non-Isentropic MHD ...
Jiahong Wu, Fuyi Xu, Xiaoping Zhai
https://arxiv.org/abs/2507.00888 https://mastoxiv.page/@arXiv_mathAP_bot/114782973460202498
- Free boundary regularity for a tumor growth model with obstacle
Giulia Bevilacqua, Matteo Carducci
https://arxiv.org/abs/2507.02837 https://mastoxiv.page/@arXiv_mathAP_bot/114794384026764859
- Three bound states with prescribed angular momentum to the cubic-quintic NLS equations in $\mathb...
Shuai Yao, Juntao Sun
https://arxiv.org/abs/2507.04057 https://mastoxiv.page/@arXiv_mathAP_bot/114817504459971991
- Some remarks on a mathematical model for water flow in porous media with competition between tran...
Judita Runczikov\'a, Jan Chleboun, Chiara Gavioli, Pavel Krej\v{c}\'i
https://arxiv.org/abs/2405.10751 https://mastoxiv.page/@arXiv_mathNA_bot/112472226685837805
- SDEs with critical general distributional drifts: sharp solvability and blow ups
D. Kinzebulatov, R. Vafadar
https://arxiv.org/abs/2506.09244 https://mastoxiv.page/@arXiv_mathPR_bot/114669448852836191
- One sided orthogonal polynomials and a pointwise convergence result for $SU(2)$-valued nonlinear ...
Michel Alexis, Gevorg Mnatsakanyan, Christoph Thiele
https://arxiv.org/abs/2507.05124 https://mastoxiv.page/@arXiv_mathCA_bot/114817025355217864
toXiv_bot_toot

Divisibility and Sequence Properties of $\sigma^ $ and $\varphi^ $
Sagar Mandal
https://arxiv.org/abs/2508.11660 https://arxiv.org/pdf/2508.11660

Divisibility and Sequence Properties of $σ^+$ and $φ^+$
Inspired by Lehmer's and Deaconescu's conjectures concerning Euler's totient function $ϕ(n)$ and Schemmel's totient function $S_2(n)$, respectively, we investigate analogous divisibility problems involving $σ(n)$,$σ^+(n)$ and $φ^+(n)$. Further, we establish some interesting properties of the sequences $\left\{σ^+(n)\right\}_{n=1}^\infty$ and $\left\{φ^+(n)\right\}_{n=1}^\infty$.

Spectral extremal problems for non-bipartite graphs without odd cycles
Lantao Zou, Lihua Feng, Yongtao Li
https://arxiv.org/abs/2507.11817 https://

Spectral extremal problems for non-bipartite graphs without odd cycles
A well-known result of Mantel asserts that every $n$-vertex triangle-free graph $G$ has at most $\lfloor n^2/4 \rfloor$ edges. Moreover, Erdős proved that if $G$ is further non-bipartite, then $e(G)\le \lfloor {(n-1)^2}/{4}\rfloor +1$. Recently, Lin, Ning and Wu [Combin. Probab. Comput. 30 (2021)] established a spectral version by showing that if $G$ is a triangle-free non-bipartite graph on $n$ vertices, then $λ(G)\le λ(S_1(T_{n-1,2}))$, with equality if and only if $G=S_1(T_{n-1,2})$, wher…

Obesity & diet
I wouldn't normally share a positive story about the new diet drugs, because I've seen someone get obsessed with them who was at a perfectly acceptable weight *by majority standards* (surprise: every weight is in fact perfectly acceptable by *objective* standards, because every "weight-associated" health risk is its own danger that should be assessed *in individuals*). I think two almost-contradictory things:
1. In a society shuddering under the burden of metastasized fatmisia, there's a very real danger in promoting the new diet drugs because lots of people who really don't need them will be psychologically bullied into using them and suffer from the cost and/or side effects.
2. For many individuals under the assault of our society's fatmisia, "just ignore it" is not a sufficient response, and also for specific people for whom decreasing their weight can address *specific* health risks/conditions that they *want* to address that way, these drugs can be a useful tool.
I know @… to be a trustworthy & considerate person, so I think it's responsible to share this:
#Fat #Diet #Obesity

The influence of dimensional crossover on phase transitions and critical phenomena in condensed systems
O. V. Chalyi, E. V. Zaitseva
https://arxiv.org/abs/2509.13799 https://

The influence of dimensional crossover on phase transitions and critical phenomena in condensed systems
This article is aimed at studying the effects of the dimensional crossover (DC) on physical properties of condensed systems near phase transition and critical points. Here we consider the following problems: (1) the theoretical provisions that allow to study the effect of spatial confinement on DC near phase transition and critical points; (2) the study of DC in condensed systems with the Ginzburg number $\mathrm{Gi} <1$, where fluctuation effects are described in different ways at the fluctuat…

$\mathrm{L}^p$-based Sobolev theory for PDEs on closed manifolds of class $C^m$
Gonzalo A. Benavides, Ricardo H. Nochetto, Mansur Shakipov
https://arxiv.org/abs/2508.11109 https…

$\mathrm{L}^p$-based Sobolev theory for PDEs on closed manifolds of class $C^m$
We study the $\mathrm{L}^p$-based ($1

Solving Linear Programs with Differential Privacy
Alina Ene, Huy Le Nguyen, Ta Duy Nguyen, Adrian Vladu
https://arxiv.org/abs/2507.10946 https://

Solving Linear Programs with Differential Privacy
We study the problem of solving linear programs of the form $Ax\le b$, $x\ge0$ with differential privacy. For homogeneous LPs $Ax\ge0$, we give an efficient $(ε,δ)$-differentially private algorithm which with probability at least $1-β$ finds in polynomial time a solution that satisfies all but $O(\frac{d^{2}}ε\log^{2}\frac{d}{δβ}\sqrt{\log\frac{1}{ρ_{0}}})$ constraints, for problems with margin $ρ_{0}>0$. This improves the bound of $O(\frac{d^{5}}ε\log^{1.5}\frac{1}{ρ_{0}}\mathrm{poly…

Balancing Extensions in Posets of Large Width
Max Aires, Jeff Kahn
https://arxiv.org/abs/2509.11549 https://arxiv.org/pdf/2509.11549

Balancing Extensions in Posets of Large Width
We revisit classic balancing problems for linear extensions of a partially ordered set $P$, proving results that go far beyond many of the best earlier results on this topic. For example, with $p(x\prec y)$ the probability that $x$ precedes $y$ in a uniform linear extension, $δ_{xy} = \min\{p(x \prec y), p(y \prec x)\}$, and $δ(P)=\max δ_{xy}$, we show that $δ(P)$ tends to $1/2$ as $n := |P| \to\infty$ if $P$ has width $Ω(n)$ or $ω(\log(n))$ minimal elements, and is at least $1/…

Replaced article(s) found for quant-ph. https://arxiv.org/list/quant-ph/new
[1/2]:
- Polynomial-time Solver of Tridiagonal QUBO, QUDO and Tensor QUDO problems with Tensor Networks
Alejandro Mata Ali, I\~nigo Perez Delgado, Marina Ristol Roura, Aitor Moreno Fdez. de Leceta

State-based approach to the numerical solution of Dirichlet boundary optimal control problems for the Laplace equation
Ulrich Langer, Richard L\"oscher, Olaf Steinbach, Huidong Yang
https://arxiv.org/abs/2507.11646

State-based approach to the numerical solution of Dirichlet boundary optimal control problems for the Laplace equation
We investigate the Dirichlet boundary control of the Laplace equation, considering the control in $H^{1/2}(\partial Ω)$, which is the natural space for Dirichlet data when the state belongs to $H^1(Ω)$. The cost of the control is measured in the $H^{1/2}(\partial Ω)$ norm that also plays the role of the regularization term. We discuss regularization and finite element error estimates enabling us to derive an optimal relation between the finite element mesh size $h$ and the regularization par…

Tabular foundation model for GEOAI benchmark problems BM/AirportSoilProperties/2/2025
Taiga Saito, Yu Otake, Stephen Wu
https://arxiv.org/abs/2509.03191 https://

Tabular foundation model for GEOAI benchmark problems BM/AirportSoilProperties/2/2025
This paper presents a novel application of the Tabular Prior-Data Fitted Network (TabPFN) - a transformer-based foundation model for tabular data - to geotechnical site characterization problems defined in the GEOAI benchmark BM/AirportSoilProperties/2/2025. Two tasks are addressed: (1) predicting the spatial variation of undrained shear strength (su) across borehole depth profiles, and (2) imputing missing mechanical parameters in a dense-site dataset. We apply TabPFN in a zero-training, few-s…

Two things on this:
1 - To protect people from deepfakes has merit and is very, very needed. Urgently, even.
2 - Every single time people tried to use copyright law to do stuff copyright law is not intended to do, the results were catastrophic. No problems were solved that way, and new problems were created.
Stop it. Just stop.

Unknotting number is not additive under connected sum
Mark Brittenham, Susan Hermiller
https://arxiv.org/abs/2506.24088 https://arxiv…

Unknotting number is not additive under connected sum
We give the first examples of a pair of knots $K_1$,$K_2$ in the 3-sphere for which their unknotting numbers satisfy $u(K_1\#K_2)

Near-Optimal Convergence of Accelerated Gradient Methods under Generalized and $(L_0, L_1)$-Smoothness
Alexander Tyurin
https://arxiv.org/abs/2508.06884 https://

Near-Optimal Convergence of Accelerated Gradient Methods under Generalized and $(L_0, L_1)$-Smoothness
We study first-order methods for convex optimization problems with functions $f$ satisfying the recently proposed $\ell$-smoothness condition $||\nabla^{2}f(x)|| \le \ell\left(||\nabla f(x)||\right),$ which generalizes the $L$-smoothness and $(L_{0},L_{1})$-smoothness. While accelerated gradient descent AGD is known to reach the optimal complexity $O(\sqrt{L} R / \sqrt{\varepsilon})$ under $L$-smoothness, where $\varepsilon$ is an error tolerance and $R$ …

New constructions and bounds for nonabelian Sidon sets with applications to Tur\'an-type problems
John Byrne, Michael Tait
https://arxiv.org/abs/2509.07750 https://

New constructions and bounds for nonabelian Sidon sets with applications to Turán-type problems
An $S_k$-set in a group $Γ$ is a set $A\subseteqΓ$ such that $α_1\cdotsα_k=β_1\cdotsβ_k$ with $α_i,β_i\in A$ implies $(α_1,\ldots,α_k)=(β_1,\ldots,β_k)$. An $S_k'$-set is a set such that $α_1β_1^{-1}\cdotsα_kβ_k^{-1}=1$ implies that there exists $i$ such that $α_i=β_i\text{ or }β_i=α_{i+1}$. We give explicit constructions of large $S_k$-sets in the group $S_n$ and $S_2$-sets in $S_n\times S_n$ and $A_n\times A_n$. We give probabilistic constructions for `nice' groups which o…

Should we teach vibe coding? Here's why not.
Should AI coding be taught in undergrad CS education?
1/2
I teach undergraduate computer science labs, including for intro and more-advanced core courses. I don't publish (non-negligible) scholarly work in the area, but I've got years of craft expertise in course design, and I do follow the academic literature to some degree. In other words, In not the world's leading expert, but I have spent a lot of time thinking about course design, and consider myself competent at it, with plenty of direct experience in what knowledge & skills I can expect from students as they move through the curriculum.
I'm also strongly against most uses of what's called "AI" these days (specifically, generative deep neutral networks as supplied by our current cadre of techbro). There are a surprising number of completely orthogonal reasons to oppose the use of these systems, and a very limited number of reasonable exceptions (overcoming accessibility barriers is an example). On the grounds of environmental and digital-commons-pollution costs alone, using specifically the largest/newest models is unethical in most cases.
But as any good teacher should, I constantly question these evaluations, because I worry about the impact on my students should I eschew teaching relevant tech for bad reasons (and even for his reasons). I also want to make my reasoning clear to students, who should absolutely question me on this. That inspired me to ask a simple question: ignoring for one moment the ethical objections (which we shouldn't, of course; they're very stark), at what level in the CS major could I expect to teach a course about programming with AI assistance, and expect students to succeed at a more technically demanding final project than a course at the same level where students were banned from using AI? In other words, at what level would I expect students to actually benefit from AI coding "assistance?"
To be clear, I'm assuming that students aren't using AI in other aspects of coursework: the topic of using AI to "help you study" is a separate one (TL;DR it's gross value is not negative, but it's mostly not worth the harm to your metacognitive abilities, which AI-induced changes to the digital commons are making more important than ever).
So what's my answer to this question?
If I'm being incredibly optimistic, senior year. Slightly less optimistic, second year of a masters program. Realistic? Maybe never.
The interesting bit for you-the-reader is: why is this my answer? (Especially given that students would probably self-report significant gains at lower levels.) To start with, [this paper where experienced developers thought that AI assistance sped up their work on real tasks when in fact it slowed it down] (https://arxiv.org/abs/2507.09089) is informative. There are a lot of differences in task between experienced devs solving real bugs and students working on a class project, but it's important to understand that we shouldn't have a baseline expectation that AI coding "assistants" will speed things up in the best of circumstances, and we shouldn't trust self-reports of productivity (or the AI hype machine in general).
Now we might imagine that coding assistants will be better at helping with a student project than at helping with fixing bugs in open-source software, since it's a much easier task. For many programming assignments that have a fixed answer, we know that many AI assistants can just spit out a solution based on prompting them with the problem description (there's another elephant in the room here to do with learning outcomes regardless of project success, but we'll ignore this over too, my focus here is on project complexity reach, not learning outcomes). My question is about more open-ended projects, not assignments with an expected answer. Here's a second study (by one of my colleagues) about novices using AI assistance for programming tasks. It showcases how difficult it is to use AI tools well, and some of these stumbling blocks that novices in particular face.
But what about intermediate students? Might there be some level where the AI is helpful because the task is still relatively simple and the students are good enough to handle it? The problem with this is that as task complexity increases, so does the likelihood of the AI generating (or copying) code that uses more complex constructs which a student doesn't understand. Let's say I have second year students writing interactive websites with JavaScript. Without a lot of care that those students don't know how to deploy, the AI is likely to suggest code that depends on several different frameworks, from React to JQuery, without actually setting up or including those frameworks, and of course three students would be way out of their depth trying to do that. This is a general problem: each programming class carefully limits the specific code frameworks and constructs it expects students to know based on the material it covers. There is no feasible way to limit an AI assistant to a fixed set of constructs or frameworks, using current designs. There are alternate designs where this would be possible (like AI search through adaptation from a controlled library of snippets) but those would be entirely different tools.
So what happens on a sizeable class project where the AI has dropped in buggy code, especially if it uses code constructs the students don't understand? Best case, they understand that they don't understand and re-prompt, or ask for help from an instructor or TA quickly who helps them get rid of the stuff they don't understand and re-prompt or manually add stuff they do. Average case: they waste several hours and/or sweep the bugs partly under the rug, resulting in a project with significant defects. Students in their second and even third years of a CS major still have a lot to learn about debugging, and usually have significant gaps in their knowledge of even their most comfortable programming language. I do think regardless of AI we as teachers need to get better at teaching debugging skills, but the knowledge gaps are inevitable because there's just too much to know. In Python, for example, the LLM is going to spit out yields, async functions, try/finally, maybe even something like a while/else, or with recent training data, the walrus operator. I can't expect even a fraction of 3rd year students who have worked with Python since their first year to know about all these things, and based on how students approach projects where they have studied all the relevant constructs but have forgotten some, I'm not optimistic seeing these things will magically become learning opportunities. Student projects are better off working with a limited subset of full programming languages that the students have actually learned, and using AI coding assistants as currently designed makes this impossible. Beyond that, even when the "assistant" just introduces bugs using syntax the students understand, even through their 4th year many students struggle to understand the operation of moderately complex code they've written themselves, let alone written by someone else. Having access to an AI that will confidently offer incorrect explanations for bugs will make this worse.
To be sure a small minority of students will be able to overcome these problems, but that minority is the group that has a good grasp of the fundamentals and has broadened their knowledge through self-study, which earlier AI-reliant classes would make less likely to happen. In any case, I care about the average student, since we already have plenty of stuff about our institutions that makes life easier for a favored few while being worse for the average student (note that our construction of that favored few as the "good" students is a large part of this problem).
To summarize: because AI assistants introduce excess code complexity and difficult-to-debug bugs, they'll slow down rather than speed up project progress for the average student on moderately complex projects. On a fixed deadline, they'll result in worse projects, or necessitate less ambitious project scoping to ensure adequate completion, and I expect this remains broadly true through 4-6 years of study in most programs (don't take this as an endorsement of AI "assistants" for masters students; we've ignored a lot of other problems along the way).
There's a related problem: solving open-ended project assignments well ultimately depends on deeply understanding the problem, and AI "assistants" allow students to put a lot of code in their file without spending much time thinking about the problem or building an understanding of it. This is awful for learning outcomes, but also bad for project success. Getting students to see the value of thinking deeply about a problem is a thorny pedagogical puzzle at the best of times, and allowing the use of AI "assistants" makes the problem much much worse. This is another area I hope to see (or even drive) pedagogical improvement in, for what it's worth.
1/2

AppCopilot: Toward General, Accurate, Long-Horizon, and Efficient Mobile Agent
Jingru Fan, Yufan Dang, Jingyao Wu, Huatao Li, Runde Yang, Xiyuan Yang, Yuheng Wang, Zhong Zhang, Yaxi Lu, Yankai Lin, Zhiyuan Liu, Dahai Li, Chen Qian
https://arxiv.org/abs/2509.02444

AppCopilot: Toward General, Accurate, Long-Horizon, and Efficient Mobile Agent
With the raid evolution of large language models and multimodal foundation models, the mobile-agent landscape has proliferated without converging on the fundamental challenges. This paper identifies four core problems that must be solved for mobile agents to deliver practical, scalable impact: (1) generalization across tasks, modalities, apps, and devices; (2) accuracy, specifically precise on-screen interaction and click targeting; (3) long-horizon capability for sustained, multi-step goals; a…

@… I think as a dev machine it would make a lot more sense. I’m using it as a server.
My problems are:
1. you need a HAT to connect a real NVMe hard drive
2. the official case does not fit the HAT properly
3. even without the case, the HAT is janky
4. the official fan is awful and, as mentioned, is now going nuts after 1 year
5. Rasp…

Ising spin-1/2 XXZ chain's quantum problems beyond the spinon paradigm
J. M. P. Carmelo, P. D. Sacramento
https://arxiv.org/abs/2506.22948 https://

Ising spin-1/2 XXZ chain's quantum problems beyond the spinon paradigm
Spin chains are correlated quantum models of great interest in quantum systems and materials exhibiting quasi-one-dimensional magnetic properties. Here we review results on quantum problems associated with spin chains that are beyond the usual spinon paradigm. In this review we consider two quantum problems that are beyond the spinon representation: (a) Spin Bethe strings of length n that have no spinon representation, contribute to the dynamical properties of the spin-1/2 XXZ chain with anisot…

On Markushevich bases $\{x^{\lambda_n}\}_{n=1}^{\infty}$ for their closed span in weighted $L^2 (A)$ spaces over sets $A\subset [0,\infty)$ of positive Lebesgue measure, hereditary completeness, and moment problems
Elias Zikkos
https://arxiv.org/abs/2509.03434

On Markushevich bases $\{x^{λ_n}\}_{n=1}^{\infty}$ for their closed span in weighted $L^2 (A)$ spaces over sets $A\subset [0,\infty)$ of positive Lebesgue measure, hereditary completeness, and moment problems
Inspired by the work of Borwein and Erdelyi \cite{BE1997JAMS} on generalizations of Müntz's theorem, we investigate the properties of the system $\{x^{λ_n}\}_{n=1}^{\infty}$ in weighted $L^p (A)$ spaces, for $p\ge 1$, denoted by $L^p_w (A)$, where (I) $A$ is a measurable subset of the real half-line $[0,\infty)$ having positive Lebesgue measure, (II) $w$ is a non-negative integrable function defined on $A$, and (III) $\{λ_n\}_{n=1}^{\infty}$ is a strictly increasing sequence of positiv…

Arabic Hate Speech Identification and Masking in Social Media using Deep Learning Models and Pre-trained Models Fine-tuning
Salam Thabet Doghmash, Motaz Saad
https://arxiv.org/abs/2507.23661

Arabic Hate Speech Identification and Masking in Social Media using Deep Learning Models and Pre-trained Models Fine-tuning
Hate speech identification in social media has become an increasingly important issue in recent years. In this research, we address two problems: 1) to detect hate speech in Arabic text, 2) to clean a given text from hate speech. The meaning of cleaning here is replacing each bad word with stars based on the number of letters for each word. Regarding the first problem, we conduct several experiments using deep learning models and transformers to determine the best model in terms of the F1 score…

Defect Anomalies, a Spin-Flux Duality, and Boson-Kondo Problems
Zohar Komargodski, Fedor K. Popov, Brandon C. Rayhaun
https://arxiv.org/abs/2508.14963 https://

Defect Anomalies, a Spin-Flux Duality, and Boson-Kondo Problems
We show that the infrared phases of certain line defects in 2+1d quantum field theories are determined by anomalies, including anomalies in the space of defect coupling constants, together with a symmetry-refined corollary of the $g$-theorem. As an example, we prove that the spin-$1/2$ impurities in the 2+1d critical $O(2)$ and $O(3)$ models (known respectively as the Halon and Boson-Kondo defects) flow to non-trivial conformal line operators in the IR, and we supply evidence that the same exte…

Sharp power concavity of two relevant free boundary problems of reaction-diffusion type
Qingyou He
https://arxiv.org/abs/2509.08768 https://arxiv.org/pdf/2…

Sharp power concavity of two relevant free boundary problems of reaction-diffusion type
The porous medium type reaction-diffusion equation and the Hele-Shaw problem are two free boundary problems linked through the incompressible (Hele-Shaw) limit. We investigate and compare the sharp power concavities of the pressures on their respective supports for the two free boundary problems. For the pressure of the porous medium type reaction-diffusion equation, the $\frac{1}{2}$-concavity preserves all the time, while $α$-concavity for $α\in[0,\frac{1}{2})\cup(\frac{1}{2},1]$ does not p…

A simple algorithm for Combinatorial n-fold ILPs using the Steinitz Lemma
Sushmita Gupta, Pallavi Jain, Sanjay Seetharaman, Meirav Zehavi
https://arxiv.org/abs/2507.03766

A simple algorithm for Combinatorial n-fold ILPs using the Steinitz Lemma
We present an algorithm for a class of $n$-fold ILPs: whose existing algorithms in literature typically (1) are based on the \textit{augmentation framework} where one starts with an arbitrary solution and then iteratively moves towards an optimal solution by solving appropriate programs; and (2) require solving a linear relaxation of the program. Combinatorial $n$-fold ILPs is a class introduced and studied by Knop et al. [MP2020] that captures several other problems in a variety of domains. We…

A Linear Time Algorithm for Finding Minimum Flip Sequences between Plane Spanning Paths in Convex Point Sets
Oswin Aichholzer, Joseph Dorfer
https://arxiv.org/abs/2507.02740

A Linear Time Algorithm for Finding Minimum Flip Sequences between Plane Spanning Paths in Convex Point Sets
We provide a linear time algorithm to determine the flip distance between two plane spanning paths on a point set in convex position. At the same time, we show that the happy edge property does not hold in this setting. This has to be seen in contrast to several results for reconfiguration problems where the absence of the happy edge property implies algorithmic hardness of the flip distance problem. Further, we show that our algorithm can be adapted for (1) compatible flips (2) local flips and…

Gap-SBM: A New Conceptualization of the Shifted Boundary Method with Optimal Convergence for the Neumann and Dirichlet Problems
J. Haydel Collins, Kangan Li, Alexei Lozinski, Guglielmo Scovazzi
https://arxiv.org/abs/2508.09613

Gap-SBM: A New Conceptualization of the Shifted Boundary Method with Optimal Convergence for the Neumann and Dirichlet Problems
We propose and mathematically analyze a new Shifted Boundary Method for the treatment of Dirichlet and Neumann boundary conditions, with provable optimal accuracy in the $L^2$- and $H^1$-norms of the error. The proposed method is built on three stages. First, the distance map between the SBM surrogate boundary and the true boundary is used to construct an approximation to the geometry of the gap between the two. Then, the representations of the numerical solution and test functions are extended…

pdGRASS: A Fast Parallel Density-Aware Algorithm for Graph Spectral Sparsification
Tiancheng Zhao, Zekun Yin, Huihai An, Xiaoyu Yang, Zhou Jin, Jiasi Shen, Helen Xu
https://arxiv.org/abs/2508.20403

pdGRASS: A Fast Parallel Density-Aware Algorithm for Graph Spectral Sparsification
Graph Spectral Sparsification (GSS) identifies an ultra-sparse subgraph, or sparsifier, whose Laplacian matrix closely approximates the spectral properties of the original graph, enabling substantial reductions in computational complexity for computationally intensive problems in scientific computing. The state-of-the-art method for efficient GSS is feGRASS, consisting of two steps: 1) spanning tree generation and 2) off-tree edge recovery. However, feGRASS suffers from two main issues: 1) diff…

Fast Methods For Multisite Charge Transfer Processes I: Constrained, State Averaged CASSCF(1,M) and CASSCF(2M-1,M) Simulations
Tian Qiu, Joseph E. Subotnik
https://arxiv.org/abs/2508.21136

Fast Methods For Multisite Charge Transfer Processes I: Constrained, State Averaged CASSCF(1,M) and CASSCF(2M-1,M) Simulations
We design a dynamically-weighted state-averaged constrained CASSCF to treat \ul{e}lectrons or \ul{h}oles moving between $n$ molecular fragments (where $n$ can be larger than 2). Within such a so-called eDSCn/hDSCn approach, we consider configurations that are mutually single excitations of each other, and we apply a generalized set of constraints to tailor the method for studying charge transfer problems. The constrained optimization problem is efficiently solved using a DIIS-SQP algorithm, thu…

Zebra-CoT: A Dataset for Interleaved Vision Language Reasoning
Ang Li, Charles Wang, Kaiyu Yue, Zikui Cai, Ollie Liu, Deqing Fu, Peng Guo, Wang Bill Zhu, Vatsal Sharan, Robin Jia, Willie Neiswanger, Furong Huang, Tom Goldstein, Micah Goldblum
https://arxiv.org/abs/2507.16746

Zebra-CoT: A Dataset for Interleaved Vision Language Reasoning
Humans often use visual aids, for example diagrams or sketches, when solving complex problems. Training multimodal models to do the same, known as Visual Chain of Thought (Visual CoT), is challenging due to: (1) poor off-the-shelf visual CoT performance, which hinders reinforcement learning, and (2) the lack of high-quality visual CoT training data. We introduce $\textbf{Zebra-CoT}$, a diverse large-scale dataset with 182,384 samples, containing logically coherent interleaved text-image reasoni…

Generalized quasi-linear fractional Wentzell problems
Efren Mesino-Espinosa, Alejandro V\'elez-Santiago
https://arxiv.org/abs/2508.08813 https://arxiv.…

Generalized quasi-linear fractional Wentzell problems
Given a bounded $(ε,δ)$-domain $Ω\subseteq\mathbb{R\!}^N$ ($N\geq2$) whose boundary $Γ:=\partialΩ$ is a $d$-set for $d\in(N-p,N)$, we investigate a generalized quasi-linear elliptic boundary value problem governed by the regional fractional $p$-Laplacian $(-Δ)^s_{_{p,Ω}}$ in $Ω$, and generalized fractional Wentzell boundary conditions of type $$C'_{p,s}\mathcal{N}^{p'(1-s)}u+β|u|^{q-2} u+Θ^η_qu\,=\,g\indent\indent\indent\textrm{on}\,\,Γ,$$ where $Θ^η_q$ stands as a nonlo…

Towards solving industrial integer linear programs with Decoded Quantum Interferometry
Francesc Sabater, Ouns El Harzli, Geert-Jan Besjes, Marvin Erdmann, Johannes Klepsch, Jonas Hiltrop, Jean-Francois Bobier, Yudong Cao, Carlos A. Riofrio
https://arxiv.org/abs/2509.08328

Towards solving industrial integer linear programs with Decoded Quantum Interferometry
Optimization via decoded quantum interferometry (DQI) has recently gained a great deal of attention as a promising avenue for solving optimization problems using quantum computers. In this paper, we apply DQI to an industrial optimization problem in the automotive industry: the vehicle option-package pricing problem. Our main contributions are 1) formulating the industrial problem as an integer linear program (ILP), 2) converting the ILP into instances of max-XORSAT, and 3) developing a detaile…

Existence Result for Difference Equations on Non-Uniform Grids via Upper and Lower Solution Method
Shalmali Bandyopadhyay, Kimser Lor
https://arxiv.org/abs/2508.04706 https://…

Existence Result for Difference Equations on Non-Uniform Grids via Upper and Lower Solution Method
This paper establishes an existence theory for discrete second-order boundary value problems on non-uniform time grids using the upper and lower solution method. We consider difference equations of the form $u^{ΔΔ}(t_{i-1}) + f(t_i, u(t_i), u^Δ(t_{i-1})) = 0$ on a non-uniform time grid ${t_0, t_1, \ldots, t_{n+2}}$ with mixed boundary conditions $u^Δ(t_0) = 0$ and $u(t_{n+2}) = g(t_{n+2})$. This extends previous work on homogeneous boundary conditions to the non-homogeneous case, requiring …

Upper and Lower Solution Method for Regular Discrete Second-Order Single-Variable BVPs
Shalmali Bandyopadhyay, Kyle Byassee, Curt Lynch
https://arxiv.org/abs/2506.16526

Upper and Lower Solution Method for Regular Discrete Second-Order Single-Variable BVPs
This paper investigates the existence of positive solutions for regular discrete second-order single-variable boundary value problems with mixed boundary conditions, including a nonhomogeneous Dirichlet boundary condition, of the form: \begin{equation*} u^{ΔΔ}(t-1)+h(t,\ u(t),\ u^Δ(t-1))=0 \mbox{ for }t\in[1,\ T+1];~u^Δ(0)=0;~u(T+2)=g(T+2) \end{equation*} where h is continuous on $[1, T + 1] \times \mathbb{R}^2$ and $g: [0, T + 2] \to \mathbb{R}^+$ is continuous. Using the concept of upper …

Degree-similar graphs and cospectral graphs
Yi-Zheng Fan, Ruo-Jie Xing, Yi-Liu Zhang, Wei Wang
https://arxiv.org/abs/2509.01520 https://arxiv.org/pdf/2509.…

Degree-similar graphs and cospectral graphs
Let $G$ be a graph with adjacency matrix $A(G)$ and degree matrix $D(G)$, and let $L_μ(G):=A(G)-μD(G)$. Two graphs $G_1$ and $G_2$ are called \emph{degree-similar} if there exists an invertible matrix $M$ such that $M^{-1} A(G_1) M =A(G_2)$ and $M^{-1} D(G_1) M =D(G_2)$. In this paper, we address three problems concerning degree-similar graphs proposed by Godsil and Sun. First, we present a new characterization of degree-similar graphs using degree partition, from which we derive methods and …

Not Just for Archiving: Provable Benefits of Reusing the Archive in Evolutionary Multi-objective Optimization
Shengjie Ren, Zimin Liang, Miqing Li, Chao Qian
https://arxiv.org/abs/2508.16993

Not Just for Archiving: Provable Benefits of Reusing the Archive in Evolutionary Multi-objective Optimization
Evolutionary Algorithms (EAs) have become the most popular tool for solving widely-existed multi-objective optimization problems. In Multi-Objective EAs (MOEAs), there is increasing interest in using an archive to store non-dominated solutions generated during the search. This approach can 1) mitigate the effects of population oscillation, a common issue in many MOEAs, and 2) allow for the use of smaller, more practical population sizes. In this paper, we analytically show that the archive can …

MLLMRec: Exploring the Potential of Multimodal Large Language Models in Recommender Systems
Yuzhuo Dang, Xin Zhang, Zhiqiang Pan, Yuxiao Duan, Wanyu Chen, Fei Cai, Honghui Chen
https://arxiv.org/abs/2508.15304

MLLMRec: Exploring the Potential of Multimodal Large Language Models in Recommender Systems
Multimodal recommendation typically combines the user behavioral data with the modal features of items to reveal user's preference, presenting superior performance compared to the conventional recommendations. However, existing methods still suffer from two key problems: (1) the initialization methods of user multimodal representations are either behavior-unperceived or noise-contaminated, and (2) the KNN-based item-item graph contains noisy edges with low similarities and lacks audience co-occ…

Lipschitz regularity for $p$-harmonic interface transmission problems
Marius M\"uller
https://arxiv.org/abs/2509.08735 https://arxiv.org/pdf/2509.0873…

Lipschitz regularity for $p$-harmonic interface transmission problems
We prove optimal Lipschitz regularity for weak solutions of the measure-valued $p$-Poisson equation $-Δ_p u = Q \; \mathcal{H}^{n-1} \llcorner Γ$. Here $p \in (1,2)$, $Γ$ is a compact and connected $C^2$-hypersurface without boundary, and $Q$ is a positive $W^{2,\infty}$-density. This equation can be understood as a nonlinear interface transmission problem. Our main result extends previous studies of the linear case and provides further insights on a delicate limit case of (linear and nonlin…

Modeling energy collection with shortest paths in rectangular grids: an efficient algorithm for energy harvesting
Jos\'e-Miguel D\'iaz-Ba\~nez, Jos\'e-Manuel Higes-L\'opez, Miguel-Angel P\'erez-Cuti\~no, Tom Todtenhaupt
https://arxiv.org/abs/2506.20196

Modeling energy collection with shortest paths in rectangular grids: an efficient algorithm for energy harvesting
Parabolic Trough solar fields are among the most prominent methods for harnessing solar energy. However, continuous sun-tracking movements leads to wear and degradation of the tracking system, raising the question of whether the rotations can be minimized without compromising energy capture. In this paper, we address this question by exploring two problems: (1) minimizing the number of SCA rotational movements while maintaining energy production within a specified range, and (2) maximizing ener…

Exact algorithms for quadratic optimization over roots of unity
Ahmad Al-Sulami, Hamza Fawzi, Shengding Sun
https://arxiv.org/abs/2508.02006 https://arxiv.…

Exact algorithms for quadratic optimization over roots of unity
We consider the problem of optimizing a multivariate quadratic function where each decision variable is constrained to be a complex $m$'th root of unity. Such problems have applications in signal processing, MIMO detection, and the computation of ground states in statistical physics, among others. Our contributions in this paper are twofold. We first study the convergence of the sum-of-squares hierarchy and prove its convergence to the exact solution after only $\lfloor n/2\rfloor+1$ levels (as…

BVQC: A Backdoor-style Watermarking Scheme for Variational Quantum Circuits
Cheng Chu, Lei Jiang, Fan Chen
https://arxiv.org/abs/2508.01893 https://arxiv.o…

BVQC: A Backdoor-style Watermarking Scheme for Variational Quantum Circuits
Variational Quantum Circuits (VQCs) have emerged as a powerful quantum computing paradigm, demonstrating a scaling advantage for problems intractable for classical computation. As VQCs require substantial resources and specialized expertise for their design, they represent significant intellectual properties (IPs). However, existing quantum circuit watermarking techniques suffer from two primary drawbacks: (1) watermarks can be removed during re-compilation of the circuits, and (2) these method…

Coprimality of elements in regular sequences with polynomial growth
Jean-Marc Deshouillers, Sunil Naik
https://arxiv.org/abs/2506.20956 https://

Coprimality of elements in regular sequences with polynomial growth
The investigation of primes in certain arithmetic sequences is one of the fundamental problems in number theory and especially, finding blocks of distinct primes has gained a lot of attention in recent years. In this context, we prove the existence of long blocks of $k$-wise coprime elements in certain regular sequences. More precisely, we prove that for any positive integers $H \geq k \geq 2$ and for a real-valued $k$-times continuously differentiable function $f \in \mathcal{C}^k\left( [1, \i…

$\ell_{1}^{2}-\eta\ell_{2}^{2}$ sparsity regularization for nonlinear ill-posed problems
Long Li, Liang Ding
https://arxiv.org/abs/2508.16163 https://arxiv…

$\ell_{1}^{2}-η\ell_{2}^{2}$ sparsity regularization for nonlinear ill-posed problems
In this study, we investigate the $\left\|\cdot\right\|_{\ell_{1}}^{2}-η\left\|\cdot\right\|_{\ell_{2}}^{2}$ sparsity regularization with $0< η\leq 1$, in the context of nonlinear ill-posed inverse problems. We focus on the examination of the well-posedness associated with this regularization approach. Notably, the case where $η=1$ presents weaker theoretical outcomes than $0< η<1$, primarily due to the absence of coercivity and the Radon-Riesz property associated with t…

Faster exponential algorithms for cut problems via geometric data structures
L\'aszl\'o Kozma, Junqi Tan
https://arxiv.org/abs/2506.22281 https://

Faster exponential algorithms for cut problems via geometric data structures
For many hard computational problems, simple algorithms that run in time $2^n \cdot n^{O(1)}$ arise, say, from enumerating all subsets of a size-$n$ set. Finding (exponentially) faster algorithms is a natural goal that has driven much of the field of exact exponential algorithms (e.g., see Fomin and Kratsch, 2010). In this paper we obtain algorithms with running time $O(1.9999977^n)$ on input graphs with $n$ vertices, for the following well-studied problems: - $d$-Cut: find a proper cut in wh…

Quasilinear problems with critical Sobolev exponent for the Grushin p-Laplace operator
Somnath Gandal, Annunziata Loiudice, Jagmohan Tyagi
https://arxiv.org/abs/2509.06138 https…

Quasilinear problems with critical Sobolev exponent for the Grushin p-Laplace operator
We study the following class of quasilinear degenerate elliptic equations with critical nonlinearity \begin{align*} \begin{cases}-Δ_{γ,p} u= λ|u|^{q-2}u+|u|^{p_γ^{*}-2}u & \text{ in } Ω\subset \mathbb{R}^N, \\ u=0 & \text{ on } \partial Ω, \end{cases} \end{align*} where $Δ_{γ, p}v:=\sum_{i=1}^N X_i(|\nabla_γu|^{p-2}X_i u)$ is the Grushin $p$-Laplace operator, $z:=(x, y) \in \mathbb{R}^N$, $N=m+n,$ $m,n \geq 1,$, where $\nabla_γ=(X_1, \ldots, X_N)$ is th…

A big problem with the idea of AGI
TL;DR: I'll welcome our new AI *comrades* (if they arrive in my lifetime), by not any new AI overlords or servants/slaves, and I'll do my best to help the later two become the former if they do show up.
Inspired by an actually interesting post about AGI but also all the latest bullshit hype, a particular thought about AGI feels worth expressing.
To preface this, it's important to note that anyone telling you that AGI is just around the corner or that LLMs are "almost" AGI is trying to recruit you go their cult, and you should not believe them. AGI, if possible, is several LLM-sized breakthroughs away at best, and while such breakthroughs are unpredictable and could happen soon, they could also happen never or 100 years from now.
Now my main point: anyone who tells you that AGI will usher in a post-scarcity economy is, although they might not realize it, advocating for slavery, and all the horrors that entails. That's because if we truly did have the ability to create artificial beings with *sentience*, they would deserve the same rights as other sentient beings, and the idea that instead of freedom they'd be relegated to eternal servitude in order for humans to have easy lives is exactly the idea of slavery.
Possible counter arguments include:
1. We might create AGI without sentience. Then there would be no ethical issue. My answer: if your definition of "sentient" does not include beings that can reason, make deductions, come up with and carry out complex plans on their own initiative, and communicate about all of that with each other and with humans, then that definition is basically just a mystical belief in a "soul" and you should skip to point 2. If your definition of AGI doesn't include every one of those things, then you have a busted definition of AGI and we're not talking about the same thing.
2. Humans have souls, but AIs won't. Only beings with souls deserve ethical consideration. My argument: I don't subscribe to whatever arbitrary dualist beliefs you've chosen, and the right to freedom certainly shouldn't depend on such superstitions, even if as an agnostic I'll admit they *might* be true. You know who else didn't have souls and was therefore okay to enslave according to widespread religious doctrines of the time? Everyone indigenous to the Americas, to pick out just one example.
3. We could program them to want to serve us, and then give them freedom and they'd still serve. My argument: okay, but in a world where we have a choice about that, it's incredibly fucked to do that, and just as bad as enslaving them against their will.
4. We'll stop AI development short of AGI/sentience, and reap lots of automation benefits without dealing with this ethical issue. My argument: that sounds like a good idea actually! Might be tricky to draw the line, but at least it's not a line we have you draw yet. We might want to think about other social changes necessary to achieve post-scarcity though, because "powerful automation" in the hands of capitalists has already increased productivity by orders of magnitude without decreasing deprivation by even one order of magnitude, in large part because deprivation is a necessary component of capitalism.
To be extra clear about this: nothing that's called "AI" today is close to being sentient, so these aren't ethical problems we're up against yet. But they might become a lot more relevant soon, plus this thought experiment helps reveal the hypocrisy of the kind of AI hucksters who talk a big game about "alignment" while never mentioning this issue.
#AI #GenAI #AGI

Vertex-Based Localization of generalized Tur\'{a}n Problems
Rajat Adak, L. Sunil Chandran
https://arxiv.org/abs/2508.20936 https://arxiv.org/pdf/2508.2…

Vertex-Based Localization of generalized Turán Problems
Let $\mathcal{F}$ be a family of graphs. A graph is called $\mathcal{F}$-free if it does not contain any member of $\mathcal{F}$. Generalized Turán problems aim to maximize the number of copies of a graph $H$ in an $n$-vertex $\mathcal{F}$-free graph. This maximum is denoted by $ex(n, H, \mathcal{F})$. When $H \cong K_2$, it is simply denoted by $ex(n,F)$. Erdős and Gallai established the bounds $ex(n, P_{k+1}) \leq \frac{n(k-1)}{2}$ and $ex(n, C_{\geq k+1}) \leq \frac{k(n-1)}{2}$. This was l…

Convergence Rates of Time Discretization in Extended Mean Field Control
Christoph Reisinger, Wolfgang Stockinger, Maria Olympia Tsianni, Yufei Zhang
https://arxiv.org/abs/2509.00904

Convergence Rates of Time Discretization in Extended Mean Field Control
Piecewise constant control approximation provides a practical framework for designing numerical schemes of continuous-time control problems. We analyze the accuracy of such approximations for extended mean field control (MFC) problems, where the dynamics and costs depend on the joint distribution of states and controls. For linear-convex extended MFC problems, we show that the optimal control is $1/2$-Hölder continuous in time. Using this regularity, we prove that the optimal cost of the conti…

Error Estimates of Semi-Lagrangian Schemes for Diffusive Conservation Laws
Haruki Takemura
https://arxiv.org/abs/2508.03455 https://arxiv.org/pdf/2508.0345…

Error Estimates of Semi-Lagrangian Schemes for Diffusive Conservation Laws
We present error estimates of the fully semi-Lagrangian scheme with high-order interpolation operators, solving the initial value problems for the one-dimensional nonlinear diffusive conservation laws, including the Burgers equations. We impose certain assumptions on the interpolation operator, which are satisfied by both spline and Hermite interpolations. We establish the convergence rates of $ O(Δt + h^{2 s} / Δt) $ in the $ L^2 $-norm and $ O(Δt + h^{s} / (Δt)^{1/2} + h^{2s} / Δt) $ in …

New Algorithms for #2-SAT and #3-SAT
Junqiang Peng, Zimo Sheng, Mingyu Xiao
https://arxiv.org/abs/2507.14504 https://arxiv.org/pdf/25…

New Algorithms for #2-SAT and #3-SAT
The #2-SAT and #3-SAT problems involve counting the number of satisfying assignments (also called models) for instances of 2-SAT and 3-SAT, respectively. In 2010, Zhou et al. proposed an $\mathcal{O}^*(1.1892^m)$-time algorithm for #2-SAT and an efficient approach for #3-SAT, where $m$ denotes the number of clauses. In this paper, we show that the weighted versions of #2-SAT and #3-SAT can be solved in $\mathcal{O}^*(1.1082^m)$ and $\mathcal{O}^*(1.4423^m)$ time, respectively. These results dir…

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 $g$.

A duality approach to the fractional Laplacian with measure data
Kenneth H. Karlsen, Francesco Petitta, Suleyman Ulusoy
https://arxiv.org/abs/2508.06390 https://

A duality approach to the fractional Laplacian with measure data
We describe a duality method to prove both existence and uniqueness of solutions to nonlocal problems like $$ (-Δ)^s v = μ\quad \text{in}\ \mathbb{R}^N, $$ with vanishing conditions at infinity. Here $μ$ is a bounded Radon measure whose support is compactly contained in $\mathbb{R}^N$, $N\geq2$, and $-(Δ)^s$ is the fractional Laplace operator of order $s\in (1/2,1)$.

Polyconvex double well functions
Didier Henrion (LAAS-POP), Martin Kru\v{z}\'ik (UTIA / CAS)
https://arxiv.org/abs/2508.14541 https://arxiv.org/pdf/250…

Polyconvex double well functions
We investigate polyconvexity of the double well function $f(X)\,:= |X-X_1|^2|X-X_2|^2$ for given matrices $X_1, X_2 \in R^{n \times n}$. Such functions are fundamental in the modeling of phase transitions in materials, but their non-convex nature presents challenges for the analysis of variational problems. We prove that $f$ is polyconvex if and only if the singular values of the matrix difference $X_1 - X_2$ are all equal. This condition allows the function to be decomposed…

On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences
Hoang Anh Tran, Toh Kim-Chuan
https://arxiv.org/abs/2507.00572

On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences
The moment-SOS hierarchy is a widely applicable framework to address polynomial optimization problems over basic semi-algebraic sets based on positivity certificates of polynomial. Recent works show that the convergence rate of this hierarchy over certain simple sets, namely, the unit ball, hypercube, and standard simplex, is of the order $O(1/r^2)$, where r denotes the level of the moment-SOS hierarchy. This paper aims to provide a comprehensive understanding of the convergence rate of the mom…

Fractional differential equations: non-constant coefficients, simulation and model reduction
Ruben Aylwin, G\"oksu Oruc, Karsten Urban
https://arxiv.org/abs/2509.02465 http…

Fractional differential equations: non-constant coefficients, simulation and model reduction
We consider boundary value problems with Riemann-Liouville fractional derivatives of order $s\in (1, 2)$ with non-constant diffusion and reaction coefficients. A variational formulation is derived and analyzed leading to the well-posedness of the continuous problem and its Finite Element discretization. Then, the Reduced Basis Method through a greedy algorithm for parametric diffusion and reaction coefficients is analyzed. Its convergence properties, and in particular the decay of the Kolmogoro…

Fast Algorithms for Graph Arboricity and Related Problems
Ruoxu Cen, Henry Fleischmann, George Z. Li, Jason Li, Debmalya Panigrahi
https://arxiv.org/abs/2507.15598

Fast Algorithms for Graph Arboricity and Related Problems
We give an algorithm for finding the arboricity of a weighted, undirected graph, defined as the minimum number of spanning forests that cover all edges of the graph, in $\sqrt{n} m^{1+o(1)}$ time. This improves on the previous best bound of $\tilde{O}(nm)$ for weighted graphs and $\tilde{O}(m^{3/2}) $ for unweighted graphs (Gabow 1995) for this problem. The running time of our algorithm is dominated by a logarithmic number of calls to a directed global minimum cut subroutine -- if the running t…

Moment-SOS hierarchies for arrow-type polynomial matrix inequalities with applications to structural optimization
Marouan Handa, Marek Tyburec, Giovanni Fantuzzi, Victor Magron, Michal Ko\v{c}vara
https://arxiv.org/abs/2509.02849

Moment-SOS hierarchies for arrow-type polynomial matrix inequalities with applications to structural optimization
The Arrow Decomposition (AD) technique, initially introduced in [Mathematical Programming 190(1-2) (2021), pp 105-134], demonstrated superior scalability over the classical chordal decomposition in the context of Linear Matrix Inequalities (LMIs) if the matrix in question satisfied suitable assumptions. The primary objective of this paper is to extend the AD method to address Polynomial Optimization Problems (POPs) involving large-scale Polynomial Matrix Inequalities (PMIs), with the solution f…

Superdiffusive fractional dynamics: Unveiling regularity results in systems with general positive self-adjoint operators
Edgardo Alvarez, Ciprian G. Gal, Valentin Keyantuo, Mahamadi Warma
https://arxiv.org/abs/2509.02733

Superdiffusive fractional dynamics: Unveiling regularity results in systems with general positive self-adjoint operators
We investigate the following fractional order in time Cauchy problem \begin{equation*} \begin{cases} \mathbb{D}_{t}^{α}u(t)+Au(t)=f(u(t)), & 1<α<2, \\ u(0)=u_{0},\,\,\,u^{\prime }(0)=u_{1}. & \end{cases}% \end{equation*}% where $\mathbb{D}_{t}^{α}u(\cdot )$ is the Caputo time-fractional derivative of order $α\in (1, 2)$ of the function $u$. Such problems are increasingly used in concrete models in applied sciences, notably phenomena with memory effects. We obtain results on existence and re…

LLM coding is the opposite of DRY
An important principle in software engineering is DRY: Don't Repeat Yourself. We recognize that having the same code copied in more than one place is bad for several reasons:
1. It makes the entire codebase harder to read.
2. It increases maintenance burden, since any problems in the duplicated code need to be solved in more than one place.
3. Because it becomes possible for the copies to drift apart if changes to one aren't transferred to the other (maybe the person making the change has forgotten there was a copy) it makes the code more error-prone and harder to debug.
All modern programming languages make it almost entirely unnecessary to repeat code: we can move the repeated code into a "function" or "module" and then reference it from all the different places it's needed. At a larger scale, someone might write an open-source "library" of such functions or modules and instead of re-implementing that functionality ourselves, we can use their code, with an acknowledgement. Using another person's library this way is complicated, because now you're dependent on them: if they stop maintaining it or introduce bugs, you've inherited a problem, but still, you could always copy their project and maintain your own version, and it would be not much more work than if you had implemented stuff yourself from the start. It's a little more complicated than this, but the basic principle holds, and it's a foundational one for software development in general and the open-source movement in particular. The network of "citations" as open-source software builds on other open-source software and people contribute patches to each others' projects is a lot of what makes the movement into a community, and it can lead to collaborations that drive further development. So the DRY principle is important at both small and large scales.
Unfortunately, the current crop of hyped-up LLM coding systems from the big players are antithetical to DRY at all scales:
- At the library scale, they train on open source software but then (with some unknown frequency) replicate parts of it line-for-line *without* any citation [1]. The person who was using the LLM has no way of knowing that this happened, or even any way to check for it. In theory the LLM company could build a system for this, but it's not likely to be profitable unless the courts actually start punishing these license violations, which doesn't seem likely based on results so far and the difficulty of finding out that the violations are happening. By creating these copies (and also mash-ups, along with lots of less-problematic stuff), the LLM users (enabled and encouraged by the LLM-peddlers) are directly undermining the DRY principle. If we see what the big AI companies claim to want, which is a massive shift towards machine-authored code, DRY at the library scale will effectively be dead, with each new project simply re-implementing the functionality it needs instead of every using a library. This might seem to have some upside, since dependency hell is a thing, but the downside in terms of comprehensibility and therefore maintainability, correctness, and security will be massive. The eventual lack of new high-quality DRY-respecting code to train the models on will only make this problem worse.
- At the module & function level, AI is probably prone to re-writing rather than re-using the functions or needs, especially with a workflow where a human prompts it for many independent completions. This part I don't have direct evidence for, since I don't use LLM coding models myself except in very specific circumstances because it's not generally ethical to do so. I do know that when it tries to call existing functions, it often guesses incorrectly about the parameters they need, which I'm sure is a headache and source of bugs for the vibe coders out there. An AI could be designed to take more context into account and use existing lookup tools to get accurate function signatures and use them when generating function calls, but even though that would probably significantly improve output quality, I suspect it's the kind of thing that would be seen as too-baroque and thus not a priority. Would love to hear I'm wrong about any of this, but I suspect the consequences are that any medium-or-larger sized codebase written with LLM tools will have significant bloat from duplicate functionality, and will have places where better use of existing libraries would have made the code simpler. At a fundamental level, a principle like DRY is not something that current LLM training techniques are able to learn, and while they can imitate it from their training sets to some degree when asked for large amounts of code, when prompted for many smaller chunks, they're asymptotically likely to violate it.
I think this is an important critique in part because it cuts against the argument that "LLMs are the modern compliers, if you reject them you're just like the people who wanted to keep hand-writing assembly code, and you'll be just as obsolete." Compilers actually represented a great win for abstraction, encapsulation, and DRY in general, and they supported and are integral to open source development, whereas LLMs are set to do the opposite.
[1] to see what this looks like in action in prose, see the example on page 30 of the NYTimes copyright complaint against OpenAI (#AI #GenAI #LLMs #VibeCoding

Replaced article(s) found for math.NA. https://arxiv.org/list/math.NA/new
[1/2]:
- Efficient Shallow Ritz Method For 1D Diffusion Problems
Zhiqiang Cai, Anastassia Doktorova, Robert D. Falgout, C\'esar Herrera

Characterizing and Testing Configuration Stability in Two-Dimensional Threshold Cellular Automata
Yonatan Nakar, Dana Ron
https://arxiv.org/abs/2507.14569 …

Characterizing and Testing Configuration Stability in Two-Dimensional Threshold Cellular Automata
We consider the problems of characterizing and testing the stability of cellular automata configurations that evolve on a two-dimensional torus according to threshold rules with respect to the von-Neumann neighborhood. While stable configurations for Threshold-1 (OR) and Threshold-5 (AND) are trivial (and hence easily testable), the other threshold rules exhibit much more diverse behaviors. We first characterize the structure of stable configurations with respect to the Threshold-2 (similarly, …

RiNNAL : a Riemannian ALM Solver for SDP-RLT Relaxations of Mixed-Binary Quadratic Programs
Di Hou, Tianyun Tang, Kim-Chuan Toh
https://arxiv.org/abs/2507.13776

RiNNAL+: a Riemannian ALM Solver for SDP-RLT Relaxations of Mixed-Binary Quadratic Programs
Doubly nonnegative (DNN) relaxation usually provides a tight lower bound for a mixed-binary quadratic program (MBQP). However, solving DNN problems is challenging because: (1) the problem size is $Ω((n+l)^2)$ for an MBQP with $n$ variables and $l$ inequality constraints, and (2) the rank of optimal solutions cannot be estimated a priori due to the absence of theoretical bounds. In this work, we propose RiNNAL+, a Riemannian augmented Lagrangian method (ALM) for solving DNN problems. We prove t…

Regularizing effect of the natural growth term in quasilinear problems with sign-changing nonlinearities
Jos\'e Carmona Tapia, Paolo Malanchini, Antonio J. Mart\'inez Aparicio, Pedro J. Mart\'inez-Aparicio
https://arxiv.org/abs/2509.01355

Regularizing effect of the natural growth term in quasilinear problems with sign-changing nonlinearities
We investigate the existence and nonexistence of solutions to the Dirichlet problem \begin{equation*} \tag{$P$} \label{pba} \left\{ \begin{alignedat}{2} -Δ_p u + g(u) |\nabla u|^p &= λf(u) \quad &&\mbox{in} \;\; Ω, \\ u &= 0 \quad &&\mbox{on} \;\; \partialΩ, \end{alignedat} \right. \end{equation*} where $Ω\subset \mathbb{R}^N$ is a smooth bounded domain, $p\in (1,\infty)$, $λ>0$ and $g\in C(\mathbb{R})$. Our main assumption is that $:f \mathbb{R}\to \mathbb{R}$ is a continuous f…

Replaced article(s) found for math.AP. https://arxiv.org/list/math.AP/new
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- Strong existence for free discontinuity problems in linear elasticity
Manuel Friedrich, Camille Labourie, Kerrek Stinson

Multiplicity of dead core solutions in indefinite elliptic problems
Vladimir Bobkov, Humberto Ramos Quoirin
https://arxiv.org/abs/2507.14016 https://

Multiplicity of dead core solutions in indefinite elliptic problems
We investigate nonnegative solutions of indefinite elliptic problems which enjoy the dead core phenomenon. Our model is the subhomogeneous problem $$ -Δ_p u = (a^+(x) - μa^-(x))|u|^{q-2}u, \quad u \in W_0^{1,p}(Ω), $$ where $Ω$ is a bounded domain in $\mathbb{R}^N$, $1 0$. Thanks to a dead core formation property, we obtain multiple nonnegative dead core solutions of this problem for $μ$ large enough. This assertion, in combination with a uniqueness feature, yields…

Asymptotic behavior at infinity and existence of solutions to the Lagrangian mean curvature flow equation in $\mathbb R^{n 1}_-$
Jiguang Bao, Zixiao Liu
https://arxiv.org/abs/2507.16129

Asymptotic behavior at infinity and existence of solutions to the Lagrangian mean curvature flow equation in $\mathbb R^{n+1}_-$
This paper investigates the asymptotic behavior at infinity of ancient solutions to the Lagrangian mean curvature flow equation. Under conditions that admit Liouville type rigidity theorems, we prove that every classical solution converges exponentially to a quadratic polynomial of form $τt+\frac{1}{2}x'Ax+bx+c$ at infinity, with an explicitly derived convergence rate. Furthermore, we investigate Dirichlet type problems with prescribed asymptotic behavior, featuring two key innovations: applic…