Tootfinder

This is a public service announcement for all the dollar-store Sherlock Holmes’s out there who clearly have nothing better to do than to concoct conspiracy theories about people from Gaza on the fediverse who are faced with genocide and famine:
Stop.
Have some humanity.
Case in point, do not do what Daniel (@helmet91@mastodon.social) is doing here:

The Diophantine Frobenius Problem revisited
Yuchen Ding, Weijia Wang, Hao Zhang
https://arxiv.org/abs/2509.08599 https://arxiv.org/pdf/2509.08599

The Diophantine Frobenius Problem revisited
Let $k\ge 2$ and $a_1, a_2, \cdots, a_k$ be positive integers with \[ \gcd(a_1, a_2, \cdots, a_k)=1. \] It is proved that there exists a positive integer $G_{a_1, a_2, \cdots, a_k}$ such that every integer $n$ strictly greater than it can be represented as the form \[ n=a_1x_1+a_2x_2+\cdots+a_kx_k, \quad (x_1, x_2, \cdots, x_k\in\mathbb{Z}_{\ge 0},~\gcd(x_1, x_2, \cdots, x_k)=1). \] We then investigate the size of $G_{a_1, a_2}$ explicitly. Our result strengthens the primality requirement of $x…

Randomised algebraic constructions for the no-$(k 1)$-in-line problem
Benedek Kov\'acs, Zolt\'an L\'or\'ant Nagy, D\'avid R. Szab\'o
https://arxiv.org/abs/2508.07632

Randomised algebraic constructions for the no-$(k+1)$-in-line problem
The no-(k+1)-in line problem seeks the maximum number of points that can be selected from an $n \times n$ square lattice such that no $k+1$ of them are collinear. The problem was first posed more than $100$ years ago for the special case $k=2$ and has remained open ever since. The general problem was recently resolved in the case $k$ is not small compared to $n$, as Kovács, Nagy and Szabó proved that the upper bound $kn$ can be attained, provided that $k>C\sqrt{n\log{n}}$ for an absolute cons…

Exact solution of the two-magnon problem in the $k=-\pi/2$ sector of a finite-size anisotropic spin-$1/2$ frustrated ferromagnetic chain
Zimeng Li, Ning Wu
https://arxiv.org/abs/2509.09659

Exact solution of the two-magnon problem in the $k=-π/2$ sector of a finite-size anisotropic spin-$1/2$ frustrated ferromagnetic chain
The two-magnon problem in the $k=-π/2$ sector of a \emph{finite-size} spin-1/2 chain with ferromagnetic nearest-neighbor (NN) interaction $(J_1>0)$ and antiferromagnetic next-nearest-neighbor (NNN) interaction $(J_2<0)$ and anisotropy parameters $Δ_1$ and $Δ_2$ is solved exactly by combining a set of exact two-magnon Bloch states and a plane-wave ansatz. Two types of two-magnon bound states (BSs), i.e., the NN and NNN exchange BSs, are revealed. We establish a phase diagram in the $J_1/(…

@helmet91@mastodon.social These people are literally faced with genocide and famine and you’re out here acting like a dollar-store Sherlock Holmes.
I’ve told you several times now that I’ve had live video conversations over Signal with Nouran and her brother Yousef.
I don’t know what your problem is but what you’re doing by spreading this FUD is deplorable. I just saw that you wrote this blog post also:

How not to get scammed
Give yourself a chance before you become a prey.

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

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

Deep holes of a class of twisted Reed-Solomon codes
Haojie Gu, Nan Wang, Jun Zhang
https://arxiv.org/abs/2509.08526 https://arxiv.org/pdf/2509.08526…

Deep holes of a class of twisted Reed-Solomon codes
The deep hole problem is a fundamental problem in coding theory, and it has many important applications in code constructions and cryptography. The deep hole problem of Reed-Solomon codes has gained a lot of attention. As a generalization of Reed-Solomon codes, we investigate the problem of deep holes of a class of twisted Reed-Solomon codes in this paper. Firstly, we provide the necessary and sufficient conditions for $\boldsymbol{a}=(a_{0},a_{1},\cdots,a_{n-k-1})\in\mathbb{F}_{q}^{n-k}$ to …

#Reform der Pflegevericherung #Interview mit Katarina Planer, Professorin für #Pflege und Pflegemangement

Abschaffung des Pflegegrad 1: Bringt sie überhaupt etwas?
Die Bundesregierung überlegt, den Pflegegrad 1 abzuschaffen. Warum das Problem nicht am Pflegegrad 1, sondern woanders liegt, erklärt Pflegewirtin Katarina Planer von der Hochschule Esslingen.

Variational Construction of Homoclinic and Heteroclinic Orbits in the Planar Sitnikov Problem
Yuika Kajihara, Mitsuru Shibayama, Guowei Yu
https://arxiv.org/abs/2508.08051 https…

Variational Construction of Homoclinic and Heteroclinic Orbits in the Planar Sitnikov Problem
The Sitnikov problem is a special case of the three-body problem. The system is known to be chaotic and has been studied by symbolic dynamics (J. Moser, Stable and random motions in dynamical systems, Princeton University Press, 1973). We study the limiting case of the Sitnikov problem as the eccentricity of the massive particles tends to 1. By variational method, we show the existence of infinitely many homoclinic and heteroclinic solutions in the planar Sitnikov problem. In a previous work, f…

Efficient Reward Identification In Max Entropy Reinforcement Learning with Sparsity and Rank Priors
Mohamad Louai Shehab, Alperen Tercan, Necmiye Ozay
https://arxiv.org/abs/2508.07400

Efficient Reward Identification In Max Entropy Reinforcement Learning with Sparsity and Rank Priors
In this paper, we consider the problem of recovering time-varying reward functions from either optimal policies or demonstrations coming from a max entropy reinforcement learning problem. This problem is highly ill-posed without additional assumptions on the underlying rewards. However, in many applications, the rewards are indeed parsimonious, and some prior information is available. We consider two such priors on the rewards: 1) rewards are mostly constant and they change infrequently, 2) rew…

Descent problem for certificate of non-negativity on semi-algebraic sets
Manoj K. Keshari, Debapriya Ojha, Niladri Sekhar Patra
https://arxiv.org/abs/2508.07060 https://

Descent problem for certificate of non-negativity on semi-algebraic sets
Let $F$ be a subfield of $\mathbb R$ and let $K$ be a basic closed semi-algebraic set in $\mathbb R$ with $\partial K\subset F$. Let $\mathcal N$ be the natural choice of generators of $K$. We show that if $f\in F[x]$ is $\geq 0$ on $K$, then $f$ can be written as $$f=\sum_{e\in\{0,1\}^s } a_eσ_e g^e $$ where $a_e\in F_{\geq 0}$, $σ_e\in \sum F[x]^2$ and $g^{e}=g_1^{e_1} \cdots g_s^{e_s}$. In other words, the preordering $T_{\mathcal N}$ of $F[x]$ is saturated. In case $F=\mathbb R$, this res…

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…

Decentralized Stochastic Nonconvex Optimization under the Relaxed Smoothness
Luo Luo, Xue Cui, Tingkai Jia, Cheng Chen
https://arxiv.org/abs/2509.08726 https://

Decentralized Stochastic Nonconvex Optimization under the Relaxed Smoothness
This paper studies decentralized optimization problem $f(\mathbf{x})=\frac{1}{m}\sum_{i=1}^m f_i(\mathbf{x})$, where each local function has the form of $f_i(\mathbf{x}) = {\mathbb E}\left[F(\mathbf{x};ξ_i)\right]$ which is $(L_0,L_1)$-smooth but possibly nonconvex and the random variable $ξ_i$ follows distribution ${\mathcal D}_i$. We propose a novel algorithm called decentralized normalized stochastic gradient descent (DNSGD), which can achieve the $ε$-stationary point on each local agent.…

Generative Diffusion Contrastive Network for Multi-View Clustering
Jian Zhu, Xin Zou, Xi Wang, Ning Zhang, Bian Wu, Yao Yang, Ying Zhou, Lingfang Zeng, Chang Tang, Cheng Luo
https://arxiv.org/abs/2509.09527

Generative Diffusion Contrastive Network for Multi-View Clustering
In recent years, Multi-View Clustering (MVC) has been significantly advanced under the influence of deep learning. By integrating heterogeneous data from multiple views, MVC enhances clustering analysis, making multi-view fusion critical to clustering performance. However, there is a problem of low-quality data in multi-view fusion. This problem primarily arises from two reasons: 1) Certain views are contaminated by noisy data. 2) Some views suffer from missing data. This paper proposes a novel…

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

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

Nearly Optimal Bounds for Stochastic Online Sorting
Yang Hu
https://arxiv.org/abs/2508.07823 https://arxiv.org/pdf/2508.07823

Nearly Optimal Bounds for Stochastic Online Sorting
In the online sorting problem, we have an array $A$ of $n$ cells, and receive a stream of $n$ items $x_1,\dots,x_n\in [0,1]$. When an item arrives, we need to immediately and irrevocably place it into an empty cell. The goal is to minimize the sum of absolute differences between adjacent items, which is called the \emph{cost} of the algorithm. It has been shown by Aamand, Abrahamsen, Beretta, and Kleist (SODA 2023) that when the stream $x_1,\dots,x_n$ is generated adversarially, the optimal cos…

Estimating the size of a set using cascading exclusion
Sourav Chatterjee, Persi Diaconis, Susan Holmes
https://arxiv.org/abs/2508.05901 https://arxiv.org/p…

Estimating the size of a set using cascading exclusion
Let $S$ be a finite set, and $X_1,\ldots,X_n$ an i.i.d. uniform sample from $S$. To estimate the size $|S|$, without further structure, one can wait for repeats and use the birthday problem. This requires a sample size of the order $|S|^\frac{1}{2}$. On the other hand, if $S=\{1,2,\ldots,|S|\}$, the maximum of the sample blown up by $n/(n-1)$ gives an efficient estimator based on any growing sample size. This paper gives refinements that interpolate between these e…

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

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

Titans coach Brian Callahan was a problem in sickening Week 1 loss to Broncos

https://www.cbssports.com/nfl/news/titans-coach-brian-callahan-was-a-probl…

Self-dual monopole loops, instantons and confinement
Mendel Nguyen, Mithat \"Unsal
https://arxiv.org/abs/2509.09625 https://arxiv.org/pdf/2509.09625…

Self-dual monopole loops, instantons and confinement
It is well-known that the standard instanton analysis in 4d Yang-Mills is plagued with the instanton size moduli problem, which renders the instanton contribution to vacuum energy density (or one-instanton partition function) infrared divergent. The formalism also ignores the implications of long range (magnetic dipole type) $1/r^4$ interaction between the small instantons, since it is weaker than Coulomb interaction. We show that in $U(1)$ lattice gauge theory, where finite action configuratio…

Oh wow.
https://www.linkedin.com/pulse/innovation-starts-problem-technology-martijn-van-dijk-sfbye/
Die Story mit dem Fahrzeug, das in der Regennacht einfach weiter beschleunigt... erklärt einiges!
Falls sich jemand fragt, warum unsere Zulassungsregeln so "fürchterlich streng" sind, dann darum: Weil es wieder und wieder Buden oder Bastler gibt, die echt Scheisse bauen.
Unter anderem wird nämlich genau das geprüft. Wenn gebremst wird, darf der Motor nicht mehr beschleunigen. Aus Gründen.

Replaced article(s) found for cs.FL. https://arxiv.org/list/cs.FL/new
[1/1]:
- On the Separability Problem of VASS Reachability Languages
Eren Keskin, Roland Meyer

Crosslisted article(s) found for math.GR. https://arxiv.org/list/math.GR/new
[1/1]:
- Ordered groups of formal series, and a conjugacy problem
Vincent Bagayoko
…

Two sets of integers such that all elements of the sumset of the two sets are perfect squares
Ajai Choudhry
https://arxiv.org/abs/2508.07806 https://arxiv.…

Two sets of integers such that all elements of the sumset of the two sets are perfect squares
This paper is concerned with the problem of finding two sets of integers, $\{a_1, a_2, \ldots$, $a_m\}$ and $\{b_1, b_2, \ldots, b_n\}$, such that all the $mn$ sums $a_i+b_j, i=1, \ldots, m, j=1, \ldots, n$, are perfect squares. A method is known for generating numerical examples of such sets when $m=2$ or 3 and $n$ is arbitrary. When both $m$ and $n$ exceed 2, only one two-parameter solution with $(m, n)=(4, 4)$ has been published. In this paper we obtain several multi-parameter solutions of t…

Truthful Two-Obnoxious-Facility Location Games with Optional Preferences and Minimum Distance Constraint
Xiaojia Han, Wenjing Liu, Qizhi Fang
https://arxiv.org/abs/2508.08036 ht…

Truthful Two-Obnoxious-Facility Location Games with Optional Preferences and Minimum Distance Constraint
In this paper, we study a truthful two-obnoxious-facility location problem, in which each agent has a private location in [0, 1] and a public optional preference over two obnoxious facilities, and there is a minimum distance constraint d between the two facilities. Each agent wants to be as far away as possible from the facilities that affect her, and the utility of each agent is the total distance from her to these facilities. The goal is to decide how to place the facilities in [0, 1] so as t…

Checking Consistency of Event-driven Traces
Parosh Aziz Abdulla, Mohamed Faouzi Atig, R. Govind, Samuel Grahn, Ramanathan S. Thinniyam
https://arxiv.org/abs/2508.07855 https://

Checking Consistency of Event-driven Traces
Event-driven programming is a popular paradigm where the flow of execution is controlled by two features: (1) shared memory and (2) sending and receiving of messages between multiple handler threads (just called handler). Each handler has a mailbox (modelled as a queue) for receiving messages, with the constraint that the handler processes its messages sequentially. Executions of messages by different handlers may be interleaved. A central problem in this setting is checking whether a candidate…

Axion Quality Problem: Keep Calm and Baryon
Prateek Agrawal, Anson Hook, Vazha Loladze, Mario Reig
https://arxiv.org/abs/2510.07366 https://arxiv.org/pdf/2…

Axion Quality Problem: Keep Calm and Baryon
Axion models generically suffer from a severe quality problem when coupled to gravity. In this article we provide a very simple model with a high quality axion. The axion is a pseudo-Nambu-Goldstone boson of the baryon number symmetry, $U(1)_B$, of a new composite sector that breaks $U(1)_B$ spontaneously when it confines. A controlled example is a supersymmetric QCD (SQCD) with $N_c = N_f$. The axion shift symmetry is automatically protected due to the high dimension of the gauge-invariant bar…

Crosslisted article(s) found for physics.flu-dyn. https://arxiv.org/list/physics.flu-dyn/new
[1/1]:
- The reflection-transmission problem for inertial waves on geostrophic shear layers
Lennart Kira, Jerome Noir, Daniel Lecoanet

Replaced article(s) found for q-bio.NC. https://arxiv.org/list/q-bio.NC/new
[1/1]:
- From Transformer to Biology: A Hierarchical Model for Attention in Complex Problem-Solving
Zhongqiao Lin, Yunwei Li, Tianming Yang

Computer-aided solution to the $k$-bonacci pick-up sticks problem
Julian Kern
https://arxiv.org/abs/2508.07943 https://arxiv.org/pdf/2508.07943

Computer-aided solution to the $k$-bonacci pick-up sticks problem
A full solution to the recently proposed problem of determining the probability that no $k$-gon can be built from $n$ independently and uniformly chosen sticks in $[0,1]$ is proposed. This extends the known results for triangles and quadrilaterals to general $k$-gons and offers a clearer interpretation of the connection to products of $k$-bonacci numbers.

Estimated Phase II Weibull control chart for monitoring times between events
Tanuja Negi
https://arxiv.org/abs/2508.05790 https://arxiv.org/pdf/2508.05790

Estimated Phase II Weibull control chart for monitoring times between events
In statistical process control Weibull distribution can be used to model the time between events or failures (TBE) in a process with increasing decreasing or constant failure rates. Specifically it helps in monitoring processes where the time between defect occurrences is of interest providing insight into the process reliability and performance. In this paper we consider the two sided problem of monitoring either an increase or a decrease in the scale parameter of the Weibull distribution with…

An Approximate Maximum Likelihood Estimator for Discretely Observed Linear Birth-and-Death Processes
Xiaochen Long, Marek Kimmel
https://arxiv.org/abs/2508.07527 https://…

An Approximate Maximum Likelihood Estimator for Discretely Observed Linear Birth-and-Death Processes
Linear birth-and-death processes (LBDPs) are foundational stochastic models in population dynamics, evolutionary biology, and hematopoiesis. Estimating parameters from discretely observed data is computationally demanding due to irregular sampling, noise, and missing values. We propose a novel approximate maximum likelihood estimator (MLE) for LBDPs based on a Gaussian approximation to transition probabilities. The approach transforms estimation into a univariate optimization problem, achieving…

Aw, flat tires, so sad. Hopefully that's not a sign of low quality tires, it would be tough situation if that became a common problem for ICE! https://kolektiva.social/@615ANTIFASCIST/115180400255033086

ANTIFASCIST 615 (@615ANTIFASCIST@kolektiva.social)
Attached: 1 image Crowd Jeers as Border Patrol vehicle with flattened tires leaves Rochester neighborhood. https://13wham.com/news/local/crowd-jeers-as-border-patrol-vehicle-with-flattened-tires-leaves-rochester-neighborhood-park-avenue-westminster-road-us-ice-customs-and-border-protection-federal-agents-trump-administration-immigration

Dynamical Systems with Bounded Condition and $C^{*}$-algebras
Takehiko Mori
https://arxiv.org/abs/2508.05713 https://arxiv.org/pdf/2508.05713

Dynamical Systems with Bounded Condition and $C^{*}$-algebras
By introducing the totally uniqueness condition for maps, we establish a one-to-one correspondence between the family of invariant sets for the $q x{+}d$-function (e.g. the $3 x{+}1$-map, also known as the Collatz map), where $q$ and $d$ are arbitrary positive odd numbers, and the family of reducing subspaces for the associated $C^{*}$-algebra. This extends the connection between the Collatz conjecture (also known as the $3 n{+}1$-problem) and the irreducibility of its associated $C^{*}$-algebr…

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…

Does block size matter in randomized block Krylov low-rank approximation?
Tyler Chen, Ethan N. Epperly, Raphael A. Meyer, Christopher Musco, Akash Rao
https://arxiv.org/abs/2508.06486

Does block size matter in randomized block Krylov low-rank approximation?
We study the problem of computing a rank-$k$ approximation of a matrix using randomized block Krylov iteration. Prior work has shown that, for block size $b = 1$ or $b = k$, a $(1 + \varepsilon)$-factor approximation to the best rank-$k$ approximation can be obtained after $\tilde O(k/\sqrt{\varepsilon})$ matrix-vector products with the target matrix. On the other hand, when $b$ is between $1$ and $k$, the best known bound on the number of matrix-vector products scales with $b(k-b)$, which coul…

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.
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On the Direct Problem in Differential Galois Theory for the Classical Groups
Daniel Robertz, Matthias Seiss
https://arxiv.org/abs/2510.07323 https://arxiv.…

On the Direct Problem in Differential Galois Theory for the Classical Groups
Let $G$ be a classical group of Lie rank $l$ and let $C$ be an algebraically closed field of characteristic zero. For $l$ differential indeterminates $\boldsymbol{v}=(v_1,\dots,v_l)$ over $C$ we constructed in a previous paper a general Picard-Vessiot extension $\mathcal{E}$ of the differential field $C\langle \boldsymbol{s}(\boldsymbol{v})\rangle$ having differential Galois group $G(C)$. Here $ \boldsymbol{s}(\boldsymbol{v})=(s_1(\boldsymbol{v}),\dots,s_l(\boldsymbol{v}))$ are certain differen…

Rational minimax approximation of matrix-valued functions
Lei-Hong Zhang, Ya-Nan Zhang, Chenkun Zhang, Shanheng Han
https://arxiv.org/abs/2508.06378 https://

Rational minimax approximation of matrix-valued functions
In this paper, we present a rigorous framework for rational minimax approximation of matrix-valued functions that generalizes classical scalar approximation theory. Given sampled data $\{(x_\ell, {F}(x_\ell))\}_{\ell=1}^m$ where ${F}:\mathbb{C} \to \mathbb{C}^{s \times t}$ is a matrix-valued function, we study the problem of finding a matrix-valued rational approximant ${R}(x) = {P}(x)/q(x)$ (with ${P}:\mathbb{C} \to \mathbb{C}^{s \times t}$ a matrix-valued polynomial and $q(x)$ a nonzero scala…

On Lagrangian formulations for (ir)reducible mixed-antisymmetric higher integer spin fields in Minkowski spaces
Alexander A. Reshetnyak, Julia V. Bogdanova, Vipul K. Pandey
https://arxiv.org/abs/2509.09490

On Lagrangian formulations for (ir)reducible mixed-antisymmetric higher integer spin fields in Minkowski spaces
We extend the results of Lagrangian formulations study to construct gauge-invariant Lagrangians for (ir)reducible integer higher-spin massless and massive representations of the Poincare group with a Young tableau $Y[\hat{s}_1,\hat{s}_2,\hat{s}_3]$ in $d$-dimensional flat space-time (as the probable candidates to describe the Dark Matter problem beyond the SM). These particles are described within a metric-like formulation by tensor fields with 3 groups of antisymmetric Lorentz indices $Φ_{μ^…

Crosslisted article(s) found for cs.CC. https://arxiv.org/list/cs.CC/new
[1/1]:
- 3-Local Hamiltonian Problem and Constant Relative Error Quantum Partition Function Approximation:...
Nai-Hui Chia, Yu-Ching Shen

Cowboys Have 1 Glaring Problem Going Into the New Season https://heavy.com/sports/nfl/dallas-cowboys/cowboys-have-1-glaring-problem-season/?adt_ei=[email]

Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications
Weiyuan Gong, Tongyang Li, Xinzhao Wang, Zhiyu Zhang
https://arxiv.org/abs/2509.08911 https://

Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications
The Matrix Multiplicative Weight Update (MMWU) is a seminal online learning algorithm with numerous applications. Applied to the matrix version of the Learning from Expert Advice (LEA) problem on the $d$-dimensional spectraplex, it is well known that MMWU achieves the minimax-optimal regret bound of $O(\sqrt{T\log d})$, where $T$ is the time horizon. In this paper, we present an improved algorithm achieving the instance-optimal regret bound of $O(\sqrt{T\cdot S(X||d^{-1}I_d)})$, where…

On the inverse transmission eigenvalue problem with a piecewise $W_2^1$ refractive index
Tao Liu, Kang Lyu, Guangsheng Wei, Chuan-Fu Yang
https://arxiv.org/abs/2509.06520 https:…

On the inverse transmission eigenvalue problem with a piecewise $W_2^1$ refractive index
In this paper, we consider the inverse spectral problem of determining the spherically symmetric refractive index in a bounded spherical region of radius $b$. Instead of the usual case of the refractive index $ρ\in W^2_2$, by using singular Sturm-Liouville theory, we {first} discuss the case when the refractive index $ρ$ is a piecewise $ W^1_2$ function. We prove that if $\int_0^b \sqrt{ρ(r)} dr

Approximating High-Dimensional Earth Mover's Distance as Fast as Closest Pair
Lorenzo Beretta, Vincent Cohen-Addad, Rajesh Jayaram, Erik Waingarten
https://arxiv.org/abs/2508.06774

Approximating High-Dimensional Earth Mover's Distance as Fast as Closest Pair
We give a reduction from $(1+\varepsilon)$-approximate Earth Mover's Distance (EMD) to $(1+\varepsilon)$-approximate Closest Pair (CP). As a consequence, we improve the fastest known approximation algorithm for high-dimensional EMD. Here, given $p\in [1, 2]$ and two sets of $n$ points $X,Y \subseteq (\mathbb R^d,\ell_p)$, their EMD is the minimum cost of a perfect matching between $X$ and $Y$, where the cost of matching two vectors is their $\ell_p$ distance. Further, CP is the basic problem of…

The Exact $\varepsilon$-Hypercyclicity Threshold
Geivison Ribeiro
https://arxiv.org/abs/2509.09406 https://arxiv.org/pdf/2509.09406

The Exact $\varepsilon$-Hypercyclicity Threshold
In this paper we give an affirmative answer to the problem proposed by Bayart in 2024 \cite{Bayart2024JMAA}: given $\varepsilon\in(0,1)$, there exists an operator which is $δ$-hypercyclic if and only if $δ\in[\varepsilon,1)$.

A Computer-Assisted Proof of the Optimal Density Bound for Pinwheel Covering
Akitoshi Kawamura, Yusuke Kobayashi
https://arxiv.org/abs/2510.06533 https://a…

A Computer-Assisted Proof of the Optimal Density Bound for Pinwheel Covering
In the covering version of the pinwheel scheduling problem, a daily task must be assigned to agents under the constraint that agent $i$ can perform the task at most once in any $a_i$-day interval. In this paper, we determine the optimal constant $α^* = 1.264\ldots {}$ such that every instance with $\sum_{i} \frac{1}{a_i} \ge α^*$ is schedulable. This resolves an open problem posed by Soejima and Kawamura (2020). Our proof combines Kawamura's (2024) techniques for the packing version with new …

On the ternary Estermann problem with almost proportional summands
Firuz Rakhmonov
https://arxiv.org/abs/2510.05602 https://arxiv.org/pdf/2510.05602…

On the ternary Estermann problem with almost proportional summands
For $n \geq 3$, an asymptotic formula is derived for the number of representations of a sufficiently large natural number $N$ in the form $p_1+p_2+m^n=N$, where $p_1$, $p_2$ $-$ prime numbers, $m$ $-$ natural number satisfying the conditions $$ \left|p_k-μ_kN\right|\le H, \quad k=1,2,\qquad \left|m^n-μ_3N\right|\le H,\qquad H \ge N^{1-\frac1{n(n-1)}} {\mathscr{L}}^{\frac{2^{n+1}}{n-1}+n-1},$$ for $μ_1+μ_2+μ_3=1, \ \ μ_i >0, \mathscr{L} = \ln{N}. $ Keywords: Estermann…

MuFASA -- Asynchronous Checkpoint for Weakly Consistent Fully Replicated Databases
Raaghav Ravishankar, Sandeep Kulkarni, Nitin H Vaidya
https://arxiv.org/abs/2510.06404 https:/…

MuFASA -- Asynchronous Checkpoint for Weakly Consistent Fully Replicated Databases
We focus on the problem of checkpointing in fully replicated weakly consistent distributed databases, which we refer to as Distributed Transaction Consistent Snapshot (DTCS). A typical example of such a system is a main-memory database that provides strong eventual consistency. This problem is important and challenging for several reasons: (1) eventual consistency often creates anomalies that the users do not anticipate. Hence, frequent checkpoints to ascertain desired invariants is highly bene…

Crosslisted article(s) found for math.RA. https://arxiv.org/list/math.RA/new
[1/1]:
- On the Direct Problem in Differential Galois Theory for the Classical Groups
Daniel Robertz, Matthias Seiss

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

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

The probabilities for the number of intersections in the Buffon-Laplace needle problem in $\mathbb{R}^d$
Uwe B\"asel
https://arxiv.org/abs/2508.04640 https://

The probabilities for the number of intersections in the Buffon-Laplace needle problem in $\mathbb{R}^d$
In 1974, Stoka solved Buffon's needle problem in $\mathbb{R}^d$, $d \ge 2$, i.e. he found a closed form solution for the probability that a line segment ("needle") with length $\ell$ intersects a grid of parallel hyperplanes with mutual distance $a\ge\ell$. For the Laplace needle problem in $\mathbb{R}^d$, where there are $d$ families of parallel hyperplanes with distances $a_1,\ldots,a_d$ fulfilling $\min(a_1,\ldots,a_d)\ge\ell$, and normal vectors in the direction of the coordinate axes $x_1,…

Crosslisted article(s) found for math.AT. https://arxiv.org/list/math.AT/new
[1/1]:
- Computational complexity of the homology problem with orientable filtration: MA-completeness
Ryu Hayakawa, Casper Gyurik, Mahtab Yaghubi Rad, Vedran Dunjko

Consistency of variational inference for Besov priors in non-linear inverse problems
Shaokang Zu, Junxiong Jia, Zhiguo Wang
https://arxiv.org/abs/2508.06179 https://

Consistency of variational inference for Besov priors in non-linear inverse problems
This study investigates the variational posterior convergence rates of inverse problems for partial differential equations (PDEs) with parameters in Besov spaces $B_{pp}^α$ ($p \geq 1$) which are modeled naturally in a Bayesian manner using Besov priors constructed via random wavelet expansions with $p$-exponentially distributed coefficients. Departing from exact Bayesian inference, variational inference transforms the inference problem into an optimization problem by introducing variational s…

Threshold dynamics in time-delay systems: polynomial $\beta$-control in a pressing process and connections to blow-up
Masato Kimura, Hirotaka Kuma, Yikan Liu, Kazunori Matsui, Masahiro Yamamoto, Zhenxing Yang
https://arxiv.org/abs/2508.07268

Threshold dynamics in time-delay systems: polynomial $β$-control in a pressing process and connections to blow-up
This paper addresses a press control problem in straightening machines with small time delays due to system communication. To handle this, we propose a generalized $β$-control method, which replaces conventional linear velocity control with a polynomial of degree $β\ge 1$. The resulting model is a delay differential equation (DDE), for which we derive basic properties through nondimensionalization and analysis. Numerical experiments suggest the existence of a threshold initial velocity separa…

On the global linear Zarankiewicz problem
Pantelis E. Eleftheriou, Aris Papadopoulos
https://arxiv.org/abs/2510.03546 https://arxiv.org/pdf/2510.03546

On the global linear Zarankiewicz problem
The `global' Zarankiewicz problem for hypergraphs asks for an upper bound on the number of edges of a finite $r$-hypergraph $V$ in terms of the number $|V|$ of its vertices, assuming the edge relation is induced by a fixed $K_{k, \dots, k}$-free $r$-hypergraph $E$, for some $k\in\mathbb N$. In [4], such bounds of size $O(|V|^{r-1})$ were achieved for a semilinear $E$, namely, definable in a linear o-minimal structure. We establish the same bounds in five new settings: when $…

Crosslisted article(s) found for astro-ph.SR. https://arxiv.org/list/astro-ph.SR/new
[1/1]:
- Rotational Metric: A Solution to Einstein's Clock-Rate Problem and Its Magnetospheric Applications
Zhen Zhang, Rui Zhang

#Mathematics #Maths

Crosslisted article(s) found for cs.RO. https://arxiv.org/list/cs.RO/new
[1/1]:
- The best approximation pair problem relative to two subsets in a normed space
Daniel Reem, Yair Censor

Replaced article(s) found for q-fin.RM. https://arxiv.org/list/q-fin.RM/new
[1/1]:
- De Finetti's problem with fixed transaction costs and regime switching
Wenyuan Wang, Zuo Quan Xu, Kazutoshi Yamazaki, Kaixin Yan, Xiaowen Zhou

Replaced article(s) found for physics.gen-ph. https://arxiv.org/list/physics.gen-ph/new
[1/1]:
- Test of a theory of the Mott quantum-measurement problem
Jonathan F. Schonfeld

Twisted conjugacy in $BS(n, 1)$
Oorna Mitra, Mallika Roy, Enric Ventura
https://arxiv.org/abs/2508.04397 https://arxiv.org/pdf/2508.04397

Twisted conjugacy in $BS(n, 1)$
In this article, we solve the twisted conjugacy problem for solvable Baumslag--Solitar groups $BS(n,1)$, i.e., we propose an algorithm which, given two elements $u,v \in BS(n,1)$ and an automorphism $φ\in \Aut(BS(n,1))$, decides whether $v=(wφ)^{-1} u w$ for some $w\in BS(n,1)$. Also we prove that the automorphism group $\Aut(BS(n,1))$ is orbit decidable -- given two words on the generators $u,v\in F(X)$, decide whether the corresponding elements $u,v\in G$ can be mapped to each other by some…

Prescribed $p$-curvature problem on Riemannian manifolds with negative curvature
Jiaogen Zhang
https://arxiv.org/abs/2510.06577 https://arxiv.org/pdf/2510.…

Prescribed $p$-curvature problem on Riemannian manifolds with negative curvature
Let $(N,g)$ be a compact Riemannian manifold with negative curvature of dimension $n\geq 3$. This paper investigates the prescribed curvature problem defined by the $p$-fold sum of the modified Shouten tensor for $1\leq p\leq n$. As an application, we establish the existence of a metric $\tilde{g}$ conformal to $g$ such that \[ \mathcal{M}_{p}(\mathrm{Ric}_{\tilde{g}})=constant. \] In the case $p=1$, this resolves a well-known result of Gursky and Viaclovsky [Indiana Univ. Math. J. 52 (2003), n…

Optimization of a Nonlinear Acoustics -- Structure Interaction Model
Barbara Kaltenbacher, Amjad Tuffaha
https://arxiv.org/abs/2508.07728 https://arxiv.org…

Optimization of a Nonlinear Acoustics -- Structure Interaction Model
In this paper, we consider a control/shape optimization problem of a nonlinear acoustics-structure interaction model of PDEs, whereby acoustic wave propagation in a chamber is governed by the Westervelt equation, and the motion of the elastic part of the boundary is governed by a 4th order Kirchoff equation. We consider a quadratic objective functional capturing the tracking of prescribed desired states, with three types of controls: 1) An excitation control represented by prescribed Neumann da…

Algorithm for constructing optimal explicit finite-difference formulas in the Hilbert space
R. S. Karimov, D. D. Atoev
https://arxiv.org/abs/2510.06643 https://

Algorithm for constructing optimal explicit finite-difference formulas in the Hilbert space
This work presents problems of constructing finite-difference formulas in the Hilbert space, i.e., setting problems of constructing finite-difference formulas using functional methods. The work presents a functional statement of the problem of optimizing finite-difference formulas in the space $W_{2}^{\left(m,m-1\right)} \left(0,1\right)$. Here, representations of optimal coefficients of explicit finite-difference formulas of the Adams type on classes $W_{2}^{\left(m,m-1\right)} \left(0,1\right…

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

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

Eagles and Cowboys begin their season seeking answers to an old problem https://theeagleswire.usatoday.com/story/sports/nfl/eagles/2025/09/03/eagles-cowboys-share-week-1-mission-ending-old-problem/85955081007…

Tight Bounds for Low-Error Frequency Moment Estimation and the Power of Multiple Passes
Naomi Green-Maimon, Or Zamir
https://arxiv.org/abs/2509.07599 https://

Tight Bounds for Low-Error Frequency Moment Estimation and the Power of Multiple Passes
Estimating the second frequency moment $F_2$ of a data stream up to a $(1 \pm \varepsilon)$ factor is a central problem in the streaming literature. For errors $\varepsilon > Ω(1/\sqrt{n})$, the tight bound $Θ\left(\log(\varepsilon^2 n)/\varepsilon^2\right)$ was recently established by Braverman and Zamir. In this work, we complete the picture by resolving the remaining regime of small error, $\varepsilon < 1/\sqrt{n}$, showing that the optimal space complexity is $Θ\left( \min\left(n, \frac…

Simple Quantum Algorithm for Approximate $k$-Mismatch Problem
Ruhan Habib
https://arxiv.org/abs/2510.02399 https://arxiv.org/pdf/2510.02399

Simple Quantum Algorithm for Approximate $k$-Mismatch Problem
In the $k$-mismatch problem, given a pattern and a text of length $n$ and $m$ respectively, we have to find if the text has a sub-string with a Hamming distance of at most $k$ from the pattern. This has been studied in the classical setting since 1982 and recently in the quantum computational setting by Jin and Nogler and Kociumaka, Nogler, and Wellnitz. We provide a simple quantum algorithm that solves the problem in an approximate manner, given a parameter $ε\in (0, 1]$. It returns an occurr…

Crosslisted article(s) found for hep-th. https://arxiv.org/list/hep-th/new
[1/1]:
- Axion Quality Problem: Keep Calm and Baryon
Prateek Agrawal, Anson Hook, Vazha Loladze, Mario Reig

Exponential Error Bounds for Information Bottleneck Source Coding Problems
Han Wu, Hamdi Joudeh
https://arxiv.org/abs/2510.08364 https://arxiv.org/pdf/2510…

Exponential Error Bounds for Information Bottleneck Source Coding Problems
We study the information bottleneck (IB) source coding problem, also known as remote lossy source coding under logarithmic loss. Based on a rate-limited description of noisy observations, the receiver produces a soft estimate for the remote source, i.e., a probability distribution, evaluated under the logarithmic loss. We focus on the excess distortion probability of IB source coding and investigate how fast it converges to 0 or 1, depending on whether the rate is above or below the rate-distor…

Nesterov acceleration for strongly convex-strongly concave bilinear saddle point problems: discrete and continuous-time approaches
Xin He, Ya-Ping Fang
https://arxiv.org/abs/2509.08258

Nesterov acceleration for strongly convex-strongly concave bilinear saddle point problems: discrete and continuous-time approaches
In this paper, we study a bilinear saddle point problem of the form $\min_{x}\max_{y} F(x) + \langle Ax, y \rangle - G(y)$, where $F$ and $G$ are $μ_F$- and $μ_G$-strongly convex functions, respectively. By incorporating Nesterov acceleration for strongly convex optimization, we first propose an optimal first-order discrete primal-dual gradient algorithm. We show that it achieves the optimal convergence rate $\mathcal{O}\left(\left(1 - \min\left\{\sqrt{\frac{μ_F}{L_F}}, \sqrt{\frac{μ_G}{L_G…

An axiomatic approach to analytic $1$-affineness
Matteo Montagnani, Emanuele Pavia
https://arxiv.org/abs/2509.04341 https://arxiv.org/pdf/2509.04341…

An axiomatic approach to analytic $1$-affineness
The notion of $1$-affineness was originally formulated by Gaitsgory in the context of derived algebraic geometry. Motivated by applications to rigid and analytic geometry, we introduce two very general and abstract frameworks where it makes to ask for objects to be $1$-affine with respect to some sheaf of categories. The first framework is suited for studying the problem of $1$-affineness when the sheaf of categories arises from an operation in a six-functor formalism over $\mathscr{C}$; we app…

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…

Replaced article(s) found for math.GR. https://arxiv.org/list/math.GR/new
[1/1]:
- On the complexity of the word problem of the R. Thompson group V
J. C. Birget

Concept Retrieval -- What and How?
Ori nizan, Oren Shrout, Ayellet Tal
https://arxiv.org/abs/2510.07058 https://arxiv.org/pdf/2510.07058

Concept Retrieval - What and How?
A concept may reflect either a concrete or abstract idea. Given an input image, this paper seeks to retrieve other images that share its central concepts, capturing aspects of the underlying narrative. This goes beyond conventional retrieval or clustering methods, which emphasize visual or semantic similarity. We formally define the problem, outline key requirements, and introduce appropriate evaluation metrics. We propose a novel approach grounded in two key observations: (1) While each neighb…

You cannot capture the essence of capitalism in a single pho- https://me.dm/@davidtoddmccarty/114944150346707896

David Todd McCarty (@davidtoddmccarty@me.dm)
Attached: 1 image So clearly the most hateful and soulless solution to a problem that might exist.

Finite element approximation to linear, second order, parabolic problems with $L^1$ data
Gabriel Barrenechea, Abner J. Salgado
https://arxiv.org/abs/2510.05331 https://

Finite element approximation to linear, second order, parabolic problems with $L^1$ data
We consider the approximation to the solution of the initial boundary value problem for the heat equation with right hand side and initial condition that merely belong to $L^1$. Due to the low integrability of the data, to guarantee well-posedness, we must understand solutions in the renormalized sense. We prove that, under an inverse CFL condition, the solution of the standard implicit Euler scheme with mass lumping converges, in $L^\infty(0,T;L^1(Ω))$ and $L^q(0,T;W^{1,q}_0(Ω))$ ($q<\tfrac{…

Solving Skolem problem for negative indexed $k-$generalized Pell numbers
Monalisa Mohapatra, Pritam Kumar Bhoi, Gopal Krishna Panda
https://arxiv.org/abs/2509.04503 https://

Solving Skolem problem for negative indexed $k-$generalized Pell numbers
In this paper, we address the Skolem problem for the $k-$Generalized Pell numbers ($P_n^{(k)}$) extended to negative indices. We focus on identifying and bounding the indices $n<0$ for which $P_n^{(k)}=0.$ In particular, we establish that the zero multiplicity is $ χ_k = 1 + (k(k-2)/4),$ if $k$ is even and $1 + ((k - 1)^2/4)$, if $k$ is odd for all $k \in [4, 500].$

On the recognition problem for limits of entropy functions
Geva Yashfe
https://arxiv.org/abs/2509.06302 https://arxiv.org/pdf/2509.06302

On the recognition problem for limits of entropy functions
We prove that there is no algorithm to decide whether a given integer vector is in the closure of the entropic cone $\overline{Γ_{n}^{*}}$. Equivalently, there is no decision procedure to determine whether a given integer-valued function $h:\mathcal{P}(\{1,\ldots,n\})\rightarrow\mathbb{Z}_{\ge 0}$ is a pointwise limit of joint entropy functions. In other words, given such an $h$, it is undecidable whether for all $\varepsilon > 0$ there exists a finite probability space $(Ω,P)$ with random va…

Crosslisted article(s) found for math.AP. https://arxiv.org/list/math.AP/new
[1/1]:
- Numerical Approximation and Bifurcation Results for an Elliptic Problem with Superlinear Subcriti...
Shalmali Bandyopadhyay, Thomas Lewis, Dustin Nichols

Debiasing Polynomial and Fourier Regression
Chris Cama\~no, Raphael A. Meyer, Kevin Shu
https://arxiv.org/abs/2508.05920 https://arxiv.org/pdf/2508.05920…

Debiasing Polynomial and Fourier Regression
We study the problem of approximating an unknown function $f:\mathbb{R}\to\mathbb{R}$ by a degree-$d$ polynomial using as few function evaluations as possible, where error is measured with respect to a probability distribution $μ$. Existing randomized algorithms achieve near-optimal sample complexities to recover a $ (1+\varepsilon) $-optimal polynomial but produce biased estimates of the best polynomial approximation, which is undesirable. We propose a simple debiasing method based on a con…

List Recoverable Codes: The Good, the Bad, and the Unknown (hopefully not Ugly)
Nicolas Resch, S. Venkitesh
https://arxiv.org/abs/2510.07597 https://arxiv.…

List Recoverable Codes: The Good, the Bad, and the Unknown (hopefully not Ugly)
List recovery is a fundamental task for error-correcting codes, vastly generalizing unique decoding from worst-case errors and list decoding. Briefly, one is given ''soft information'' in the form of input lists S_1,...,S_n of bounded size, and one argues that there are not too many codewords that agree a lot with this soft information. This general problem appears in many guises, both within coding theory and in theoretical computer science more broadly. In this article we survey recent resu…

Crosslisted article(s) found for math.NT. https://arxiv.org/list/math.NT/new
[1/1]:
- On the Direct Problem in Differential Galois Theory for the Classical Groups
Daniel Robertz, Matthias Seiss

The $L^p$ regularity problem for parabolic operators with transversally independent coefficients
Martin Dindo\v{s}, Jill Pipher, Martin Ulmer
https://arxiv.org/abs/2509.06627 ht…

The $L^p$ regularity problem for parabolic operators with transversally independent coefficients
In this paper, we fully resolve the question of whether the Regularity problem for the parabolic PDE $\partial_tu - \mbox{div}(A\nabla u)=0$ on the domain $\mathbb R^{n+1}_+\times\mathbb R$ is solvable for some $p\in (1,\infty)$ under the assumption that the matrix $A$ is elliptic, has bounded and measurable coefficients and its coefficients are independent of the spatial variable $x_{n+1}$ (which is transversal to the boundary). We prove that for some $p_0>1$ the Regularity problem is solvable…

A Generalisation on Erd\H{o}s Distinct Subset Sums Problem
Zijie Gu
https://arxiv.org/abs/2510.06032 https://arxiv.org/pdf/2510.06032

A Generalisation on Erdős Distinct Subset Sums Problem
This paper investigates the Erdős distinct subset sums problem in $\mathbb{Z}^k$. Beyond the classical variance method, using alternative statistical quantities like $\mathbb{E}[\|X\|_1]$ and $\mathbb{E}[\|X\|_3^3]$ can yield better bounds in certain dimensions. This innovation improves previous low-dimensional results and provides a framework for choosing suitable methods depending on the dimension.

HNN extensions of free groups with equal associated subgroups of finite index: polynomial time word problem
Hanwen Shen, Alexander Ushakov
https://arxiv.org/abs/2510.03801 https…

HNN extensions of free groups with equal associated subgroups of finite index: polynomial time word problem
Let $G=F\ast_φt$ be an HNN extension of a free group $F$ with two equal associated normal subgroups $H_1 = H_2$ of finite index. We prove that the word problem in $G$ is decidable in polynomial time. This result extends to the case where the subgroups $H_1=H_2$ are not normal, provided that the isomorphism $φ:H_1\to H_2$ satisfies an additional condition described in Section 5.

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

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

On certain root number $1$ cases of the cube sum problem
Shamik Das, Somnath Jha
https://arxiv.org/abs/2508.05361 https://arxiv.org/pdf/2508.05361

On certain root number $1$ cases of the cube sum problem
We consider certain families of integers $n$ determined by some congruence condition, such that the global root number of the elliptic curve $E_{-432n^2}: Y^2=X^3-432n^2$ is $1$ for every $n$, however a given $n$ may or may not be a sum of two rational cubes. We give explicit criteria in terms of the $2$-parts and $3$-parts of the ideal class groups of certain cubic number fields to determine whether such an $n$ is a cube sum. In particular, we study integers $n$ divisible by $3$ such that the …

An Improved Approximation Algorithm for the Capacitated Arc Routing Problem
Jingyang Zhao, Mingyu Xiao
https://arxiv.org/abs/2508.05471 https://arxiv.org/p…

An Improved Approximation Algorithm for the Capacitated Arc Routing Problem
The Capacitated Arc Routing Problem (CARP), introduced by Golden and Wong in 1981, is an important arc routing problem in Operations Research, which generalizes the famous Capacitated Vehicle Routing Problem (CVRP). When every customer has a unit demand, the best known approximation ratio for CARP, given by Jansen in 1993, remains $\frac{5}{2}-\frac{1.5}{k}$, where $k$ denotes the vehicle capacity. Based on recent progress in approximating CVRP, we improve this result by proposing a $(\frac{5}{…

On the Modular Chromatic Index of Random Hypergraphs
Gaia Carenini, Samuel Coulomb
https://arxiv.org/abs/2510.04334 https://arxiv.org/pdf/2510.04334…

On the Modular Chromatic Index of Random Hypergraphs
Let $k,r \geq 2$ be two integers. We consider the problem of partitioning the hyperedge set of an $r$-uniform hypergraph $H$ into the minimum number $χ_k'(H)$ of edge-disjoint subhypergraphs in which every vertex has either degree $0$ or degree congruent to $1$ modulo $k$. For a random hypergraph $H$ drawn from the binomial model $\mathbf{H}(n,p,r)$, with edge probability $p \in (C\log(n)/n,1)$ for a large enough constant $C>0$ independent of $n$ and satisfying $n^{r-1}p(1-p)\to\infty$ as $n\t…

Box Allocation Optimization in Meal Kit Delivery
Thi Minh Thu Nguyen, Loic Genest, Alain Zemkoho
https://arxiv.org/abs/2509.06157 https://arxiv.org/pdf/250…

Box Allocation Optimization in Meal Kit Delivery
This study introduces the Box Allocation Problem (BAP), a novel optimization challenge in the $1.4 billion UK meal kit delivery market. BAP involves assigning orders across multiple production facilities to minimize daily recipe variations while adhering to capacity and eligibility constraints over a 15-day planning horizon. We formulate BAP as a mixed-integer linear programming (MILP) problem and systematically compare the performance of the COIN-OR Branch and Cut (CBC) solver with heuristic m…

Sharp non-existence threshold for a parabolic Hardy-H{\'e}non equation with quasilinear diffusion
Razvan Gabriel Iagar (LAMA), Philippe Lauren\c{c}ot (LAMA)
https://arxiv.org/abs/2508.06164

Sharp non-existence threshold for a parabolic Hardy-H{é}non equation with quasilinear diffusion
Optimal conditions for initial data leading to non-existence of non-negative solutions to the Cauchy problem for the parabolic Hardy-H{é}non equation $$ \partial\_tu=Δu^m+|x|^σu^p, \quad (t,x)\in(0,\infty)\times\mathbb{R}^N, $$ with $m>0$, $σ>0$ and $p>\max\{1,m\}$, are identified. Assuming that the initial condition satisfies $$ u\_0\in L^{\infty}(\mathbb{R}^N), \quad \lim\limits\_{|x|\to\infty}|x|^γu\_0(x)=L\in(0,\infty), \quad u\_0\geq0, $$ it is shown that…

Blow-up for a Nonlocal Diffusion Equation with Time Regularly Varying Nonlinearity and Forcing
Rihab Ben Belgacem, Mohamed Majdoub
https://arxiv.org/abs/2509.07405 https://

Blow-up for a Nonlocal Diffusion Equation with Time Regularly Varying Nonlinearity and Forcing
We investigate the Cauchy problem for a semilinear parabolic equation driven by a mixed local-nonlocal diffusion operator of the form \[ \partial_t u - (Δ- (-Δ)^{\mathsf{s}})u = \mathsf{h}(t)|x|^{-b}|u|^p + t^\varrho \mathbf{w}(x), \qquad (x,t)\in \mathbb{R}^N\times (0,\infty), \] where $\mathsf{s}\in (0,1)$, $p>1$, $b\geq 0$, and $\varrho>-1$. The function $\mathsf{h}(t)$ is assumed to belong to the generalized class of regularly varying functions, while $\mathbf{w}$ is a…

A Finer View of the Parameterized Landscape of Labeled Graph Contractions
Yashaswini Mathur, Prafullkumar Tale
https://arxiv.org/abs/2510.06102 https://arx…

A Finer View of the Parameterized Landscape of Labeled Graph Contractions
We study the \textsc{Labeled Contractibility} problem, where the input consists of two vertex-labeled graphs $G$ and $H$, and the goal is to determine whether $H$ can be obtained from $G$ via a sequence of edge contractions. Lafond and Marchand~[WADS 2025] initiated the parameterized complexity study of this problem, showing it to be \(\W[1]\)-hard when parameterized by the number \(k\) of allowed contractions. They also proved that the problem is fixed-parameter tractable when parameterized …

Existence and Nonexistence Breaking Results For a Weighted Elliptic Problem in Half-Space
J. M. Do \'O, R. F. Freire, J. Giacomoni, E. S. Medeiros
https://arxiv.org/abs/2510.05999

Existence and Nonexistence Breaking Results For a Weighted Elliptic Problem in Half-Space
In this paper we study the problem $-\mathrm{div}(ρ(x_N)\nabla u)=a|u|^{p-2}u$ in $\mathbb{R}^N_+$, $-\partial u/\partial x_N=b|u|^{q-2}u$ in $\mathbb{R}^{N-1}$ where $a,b \in \mathbb{R}$, $p,q\in (1,\infty)$ and $ρ$ is a positive weight. We establish regularity results for weak solutions and, using a variational approach combined with a new Pohozaev-type identity, we show that the introduction of the weighted operator $-\mathrm{div}(ρ(x_N)\nabla u)$ can reverse the known…

A Characterization of Solvability of the Parabolic $L^p$ Dirichlet Problem on Lipschitz Graph Domains Via Carleson Measure Estimates of Bounded Solutions
James Warta, Steve Hofmann
https://arxiv.org/abs/2509.04701

A Characterization of Solvability of the Parabolic $L^p$ Dirichlet Problem on Lipschitz Graph Domains Via Carleson Measure Estimates of Bounded Solutions
In this paper, we show that if the bounded solutions to the parabolic Dirichlet problem on a Lipshitz-$\left[1,\frac{1}{2}\right]$ domain obey a Carleson measure estimate, then the corresponding parabolic measure on the boundary will belong to class $A^\infty$, which is equivalent to $L^p$ solvability for some $p<\infty$. This improves the existing literature which places additional assumptions on the parabolic uniform rectifiability or, equivalently, on the half-order time derivative of the fu…

Capillary $L_p$ Minkowski Flows
Jinrong Hu, Yingxiang Hu, Mohammad N. Ivaki
https://arxiv.org/abs/2509.06110 https://arxiv.org/pdf/2509.06110

Capillary $L_p$ Minkowski Flows
We study the long-time existence and asymptotic behavior of a class of anisotropic capillary Gauss curvature flows. As an application, we provide a flow approach to the existence of smooth solutions to the capillary even $L_p$ Minkowski problem in the Euclidean half-space for all $p \in (-n-1, \infty)$ and capillary $L_p$ Minkowski problem for $p > n+1$.

Evolution problem for the $1$-Laplacian with mixed boundary conditions
N. Igbida, J. M. Maz\'on, J. Toledo
https://arxiv.org/abs/2508.01809 https://arx…

Evolution problem for the $1$-Laplacian with mixed boundary conditions
This paper deals with evolution problem for the $1$-Laplacian with mixed boundary conditions on a bounded open set $Ω$ of $\R^N$. We prove existence and uniqueness of strong solutions for data in $L^2(Ω)$ by mean of the theory of maximal monotone operator. We also see that if the flux on the boundary is~$1$ (that is, the maximum possible) then these strong solutions can be seen as the large solutions introduced in \cite{MP}. We give explicit examples of solutions.