Tootfinder

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…

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 construction for the triangle removal lemma
Zach Hunter
https://arxiv.org/abs/2507.05231 https://arxiv.org/pdf/2507.05231…

An improved construction for the triangle removal lemma
We construct $n$-vertex graphs $G$ where $εn^2$ edges must be deleted to become triangle-free, which contain less than $ε^{(C_{\text{new}}-o(1))\log_2 1/ε}n^3$ triangles for $C_{\text{new}}= \frac{1}{4\log_2(4/3)} \approx 1.6601$. Previously, a bound of the same shape was known, but with $C_{\text{new}}$ replaced by $C_{\text{old}} := C_{\text{new}}/2$. Our construction uses ideas from additive combinatorics, drawing especially from the corners problem, but does not yield new bounds for thos…

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,…

Color Distance Oracles and Snippets: Separation Between Exact and Approximate Solutions
Noam Horowicz, Tsvi Kopelowitz
https://arxiv.org/abs/2507.04578 htt…

Color Distance Oracles and Snippets: Separation Between Exact and Approximate Solutions
In the snippets problem, the goal is to preprocess text $T$ so that given two patterns $P_1$ and $P_2$, one can locate the occurrences of the two patterns in $T$ that are closest to each other, or report their distance. Kopelowitz and Krauthgamer [CPM2016] showed upper bound tradeoffs and conditional lower bounds tradeoffs for the snippets problem, by utilizing connections between the snippets problem and the problem of constructing a color distance oracle (CDO), which is a data structure that …

The occupation dependent DFT-1/2 method
Shengxin Yang, Jiangzhen Shi, Kan-Hao Xue, Jun-Hui Yuan, Xiangshui Miao
https://arxiv.org/abs/2507.04804 https://…

The occupation dependent DFT-1/2 method
There has been a high demand in rectifying the band gap under-estimation problem in density functional theory (DFT), while keeping the computational load at the same level as local density approximation. DFT-1/2 and shell DFT-1/2 are useful attempts, as they correct the spurious electron self-interaction through the application of self-energy potentials, which pull down the valence band. Nevertheless, the self-energy potential inevitably disturbs the conduction band, and these two methods fail …

Day 1: Gene starts thread asking why his Thunderbird looks weird.
https://lists.debian.org/msgid-search/acb28fa6-4521-4848-ae20-7fc5b5b72a76@shentel.net
Day 3, 32 mails in: Gene works out which desktop environment he is using.

"Two final considerations include (1) the necessity of being both deliberate and strategic and (2) the importance of being flexible and even whimsical about your future."
https://journals.plos.org/plosbiology/article?id=10.1371/journal.pbio.…

Rational lemniscates and the matching problem
Kirill Lazebnik, Pierre-Olivier Paris\'e, Malik Younsi
https://arxiv.org/abs/2507.03547 https://

Rational lemniscates and the matching problem
The matching problem for a given Jordan curve in the complex plane asks to find two nonconstant functions, one analytic in the bounded complementary component of the curve and the other analytic in the unbounded complementary component of the curve, which are continuous up to the curve and complex conjugate to each other on the curve. We prove that there exist Jordan curves of any Hausdorff dimension between $1$ and $2$ for which the matching problem has a solution. This answers a question of E…

#Mathematics #Maths

I am ignorant on what it is to be trans or a woman or a world-class athlete, but I THINK the problem here is a doomed project of representing a multidimensional continuously variable attribute with a single Boolean https://infosec.exchange/@JessTheUnstill/114639211101368863

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

On the conjugacy problem for subdirect products of hyperbolic groups
Martin R. Bridson
https://arxiv.org/abs/2507.05087 https://arxiv…

On the conjugacy problem for subdirect products of hyperbolic groups
If $G_1$ and $G_2$ are torsion-free hyperbolic groups and $P

An old friend of mine is a Hasher. Shout-out to Pollywaffle from Canberra. https://sudomakecake.com/@woollypigs/114640950327552671

On Shelah's Approachability Ideal
Hannes Jakob, Alejandro Poveda
https://arxiv.org/abs/2508.04374 https://arxiv.org/pdf/2508.04374

On Shelah's Approachability Ideal
We solve a long-standing open problem of Shelah regarding the \emph{Approachability Ideal} $I[κ^+]$. Given a singular cardinal $\aleph_γ$, a regular cardinal $μ\in (\mathrm{cf}(γ),\aleph_γ)$ and assuming appropriate large cardinal hypotheses, we construct a model of $\mathsf{ZFC}$ in which $\aleph_{γ+1} \cap \mathrm{cof}(μ) \notin I[\aleph_{γ+1}]$. This provides a definitive answer to a question of Shelah from the 80's. In addition, assuming large cardinals, we construct a model of $\ma…

MD-LLM-1: A Large Language Model for Molecular Dynamics
Mhd Hussein Murtada, Z. Faidon Brotzakis, Michele Vendruscolo
https://arxiv.org/abs/2508.03709 https://

MD-LLM-1: A Large Language Model for Molecular Dynamics
Molecular dynamics (MD) is a powerful approach for modelling molecular systems, but it remains computationally intensive on spatial and time scales of many macromolecular systems of biological interest. To explore the opportunities offered by deep learning to address this problem, we introduce a Molecular Dynamics Large Language Model (MD-LLM) framework to illustrate how LLMs can be leveraged to learn protein dynamics and discover states not seen in training. By applying MD-LLM-1, the first imp…

Retrodicting Chaotic Systems: An Algorithmic Information Theory Approach
Kamal Dingle, Boumediene Hamzi, Marcus Hutter, Houman Owhadi
https://arxiv.org/abs/2507.04780

Retrodicting Chaotic Systems: An Algorithmic Information Theory Approach
Making accurate inferences about data is a key task in science and mathematics. Here we study the problem of \emph{retrodiction}, inferring past values of a series, in the context of chaotic dynamical systems. Specifically, we are interested in inferring the starting value $x_0$ in the series $x_0,x_1,x_2,\dots,x_n$ given the value of $x_n$, and the associated function $f$ which determines the series as $f(x_i)=x_{i+1}$. Even in the deterministic case this is a challenging problem, due to mixin…

This is the first numerical problem I ever did. It demonstrates the
power of computers:
Enter lots of data on calorie & nutritive content of foods. Instruct
the thing to maximize a function describing nutritive content, with a
minimum level of each component, for fixed caloric content. The
results are that one should eat each day:
1/2 chicken
1 egg
1 glass of skim milk
27 heads of lettuce.
-- Rev. Adrian Melott

Replaced article(s) found for cs.NE. https://arxiv.org/list/cs.NE/new
[1/1]:
- A Census-Based Genetic Algorithm for Target Set Selection Problem in Social Networks
Md. Samiur Rahman, Mohammad Shamim Ahsan, Cheng-Wu Chen, Vijayakumar Varadarajan

Gordian split links in the Gehring ropelength problem
Friedrich Bauermeister
https://arxiv.org/abs/2506.04644 https://arxiv.org/pdf/2…

Gordian split links in the Gehring ropelength problem
A thick link is a link in Euclidean three-space such that each component of the link lies at distance at least 1 from every other component. Strengthening the notion of thickness, we define a thickly embedded link to be a thick link whose open radius-1/2 normal disk bundles of all components are embedded. The Gehring ropelength problem asks how large the sum of the lengths of the components of a thick (respectively thickly embedded) link must be, given the link homotopy (respectively isotopy) c…

Global strong solution of the 3D compressible liquid crystal flows with density-dependent viscosity and large velocity
Jiaxu Li, Yu Mei, Rong Zhang
https://arxiv.org/abs/2507.04760

Global strong solution of the 3D compressible liquid crystal flows with density-dependent viscosity and large velocity
This paper concerns the Cauchy problem of three-dimensional compressible liquid crystal flows with density-dependent viscosity. When the viscosity coefficients $μ_1(ρ),μ_2(ρ)$ are power functions of the density with the power larger than $1$, it is proved that the system exists a unique global strong solution as long as the initial density is sufficiently large and $L^3$-norm of the derivative of the initial director is sufficiently small. This is the first result concerning the global stro…

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]

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.

Communication Round and Computation Efficient Exclusive Prefix-Sums Algorithms (for MPI_Exscan)
Jesper Larsson Tr\"aff
https://arxiv.org/abs/2507.04785

Communication Round and Computation Efficient Exclusive Prefix-Sums Algorithms (for MPI_Exscan)
Parallel scan primitives compute element-wise inclusive or exclusive prefix sums of input vectors contributed by $p$ consecutively ranked processors under an associative, binary operator $\oplus$. In message-passing systems with bounded, one-ported communication capabilities, at least $\lceil\log_2 p\rceil$ or $\lceil\log_2 (p-1)\rceil$ communication rounds are required to perform the scans. While there are well-known, simple algorithms for the inclusive scan that solve the problem in $\lceil\l…

Spectral Tur\'{a}n problem of non-bipartite graphs: Forbidden books
Ruifang Liu, Lu Miao
https://arxiv.org/abs/2506.04884 https://

Spectral Turán problem of non-bipartite graphs: Forbidden books
A book graph $B_{r+1}$ is a set of $r+1$ triangles with a common edge, where $r\geq0$ is an integer. Zhai and Lin [J. Graph Theory 102 (2023) 502-520] proved that for $n\geq\frac{13}{2}r$, if $G$ is a $B_{r+1}$-free graph of order $n$, then $ρ(G)\leqρ(T_{n,2})$, with equality if and only if $G\cong T_{n,2}$. Note that the extremal graph $T_{n,2}$ is bipartite. Motivated by the above elegant result, we investigate the spectral Turán problem of non-bipartite $B_{r+1}$-free graphs of order $n$.…

Multi-Modal Multi-Behavior Sequential Recommendation with Conditional Diffusion-Based Feature Denoising
Xiaoxi Cui, Weihai Lu, Yu Tong, Yiheng Li, Zhejun Zhao
https://arxiv.org/abs/2508.05352

Multi-Modal Multi-Behavior Sequential Recommendation with Conditional Diffusion-Based Feature Denoising
The sequential recommendation system utilizes historical user interactions to predict preferences. Effectively integrating diverse user behavior patterns with rich multimodal information of items to enhance the accuracy of sequential recommendations is an emerging and challenging research direction. This paper focuses on the problem of multi-modal multi-behavior sequential recommendation, aiming to address the following challenges: (1) the lack of effective characterization of modal preferences…

Covariant and Gauge-invariant Metric-based Gravitational-waves Extraction in Numerical Relativity
Joan Fontbut\'e, Sebastiano Bernuzzi, Simone Albanesi, David Radice, Alireza Rashti, William Cook, Boris Daszuta, Alessandro Nagar
https://arxiv.org/abs/2508.03799

Covariant and Gauge-invariant Metric-based Gravitational-waves Extraction in Numerical Relativity
We revisit the problem of gravitational-wave extraction in numerical relativity with gauge-invariant metric perturbation theory of spherical spacetimes. Our extraction algorithm allows the computation of even-parity (Zerilli-Moncrief) and odd-parity (Regge-Wheeler) multipoles of the strain from a (3+1) metric without the assumption that the spherical background is in Schwarzschild coordinates. The algorithm is validated with a comprehensive suite of 3D problems including fluid ($f$-modes) and s…

Best approximation of a three-variable function by sum of one-variable coordinate functions
Rashid A. Aliev, Vugar A. Guliyev, Amil F. Jabiyev
https://arxiv.org/abs/2507.04747

Best approximation of a three-variable function by sum of one-variable coordinate functions
Consider the following approximation problem of a continuous function of three variables by the sum of three continuous functions of one variable: \[ E(f,Ω)=\inf||f(x,y,z)-ϕ(x)-ψ(y)-ω(z)||_{\infty}=? \] where $f(x,y,z)$ is a given continuous function defined on $Ω=[0,1]^3$ and the infimum runs over all triplets of continuous functions $ϕ(x),ψ(y),ω(z)$ defined on the unit interval $[0,1]$. In this paper, we will prove a formula to calculate the error $E(f,Ω)$ und…

P\'olya's conjecture up to $\epsilon$-loss and quantitative estimates for the remainder of Weyl's law
Renjin Jiang, Fanghua Lin
https://arxiv.org/abs/2507.04307

Pólya's conjecture up to $ε$-loss and quantitative estimates for the remainder of Weyl's law
Let $Ω\subset\mathbb{R}^n$ be a bounded Lipschitz domain. For any $ε\in (0,1)$ we show that for any Dirichlet eigenvalue $λ_k(Ω)>Λ(ε,Ω)$, it holds \begin{align*} k&\le (1+ε)\frac{|Ω|ω(n)}{(2π)^n}λ_k(Ω)^{n/2}, \end{align*} where $Λ(ε,Ω)$ is given explicitly. This reduces the $ε$-loss version of Pólya's conjecture to a computational problem. This estimate is based on a uniform estimate on the remainder of the Weyl law on Lipschitz domains, which appears to be the first…

The Value of Scaffolding https://johnmdavismusic.com/2025/06/12/the-value-of-scaffolding/comment-page-1/?utm_source=dlvr.it&utm_medium=mastodon#respond

The Value of Scaffolding
Image from pexels.com I have a real problem with the blank page. I would never make it as a writer. That empty expanse of void waiting for words… I feel that here but I’m not a writer so I just bla…

Asymptotic Plateau problem for $2$-convex hypersurface in $\mathbb{H}^4$
Defa Chen, Zhenan Sui, Letao Sun
https://arxiv.org/abs/2506.00565 https://

Asymptotic Plateau problem for $2$-convex hypersurface in $\mathbb{H}^4$
We prove the existence of smooth complete $2$-convex hypersurface which satisfies prescribed curvature equation $(κ_1 + κ_2)(κ_1 + κ_3)(κ_2 + κ_3) = (2 σ)^3$ and has prescribed asymptotic boundary at infinity of hyperbolic space of dimension 4, where $σ\in (0, 1)$ is a constant. We also prove the existence for $σ_k (κ_2 + \cdots + κ_n, \cdots, κ_1 + \cdots + κ_{n - 1}) = C_n^k (n - 1)^k σ^k$ with $k < n$ in $\mathbb{H}^{n + 1}$.

Tired of how much Canadian journalism focus on the US. Sure let's do it about trade policies that impact us.. but their non-stop stupidity and fuckery, we just don't need to see that.
They are gerrymandering in Texas, this is their fucking problem. Why should it be the #1 news of the Canadian public broadcaster? What can I do? How does that concern me?
And yes, human rights abuse should be denounced.
Are we running out of problems in Canada to talk about? I don…

Counting linear congruence systems with a fixed number of solutions
Marcus Nilsson
https://arxiv.org/abs/2507.04688 https://arxiv.org…

Counting linear congruence systems with a fixed number of solutions
For a prime p and a positive integer s consider a homogeneous linear system over the ring Z_p^s (the ring of integers modulo p^s) described by an n x m-matrix. The possible number of solutions to such a system is p^j, where j=0,1,..., sm. We study the problem of how many n x m -matrices over Z_p^s there are given that we have exactly p^j homogeneous solutions. For the case s=1 (when Z_p^s is a field) George von Landsberg proved a general formula in 1893. However, there seems to be few published…

MoDA: Multi-modal Diffusion Architecture for Talking Head Generation
Xinyang Li, Gen Li, Zhihui Lin, Yichen Qian, GongXin Yao, Weinan Jia, Weihua Chen, Fan Wang
https://arxiv.org/abs/2507.03256

MoDA: Multi-modal Diffusion Architecture for Talking Head Generation
Talking head generation with arbitrary identities and speech audio remains a crucial problem in the realm of digital humans and the virtual metaverse. Recently, diffusion models have become a popular generative technique in this field with their strong generation and generalization capabilities. However, several challenges remain for diffusion-based methods: 1) inefficient inference and visual artifacts, which arise from the implicit latent space of Variational Auto-Encoders (VAE), complicating…

Bicriteria approximation for $k$-edge-connectivity
Zeev Nutov, Reut Cohen
https://arxiv.org/abs/2507.03786 https://arxiv.org/pdf/2507…

Bicriteria approximation for $k$-edge-connectivity
In the $k$-Edge Connected Spanning Subgraph ($k$-ECSS) problem we are given a (multi-)graph $G=(V,E)$ with edge costs and an integer $k$, and seek a min-cost $k$-edge-connected spanning subgraph of $G$. The problem admits a $2$-approximation algorithm and no better approximation ratio is known. Recently, Hershkowitz, Klein, and Zenklusen [STOC 24] gave a bicriteria $(1,k-10)$-approximation algorithm that computes a $(k-10)$-edge-connected spanning subgraph of cost at most the optimal value of a…

Die Erde speichert derzeit mehr als doppelt so viel Wärme, wie #Klimamodelle es erwarten.
Die #Energieungleichgewicht liegt 2023 bei 1,8 W/m² und übersteigt die Prognosen deutlich. Forscher vermuten eine abnehmende

Greenhouse Gases Are Trapping Twice As Much Heat As They Should, Leading To A Record-Breaking Energy Imbalance
Only by phasing out fossil fuels immediately can this problem be fixed.

And this, people, is why Europe ABSOLUTELY NEEDS RIGHT FREAKING NOW its own human-graded space access system.
I'll never understand why nobody at #ESA thought of developping further the ATV in order to be also used to send people up instead of just cargo.
I know, the problem was mostly in bringing people down, as the ATV was designed to burn up in the atmosphere. But still. Now we…

rickf (@rickf@indieweb.social)
Attached: 1 image Dragon is what the US uses to resupply the ISS, for those that don't know...

Hypergraph Tur\'an problem of the generalized triangle with bounded matching number
Jian Wang, Wenbin Wang, Weihua Yang
https://arxiv.org/abs/2507.04579

Hypergraph Turán problem of the generalized triangle with bounded matching number
Let $\mathcal{H}$ be a 3-graph on $n$ vertices. The matching number $ν(\mathcal{H})$ is defined as the maximum number of disjoint edges in $\mathcal{H}$. The generalized triangle $F_5$ is a 3-graph on the vertex set $\{a,b,c,d,e\}$ with the edge set $\{abc, abd,cde\}$. In this paper, we showed that an $F_5$-free 3-graph $\mathcal{H}$ with matching number at most $s$ has at most $s\lfloor (n-s)^2/4\rfloor$ edges for $n\geq 30(s+1)$ and $s\geq 3$. For the proof, we establish a 2-colored version …

"The big problem is 'bottlenecks' that make it harder to produce housing, expand energy production, or build new roads and bridges."
vs.
"The big problem is that big corporations have way too much power over our economy and our government."
By 12pts all voters and by 42pts Dem voters prefer the second statement. They're right!

Poll: Democratic voters prefer "populism" over "abundance"
Democrats are asking themselves some hard questions as they ponder how they lost the 2024 election.

Johann Steurer und Erich W. Russi konnten als Ärzte 120% arbeiten, weil sie im Backoffice eine Frau hatten, die sich um Haushalt und Kinder kümmerte. Dass dies ein Problem sein kann, sehen sie nicht.
https://www.tagesanzeiger.ch/zuerich-rueckzahlung-der-studienkosten-gegen-aerztemangel-672603559843

Green\'s Mapping and Julia Sets
Ilia Binder, Paul F. X. M\"uller, Peter Yuditskii
https://arxiv.org/abs/2508.04207 https://arxiv.org/pdf/2508.0420…

Greenś Mapping and Julia Sets
In March 1999, the first named author (Binder) posed the problem of showing that a ``good direction'' $ψ\in [0,2]$ exists, for any Green's mapping $T:H\rightarrow\tilde Ω$, i.e., \begin{equation}\label{binder} \int\limits_0\limits^{1} |T''(re^{iπψ})|dr <\infty, \quad\text{ for at least one } \quad ψ\in [0,2]. \end{equation} Presently this problem is open even in the special case where $\partial Ω$ is a uniformly perfect subset of the real line. In this paper we obtain a posi…

Comments on QED$_3$ in a Magnetic Field
Thomas T. Dumitrescu, Juan Maldacena
https://arxiv.org/abs/2508.03532 https://arxiv.org/pdf/2508.03532

Comments on QED$_3$ in a Magnetic Field
We discuss the low-energy dynamics of massless Dirac fermions interacting with a propagating, relativistic photon in 2+1 spacetime dimensions, when we turn on a uniform magnetic field. This problem can be solved when the magnetic field is sufficiently strong. As observed previously, we find that the vacuum spontaneously breaks some of the global symmetries. We also determine the spectrum of excitations around this vacuum, and compute the resulting low-energy effective action. We use techniques …

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.

Constructing and characterizing prime $\mathbb{Q}$-Fano threefolds of genus one and with six $1/2(1,1,1)$-singularites via key varieties
Hiromichi Takagi
https://arxiv.org/abs/2507.13657

Constructing and characterizing prime $\mathbb{Q}$-Fano threefolds of genus one and with six $1/2(1,1,1)$-singularites via key varieties
We consider the classification problem of prime $\mathbb{Q}$-Fano 3-folds with at most $1/2(1,1,1)$-singularities, which was initiated in [Taka2]. We construct two distinct classes of such 3-folds with genus one and six $1/2(1,1,1)$-singularities, each equipped with a prescribed Sarkisov link. Our method involves constructing certain higher-dimensional $\mathbb{Q}$-Fano varieties $Σ$, referred to as key varieties, by extending the Sarkisov links to higher dimensions. We prove that each such 3-…

Reducing Profile-Based Matching to the Maximum Weight Matching Problem
Seongbeom Park
https://arxiv.org/abs/2507.00047 https://arxiv.…

Reducing Profile-Based Matching to the Maximum Weight Matching Problem
The profile-based matching problem is the problem of finding a matching that optimizes profile from an instance $(G, r, \langle u_1, \dots, u_r \rangle)$, where $G$ is a bipartite graph $(A \cup B, E)$, $r$ is the number of utility functions, and $u_i: E \to \{ 0, 1, \dots, U_i \}$ is utility functions for $1 \le i \le r$. A matching is optimal if the matching maximizes the sum of the 1st utility, subject to this, maximizes the sum of the 2nd utility, and so on. The profile-based matching can e…

Squares, three fleas, sporadic integer sets, and squares
Giedrius Alkauskas
https://arxiv.org/abs/2508.05347 https://arxiv.org/pdf/2508.05347

Squares, three fleas, sporadic integer sets, and squares
In the plane, three integer points ("fleas") are given. At every tick of time, two of them (say, P,Q) instantly jump to two vacant points R,S, so that PQRS is a square with that order of vertices. Description of all integers and half-integers which occur as areas of spanned triangles turns out to be unexpectedly intricate problem. For example, if one starts from a triple (0,0), (2,0), (4,1), these positive integers are missed: 2*{0, 1, 4, 15, 16, 20, 79, 84, 95, 119, 156}, with no other up to 3…

Replaced article(s) found for cs.CC. https://arxiv.org/list/cs.CC/new
[1/1]:
- On the Counting Complexity of the Skolem Problem
Gorav Jindal, Jo\"el Ouaknine

Czy ktoś jeszcze ma taki problem na moim blogu?
https://pol.social/@mstankiewicz_prywatnie/114953802904907641

Orbit recovery for spherical functions
Tamir Bendory, Dan Edidin, Josh Katz, Shay Kreymer
https://arxiv.org/abs/2508.02674 https://arxiv.org/pdf/2508.02674…

Orbit recovery for spherical functions
Orbit recovery is a central problem in both mathematics and applied sciences, with important applications to structural biology. This paper focuses on recovering generic orbits of functions on ${\mathbb R}^{n}$ and the sphere $S^{n-1}$ under the rotation action of $SO(n)$. Specifically, we demonstrate that invariants of degree three (called the bispectrum) suffice to recover generic orbits of functions in finite-dimensional approximations of $L^2({\mathbb R}^n)$ obtained by band-limiting the sp…

Iteration Steps of 3x 1 Problem
Youchun Luo
https://arxiv.org/abs/2506.23070 https://arxiv.org/pdf/2506.23070

Iteration Steps of 3x+1 Problem
On the 3x+1 problem, given a positive integer $N$, let $D\left( N \right) $, $O\left( N \right) $, $E\left( N \right) $ be the total iteration steps, the odd iteration steps and the even iteration steps when $N$ iterates to 1(except 1) respectively. Trivially, we have $D\left( N \right) =O\left( N \right) +E\left( N \right) $. In this paper, we propose a so-called weak residue conjecture(i.e., $\frac{2^{E\left( N \right)}}{3^{O\left( N \right)}\cdot N}\le 2$). We prove that if 3x+1 conjecture i…

Sufficient conditions of $k$-leaf-connected graphs and spanning trees with bounded total $k$-excess
Guoyan Ao, Ruifang Liu, Jinjiang Yuan
https://arxiv.org/abs/2507.04400

Sufficient conditions of $k$-leaf-connected graphs and spanning trees with bounded total $k$-excess
Chvátal and Erdös [Discrete Math. 2 (1972) 111-113] stated that, for an $m$-connected graph $G$, if its independence number $α(G)\leq m-1$, then $G$ is Hamilton-connected. Note that $k$-leaf-connectedness is a natural generalization of Hamilton-connectedness of a graph. Ozeki and Yamashita [Graphs Combin. 27 (2011) 1-26] posed an open problem: What is the sufficient condition based on the independence number for an $m$-connected graph to be $k$-leaf-connected? In this paper, we prove that if…

Replaced article(s) found for cs.LO. https://arxiv.org/list/cs.LO/new
[1/1]:
- The Boolean Solution Problem from the Perspective of Predicate Logic -- Extended Version
Christoph Wernhard

housing ownership law possibilities
Should we maybe have a law that says any one person or entity can only own a max of 2 houses? Or that you can only own 1 not being lived in by your immediate family?
I can see several reasonable use cases for having 1 extra house, including when an old person dies and the family takes a while to decide what's happening with their previous house. And we could debate those cases, and maybe even decide it's not worth arguing over 2 or 3 extra, because that isn't the biggest problem.
But I think we could possibly mostly agree that having one person or company own 5 or 10 or 50 or 500 houses just to extract profit from them is not good for overall wellbeing.
#housing #law #HouseOwnership #HousingMarket #renting #RentalMarket

Faster MPC Algorithms for Approximate Allocation in Uniformly Sparse Graphs
Jakub {\L}\k{a}cki, Slobodan Mitrovi\'c, Srikkanth Ramachandran, Wen-Horng Sheu
https://arxiv.org/abs/2506.04524

Faster MPC Algorithms for Approximate Allocation in Uniformly Sparse Graphs
We study the allocation problem in the Massively Parallel Computation (MPC) model. This problem is a special case of $b$-matching, in which the input is a bipartite graph with capacities greater than $1$ in only one part of the bipartition. We give a $(1+ε)$ approximate algorithm for the problem, which runs in $\tilde{O}(\sqrt{\log λ})$ MPC rounds, using sublinear space per machine and $\tilde{O}(λn)$ total space, where $λ$ is the arboricity of the input graph. Our result is obtained by pro…

I am looking at switching away from Spotify and currently looking at Apple Music.
I can understand artists/labels not publishing to Apple Music, no problem with that.
The problem I have is that 1 track on the album (which just happens to be my favourite of the album) is just not there on Apple Music.
It's not geo-locked (I'll get onto that in a min) but my god, it is so stupid.
Thankfully this particular artist, I support on Bandcamp, so no major loss there.

Great article from NYT about sheikh Mansour bin Zayed al-Nahyan from the UAE. For me it illustrates the bigger problem of the middle-east/gulfstates, the absence of any meaningful democracy, too rich oligarchs with too much power. Politically the people are living in medieval times there.

Conquering Soccer and Arming Warlords
The Emirati vice president is best known as the owner of Manchester City, a top English soccer team. Behind the scenes, he has been described as the “handler” guiding his country’s secret foreign wars.

Prediction of acoustic field in 1-D uniform duct with varying mean flow and temperature using neural networks
D. Veerababu, Prasanta K. Ghosh
https://arxiv.org/abs/2507.22370 ht…

Prediction of acoustic field in 1-D uniform duct with varying mean flow and temperature using neural networks
Neural networks constrained by the physical laws emerged as an alternate numerical tool. In this paper, the governing equation that represents the propagation of sound inside a one-dimensional duct carrying a heterogeneous medium is derived. The problem is converted into an unconstrained optimization problem and solved using neural networks. Both the acoustic state variables: acoustic pressure and particle velocity are predicted and validated with the traditional Runge-Kutta solver. The effect …

There’s exactly 1 narrow way that it’s true. Before widespread #WFH, attackers often had an insurmountable barrier: no way into the business network from the Internet. At the last gig (2008) where I had to visit a “workplace” regularly, inbound remote access was officially non-existent & outbound Internet access all went through restrictive web proxies.

Kevin Beaumont (@GossiTheDog@cyberplace.social)
Attached: 1 image This Daily Mail piece about security leaders thinking work-from-home means they will be crippled is horseshit, I'm not linking it. They've taken a survey about how security people think their businesses couldn't survive ransomware, and linked it to working from home. WFH isn't the problem: business IT and resilience being built on quicksand is the problem.

Solving a real-world modular logistic scheduling problem with a quantum-classical metaheuristics
Florian Krellner, Abhishek Awasthi, Nico Kraus, Sarah Braun, Michael Poppel, Daniel Porawski
https://arxiv.org/abs/2507.21701

Solving a real-world modular logistic scheduling problem with a quantum-classical metaheuristics
This study evaluates the performance of a quantum-classical metaheuristic and a traditional classical mathematical programming solver, applied to two mathematical optimization models for an industry-relevant scheduling problem with autonomous guided vehicles (AGVs). The two models are: (1) a time-indexed mixed-integer linear program, and (2) a novel binary optimization problem with linear and quadratic constraints and a linear objective. Our experiments indicate that optimization methods are ve…

Replaced article(s) found for cs.CE. https://arxiv.org/list/cs.CE/new
[1/1]:
- The time slot allocation problem in liberalised passenger railway markets: a multi-objective appr...
Be\v{s}inovi\'c, Garc\'ia-R\'odenas, L\'opez-Garc\'ia, L\'opez-G\'omez, Mart\'i…

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…

On the dynamics of a semigroup and its relation with the Riemann Hypothesis
Carlos F. \'Alvarez, Juan Manzur
https://arxiv.org/abs/2507.03625 https://

On the dynamics of a semigroup and its relation with the Riemann Hypothesis
The semigroup of weighted composition operators $(W_n)_{n\in \mathbb{N}}$, defined by $$W_nf(z)=(1+z+\cdots +z^n)f(z^n),$$ acts on the classical Hardy-Hilbert space $H^{2}(\mathbb{D})$, and exhibits intriguing connections with both the Riemann Hypothesis (RH) and the Invariant Subspace Problem (ISP). In this paper, we prove that the adjoint operators $W^{\ast}_{n}$, for $n\geq 2$, are Devaney chaotic, frequently hypercyclic and mixing. In particular, these operators are hypercyclic and discuss …

Resilient Pattern Mining
Pengxin Bian, Panagiotis Charalampopoulos, Lorraine A. K. Ayad, Manal Mohamed, Solon P. Pissis, Grigorios Loukides
https://arxiv.org/abs/2506.04935

Resilient Pattern Mining
Frequent pattern mining is a flagship problem in data mining. In its most basic form, it asks for the set of substrings of a given string $S$ of length $n$ that occur at least $τ$ times in $S$, for some integer $τ\in[1,n]$. We introduce a resilient version of this classic problem, which we term the $(τ, k)$-Resilient Pattern Mining (RPM) problem. Given a string $S$ of length $n$ and two integers $τ, k\in[1,n]$, RPM asks for the set of substrings of $S$ that occur at least $τ$ times in $S$,…

Factorization of Basic Hypergeometric Series
Jonathan G. Bradley-Thrush
https://arxiv.org/abs/2507.04313 https://arxiv.org/pdf/2507.0…

Factorization of Basic Hypergeometric Series
The general problem of the factorization of a basic hypergeometric series is presented and discussed. The case of the general $_2ψ_2$ series is examined in detail. Connections are found with the theory of basic hypergeometric series on root systems. Alternative proofs of several well-known summation and transformation formulae, including Gustafson's generalization of Ramanujan's $_1ψ_1$ summation, are obtained incidentally.

Fractional Infinity Laplacian with Obstacle
Samer Dweik, Ahmad Sabra
https://arxiv.org/abs/2507.04328 https://arxiv.org/pdf/2507.0432…

Fractional Infinity Laplacian with Obstacle
This paper deals with the obstacle problem for the fractional infinity Laplacian with nonhomogeneous term $f(u)$, where $f:\mathbb{R}^+ \mapsto \mathbb{R}^+$: $$\begin{cases} L[u]=f(u) &\qquad in \{u>0\}\\ u \geq 0 &\qquad in\, Ω\\ u=g &\qquad on\, \partial Ω\end{cases},$$ with $$L[u](x)=\sup_{y\in Ω,\,y\neq x}\dfrac{u(y)-u(x)}{|y-x|^α}+\inf_{y\in Ω,\,y\neq x} \dfrac{u(y)-u(x)}{|y-x|^α},\qquad 0<α<1.$$ Under the assumptions that $f$ is a continuous and monotone functi…

This https://arxiv.org/abs/2501.00671 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Sylvester's problem for beta-type distributions
Consider $d+2$ i.i.d. random points $X_1,\ldots, X_{d+2}$ in $\mathbb R^d$. In this note, we compute the probability that their convex hull is a simplex focusing on three specific distributional settings: (i) the distribution of $X_1$ is multivariate standard normal; (ii) the density of $X_1$ is proportional to $(1-\|x\|^2)^β$ on the unit ball (the beta distribution); (iii) the density of $X_1$ is proportional to $(1+\|x\|^2)^{-β}$ (the beta prime distribution). In the Gau…

Computing $H$-equations with 2-by-2 integral matrices
Gemma Bastardas, Enric Ventura
https://arxiv.org/abs/2506.05272 https://arxiv.o…

Computing $H$-equations with 2-by-2 integral matrices
We study the transference through finite index extensions of the notion of equational coherence, as well as its effective counterpart. We deduce an explicit algorithm for solving the following algorithmic problem about size two integral invertible matrices: ''given $h_1,\ldots, h_r; g\in \operatorname{PSL}_2(\mathbb{Z})$, decide whether $g$ is algebraic over the subgroup $H=\langle h_1,\ldots ,h_r\rangle \leqslant \operatorname{PSL}_2(\mathbb{Z})$ (i.e., whether there exist a non-trivial $H$-eq…

When Are Standard Graph Products Isomorphic?
Priti Prasanna Mondal, M. Rajesh Kannan, Fouzul Atik
https://arxiv.org/abs/2508.04137 https://arxiv.org/pdf/25…

When Are Standard Graph Products Isomorphic?
This article investigates the isomorphism problem for graphs derived from the four standard graph products: Cartesian, Kronecker (direct), strong, and lexicographic product. We provide a complete characterization of all simple connected graphs for which their corresponding products are isomorphic. As a by-product, we identify a novel family of non-distance-regular graphs that possess fewer than d+1 distinct distance eigenvalues, where d represents the diameter of the graph. This result offers a…

Error analysis for a Finite Element Discretization of a radially symmetric harmonic map heat flow problem
Nam Anh Nguyen, Arnold Reusken
https://arxiv.org/abs/2506.23748

Error analysis for a Finite Element Discretization of a radially symmetric harmonic map heat flow problem
We consider the harmonic map heat flow problem for a radially symmetric case. For discretization of this problem we apply a $H^1$-conforming finite element method in space combined with a semi-implicit Euler time stepping. The semi-implicit Euler method results in a linear problem in each time step. We restrict to the regime of smooth solutions of the continuous problem and present an error analysis of this discretization method. This results in optimal order discretization error bounds. Key in…

Non-radial minimizers for Hardy--Sobolev inequalities in non-convex cones
A. I. Nazarov, N. V. Rastegaev
https://arxiv.org/abs/2507.04470 https://

Non-radial minimizers for Hardy--Sobolev inequalities in non-convex cones
The symmetry breaking is obtained for Neumann problems driven by $p$-Laplacian in certain non-convex cones. These problems are generated by the Hardy--Sobolev inequalities. In the case of the Sobolev inequality for the ordinary Laplacian this problem was investigated in (Ciraolo, Pacella, Polvara, 2024). Such problems have obvious radial solutions -- Talenti--Bliss type functions of $|x|$. However, under a certain restriction on the first Neumann eigenvalue $λ_1(D)$ of the Beltrami…

Generalized Hardy's identity for the astroid-type p-circle lattice point problem
Masaya Kitajima
https://arxiv.org/abs/2506.03331 https://

Generalized Hardy's identity for the astroid-type p-circle lattice point problem
Let $r$ be a positive real number and $p$ satisfy $(2/p)\in\mathbb{N}$. Then, we consider the lattice point problem of the closed curves astroid-type $p$-circle $\{x\in\mathbb{R}^{2}|\ |x_{1}|^{p}+|x_{2}|^{p}=r^{p}\}$ which generalize the circle. In investigating the asymptotic behavior of the error term in the area approximation of the circle, G.H. Hardy conjectured an infimum for the evaluation in 1917. One of the grounds for this conjecture is the Hardy's identity, w…

Tight Guarantees for Cut-Relative Survivable Network Design via a Decomposition Technique
Nikhil Kumar, JJ Nan, Chaitanya Swamy
https://arxiv.org/abs/2507.04473

Tight Guarantees for Cut-Relative Survivable Network Design via a Decomposition Technique
In the classical \emph{survivable-network-design problem} (SNDP), we are given an undirected graph $G = (V, E)$, non-negative edge costs, and some $(s_i,t_i,r_i)$ tuples, where $s_i,t_i\in V$ and $r_i\in\mathbb{Z}_+$. We seek a minimum-cost subset $H \subseteq E$ such that each $s_i$-$t_i$ pair remains connected even if any $r_i-1$ edges fail. It is well-known that SNDP can be equivalently modeled using a weakly-supermodular \emph{cut-requirement function} $f$, where we seek a minimum-cost edge…

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)

Faster Distributed $\Delta$-Coloring via a Reduction to MIS
Yann Bourreau, Sebastian Brandt, Alexandre Nolin
https://arxiv.org/abs/2508.01762 https://arxiv…

Faster Distributed $Δ$-Coloring via a Reduction to MIS
Recent improvements on the deterministic complexities of fundamental graph problems in the LOCAL model of distributed computing have yielded state-of-the-art upper bounds of $\tilde{O}(\log^{5/3} n)$ rounds for maximal independent set (MIS) and $(Δ+ 1)$-coloring [Ghaffari, Grunau, FOCS'24] and $\tilde{O}(\log^{19/9} n)$ rounds for the more restrictive $Δ$-coloring problem [Ghaffari, Kuhn, FOCS'21; Ghaffari, Grunau, FOCS'24; Bourreau, Brandt, Nolin, STOC'25]. In our work, we show that $Δ$-col…

On embedding of ample semigroups in inverse semigroups
Nasir Sohail, Aftab Hussain Shah, Kristo V\"aljako
https://arxiv.org/abs/2508.01949 https://arx…

On embedding of ample semigroups in inverse semigroups
The problem of embedding an ample semigroup in an inverse semigroup as a (2, 1, 1)-type subalgebra is known to be undecidable. In this article, we investigate the problem for certain classes of ample semigroups. We also give examples of semigroups that are left (respectively, right) but not right (respectively, left) ample.

This https://arxiv.org/abs/2501.10302 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Martingale Approach to Gambler's Ruin Problem for Correlated Random Walks
The gambler's ruin problem for correlated random walks (CRW), both with and without delays, is addressed using the Optional Stopping Theorem for martingales. We derive closed-form expressions for the ruin probabilities and the expected game duration for CRW with increments $\{1,-1\}$ and for symmetric CRW with increments $\{1,0,-1\}$ (CRW with delays). Additionally, a martingale technique is developed for general CRW with delays. The gambler's ruin probability for a game involving bets on two a…

Spectral extremal problem for the odd prism
Xinhui Duan, Lu Lu
https://arxiv.org/abs/2507.01266 https://arxiv.org/pdf/2507.01266

Spectral extremal problem for the odd prism
The spectral Turán number $\spex(n, F)$ denotes the maximum spectral radius $ρ(G)$ of an $F$-free graph $G$ of order $n$. This paper determines $\spex\left(n, C_{2k+1}^{\square}\right)$ for all sufficiently large $n$, establishing the unique extremal graph. Here, $C_{2k+1}^{\square}$ is the odd prism -- the Cartesian product $C_{2k+1} \square K_2$ -- where the Cartesian product $G \square F$ has vertex set $V(G) \times V(F)$, and edges between $(u_1,v_1)$ and $(u_2,v_2)$ if either $u_1 = u_2$…

A weighted divisor problem and exponential sum
Kritika Aggarwal, Debika Banerjee
https://arxiv.org/abs/2507.01891 https://arxiv.org/p…

A weighted divisor problem and exponential sum
In this paper, we investigate a weighted divisor problem involving the exponential sum of $D_{(1)}(n)$, the $n$th coefficient in the Dirichlet series expansion of $ζ'(s)^2$. We establish a truncated Voronoï type formula for the error term of $\sum_{n\leq x}D_{(1)}(n)e(nh/k)$, analogous to the results obtained by Jutila. Utilizing this truncated formula, we derive a mean square estimate of the error term. In addition, we study the associated Riesz sum and the corresponding error term, along wi…

Bootstrap Percolation, Indecomposable Permutations, and the n-Kings problem
Mark Huibregtse, Cristobal Lemus-Vidales, David Vella
https://arxiv.org/abs/2508.02030 https://

Bootstrap Percolation, Indecomposable Permutations, and the n-Kings problem
We study the process of bootstrap percolation on n x n permutation matrices, inspired by the work of Shapiro and Stephens [5]. In this percolation model, cells mutate (from 0 to 1) if at least two of their cardinal neighbors contain a 1, and thereafter remain unchanged; the process continues until no further mutations are possible. After carefully analyzing this process, we consider how it interacts with the notion of (in)decomposable permutations. We prove that the number of indecomposable per…

Determining unit groups and $\mathrm{K}_1$ of finite rings
Tommy Hofmann
https://arxiv.org/abs/2506.00266 https://arxiv.org/pdf/2506.…

Determining unit groups and $\mathrm{K}_1$ of finite rings
We consider the computational problem of determining the unit group of a finite ring, by which we mean the computation of a finite presentation together with an algorithm to express units as words in the generators. We show that the problem is equivalent to the number theoretic problems of factoring integers and solving discrete logarithms in finite fields. A similar equivalence is shown for the problem of determining the abelianization of the unit group or the first $K$-group of finite rings.

$C^{1,\alpha}$ regularity of the solution for the obstacle problem for the linearized Monge-Amp\`ere operator
Meng Ji
https://arxiv.org/abs/2505.24410 http…

$C^{1,α}$ regularity of the solution for the obstacle problem for the linearized Monge-Ampère operator
In this paper, we study the regularity of the solution for the obstacle problem associated with the linearized Monge-Ampère operator: \begin{align*} \begin{cases} &u\geqφ\text{\quad in } Ω &L_{ w}u=\tr( W D^{2}u)\leq 0 \text{\quad in } Ω &L_{ w}u= 0 \text{\quad in } \{u>φ\} &u=0 \text{\quad on } \partialΩ, \end{cases} \end{align*} where $ W=(\det D^{2} w) D^{2} w^{-1}$ is the matrix of cofactor of $D^{2} w$, $w$ satisfies $λ\leq \det D^{2} w \leq Λ$ and $ w=0$ on $\partial �…

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition
Anders Aamand, Justin Y. Chen, Mina Dalirrooyfard, Slobodan Mitrovi\'c, Yuriy Nevmyvaka, Sandeep Silwal, Yinzhan Xu
https://arxiv.org/abs/2507.01873

Breaking the $n^{1.5}$ Additive Error Barrier for Private and Efficient Graph Sparsification via Private Expander Decomposition
We study differentially private algorithms for graph cut sparsification, a fundamental problem in algorithms, privacy, and machine learning. While significant progress has been made, the best-known private and efficient cut sparsifiers on $n$-node graphs approximate each cut within $\widetilde{O}(n^{1.5})$ additive error and $1+γ$ multiplicative error for any $γ> 0$ [Gupta, Roth, Ullman TCC'12]. In contrast, "inefficient" algorithms, i.e., those requiring exponential time, can achieve an $\wi…

On one of Erd\H{o}s' Problems -- An Efficient Search for Benelux Pairs
Christian Hercher
https://arxiv.org/abs/2506.01099 https://

On one of Erdős' Problems -- An Efficient Search for Benelux Pairs
Erdős asked for positive integers $m

Replaced article(s) found for cs.DS. https://arxiv.org/list/cs.DS/new
[1/1]:
- A Maximum Linear Arrangement Problem on Directed Graphs
Matt DeVos, Kathryn Nurse
h…

Replaced article(s) found for math.AP. https://arxiv.org/list/math.AP/new
[1/1]:
- Subelliptic $p$-Laplacian spectral problem for H\"ormander vector fields
Mukhtar Karazym, Durvudkhan Suragan

On the Erd\H{o}s-Ko-Rado problem of flags with type $\{1, n-3 \}$ of finite sets
Philipp Heering
https://arxiv.org/abs/2506.20556 https://

On the Erdős-Ko-Rado problem of flags with type $\{1, n-3 \}$ of finite sets
A flag of a finite set $S$ is a set $f$ of non-empty, proper subsets of $S$, such that $X\subseteq Y$ or $Y\subseteq X$ for all $X,Y\in f$. Two flags $f_1$ and $f_2$ of $S$ are opposite if $X_1\cap X_2=\emptyset$, or $X_1\cup X_2=S$ for all $X_1\in f_1$ and $X_2\in f_2$. The set $\{|X| \mid X\in f \}$ is the type of a flag $f$. A set of pairwise non-opposite flags is an Erdős-Ko-Rado set. In 2022 Metsch posed the problem of determining the maximum size of all Erdős-Ko-Rado sets of f…

A Refined Kernel for $d$-Hitting Set
Yuxi Liu, Mingyu Xiao
https://arxiv.org/abs/2506.24114 https://arxiv.org/pdf/2506.24114

A Refined Kernel for $d$-Hitting Set
The $d$-Hitting Set problem is a fundamental problem in parameterized complexity, which asks whether a given hypergraph contains a vertex subset $S$ of size at most $k$ that intersects every hyperedge (i.e., $S \cap e \neq \emptyset$ for each hyperedge $e$). The best known kernel for this problem, established by Abu-Khzam [1], has $(2d - 1)k^{d - 1} + k$ vertices. This result has been very widely used in the literature as many problems can be modeled as a special $d$-Hitting Set problem. In thi…

Shape derivative approach to fractional overdetermined problems
Sidy M. Djitte, Ignace A. Minlend
https://arxiv.org/abs/2506.00268 https://

Shape derivative approach to fractional overdetermined problems
We use shape derivative approach to prove that balls are the only convex and $C^{1,1}$ regular domains in which the fractional overdetermined problem \begin{equation*} \left\{\begin{aligned} \Ds u&= λ_{s, p} u^{p-1}\quad\text{in}\quad\Om \\ u &= 0\quad \text{in}\quad\R^N\setminus \Om\\ u/d^s&=C_0\quad\text{on\;\; $\partialØ$} \end{aligned} \right. \end{equation*} admits a nontrivial solution for $p\in [1, 2]$ and where $λ_{s, p}= λ_{s, p}(Ø)$ is the best constant in the family of Subcritic…

Code-based $[3,1]$-avoiders in finite affine spaces $\mathrm{AG}(n,2)$
Benedek Kov\'acs
https://arxiv.org/abs/2505.24072 https://…

Code-based $[3,1]$-avoiders in finite affine spaces $\mathrm{AG}(n,2)$
The author, together with Nagy, studied the following problem on unavoidable intersections of given size in binary affine spaces. Given an $m$-element set $S\subseteq \mathbb{F}_2^n$, is there guaranteed to be a $[k,t]$-flat, that is, a $k$-dimensional affine subspace of $\mathbb{F}_2^n$ containing exactly $t$ points of $S$? Such problems can be viewed as generalizations of the cap set problem over the binary field. They conjectured that for every fixed pair $(k,t)$ with $k\ge 1$ and $0\le t\le…

This https://arxiv.org/abs/2405.05727 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On Chen's theorem, Goldbach's conjecture and almost prime twins II
Let $N$ denote a sufficiently large even integer and $x$ denote a sufficiently large integer, we define $D_{1,2}(N)$ as the number of primes $p$ that such that $N - p$ has at most 2 prime factors. In this paper, we show that $D_{1,2}(N) \geqslant 1.9728 \frac{C(N) N}{(\log N)^2}$, which is rather near to the asymptotic constant $2$ in Hardy--Littlewood conjecture for Goldbach's conjecture. We also get similar results on twin prime problem and additive representations of integers. The proof comb…

Global existence of the solution of the modified Camassa-Holm equation with step-like boundary conditions
I. Karpenko, D. Shepelsky, G. Teschl
https://arxiv.org/abs/2507.02100

Global existence of the solution of the modified Camassa-Holm equation with step-like boundary conditions
We consider the Cauchy problem for the modified Camassa-Holm equation \[ u_t+\left((u^2-u_x^2)m\right)_x=0,\quad m\coloneqq u-u_{xx}, \quad t>0,\ \ -\infty

A 0.51-Approximation of Maximum Matching in Sublinear $n^{1.5}$ Time
Sepideh Mahabadi, Mohammad Roghani, Jakub Tarnawski
https://arxiv.org/abs/2506.01669 h…

A 0.51-Approximation of Maximum Matching in Sublinear $n^{1.5}$ Time
We study the problem of estimating the size of a maximum matching in sublinear time. The problem has been studied extensively in the literature and various algorithms and lower bounds are known for it. Our result is a $0.5109$-approximation algorithm with a running time of $\tilde{O}(n\sqrt{n})$. All previous algorithms either provide only a marginal improvement (e.g., $2^{-280}$) over the $0.5$-approximation that arises from estimating a \emph{maximal} matching, or have a running time that i…

Algebraic aspects of the polynomial Littlewood-Offord problem
Zhihan Jin, Matthew Kwan, Lisa Sauermann, Yiting Wang
https://arxiv.org/abs/2505.23335 https:…

Algebraic aspects of the polynomial Littlewood-Offord problem
Consider a degree-$d$ polynomial $f(ξ_1,\dots,ξ_n)$ of independent Rademacher random variables $ξ_1,\dots,ξ_n$. To what extent can $f(ξ_1,\dots,ξ_n)$ concentrate on a single point? This is the so-called polynomial Littlewood-Offord problem. A nearly optimal bound was proved by Meka, Nguyen and Vu: the point probabilities are always at most about $1/\sqrt n$, unless $f$ is "close to the zero polynomial" (having only $o(n^d)$ nonzero coefficients). In this paper we prove several results s…

On the Frobenius Problem for Some Generalized Fibonacci Subsequences -- II
Ryan Azim Shaikh, Amitabha Tripathi
https://arxiv.org/abs/2507.00495 https://

On the Frobenius Problem for Some Generalized Fibonacci Subsequences -- II
For a set $A$ of positive integers with $\gcd(A)=1$, let $\langle A \rangle$ denote the set of all finite linear combinations of elements of $A$ over the non-negative integers. Then it is well known that only finitely many positive integers do not belong to $\langle A \rangle$. The Frobenius number and the genus associated with the set $A$ is the largest number and the cardinality of the set of integers non-representable by $A$. By a generalized Fibonacci sequence $\{V_n\}_{n \ge 1}$ we mean an…

General monotone formula for homogeneous $k$-Hessian equation in the exterior domain and its applications
Jiabin Yin, Xingjian Zhou
https://arxiv.org/abs/2506.01434

General monotone formula for homogeneous $k$-Hessian equation in the exterior domain and its applications
In this paper, we deal with an overdetermined problem for the $k$-Hessian equation ($1\leq k<\frac n2$) in the exterior domain and prove the corresponding ball characterizations. Since that Weinberger type approach seems to fail to solve the problem, we give a new perspective to solve exterior overdetermined problem by combining two integral identities and geometric inequalities. In particular, when $k=1$, we give an alternative proof for Brandolini-Nitsch-Salani's results \cite{BNS}. Meanwhile…

Sums and differences of sets: a further improvement over AlphaEvolve
Fan Zheng
https://arxiv.org/abs/2506.01896 https://arxiv.org/pdf…

Sums and differences of sets: a further improvement over AlphaEvolve
We present a new advancement in the sum and difference of sets problem, which improves upon recent results by both DeepMind's AlphaEvolve ($θ= 1.1584$) and subsequent explicit constructions ($θ= 1.173050$). In this work, we construct a sequence of $U$ sets which in the limit establishes a new lower bound of $θ= 1.173077$.

This https://arxiv.org/abs/2505.00493 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the greatest prime factor and uniform equidistribution of quadratic polynomials
We show that the greatest prime factor of $n^2+h$ is at least $n^{1.312}$ infinitely often. This gives an unconditional proof for the range previously known under the Selberg eigenvalue conjecture. Furthermore, we get uniformity in $h \leq n^{1+o(1)}$ under a natural hypothesis on real characters. The same uniformity is obtained for the equidistribution of the roots of quadratic congruences modulo primes. We also prove a variant of the divisor problem for $ax^2+by^3$, which was used by the seco…

Improved bounds on the postage stamp problem for large numbers of stamps
Eric James Faust, Michael Tait
https://arxiv.org/abs/2507.23627 https://arxiv.org/…

Improved bounds on the postage stamp problem for large numbers of stamps
Let $F_h(n)$ denote the minimum cardinality of an additive {\em $h$-fold basis} of $\{1,2,\cdots,n\}$: a set $S$ such that any integer in $\{1,2,\cdots, n\}$ can be written as a sum of at most $h$ elements from $S$. While the trivial bounds $h!n \; \lesssim \; F_h(n)^h \; \lesssim \; h^h n$ are well-known, comparatively little has been established for $h>2$. In this paper, we make significant improvements to both of the best-known bounds on $F_h(n)$ for sufficiently large $h$. For the lower bou…