Tootfinder

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…

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.

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…

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…

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 $u_1 = u_2$…

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 $\mathbb{H}^{n + 1}$.

"The destruction of the climate by industrial processes is a real-world problem. If programming language selection has no impact on it, then maybe we’re all just wasting our time, creating shiny consumer distractions to make the last few years of humanity that little more palatable for the richest 1% of the world’s human population."

Choosing A Programming Language
Selecting the correct programming language for a particular task often feels like a bunfight. Suggestions are thrown around based on the individual's preferences and desires. The experience is very likely to leave one feeling that programming is an art, rather than a science.

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

On the heat kernel of a Cayley graph of $\operatorname{PSL}_2\mathbb{Z}$
Anders Karlsson, Kamila Kashaeva
https://arxiv.org/abs/2506.02340 https://

On the heat kernel of a Cayley graph of $\operatorname{PSL}_2\mathbb{Z}$
In this paper, we obtain an explicit formula for the heat kernel on the infinite Cayley graph of the modular group $\operatorname{PSL}_2\mathbb{Z}$, given by the presentation $\langle a,b\mid a^2=1, b^3=1\rangle$. Our approach extends the method of Chung--Yau in~\cite{MR1667452} by observing that the Cayley graph strongly and regularly covers a weighted infinite line. We solve the spectral problem on this line to obtain an integral expression for its heat kernel, and then lift this to the Cayle…

This https://arxiv.org/abs/2503.10569 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

Low-Rank Matrix Regression via Least-Angle Regression
Low-rank matrix regression is a fundamental problem in data science with various applications in systems and control. Nuclear norm regularization has been widely applied to solve this problem due to its convexity. However, it suffers from high computational complexity and the inability to directly specify the rank. This work introduces a novel framework for low-rank matrix regression that addresses both unstructured and Hankel matrices. By decomposing the low-rank matrix into rank-1 bases, the …

This https://arxiv.org/abs/2501.12261 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCG_…

A Framework for the Design of Efficient Diversification Algorithms to NP-Hard Problems
There has been considerable recent interest in computing a diverse collection of solutions to a given optimization problem, both in the AI and theory communities. Given a classical optimization problem $Π$ (e.g., spanning tree, minimum cuts, maximum matching, minimum vertex cover) with input size $n$ and an integer $k\geq 1$, the goal is to generate a collection of $k$ maximally diverse solutions to $Π$. This diverse-X paradigm not only allows the user to generate very different solutions, bu…

Boundary behavior in the Loewner-Nirenberg problem
Satyanad Kichenassamy (LMR)
https://arxiv.org/abs/2507.02484 https://arxiv.org/pdf…

Boundary behavior in the Loewner-Nirenberg problem
Let $Ω\subset\mathbb R^n$ be a bounded domain of class $C^{2+α}$, $0<α<1$. We show that if $n\geq 3$ and $u_Ω$ is the maximal solution of equation $Δu = n(n-2)u^{(n+2)/(n-2)}$ in $Ω$, then the hyperbolic radius $v_Ω=u_Ω^{-2/(n-2)}$ is of class $C^{2+α}$ up to the boundary. The argument rests on a reduction to a nonlinear Fuchsian elliptic PDE.

This https://arxiv.org/abs/2409.01198 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csRO_…

Direct Kinematics, Inverse Kinematics, and Motion Planning of 1-DoF Rational Linkages
This study presents a set of algorithms that deal with trajectory planning of rational single-loop mechanisms with one degree of freedom (DoF). Benefiting from a dual quaternion representation of a rational motion, a formula for direct (forward) kinematics, a numerical inverse kinematics algorithm, and the generation of a driving-joint trajectory are provided. A novel approach using the Gauss-Newton search for the one-parameter inverse kinematics problem is presented. Additionally, a method for…

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…

Improving LLM Agents with Reinforcement Learning on Cryptographic CTF Challenges
Lajos Muzsai, David Imolai, Andr\'as Luk\'acs
https://arxiv.org/abs/2506.02048

Improving LLM Agents with Reinforcement Learning on Cryptographic CTF Challenges
Large Language Models (LLMs) still struggle with the structured reasoning and tool-assisted computation needed for problem solving in cybersecurity applications. In this work, we introduce "random-crypto", a cryptographic Capture-the-Flag (CTF) challenge generator framework that we use to fine-tune a tool-augmented Llama-3.1-8B with Guided Reinforcement Prompt Optimisation (GRPO), allowing the agent to iteratively write and execute Python inside an isolated REPL. GRPO yields a +53% absolute jum…

Misaligned from Within: Large Language Models Reproduce Our Double-Loop Learning Blindness
Tim Rogers, Ben Teehankee
https://arxiv.org/abs/2507.02283 https…

Misaligned from Within: Large Language Models Reproduce Our Double-Loop Learning Blindness
This paper examines a critical yet unexplored dimension of the AI alignment problem: the potential for Large Language Models (LLMs) to inherit and amplify existing misalignments between human espoused theories and theories-in-use. Drawing on action science research, we argue that LLMs trained on human-generated text likely absorb and reproduce Model 1 theories-in-use - a defensive reasoning pattern that both inhibits learning and creates ongoing anti-learning dynamics at the dyad, group, and or…

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…

This https://arxiv.org/abs/2406.04231 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csMA_…

Quantifying Misalignment Between Agents: Towards a Sociotechnical Understanding of Alignment
Existing work on the alignment problem has focused mainly on (1) qualitative descriptions of the alignment problem; (2) attempting to align AI actions with human interests by focusing on value specification and learning; and/or (3) focusing on a single agent or on humanity as a monolith. Recent sociotechnical approaches highlight the need to understand complex misalignment among multiple human and AI agents. We address this gap by adapting a computational social science model of human contentio…

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…

This https://arxiv.org/abs/2409.08928 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Self-Organizing State-Space Models with Artificial Dynamics
We consider the problem of performing parameter and state inference in a state-space model (SSM) parametrized by a static parameter $θ$. A popular idea to address this problem consists of incorporating $θ$ in the state of the system and allowing its time evolution, modelled as a Markov chain $(θ_t)_{t\geq 1}$. This proxy model defines a so-called self-organizing SSM (SO-SSM) to which one may apply standard particle filters. However, the practical implementation of this idea in a theoreticall…

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…

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

Probably a good day 🥵 to remind of our CoolWalks study: https://www.nature.com/articles/s41598-025-97200-2
- Above all, stop burning fossil fuels
- Buildings (and trees) cast a lot of shade in cities. We systematically quantify the benefits for 🚶🚴
- Make sha…

CoolWalks for active mobility in urban street networks - Scientific Reports
Walking is the most sustainable form of urban mobility, but is compromised by uncomfortable or unhealthy sun exposure, which is an increasing problem due to global warming. Shade from buildings can provide cooling and protection for pedestrians, but the extent of this potential benefit is unknown. Here we explore the potential for shaded walking, using building footprints and street networks from both synthetic and real cities. We introduce a route choice model with a sun avoidance parameter $$…

This https://arxiv.org/abs/2412.06552 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCC_…

Direct Sums for Parity Decision Trees
Direct sum theorems state that the cost of solving $k$ instances of a problem is at least $Ω(k)$ times the cost of solving a single instance. We prove the first such results in the randomised parity decision tree model. We show that a direct sum theorem holds whenever (1) the lower bound for parity decision trees is proved using the discrepancy method; or (2) the lower bound is proved relative to a product distribution.

UTCS: Effective Unsupervised Temporal Community Search with Pre-training of Temporal Dynamics and Subgraph Knowledge
Yue Zhang, Yankai Chen, Yingli Zhou, Yucan Guo, Xiaolin Han, Chenhao Ma
https://arxiv.org/abs/2506.02784

UTCS: Effective Unsupervised Temporal Community Search with Pre-training of Temporal Dynamics and Subgraph Knowledge
In many real-world applications, the evolving relationships between entities can be modeled as temporal graphs, where each edge has a timestamp representing the interaction time. As a fundamental problem in graph analysis, {\it community search (CS)} in temporal graphs has received growing attention but exhibits two major limitations: (1) Traditional methods typically require predefined subgraph structures, which are not always known in advance. (2) Learning-based methods struggle to capture …

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.

Random-key genetic algorithms
Mariana A. Londe, Luciana S. Pessoa, Carlos E. Andrade, Jos\'e F. Gon\c{c}alves, Mauricio G. C. Resende
https://arxiv.org/abs/2506.02120

Random-key genetic algorithms
A random-key genetic algorithm is an evolutionary metaheuristic for discrete and global optimization. Each solution is encoded as a vector of N random keys, where a random key is a real number randomly generated in the continuous interval [0, 1). A decoder maps each vector of random keys to a solution of the optimization problem being solved and computes its cost. The benefit of this approach is that all genetic operators and transformations can be maintained within the unitary hypercube, regar…

"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.

This https://arxiv.org/abs/2501.02485 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Semi-analytic construction of global transfers between quasi-periodic orbits in the spatial R3BP
Consider the spatial restricted three-body problem, as a model for the motion of a spacecraft relative to the Sun-Earth system. We focus on the dynamics near the equilibrium point $L_1$, located between the Sun and the Earth. We show that we can transfer the spacecraft from a quasi-periodic orbit that is nearly planar relative to the ecliptic to a quasi-periodic orbit that has large vertical amplitude, at zero energy cost. (In fact, the final orbit has the maximum vertical amplitude that can be…

European Journal of Jewish Studies Volume 19 (2025): Issue 1
https://ift.tt/i1HGJwy
When did aliens become a problem? The Mediterranean Association for Marine Biology and Oceanology in…
via Input 4 RELCFP

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…

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…

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)

Tools for stability analysis of fractional reaction diffusion systems
Sofwah Ahmad, Szymon Cygan, Grzegorz Karch
https://arxiv.org/abs/2507.02094 https://

Tools for stability analysis of fractional reaction diffusion systems
The linearization principle states that the stability (or instability) of solutions to a suitable linearization of a nonlinear problem implies the stability (or instability) of solutions to the original nonlinear problem. In this work, we prove this principle for solutions of abstract fractional reaction-diffusion equations with a fractional derivative in time of order $α\in (0,1)$. Then, we apply these results to particular fractional reaction-diffusion equations, obtaining, for example, the …

Na gut, dann kleben wir die Stadt eben noch einmal mit #NolympiaHH voll
https://www.instagram.com/p/DKUj8edMeZu/

NDR Hamburg on Instagram: "Hamburg hat am Sonnabend als letzter von vier Kandidaten seine Pläne für eine mögliche deutsche Bewerbung um Olympische und Paralympische Spiele 2036, 2040 oder 2044 vorgestellt: Beachvolleyball auf dem Heiligengeistfeld, Schwimmen im Volksparkstadion, Hockey im Millerntorstadion - und Leichtathletik im Volkspark. Das fehlende Leichtathletikstadion war bislang in der Hansestadt mit Blick auf Olympische Spiele ein großes Problem. Nun entsteht in unmittelbarer Nähe zum Volksparkstadion eine ohnehin geplante Arena, die bis zu 60.000 Menschen fasst und auch ohne Olympia-Zuschlag gebaut wird. ___ #olympia #olympischespiele #hamburg #volsparkstadion #millerntorstadion #hamburg #ndr #activecity"
1,594 likes, 55 comments - ndrhamburg on May 31, 2025: "Hamburg hat am Sonnabend als letzter von vier Kandidaten seine Pläne für eine mögliche deutsche Bewerbung um Olympische und Paralympische Spiele 2036, 2040 oder 2044 vorgestellt: Beachvolleyball auf dem Heiligengeistfeld, Schwimmen im Volksparkstadion, Hockey im Millerntorstadion - und Leichtathletik im Volkspark. Das fehlende Leichtathletikstadion war bislang in der Hansestadt mit Blick auf Olympische Spiele ein großes Problem. Nun e…

This https://arxiv.org/abs/2309.01754 has been replaced.
link: https://scholar.google.com/scholar?q=a

On the success probability of the quantum algorithm for the short DLP
Ekerå and Håstad have introduced a variation of Shor's algorithm for the discrete logarithm problem (DLP). Unlike Shor's original algorithm, Ekerå-Håstad's algorithm solves the short DLP in groups of unknown order. In this work, we prove a lower bound on the probability of Ekerå-Håstad's algorithm recovering the short logarithm $d$ in a single run. By our bound, the success probability can easily be pushed as high as $1 - 10^{-10}$ for any short $d$. A key to achieving such a high success…

Marcello's completion of graphs
Johan Kok
https://arxiv.org/abs/2507.02015 https://arxiv.org/pdf/2507.02015

Marcello's completion of graphs
This paper initiates a study on a new optimization problem with regards to graph completion. The defined procedure is called, \emph{Marcello's completion} of a graph. For graph $G$ of order $n$ the \emph{Marcello number} is obtained by iteratively constructing graphs, $G_1,G_2,\dots,G_k$ by adding a maximal number of edges between pairs of distinct, non-adjacent vertices in accordance with the \emph{Marcello rule}. If for smallest $k$ the resultant graph $G_k \cong K_n$ then the Marcello number…

A Strong Kurepa Tree
John Krueger
https://arxiv.org/abs/2507.01133 https://arxiv.org/pdf/2507.01133

A Strong Kurepa Tree
We prove that it is consistent that there exists a Kurepa tree $T$ such that ${}^{ω_1}2$ is a continuous image of the topological space $[T]$ consisting of all cofinal branches of $T$ with respect to the cone topologies. This result solves an open problem due to Bergfalk, Chodounský, Guzmán, and Hrušák. We also prove that any Kurepa tree with the above property contains an Aronszajn subtree.

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.

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…

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…

Replaced article(s) found for math.FA. https://arxiv.org/list/math.FA/new
[1/1]:
- Typical properties of positive contractions and the invariant subspace problem
Valentin Gillet

I understood this in principle but for some reason this graph really drove home the shape of the problem. https://vis.social/@infobeautiful/114614345328627391

Information Is Beautiful (@infobeautiful@vis.social)
Attached: 1 image If you're aged 30 or more, then 50% of all human fossil fuel emissions happened during your lifetime

This https://arxiv.org/abs/2210.03905 has been replaced.
link: https://scholar.google.com/scholar?q=a

Empirical Bayes Selection for Value Maximization
We study the problem of selecting the best $m$ units from a set of $n$ as $m / n \to α\in (0, 1)$, where noisy, heteroskedastic measurements of the units' true values are available and the decision-maker wishes to maximize the aggregate true value of the units selected. Given a parametric prior distribution, the empirical Bayes decision rule incurs $O_p(n^{-1})$ regret relative to the Bayesian oracle that knows the true prior. More generally, if the error in the estimated prior is of order $O_…

An application of the hit problem to the algebraic transfer
Nguyen Sum
https://arxiv.org/abs/2505.23218 https://arxiv.org/pdf/2505.23…

An application of the hit problem to the algebraic transfer
Let $P_k$ be the polynomial algebra $\mathbb F_2[x_1,x_2,\ldots ,x_k]$ over the field $\mathbb F_2$ with two elements, in $k$ variables $x_1, x_2, \ldots , x_k$, each variable of degree 1. Denote by $GL_k$ the general linear group over $\mathbb F_2$ which regularly acts on $P_k$. The algebra $P_k$ is a module over the mod-2 Steenrod algebra $\mathcal A$. In 1989, Singer [22] defined the $k$-th homological algebraic transfer, which is a homomorphism $$φ_k=(φ_k)_m :{\rm Tor}^{\mathcal A}_{k,k+m…

This https://arxiv.org/abs/2212.06782 has been replaced.
link: https://scholar.google.com/scholar?q=a

On Computing Vertex Connectivity of 1-Plane Graphs
The vertex connectivity of a graph $G$ is the size of the smallest set of vertices $S$ such that $G \setminus S$ is disconnected. For the class of planar graphs, the problem of vertex connectivity is well-studied, both from structural and algorithmic perspectives. Let $G$ be a plane embedded graph, and $Λ(G)$ be an auxiliary graph obtained by inserting a face vertex inside each face and connecting it to all vertices of $G$ incident with the face. If $S$ is a minimal vertex cut of $G$, then the…

Replaced article(s) found for q-bio.MN. https://arxiv.org/list/q-bio.MN/new
[1/1]:
- Modeling the Monty Hall Decision Problem with Reaction Kinetics
Oliver Steinbock, Wen Zhu

This https://arxiv.org/abs/2506.02120 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csNE_…

Random-key genetic algorithms
A random-key genetic algorithm is an evolutionary metaheuristic for discrete and global optimization. Each solution is encoded as a vector of N random keys, where a random key is a real number randomly generated in the continuous interval [0, 1). A decoder maps each vector of random keys to a solution of the optimization problem being solved and computes its cost. The benefit of this approach is that all genetic operators and transformations can be maintained within the unitary hypercube, regar…

Once upon a time the French had a real problem with the 1%. THEY SOLVED IT.

Improving statistical learning methods via features selection without replacement sampling and random projection
Sulaiman khan, Muhammad Ahmad, Fida Ullah, Carlos Aguilar Iba\~nez, Jos\'e Eduardo Valdez Rodriguez
https://arxiv.org/abs/2506.00053

Improving statistical learning methods via features selection without replacement sampling and random projection
Cancer is fundamentally a genetic disease characterized by genetic and epigenetic alterations that disrupt normal gene expression, leading to uncontrolled cell growth and metastasis. High-dimensional microarray datasets pose challenges for classification models due to the "small n, large p" problem, resulting in overfitting. This study makes three different key contributions: 1) we propose a machine learning-based approach integrating the Feature Selection Without Re-placement (FSWOR) technique…

Weyl formula improvement for product of Zoll manifolds
Yanfei Wang
https://arxiv.org/abs/2506.02299 https://arxiv.org/pdf/2506.02299

Weyl formula improvement for product of Zoll manifolds
Iosevich and Wyman have proved in ~\cite{IoWy} that the remainder term in classical Weyl law can be improved from $O(λ^{d-1})$ to $o(λ^{d-1})$ in the case of product manifold by using a famous result of Duistermaat and Guillemin. They also showed that we could have polynomial improvement in the special case of Cartesian product of round spheres by reducing the problem to the study of the distribution of weighted integer lattice points. In this paper, we show that we can extend this result to …

@… Gutachten gehören explizit zu meinen aufgaben, es stellt sich für mich da eher die frage, (1) ob ich dafür überhaupt geld nehmen dürfte (oder es z. b. an die uni abführen müsste), (2) ob das dann eine nebentätigkeit ist, und (3) ab wann diese einkünfte zu versteuern sind.
Aber das problem ist doch, dass völlig falsche anreize gesetzt werden, ohne das eigen…

@… Gutachten gehören explizit zu meinen aufgaben, es stellt sich für mich da eher die frage, (1) ob ich dafür überhaupt geld nehmen dürfte (oder es z. b. an die uni abführen müsste), (2) ob das dann eine nebentätigkeit ist, und (3) ab wann diese einkünfte zu versteuern sind.
Aber das problem ist doch, dass völlig falsche anreize gesetzt werden, ohne das eigen…

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 $θ= 1.173077$.

STIP: Forschungsstipendium ‚Kritik im Widerstreit‘, Halle (28.6.2025)
https://ift.tt/hjdRtZJ
When did aliens become a problem? The Mediterranean Association for Marine Biology and Oceanology in…
via Input 4 RELCFP …

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.

On the convergence of critical points on real algebraic sets and applications to optimization
Saugata Basu, Ali Mohammad-Nezhad
https://arxiv.org/abs/2506.20565

On the convergence of critical points on real algebraic sets and applications to optimization
Let $F \in \R[X_1,\ldots,X_n]$ and the zero set $V=\zero(\mathcal{P},\R^n)$, where $\mathcal{P}:=\{P_1,\ldots,P_s\} \subset \R[X_1,\ldots,X_n]$ is a finite set of polynomials. We investigate existence of critical points of $F$ on an infinitesimal perturbation $V_ξ = \zero(\{P_1-ξ_1.\ldots,P_s-ξ_s\},\R^n)$. Our motivation is to understand the limiting behavior of central paths in polynomial optimization, which is an important problem in the theory of interior point methods for polynomial opti…

Incremental Gain Computation and Regulation of Discrete-time Positive Lur\'e Systems using Linear Programming
Jared Miller
https://arxiv.org/abs/2505.24386

Incremental Gain Computation and Regulation of Discrete-time Positive Luré Systems using Linear Programming
This work approaches the problem of computing incremental $\ell_1$ and $\ell_\infty$ gains for discrete-time positive systems in \lure feedback with static memoryless nonlinearities, and regulating the $\ell_\infty$ gain through the design of a state-feedback controller. Finite incremental gains provide a quantitative measure of robustness for trajectories, and will ensure that all pairs of trajectories will converge to a fixed point or will diverge together in the absence of an applied input. …

A coding problem that sounded simple, but to implement it with good performance was quite a challenge::
Given a number n, find the next number m where m > n, with m containing the same digits as n
So given 12 this would be 21
113 -> 131
534987 -> 537489
111 -> no solution, -1, error or whatever
EDIT: changed the solution of example for 534987
#programming

The Minkowski problem for the $k$-torsional rigidity
Xia Zhao, Peibiao Zhao
https://arxiv.org/abs/2505.24494 https://arxiv.org/pdf/25…

The Minkowski problem for the $k$-torsional rigidity
P. Salani [Adv. Math., 229 (2012)] introduced the $k$-torsional rigidity associated with a $k$-Hessian equation and obtained the Brunn-Minkowski inequalities $w.r.t.$ the torsional rigidity in $\mathbb{R}^3$. Following this work, we first construct, in the present paper, a Hadamard variational formula for the $k$-torsional rigidity with $1\leq k\leq n-1$, then we can deduce a $k$-torsional measure from the Hadamard variational formula. Based on the $k$-torsional measure, we propose the Minkowsk…

This https://arxiv.org/abs/2407.20941 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csDS_…

Random-Order Interval Selection
In the problem of online unweighted interval selection, the objective is to maximize the number of non-conflicting intervals accepted by the algorithm. In the conventional online model of irrevocable decisions, there is an Omega(n) lower bound on the competitive ratio, even for randomized algorithms [Bachmann et al. 2013]. In a line of work that allows for revocable acceptances, [Faigle and Nawijn 1995] gave a greedy 1-competitive (i.e. optimal) algorithm in the real-time model, where intervals…

Replaced article(s) found for math.NA. https://arxiv.org/list/math.NA/new
[1/1]:
- SFEM for the Lagrangian formulation of the surface Stokes problem
Charles M. Elliott, Achilleas Mavrakis

Replaced article(s) found for cs.DM. https://arxiv.org/list/cs.DM/new
[1/1]:
- The EnvDesign Model: A Method to Solve the Environment Design Problem
Akshay Sathiya, Rohit Pandey

Ill-posedness of the Euler equations and inviscid limit of the Navie-Stokes equations in Besov spaces
Jinlu Li, Xing Wu, Yanghai Yu
https://arxiv.org/abs/2507.02247

Ill-posedness of the Euler equations and inviscid limit of the Navie-Stokes equations in Besov spaces
In this paper, we consider the Cauchy problem to the incompressible Euler and Navie-Stokes equations on the d-dimensional torus.Our aim of this paper is two fold. Firstly, we construct a new initial data and present a simple proof of the ill-posedness of the Euler equations in different senses: (1) the solution map of the Euler equations starting from $u_0$ is discontinuous at $t = 0$ in $B^s_{p,\infty}$ with $s>0$ and $1\leq p \leq \infty$, which covers the result obtained by Cheskidov and Shv…

Na gut, dann kleben wir die Stadt eben noch einmal mit #NolympiaHH voll
https://www.instagram.com/p/DKUj8edMeZu/

NDR Hamburg on Instagram: "Hamburg hat am Sonnabend als letzter von vier Kandidaten seine Pläne für eine mögliche deutsche Bewerbung um Olympische und Paralympische Spiele 2036, 2040 oder 2044 vorgestellt: Beachvolleyball auf dem Heiligengeistfeld, Schwimmen im Volksparkstadion, Hockey im Millerntorstadion - und Leichtathletik im Volkspark. Das fehlende Leichtathletikstadion war bislang in der Hansestadt mit Blick auf Olympische Spiele ein großes Problem. Nun entsteht in unmittelbarer Nähe zum Volksparkstadion eine ohnehin geplante Arena, die bis zu 60.000 Menschen fasst und auch ohne Olympia-Zuschlag gebaut wird. ___ #olympia #olympischespiele #hamburg #volsparkstadion #millerntorstadion #hamburg #ndr #activecity"
1,594 likes, 55 comments - ndrhamburg on May 31, 2025: "Hamburg hat am Sonnabend als letzter von vier Kandidaten seine Pläne für eine mögliche deutsche Bewerbung um Olympische und Paralympische Spiele 2036, 2040 oder 2044 vorgestellt: Beachvolleyball auf dem Heiligengeistfeld, Schwimmen im Volksparkstadion, Hockey im Millerntorstadion - und Leichtathletik im Volkspark. Das fehlende Leichtathletikstadion war bislang in der Hansestadt mit Blick auf Olympische Spiele ein großes Problem. Nun e…

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

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

Replaced article(s) found for math.CV. https://arxiv.org/list/math.CV/new
[1/1]:
- Holomorphic bundles framed along a real hypersurface and the Riemann-Hilbert problem
Andrei Teleman

On a Variation of Gambler's Ruin Problem
Zhiyi Chi, Vladimir Pozdnyakov
https://arxiv.org/abs/2506.00990 https://arxiv.org/pdf/25…

On a Variation of Gambler's Ruin Problem
Assume that letters (from a finite alphabet) in a text form a Markov chain. We track two distinct words, $U$ and $D$. A gambler gains 1 point for each occurrence of $U$ (including overlapping occurrences) and loses 1 point for each occurrence of $D$ (also including overlapping occurrences). We determine the probability of gaining $A$ points before losing $B$ points, where $A$ and $B$ are integers. Additionally, we find the expected waiting time until one of the two events -- gaining $A$ points …

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

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/2502.06200 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csDS_…

On the query complexity of sampling from non-log-concave distributions
We study the problem of sampling from a $d$-dimensional distribution with density $p(x)\propto e^{-f(x)}$, which does not necessarily satisfy good isoperimetric conditions. Specifically, we show that for any $L,M$ satisfying $LM\ge d\ge 5$, $ε\in \left(0,\frac{1}{32}\right)$, and any algorithm with query accesses to the value of $f(x)$ and $\nabla f(x)$, there exists an $L$-log-smooth distribution with second moment at most $M$ such that the algorithm requires $\left(\frac{LM}{dε}\right)^{�…

Restricted (2 1)-TQFTs supported by thickened and solid tori
Du\v{s}an {\DJ}or{\dj}evi\'c, Danica Kosanovi\'c, Jovana Nikoli\'c, Zoran Petri\'c
https://arxiv.org/abs/2505.21373

Restricted (2+1)-TQFTs supported by thickened and solid tori
A faithful $(1+1)$ TQFT has recently been constructed, but the existence of a faithful $(2+1)$ TQFT remains an open question, that subsumes the hard problem of linearity of mapping class groups of surfaces. To circumvent the latter problem we construct a subcategory of the category of 3-cobordisms, containing disjoint unions of tori and simplest cobordisms between them. On this we define TQFTs that are able to distinguish pairs of torus bundles and lens spaces, previously shown not to be distin…

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…

Exploring Advanced LLM Multi-Agent Systems Based on Blackboard Architecture
Bochen Han, Songmao Zhang
https://arxiv.org/abs/2507.01701 https://

Exploring Advanced LLM Multi-Agent Systems Based on Blackboard Architecture
In this paper, we propose to incorporate the blackboard architecture into LLM multi-agent systems (MASs) so that (1) agents with various roles can share all the information and others' messages during the whole problem-solving process, (2) agents that will take actions are selected based on the current content of the blackboard, and (3) the selection and execution round is repeated until a consensus is reached on the blackboard. We develop the first implementation of this proposal and conduct e…

The Dirichlet problem for the minimal surface system on smooth domains
Caiyan Li, Hengyu Zhou
https://arxiv.org/abs/2506.23245 https://

The Dirichlet problem for the minimal surface system on smooth domains
In this paper, we propose a new assumption (1.2) that involves a small oscillation and $C^2$ norms for maps from smooth bounded domains into Euclidean spaces. Furthermore, by assuming that the domain has non-negative Ricci curvature, we establish the Dirichlet problem for the minimal surface system via the mean curvature flow (MCF) with boundary. The long-time existence of such flow is derived using Bernstein-type theorems of higher codimensional self-shrinkers in the whole space and the half-s…

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…

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…

On the local metric dimension of $K_4$-free graphs
Ali Ghalavand, Sandi Klav\v{z}ar, Xueliang Li
https://arxiv.org/abs/2506.00414 https://

On the local metric dimension of $K_4$-free graphs
Let $G$ be a graph of order $ n(G) $, local metric dimension $ \dim_l(G) $, and clique number $ ω(G) $. It has been conjectured that if $ n(G) \geq ω(G) + 1 \geq 4 $, then $ \dim_l(G) \leq \left( \frac{ω(G) - 2}{ω(G) - 1} \right) n(G) $. In this paper the conjecture is confirmed for the case $ ω(G) = 3 $. Consequently, a problem regarding the local metric dimension of planar graphs is also resolved.

Computing Diverse and Nice Triangulations
Waldo G\'alvez, Mayank Goswami, Arturo Merino, GiBeom Park, Meng-Tsung Tsai
https://arxiv.org/abs/2506.01323 …

Computing Diverse and Nice Triangulations
We initiate the study of computing diverse triangulations to a given polygon. Given a simple $n$-gon $P$, an integer $ k \geq 2 $, a quality measure $σ$ on the set of triangulations of $P$ and a factor $ α\geq 1 $, we formulate the Diverse and Nice Triangulations (DNT) problem that asks to compute $k$ \emph{distinct} triangulations $T_1,\dots,T_k$ of $P$ such that a) their diversity, $\sum_{i < j} d(T_i,T_j) $, is as large as possible \emph{and} b) they are nice, i.e., $σ(T_i) \leq ασ^* $ …

Replaced article(s) found for cs.DM. https://arxiv.org/list/cs.DM/new
[1/1]:
- The Fagnano Triangle Patrolling Problem
Konstantinos Georgiou, Somnath Kundu, Pawel Pralat

Analysis of A Mixed Finite Element Method for Poisson's Equation with Rough Boundary Data
Huadong Gao, Yuhui Huang, Wen Xie
https://arxiv.org/abs/2507.00697

Analysis of A Mixed Finite Element Method for Poisson's Equation with Rough Boundary Data
This paper is concerned with finite element methods for Poisson's equation with rough boundary data. Conventional methods require that the boundary data $g$ of the problem belongs to $H^{1/2} (\partial Ω)$. However, in many applications one has to consider the case when $g$ is in $L^2(\partial Ω)$ only. To this end, very weak solutions are considered to establish the well-posedness of the problem. Most previously proposed numerical methods use regularizations of the boundary data. The main pu…

Replaced article(s) found for math.NT. https://arxiv.org/list/math.NT/new
[1/1]:
- Local square mean in the hyperbolic circle problem
Andr\'as Bir\'o

On the Dirichlet Problem at Infinity and Poisson Boundary for Certain Manifolds without Conjugate Points
Fei Liu, Yinghan Zhang
https://arxiv.org/abs/2506.22883

On the Dirichlet Problem at Infinity and Poisson Boundary for Certain Manifolds without Conjugate Points
In this paper, we investigate the problem of the existence of the bounded harmonic functions on a simply connected Riemannian manifold $\widetilde{M}$ without conjugate points, which can be compactified via the ideal boundary $\widetilde{M}(\infty)$. Let $\widetilde{M}$ be a uniform visibility manifold which satisfy the Axiom $2$, or a rank $1$ manifold without focal points, suppose that $Γ$ is a cocompact discrete subgroup of $Iso(\widetilde{M})$, we show that for a given continuous function …

$C^{1,\alpha}$ 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 �…

Two $2/5$-level mock theta conjecture-like identities
Stepan Konenkov, Eric T. Mortenson
https://arxiv.org/abs/2506.01886 https://arx…

Two $2/5$-level mock theta conjecture-like identities
Determining the explicit forms and modularity for string functions and branching coefficients for Kac--Moody algebras after Kac, Peterson, and Wakimoto is an important problem. In a pair of papers, Borozenets and Mortenson determined the explicit forms for fractional-level string functions for the Kac--Moody algebra $A_{1}^{(1)}$. For positive fractional-level string functions they obtained mock theta conjecture-like identities, and for negative fractional-level string functions, they obtained …

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…

Computing Maximum Cliques in Unit Disk Graphs
Anastasiia Tkachenko, Haitao Wang
https://arxiv.org/abs/2506.21926 https://arxiv.org/pd…

Computing Maximum Cliques in Unit Disk Graphs
Given a set $P$ of $n$ points in the plane, the unit-disk graph $G(P)$ is a graph with $P$ as its vertex set such that two points of $P$ have an edge if their Euclidean distance is at most $1$. We consider the problem of computing a maximum clique in $G(P)$. The previously best algorithm for the problem runs in $O(n^{7/3+o(1)})$ time. We show that the problem can be solved in $O(n \log n + n K^{4/3+o(1)})$ time, where $K$ is the maximum clique size. The algorithm is faster than the previous one…

Structured Column Subset Selection for Bayesian Optimal Experimental Design
Hugo D\'iaz, Arvind K. Saibaba, Srinivas Eswar, Vishwas Rao, Zichao Wendy Di
https://arxiv.org/abs/2506.00336

Structured Column Subset Selection for Bayesian Optimal Experimental Design
We consider optimal experimental design (OED) for Bayesian inverse problems, where the experimental design variables have a certain multiway structure. Given $d$ different experimental variables with $m_i$ choices per design variable $1 \le i\le d$, the goal is to select $k_i \le m_i$ experiments per design variable. Previous work has related OED to the column subset selection problem by mapping the design variables to the columns of a matrix $\mathbf{A}$. However, this approach is applicable o…

This https://arxiv.org/abs/2505.24206 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the time-decay with the diffusion wave phenomenon of the solution to the compressible Navier-Stokes-Korteweg system in critical spaces
We consider the initial value problem of the compressible Navier-Stokes-Korteweg equations in the whole space $\mathbb{R}^d$ ($d \ge 2$). The purposes of this paper are to obtain the global-in-time solution around the constant equilibrium states $(ρ_*,0)$ and investigate the $L^p$-$L^1$ type time-decay estimates in a scaling critical framework, where $ρ_*>0$ is a constant. In addition, we study the diffusion wave property came from the wave equation with strong damping for the solution with t…

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…

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…

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…

Minimum Selective Subset on Some Graph Classes
Bubai Manna
https://arxiv.org/abs/2507.00235 https://arxiv.org/pdf/2507.00235

Minimum Selective Subset on Some Graph Classes
In a connected simple graph G = (V(G),E(G)), each vertex is assigned a color from the set of colors C={1, 2,..., c}. The set of vertices V(G) is partitioned as V_1, V_2, ... ,V_c, where all vertices in V_j share the same color j. A subset S of V(G) is called Selective Subset if, for every vertex v in V(G), and if v is in V_j, at least one of its nearest neighbors in (S union (V(G)\ V_j)) has the same color as v. The Minimum Selective Subset (MSS) problem seeks to find a selective subset of mini…

The Price of Being Partial: Complexity of Partial Generalized Dominating Set on Bounded-Treewidth Graphs
Jakob Greilhuber, D\'aniel Marx
https://arxiv.org/abs/2506.01645

The Price of Being Partial: Complexity of Partial Generalized Dominating Set on Bounded-Treewidth Graphs
The $(σ, ρ)$-domination framework introduced by Telle [Nord. J. Comput.'94] captures many classical graph problems. For fixed sets $σ, ρ$ of non-negative integers, a $(σ,ρ)$-set of a graph $G$ is a set $S$ such that for every $v\in V(G)$, we have (1) if $v \in S$, then $|N(v) \cap S| \in σ$, and (2) if $v \not\in S$, then $|N(v) \cap S| \in ρ$. We initiate the study of a natural partial variant of the problem, in which the constraints given by $σ, ρ$ need not be fu…

The minimum size of maximal bipartite IC-plane graphs with given connectivity
Guiping Wang, Yuanqiu Huang, Zhangdong Ouyang, Licheng Zhang
https://arxiv.org/abs/2506.00878

The minimum size of maximal bipartite IC-plane graphs with given connectivity
Recently, the problem of establishing bounds on the edge density of 1-planar graphs, including their subclass IC-planar graphs, has received considerable attention. In 2018, Angelini et al. showed that any n-vertex bipartite IC-planar graph has at most 2.25n-4 edges, which implies that bipartite IC-planar graphs have vertex-connectivity at most 4. In this paper, we prove that any n-vertex maximal bipartite IC-plane graph with connectivity 2 has at least 3/2n-2 edges, and those with connectivity…

The independence and clique cover numbers of the squarefree graph
Boris Alexeev, Dustin G. Mixon, Will Sawin
https://arxiv.org/abs/2507.01928 https://

The independence and clique cover numbers of the squarefree graph
We determine the largest subset $A\subseteq \{1,\dotsc,n\}$ such that for all $a,b\in A$, the product $ab$ is not squarefree. Specifically, the maximum size is achieved by the \emph{complement} of the odd squarefree numbers. This resolves a problem of Paul Erdős and András Sárközy from 1992.

Multi-peak solutions for the fractional Schr\"odinger equation with Dirichlet datum
Maria Medina, Jing Wu
https://arxiv.org/abs/2507.00806 https://

Multi-peak solutions for the fractional Schrödinger equation with Dirichlet datum
Let $s\in (0,1)$, $\varepsilon>0$ and let $Ω$ be a bounded smooth domain. Given the problem $$\varepsilon^{2s}(-Δ)^{s} u + V(x)u = |u|^{p-1}u \quad \mbox{in }\; Ω,$$ with Dirichlet boundary conditions and $1

Regularity and pointwise convergence for dispersive equations with asymptotically concave phase on Damek-Ricci spaces
Utsav Dewan
https://arxiv.org/abs/2506.00881

Regularity and pointwise convergence for dispersive equations with asymptotically concave phase on Damek-Ricci spaces
We study the Carleson's problem on Damek-Ricci spaces $S$ for dispersive equations: \begin{equation*} \begin{cases} i\frac{\partial u}{\partial t} +Ψ(\sqrt{-\mathcal{L}} )u=0\:,\: (x,t) \in S \times \mathbb{R} \:, \\ u(0,\cdot)=f\:,\: \text{ on } S \:, \end{cases} \end{equation*} where $\mathcal{L}= Δ$, the Laplace-Beltrami operator or $\tildeΔ$, the shifted Laplace-Beltrami operator, so that the corresponding phase function $ψ$ satisfies for some $a \in (0,1)$, the large frequency as…

This https://arxiv.org/abs/2404.11389 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Finding $d$-Cuts in Graphs of Bounded Diameter, Graphs of Bounded Radius and $H$-Free Graphs
The $d$-Cut problem is to decide if a graph has an edge cut such that each vertex has at most $d$ neighbours at the opposite side of the cut. If $d=1$, we obtain the intensively studied Matching Cut problem. The $d$-Cut problem has been studied as well, but a systematic study for special graph classes was lacking. We initiate such a study and consider classes of bounded diameter, bounded radius and $H$-free graphs. We prove that for all $d\geq 2$, $d$-Cut is polynomial-time solvable for graphs …

Sharp remainder of the $L^{p}$-Poincar\'e inequality for Baouendi-Grushin vector fields
Kuralay Apseit, Nurgissa Yessirkegenov, Amir Zhangirbayev
https://arxiv.org/abs/2507.01681

Sharp remainder of the $L^{p}$-Poincaré inequality for Baouendi-Grushin vector fields
In this paper, we establish a sharp remainder formula for the Poincaré inequality for Baouendi-Grushin vector fields in the setting of $L^{p}$ for complex-valued functions. In special cases, we recover previously known results. Additionally, we provide estimates of the remainder term for $p\geq2$ and $1