Tootfinder

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-…

Beyond Pass@1: Self-Play with Variational Problem Synthesis Sustains RLVR
Xiao Liang, Zhongzhi Li, Yeyun Gong, Yelong Shen, Ying Nian Wu, Zhijiang Guo, Weizhu Chen
https://arxiv.org/abs/2508.14029

Beyond Pass@1: Self-Play with Variational Problem Synthesis Sustains RLVR
Reinforcement Learning with Verifiable Rewards (RLVR) has recently emerged as a key paradigm for post-training Large Language Models (LLMs), particularly for complex reasoning tasks. However, vanilla RLVR training has been shown to improve Pass@1 performance at the expense of policy entropy, leading to reduced generation diversity and limiting the Pass@k performance, which typically represents the upper bound of LLM reasoning capability. In this paper, we systematically analyze the policy's gen…

Qudit-based scalable quantum algorithm for solving the integer programming problem
Kapil Goswami, Peter Schmelcher, Rick Mukherjee
https://arxiv.org/abs/2508.13906 https://

Qudit-based scalable quantum algorithm for solving the integer programming problem
Integer programming (IP) is an NP-hard combinatorial optimization problem that is widely used to represent a diverse set of real-world problems spanning multiple fields, such as finance, engineering, logistics, and operations research. It is a hard problem to solve using classical algorithms, as its complexity increases exponentially with problem size. Most quantum algorithms for solving IP are highly resource inefficient because they encode integers into qubits. In [1], the issue of resource i…

On upper bounds on the number of parts in the problem of partitioning sets into parts of smaller diameter
Arthur Igorevich Bikeev, Andrei Mikhailovich Raigorodskii
https://arxiv.org/abs/2508.14578

On upper bounds on the number of parts in the problem of partitioning sets into parts of smaller diameter
In the present paper, we study problems related to the classical Borsuk's problem. Recall that the Borsuk's problem consists in finding the smallest number $ f(n) $ of parts of smaller diameter into which an arbitrary set of diameter 1 in Euclidean space $ {\mathbb R}^n $ can be divided. Here we will discuss the quantity $ χ(n,b) $ which differs from the quantity $ f(n) $ in that in its definition an arbitrary set of diameter 1 in $ {\mathbb R}^n $ must be partitioned into parts whose diameter…

Nearly Tight Bounds for the Online Sorting Problem
Yossi Azar, Debmalya Panigrahi, Or Vardi
https://arxiv.org/abs/2508.14287 https://arxiv.org/pdf/2508.142…

Nearly Tight Bounds for the Online Sorting Problem
In the online sorting problem, a sequence of $n$ numbers in $[0, 1]$ (including $\{0,1\}$) have to be inserted in an array of size $m \ge n$ so as to minimize the sum of absolute differences between pairs of numbers occupying consecutive non-empty cells. Previously, Aamand {\em et al.} (SODA 2023) gave a deterministic $2^{\sqrt{\log n} \sqrt{\log \log n + \log (1/\varepsilon)}}$-competitive algorithm when $m = (1+\varepsilon) n$ for any $\varepsilon \ge Ω(\log n/n)$. They also showed a lower b…

So am I understanding this correctly that the upcoming NPM authentication and token changes mean our only publishing workflow options henceforth are either switching to OICD Trusted Publishing[1] via GitHub Actions or using granular access tokens. The problem with the former is that I wanted to migrate my projects to Codeberg soon (which isn't supported). The problem with the latter is that granular tokens are unsuitable for publishing packages from a large monorepo, since these tokens a…

thi.ng/umbrella

“Anyone who claims to rely on the best scientific consensus today must report the current death toll in the Gaza genocide as ‘more than 115,000’ violent deaths or ‘more than 460,000’ overall.
Here, in detail, is why.”
https://www.counterpunch.org/202…

The Real Gaza Death Toll is Impossible to Know Today, But the Minimum Isn’t
The problem with leaving this sentiment at “we have no idea how many people have been killed” is that we do have a very clear idea of the minimum, based on the most rigorous, detailed analyses that statisticians, epidemiologists, and experts on urban warfare, working together under stringent peer review in the world’s leading research forums, agree on. And that minimum number is indeed much higher than the Ministry’s count. That minimum scientifically plausible number of traumatic death…

A double-phase Neumann problem with $p=1$
Alexandros Matsoukas, Nikos Yannakakis
https://arxiv.org/abs/2508.13772 https://arxiv.org/pdf/2508.13772

A double-phase Neumann problem with $p=1$
We study a double-phase Neumann problem with non-homogeneous boundary conditions, where the lowest exponent $p$ is equal to 1. The existence of a solution is established as the limit of solutions to corresponding double-phase problems with $p>1$. We also provide a variational characterization of the limit.

blew someone's mind the other day by telling them sf's sunset district is denser than the whole city of amsterdam. yup! it's car-centric but no, density is not the problem

The Rectilinear Marco Polo Problem
Ofek Gila (University of California, Irvine), Michael T. Goodrich (University of California, Irvine), Zahra Hadizadeh (University of Rochester), Daniel S. Hirschberg (University of California, Irvine), Shayan Taherijam (University of California, Irvine)
https://arxiv.org/abs/2508.14820

The Rectilinear Marco Polo Problem
We study the rectilinear Marco Polo problem, which generalizes the Euclidean version of the Marco Polo problem for performing geometric localization to rectilinear search environments, such as in geometries motivated from urban settings, and to higher dimensions. In the rectilinear Marco Polo problem, there is at least one point of interest (POI) within distance $n$, in either the $L_1$ or $L_\infty$ metric, from the origin. Motivated from a search-and-rescue application, our goal is to move a …

Approximating 1-in-3 SAT by linearly ordered hypergraph 3-colouring is NP-hard
Andrei Krokhin, Danny Vagnozzi
https://arxiv.org/abs/2508.14606 https://arxi…

Approximating 1-in-3 SAT by linearly ordered hypergraph 3-colouring is NP-hard
Given a satisfiable instance of 1-in-3 SAT, it is NP-hard to find a satisfying assignment for it, but it may be possible to efficiently find a solution subject to a weaker (not necessarily Boolean) predicate than `1-in-3'. There is a folklore conjecture predicting which choices of weaker predicates lead to tractability and for which the task remains \NP-hard. One specific predicate, corresponding to the problem of linearly ordered $3$-colouring of 3-uniform hypergraphs, has been mentioned in se…

On branching points in the Gilbert-Steiner problem
Danila Cherkashin
https://arxiv.org/abs/2507.13532 https://arxiv.org/pdf/2507.1353…

On branching points in the Gilbert-Steiner problem
The Gilbert--Steiner problem is a generalization of the Steiner tree problem and specific optimal mass transportation, which allows the use additional (branching) point in a transport plan. A specific feature of the problem is that the cost of transporting a mass $m$ along a segment of length $l$ is equal to $l \times m^p$ for a fixed $0 < p < 1$ and segments may end at points not belonging to the supports of given measures (branching points). Main result of this paper determines all pairs of…

I’ve worked over the past year to reduce the amount of noise in my consciousness on a daily basis.
By that I mean - information noise, not literal sounds “noise”. (That problem was solved long ago by some good earplugs and noise canceling earphones.)
I’ve gotten used to spending less time on social media, regularly blocking most apps on my devices (anything with a feed news, most work communication apps, etc.), putting my phone and other devices aside for extended periods of time. Often go to work places with my iPad explicitly having its WiFi turned off and selecting cafes that don’t offer WiFi at all.
Negotiated better boundaries at work and in personal life where I exchange messages with people less often but try to make those interactions more meaningful, and people rarely expect me to respond to requests in less than 24 hours. Spent a lot of time setting up custom notification settings on all apps that would allow it, so I get fewer pings. With software, choosing fewer cloud-based options and using tools that are simple and require as few interruptions as possible.
Accustomed myself to lower-tech versions of doing things I like to do: reading on paper, writing by hand, drawing in physical sketchbooks, got a typewriter for typing without a screen. Choosing to call people on audio more, trying to make more of an effort to see people in person. Going to museums to look at art instead of browsing Pinterest. Defaulting to the library when looking for information.
I’m commenting on this now for two reasons:
1. I am pretty proud of myself for how much I’ve actually managed to reduce the constant stream of modern life esp. as a remote worker in tech!
2. Now that I’ve reached a breaking point of reducing enough noise that it’s NOTICEABLE - I am struck by the silence. I don’t know what to do with it. I don’t know how to navigate it and fill it. I made this space to be able to read and write and think more deeply - for now I feel stuck in limbo where I’m just reacquainting myself with the concept of having any space in my mind at all.

my conceptual framework part is about 1,5 pages too long. The problem is that I've condenced it for approx 2 hours. So I'm stuck. I need to work on some other part for a while. Writing articles is an amazingly fun pain in the ass.

Analyzing Undergraduate Problem-Solving in Physics Through Interaction With an AI Chatbot
Syed Furqan Abbas Hashmi, N. Sanjay Rebello
https://arxiv.org/abs/2508.14778 https://…

Analyzing Undergraduate Problem-Solving in Physics Through Interaction With an AI Chatbot
Providing individualized scaffolding for physics problem solving at scale remains an instructional challenge. We investigate (1) students' perceptions of a Socratic Artificial Intelligence (AI) chatbot's impact on problem-solving skills and confidence and (2) how the specificity of students' questions during tutoring relates to performance. We deployed a custom Socratic AI chatbot in a large-enrollment introductory mechanics course at a Midwestern public university, logging full dialogue transc…

Worst-case Nonparametric Bounds for the Student T-statistic
David Edelman
https://arxiv.org/abs/2508.13226 https://arxiv.org/pdf/2508.13226

Worst-case Nonparametric Bounds for the Student T-statistic
We address the problem of finding worst-case nonparametric bounds for T-statistic bythe considering the extremal problem of maximising $\mathbb{P}(S(w)\ge t)$ over nonnegative weight vectors $w\in\mathbb{R}^n$ with $\|w\|_2=1$, where $S(w)=\sum_{i=1}^n w_i \varepsilon_i$ and $\varepsilon_i$ are independent Rademacher variables. While classical results of Hoeffding [1] and Chernoff [2] provide sub-Gaussian upper bounds, and optimal-order inequalities were later obtained by the author […

Do I at least get a poorly rushed conclusion with weird group sex at the end? https://cyberpunk.lol/@dirtwizard666/114888521066687558

> The underlying problem today was a malfunction at Amazon Web Services, where something called "DNS resolution" was not working
BBC putting quotes around "DNS resolution" there, like it's indecipherable Gen-Z slang.
https://www.bbc.co.uk/news/live/c5y8k7k6v1rt

Snapchat, Roblox and Lloyds bank hit by Amazon Web Services internet outage - live updates
More than 1,000 companies have had 6.5 million reports of disruption, including Snapchat, Reddit, Roblox and Lloyds bank.

I was just thinking about what you should do when you have a problem with an organisation you are part of, and so far (I've only just woken up) I think the steps are:
1. Wait - maybe it will pass
2. Act yourself to fix it - at the very least you will gain a better undertaking of the
3. Complain - perhaps the boss doesn't know theres a problem
4. Organise - what you can't fix alone you can fix together
5. Leave - if all else fails
And it feels lik…

Quantum algebra approach to univariate and multivariate rational functions of $q$-Racah type
Wolter Groenevelt, Carel Wagenaar
https://arxiv.org/abs/2507.13483

Quantum algebra approach to univariate and multivariate rational functions of $q$-Racah type
In this paper, we study rational functions of $q$-Racah type and a multivariate extension, using representation theory of $\mathcal U_q(\mathfrak{sl}_2)$. Eigenfunctions of twisted primitive elements in $\mathcal U_q(\mathfrak{su}_2)$ can be expressed in terms of $q^{-1}$-Krawtchouk polynomials. Using this, we show that overlap coefficients of solutions of a generalized eigenvalue problem (GEVP) and an eigenvalue problem (EVP) can be expressed in terms of a rational function of $_4φ_3$-type. W…

Replaced article(s) found for astro-ph.GA. https://arxiv.org/list/astro-ph.GA/new
[1/1]:
- Addressing the core-cusp and diversity problem of dwarf and disk galaxies using cold collisionles...
Liliya L. R. Williams, Jens Hjorth, Evan D. Skillman

An Elliptic-Parabolic Free Boundary Problem with Discontinuous Data
Dennis Kriventsov, Mar\'ia Soria-Carro
https://arxiv.org/abs/2508.13299 https://arx…

An Elliptic-Parabolic Free Boundary Problem with Discontinuous Data
We consider an elliptic-parabolic free boundary problem that models the fluid flow through a partially saturated porous medium. The free boundary arises as the interface separating the saturated and unsaturated regions. Our main goal is to investigate, for the 1+1 dimensional model, how jump discontinuities on the boundary and initial data influence the regularity of both the solution and the free boundary. We show that if the data is merely bounded, then weak solutions are Lipschitz in space a…

Amplitude maximization in stable systems, Schur positivity, and some conjectures on polynomial interpolation
Dmitrii M. Ostrovskii, Pavel S. Shcherbakov
https://arxiv.org/abs/2508.13554

Amplitude maximization in stable systems, Schur positivity, and some conjectures on polynomial interpolation
For $r > 0$ and integers $t \ge n > 0$, we consider the following ``amplitude maximization'' problem: maximize the quantity $|x_t|$ over the set of complex solutions $x = (x_0, x_1, \dots)$ of all homogeneous linear difference equations of order $n$ with the roots of characteristic polynomial in the disc $\{z \in \mathbb{C}: |z| \le r\}$, and with initial values $x_0, \dots, x_{n-1}$ in the unit disc. We find that for any $t,n,r$, the maximum is attained in the case of coinc…

Modular transformations of tau functions and conformal blocks on the torus
Fabrizio Del Monte, Harini Desiraju, Pavlo Gavrylenko
https://arxiv.org/abs/2508.14030 https://…

Modular transformations of tau functions and conformal blocks on the torus
The connection problem for isomonodromic tau functions on the one-punctured torus concerns the ratio between the tau function and its modular transform, associated to dual pants decompositions of the torus. In this paper, we study the modular transformations of the tau function and consequently derive the connection constant. Moreover, through the relation with two-dimensional Conformal Field Theory, we also obtain an exact closed formula for the $c=1$ Virasoro modular kernel, whose expression …

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

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

Nearly Optimal Bounds on the Fourier sampling numbers of Besov Spaces
Jonathan W. Siegel
https://arxiv.org/abs/2508.13991 https://arxiv.org/pdf/2508.13991

Nearly Optimal Bounds on the Fourier sampling numbers of Besov Spaces
Let $\mathbb{T}^d$ denote the $d$-dimensional torus. We consider the problem of optimally recovering a target function $f^*:\mathbb{T}^d\rightarrow \mathbb{C}$ from samples of its Fourier coefficients. We make classical smoothness assumptions on $f^*$, specifically that $f^*$ lies in a Besov space $B^s_\infty(L_q)$ with $s > 0$ and $1\leq q\leq \infty$, and measure recovery error in the $L_p$-norm with $1\leq p\leq \infty$. Abstractly, the optimal recovery error is characterized by a `restricte…

An Efficient Massively Parallel Constant-Factor Approximation Algorithm for the $k$-Means Problem
Vincent Cohen-Addad, Fabian Kuhn, Zahra Parsaeian
https://arxiv.org/abs/2507.14089

An Efficient Massively Parallel Constant-Factor Approximation Algorithm for the $k$-Means Problem
In this paper, we present an efficient massively parallel approximation algorithm for the $k$-means problem. Specifically, we provide an MPC algorithm that computes a constant-factor approximation to an arbitrary $k$-means instance in $O(\log\log n \cdot \log\log\log n)$ rounds. The algorithm uses $O(n^σ)$ bits of memory per machine, where $σ> 0$ is a constant that can be made arbitrarily small. The global memory usage is $O(n^{1+\varepsilon})$ bits for an arbitrarily small constant $\varepsi…

High-Quality Axion Dark Matter at Gravitational Wave Interferometers
Disha Bandyopadhyay, Debasish Borah, Nayan Das, Rome Samanta
https://arxiv.org/abs/2509.14323 https://

High-Quality Axion Dark Matter at Gravitational Wave Interferometers
Gravitational effects are known to violate global symmetries, threatening the Peccei-Quinn (PQ) solution to the strong CP problem. Ultraviolet completions featuring a gauged $U(1)$ symmetry, where $U(1)_{\rm PQ}$ arises as an accidental global symmetry, can suppress Planck-suppressed operators, enabling high-quality axions in a mass window where it can also account for the observed dark matter (DM) in the Universe. We show that in such models, the spontaneous breaking of the $U(1)$ gauge symmet…

The extended horizontal linear complementarity problem: iterative methods and error analysis
Shi-Liang Wu, Cui-Xia Li
https://arxiv.org/abs/2509.14491 https://

The extended horizontal linear complementarity problem: iterative methods and error analysis
To the best of our knowledge, since the extended horizontal linear complementarity problem (EHLCP) was first introduced and studied by Kaneko in 1977, no iterative methods or error analysis have been developed for it due to the interdependence of its multiple unknowns in a 'chain-like' structure. This paper aims to address these gaps by: (1) proposing an equivalent fixed-point formulation of the EHLCP by using a variable transformation technique with the max-min function; (2) developing eff…

Finite graphs and configurations of points
Joseph Malkoun
https://arxiv.org/abs/2508.13472 https://arxiv.org/pdf/2508.13472

Finite graphs and configurations of points
We generalize the Atiyah problem on configurations and the related Atiyah--Sutcliffe conjectures 1 and 2 using finite graphs, configurations of points and tensors. Our conjectures are intriguing geometric inequalities, defined using the pairwise directions of the configuration of points, just as in the original problem. The generalization of the Atiyah determinant to our setting is no longer a determinant. We call it the $G$-amplitude function, where $G$ is a finite simple graph, in analogy wit…

@… this is a tricky problem, because we have US notation and European one (1,000.00 vs 1.000,00).
People are kind of used to see both on screens so I'd say most important is to avoid confusion at all cost when it comes to money.
Space is a good way I guess. Valid for most languages and clear.

Replaced article(s) found for physics.hist-ph. https://arxiv.org/list/physics.hist-ph/new
[1/1]:
- The Algebra of the Pseudo-Observables II: The Measurement Problem
Edoardo Piparo

Crosslisted article(s) found for math.AG. https://arxiv.org/list/math.AG/new
[1/1]:
- Positive polynomials and the truncated moment problem on plane cubics
Mario Kummer, Alja\v{z} Zalar

Additive Problems with Primes from a Thin Bohr Set
Sarvagya Jain
https://arxiv.org/abs/2508.12139 https://arxiv.org/pdf/2508.12139

Additive Problems with Primes from a Thin Bohr Set
For an irrational $α\in \mathbb{R}$, we consider additive problems with the set of primes satisfying $\lVertαp\rVert\leq \frac{1}{p^τ}$ for some fixed $τ>0$. In particular, we show that there exist infinitely many non-trivial three-term arithmetic progressions in the set of primes satisfying $\lVert αp\rVert\leq \frac{1}{p^τ}$ for $τ\in(0, \tfrac18)$. We also consider a binary Goldbach-type problem.

Form factors of composite branch-point twist operators in the sinh-Gordon model on a multi-sheeted Riemann surface: semiclassical limit
Michael Lashkevich, Amir Nesturov
https://arxiv.org/abs/2508.12878

Form factors of composite branch-point twist operators in the sinh-Gordon model on a multi-sheeted Riemann surface: semiclassical limit
Quantum sinh-Gordon model in 1+1 dimensions is one of the simplest and best-studied massive integrable relativistic quantum field theories. We consider this theory on a multi-sheeted Riemann surfaces with a flat metric, which can be seen as a pile of planes connected to each other along cut lines. The cut lines end at branch points, which are represented by a twist operator ${\cal T}_n.$ Operators of such kind are interesting in the framework of the problem of computing von Neumann and Renyi en…

A Durrett-Remenik particle system in $\mathbb{R}^d$
Rami Atar
https://arxiv.org/abs/2507.13990 https://arxiv.org/pdf/2507.13990

A Durrett-Remenik particle system in $\mathbb{R}^d$
This paper studies a branching-selection model of motionless particles in $\mathbb{R}^d$, with nonlocal branching, introduced by Durrett and Remenik in dimension $1$. The assumptions on the fitness function, $F$, and on the inhomogeneous branching distribution, are mild. The evolution equation for the macroscopic density is given by an integro-differential free boundary problem in $\mathbb{R}^d$, in which the free boundary represents the least $F$-value in the population. The main result is the…

Freeze-Tag is NP-hard in 2D with $L_1$ distance
Lucas de Oliveira Silva, Lehilton Lelis Chaves Pedrosa
https://arxiv.org/abs/2509.14357 https://arxiv.org/p…

Freeze-Tag is NP-hard in 2D with $L_1$ distance
The Freeze-Tag Problem (FTP) is a scheduling problem with application in robot swarm activation and was introduced by Arkin et al. in 2002. This problem seeks an efficient way of activating a robot swarm starting with a single active robot. Activations occur through direct contact, and once a robot becomes active, it can move and help activate other robots. Although the problem has been shown to be NP-hard in the Euclidean plane $R^2$ under the $L_2$ distance, and in three-dimensional Euclide…

The Maximum Coverage Model and Recommendation System for UAV Vertiports Location Planning
Chunliang Hua, Xiao Hu, Jiayang Sun, Zeyuan Yang
https://arxiv.org/abs/2508.12651 https…

The Maximum Coverage Model and Recommendation System for UAV Vertiports Location Planning
As urban aerial mobility (UAM) infrastructure development accelerates globally, cities like Shenzhen are planning large-scale vertiport networks (e.g., 1,200+ facilities by 2026). Existing planning frameworks remain inadequate for this complexity due to historical limitations in data granularity and real-world applicability. This paper addresses these gaps by first proposing the Capacitated Dynamic Maximum Covering Location Problem (CDMCLP), a novel optimization framework that simultaneously mo…

Cislunar Resonant Transport and Heteroclinic Pathways: From 3:1 to 2:1 to L1
Bhanu Kumar, Anjali Rawat, Aaron J. Rosengren, Shane D. Ross
https://arxiv.org/abs/2509.12675 https:…

Cislunar Resonant Transport and Heteroclinic Pathways: From 3:1 to 2:1 to L1
Understanding the dynamical structure of cislunar space beyond geosynchronous orbit is critical for both lunar exploration and for high-Earth-orbiting trajectories. In this study, we investigate the role of mean-motion resonances and their associated heteroclinic connections in enabling natural semi-major axis transport in the Earth-Moon system. Working within the planar circular restricted three-body problem, we compute and analyze families of periodic orbits associated with the interior 4:1, …

Crosslisted article(s) found for cs.LO. https://arxiv.org/list/cs.LO/new
[1/1]:
- The Constraint Satisfaction Problem Over Multisorted Cores
Dejan Delic, John Marcoux

Replaced article(s) found for cs.CL. https://arxiv.org/list/cs.CL/new
[1/2]:
- G-LLaVA: Solving Geometric Problem with Multi-Modal Large Language Model
Gao, Pi, Zhang, Ye, Zhong, Wang, Hong, Han, Xu, Li, Kong

Improved Online Sorting
Jubayer Nirjhor, Nicole Wein
https://arxiv.org/abs/2508.14361 https://arxiv.org/pdf/2508.14361

Improved Online Sorting
We study the online sorting problem, where $n$ real numbers arrive in an online fashion, and the algorithm must immediately place each number into an array of size $(1+\varepsilon) n$ before seeing the next number. After all $n$ numbers are placed into the array, the cost is defined as the sum over the absolute differences of all $n-1$ pairs of adjacent numbers in the array, ignoring empty array cells. Aamand, Abrahamsen, Beretta, and Kleist introduced the problem and obtained a deterministic a…

Replaced article(s) found for quant-ph. https://arxiv.org/list/quant-ph/new
[1/2]:
- The Algebra of the Pseudo-Observables II: The Measurement Problem
Edoardo Piparo

Crosslisted article(s) found for math.DS. https://arxiv.org/list/math.DS/new
[1/1]:
- Segmentation of the spacecraft transfer problem through overdetermined and continuity constraints...
Allan Kardec de Almeida Junior

The Chapman-Enskog Divergence Problem in Plasma Transport: Structural Limitations and a Practical Regularization Approach
Justo Karell
https://arxiv.org/abs/2508.12390 https://

The Chapman-Enskog Divergence Problem in Plasma Transport: Structural Limitations and a Practical Regularization Approach
We calculate transport coefficients from the Chapman--Enskog expansion with BGK collision operators, obtaining exactly $κ= \frac{5nT}{2mν}$, and show that maximum entropy closure yields identical results when applied with the same collision operator. Through structural arguments, we suggest that this $1/ν$ divergence extends to other local collision operators of the form $\mathcal{L} = ν\hat{L}$, making the divergence fundamental to the Chapman--Enskog approach rather than a closure artifac…

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

KI soll 600.000 fehlende Beamte ersetzen? Klingt wie der Plan eines Startups, das gerade seine erste Fördermillion verbrannt hat.
Problem 1: KI ist kein Zauberstab.
Problem 2: Selbst wenn – die Infrastruktur dahinter gleicht oft noch einem Flickenteppich aus den 90ern.
Problem 3: Bürger wollen keine Algorithmen. Sie wollen funktionierende Behördengänge. Wie bei Amazon. Nur ohne Prime-Mitgliedschaft.

Gaussian Multiplier Bootstrap Procedure for the $\kappa$th Largest Coordinate of High-Dimensional Statistics
Yixi Ding, Qizhai Li, Yuke Shi, Liuquan Sun
https://arxiv.org/abs/2508.14400

Gaussian Multiplier Bootstrap Procedure for the $κ$th Largest Coordinate of High-Dimensional Statistics
We consider the problem of Gaussian and bootstrap approximations for the distribution of the $κ$th-largest statistic in high dimensions. This statistic, defined as the $κ$th-largest component of the sum of independent random vectors, is critical in numerous high-dimensional estimation and testing problems. Such a problem has been studied previously for $κ=1$ (i.e., maxima). However, in many applications, a general $κ\geq1$ is of great interest, which is addressed in this paper. By invoking …

Non-radial solutions for the critical quasi-linear H\'{e}non equation involving $p$-Laplacian in $\R^N$
Wei Dai, Lixiu Duan, Changfeng Gui, Yuan Li
https://arxiv.org/abs/2508.13539

Non-radial solutions for the critical quasi-linear Hénon equation involving $p$-Laplacian in $\R^N$
In this paper, we investigate the following $D^{1,p}$-critical quasi-linear Hénon equation involving $p$-Laplacian \begin{equation*}\label{00} \left\{ \begin{aligned} &-Δ_p u=|x|^αu^{p_\al^*-1}, & x\in \R^N, \\ &u>0, & x\in \R^N, \end{aligned} \right. \end{equation*} where $N\geq2$, $10$. By carefully studying the linearized problem and applying the approximation method and bifurcation theory, we prove that, when the parameter $\al$ ta…

Replaced article(s) found for physics.ed-ph. https://arxiv.org/list/physics.ed-ph/new
[1/1]:
- Using Large Language Models to Assign Partial Credit to Students' Explanations of Problem-Solving...
Zhongzhou Chen, Tong Wan

Re-weighting estimator for ab initio path integral Monte Carlo simulations of fictitious identical particles
Tobias Dornheim, Pontus Svensson, Paul Hamann, Sebastian Schwalbe, Zhandos Moldabekov, Panagiotis Tolias, Jan Vorberger
https://arxiv.org/abs/2508.12323

Re-weighting estimator for ab initio path integral Monte Carlo simulations of fictitious identical particles
The fermion sign problem constitutes one of the most fundamental obstacles in quantum many-body theory. Recently, it has been suggested to circumvent the sign problem by carrying out path integral simulations with a fictitious quantum statistics variable $ξ$, which allows for a smooth interpolation between the bosonic and fermionic limits [\textit{J.~Chem.~Phys.}~\textbf{157}, 094112 (2022)]. This $ξ$-extrapolation method has subsequently been applied to a variety of systems and has facilitat…

An analytical parameterization for all solutions of the two-dimensional moment problem under Carleman-type conditions
Sergey M. Zagorodnyuk
https://arxiv.org/abs/2508.10823 http…

An analytical parameterization for all solutions of the two-dimensional moment problem under Carleman-type conditions
The two-dimensional moment problem consists of finding a positive Borel measure $μ$ in $\mathbb{R}^2$ such that $\int_{\mathbb{R}^2} t_1^m t_2^n dμ= s_{m,n}$, $m,n=0,1,2,...$, where $s_{m,n}$ are prescribed real constants (moments). We study this moment problem in the case when the sequence $\{ s_{m,n} \}_{m,n=0}^\infty$ is positive semi-definite, and the following Carleman-type conditions hold: $$ \sum_{k=1}^\infty \frac{1}{ \sqrt[2k]{ s_{2m,2k} + s_{2m+2,2k} } } = \infty,\quad m=0,1,2,.... …

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

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

Spectral Tur\'an-type problem in non-$r$-partite graphs: Forbidden generalized book graph $B_{r,k}$
Yuantian Yu, Shuchao Li
https://arxiv.org/abs/2508.12034 https://

Spectral Turán-type problem in non-$r$-partite graphs: Forbidden generalized book graph $B_{r,k}$
Given a graph $H$, a graph is said to be $H$-free if it does not contain $H$ as a subgraph. A graph is color-critical when it has an edge whose removal leads to a reduction in its chromatic number. For a graph $H$ with a chromatic number of \(r + 1\), we use \(\text{spex}_{r + 1}(n, H)\) to represent the maximum spectral radius among non-$r$-partite $H$-free graphs of order $n$. The set of all non-$r$-partite $H$-free graphs of order $n$ that have a spectral radius of \(\text{spex}_{r + 1}(n, H…

Reverse Hurwitz counts of genus 1 curves
Michael Mueller
https://arxiv.org/abs/2509.11280 https://arxiv.org/pdf/2509.11280…

Reverse Hurwitz counts of genus 1 curves
In this paper, we study a problem that is in a sense a reversal of the Hurwitz counting problem. The Hurwitz problem asks: for a generic target -- $\mathbb P^1$ with a list of $n$ points $q_1,\dots,q_n\in \mathbb P^1$ -- and partitions $σ_1,\dots,σ_n$ of $d$, how many degree $d$ covers $C\to\mathbb P^1$ are there with specified ramification $σ_i$ over $q_i$? We ask: for a generic source -- an $r$-pointed curve $(C,p_1,\dots,p_r)$ of genus $1$ -- and partitions $μ, σ_1,\dots,σ_n$ of $d$ wi…

Die CDU in Stuttgart völlig fanatisch am Hallozinieren. In ihrem Wahn völlig ungeeignet ihre einfachsten privaten Probleme zu lösen. Solche Leute sollten nicht auch noch Regierungsverantwortung bekommen.
Vaihingen ist ein Stadtrandstadtteil mit freistehenden Häusern und großen Gärten. Als ich dort wohnte stand mein Auto auf unserem Grundstück und nicht auf Kosten der Gesellschaft auf der Straße. Die CDU tritt auf wie ein Baby, das sich die Windel nicht wechseln kann.

Björn (@funqr@chaos.social)
Attached: 1 image Ein Aushang der #CDU hat heute meine Aufmerksamkeit erregt. #Stuttgart #Vaihingen steht kurz vor dem Kollaps, möchte man hier denken. Das #Fahrrad ist DAS Problem.

A Nonlinear Scaling-based Design of Control Lyapunov-barrier Function for Relative Degree 2 Case and its Application to Safe Feedback Linearization
Haechan Pyon, Gyunghoon Park
https://arxiv.org/abs/2509.15071

A Nonlinear Scaling-based Design of Control Lyapunov-barrier Function for Relative Degree 2 Case and its Application to Safe Feedback Linearization
In this paper we address the problem of control Lyapunov-barrier function (CLBF)-based safe stabilization for a class of nonlinear control-affine systems. A difficulty may arise for the case when a constraint has the relative degree larger than 1, at which computing a proper CLBF is not straightforward. Instead of adding an (possibly non-existent) control barrier function (CBF) to a control Lyapunov function (CLF), our key idea is to simply scale the value of the CLF on the unsafe set, by utili…

Indoor Airflow Imaging Using Physics-Informed Background-Oriented Schlieren Tomography
Arjun Teh, Wael H. Ali, Joshua Rapp, Hassan Mansour
https://arxiv.org/abs/2509.14442 https…

Indoor Airflow Imaging Using Physics-Informed Background-Oriented Schlieren Tomography
We develop a framework for non-invasive volumetric indoor airflow estimation from a single viewpoint using background-oriented schlieren (BOS) measurements and physics-informed reconstruction. Our framework utilizes a light projector that projects a pattern onto a target back-wall and a camera that observes small distortions in the light pattern. While the single-view BOS tomography problem is severely ill-posed, our proposed framework addresses this using: (1) improved ray tracing, (2) a physi…

Should we teach vibe coding? Here's why not.
Should AI coding be taught in undergrad CS education?
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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

Surface Stokes Without Inf-Sup Condition
Ricardo H. Nochetto, Mansur Shakipov
https://arxiv.org/abs/2508.13342 https://arxiv.org/pdf/2508.13342

Surface Stokes Without Inf-Sup Condition
For a $d$-dimensional hypersurface of class $C^3$ without boundary, we reformulate the surface Stokes equations as a nonsymmetric indefinite elliptic problem governed by two Laplacians. We then use this elliptic reformulation as a basis for a numerical method based on lifted parametric FEM. Assuming no geometric error for simplicity, we prove its well-posedness, quasi-best approximation in a robust mesh-dependent $H^1$-norm for any polynomial degree, as well as an optimal $L^2$ error estimate f…

The tame Deligne-Simpson problem
Cheng Shu
https://arxiv.org/abs/2509.11841 https://arxiv.org/pdf/2509.11841

The tame Deligne-Simpson problem
The objective of this article is to prove the necessity statement in Crawley-Boevey's conjectural solution to the (tame) Deligne-Simpson problem. We use the nonabelian Hodge correspondence, variation of parabolic weights and results of Schedler-Tirelli to reduce to simpler situations, where every conjugacy class is semi-simple and the underlying quiver is (1) an affine Dynkin diagram or (2) an affine Dynkin diagram with an extra vertex. In case (1), a nonexistence result of Kostov applies. In c…

Robot Policy Evaluation for Sim-to-Real Transfer: A Benchmarking Perspective
Xuning Yang, Clemens Eppner, Jonathan Tremblay, Dieter Fox, Stan Birchfield, Fabio Ramos
https://arxiv.org/abs/2508.11117

Robot Policy Evaluation for Sim-to-Real Transfer: A Benchmarking Perspective
Current vision-based robotics simulation benchmarks have significantly advanced robotic manipulation research. However, robotics is fundamentally a real-world problem, and evaluation for real-world applications has lagged behind in evaluating generalist policies. In this paper, we discuss challenges and desiderata in designing benchmarks for generalist robotic manipulation policies for the goal of sim-to-real policy transfer. We propose 1) utilizing high visual-fidelity simulation for improved …

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

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

On the Linearization of Certain Singularities of Nijenhuis Operators
Andrey Yu. Konyaev
https://arxiv.org/abs/2509.10155 https://arxiv.org/pdf/2509.10155…

On the Linearization of Certain Singularities of Nijenhuis Operators
We consider a linearization problem for Nijenhuis operators in dimension two around a point of scalar type in analytic category. The problem was almost completely solved in arXiv:1903.06411. One case, however, namely the case of left-symmetric algebra $\mathfrak b_{1, α}$, proved to be difficult. Here we solve it and, thus, complete the solution of the linearization problem for Nijenhuis operators in dimension two. The problem turns out to be related to classical results on the linearization o…

Sample efficient likelihood-free inference for virus dynamics with different types of experiments
Yingying Xu, Ulpu Remes, Enrico Rinaldi, Henri Pesonen
https://arxiv.org/abs/2508.11042

Sample efficient likelihood-free inference for virus dynamics with different types of experiments
This study applied Bayesian optimization likelihood-free inference(BOLFI) to virus dynamics experimental data and efficiently inferred the model parameters with uncertainty measure. The computational benefit is remarkable compared to existing methodology on the same problem. No likelihood knowledge is needed in the inference. Improvement of the BOLFI algorithm with Gaussian process based classifier for treatment of extreme values are provided. Discrepancy design for combining different forms of…

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

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

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]

Efficient Algorithms for Disjoint Shortest Paths Problem and its Extensions
Keerti Choudhary, Amit Kumar, Lakshay Saggi
https://arxiv.org/abs/2509.14588 https://

Efficient Algorithms for Disjoint Shortest Paths Problem and its Extensions
We study the 2-Disjoint Shortest Paths (2-DSP) problem: given a directed weighted graph and two terminal pairs $(s_1,t_1)$ and $(s_2,t_2)$, decide whether there exist vertex-disjoint shortest paths between each pair. Building on recent advances in disjoint shortest paths for DAGs and undirected graphs (Akmal et al. 2024), we present an $O(mn \log n)$ time algorithm for this problem in weighted directed graphs that do not contain negative or zero weight cycles. This algorithm presents a signif…

The Gaussian Minkowski problem for epigraphs of convex functions
Xiao Li, Deping Ye
https://arxiv.org/abs/2508.12028 https://arxiv.org/pdf/2508.12028

The Gaussian Minkowski problem for epigraphs of convex functions
A variational formula is derived by combining the Gaussian volume of the epigraph of a convex function $φ$ and the perturbation of $φ$ via the infimal convolution. This formula naturally leads to a Borel measure on $\mathbb{R}^n$ and a Borel measure on the unit sphere $S^{n-1}$. The resulting Borel measure on $\mathbb{R}^n$ will be called the Euclidean Gaussian moment measure of the convex function $φ$, and the related Minkowski-type problem will be studied. In particular, the newly posed Mi…

Plancherel-P\'{o}lya's Type of Instability in Vibration System with Multiple Frozen Arguments
Lung-Hui Chen, Chung-Tsun Shieh
https://arxiv.org/abs/2508.11101 https://…

Plancherel-Pólya's Type of Instability in Vibration System with Multiple Frozen Arguments
We discuss the problem of the inverse spectral problem of Sturm-Liouville operator with multiple frozen arguments at $\{a_{1}, a_{2},\ldots,a_{N}\}$ in $(0,π)$. One may consider the characteristic functions as perturbation of sine or of cosine functions depending on the boundary problem prescribed. However, such perturbation is represented in the form of Fourier transform of certain function which may or may not bring in Riesz basis theory and classical perturbation theory in functional analys…

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

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

Fair distribution of bundles
Pablo Sober\'on
https://arxiv.org/abs/2507.13421 https://arxiv.org/pdf/2507.13421

Fair distribution of bundles
In this paper, we study the problem of splitting fairly bundles of items. We show that given $n$ bundles with $m$ kinds of items in them, it is possible to distribute the value of each kind of item fairly among $r$ persons by breaking apart at most $(r-1)m$ bundles. Moreover, we can guarantee that each participant will receive roughly $n/r - mr/2$ full bundles. The proof methods are topological and use a modified form of the configuration space/test map scheme. We obtain optimal results when $r…

$L^2$-solutions to stochastic reaction-diffusion equations with superlinear drifts driven by space-time white noise^
Shijie Shang, Pengyu Wang, Tusheng Zhang
https://arxiv.org/abs/2509.12744

$L^2$-solutions to stochastic reaction-diffusion equations with superlinear drifts driven by space-time white noise^
Consider the following stochastic reaction-diffusion equation with logarithmic superlinear coefficient b, driven by space-time white noise W: $$ u_t(t,x) = (1/2)u_{xx}(t,x) + b(u(t,x)) + σ(u(t,x))W(dt,dx) $$ for $t > 0$ and $x \in [0,1]$, with initial condition $$ u(0,x) = u_0(x) $$ for $x \in [0,1]$, where $u_0 \in L^2[0,1]$. In this paper, we establish existence and uniqueness of probabilistically strong solutions in $C(R_+, L^2[0,1])$. Our result resolves a problem from [Ann. Probab. 47 (…

H\"older stability of an inverse spectral problem for the magnetic Schr\"odinger operator on a simple manifold
Boya Liu, Hadrian Quan, Teemu Saksala, Lili Yan
https://arxiv.org/abs/2507.13619

Hölder stability of an inverse spectral problem for the magnetic Schrödinger operator on a simple manifold
We show that on a simple Riemannian manifold, the electric potential and the solenoidal part of the magnetic potential appearing in the magnetic Schrödinger operator can be recovered Hölder stably from the boundary spectral data. This data contains the eigenvalues and the Neumann traces of the corresponding sequence of Dirichlet eigenfunctions of the operator. Our proof contains two parts, which we present in the reverse order. (1) We show that the boundary spectral data can be stably obtaine…

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

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

Weighted First Order Model Counting for Two-variable Logic with Axioms on Two Relations
Qipeng Kuang, V\'aclav K\r{u}la, Ond\v{r}ej Ku\v{z}elka, Yuanhong Wang, Yuyi Wang
https://arxiv.org/abs/2508.11515

Weighted First Order Model Counting for Two-variable Logic with Axioms on Two Relations
The Weighted First-Order Model Counting Problem (WFOMC) asks to compute the weighted sum of models of a given first-order logic sentence over a given domain. The boundary between fragments for which WFOMC can be computed in polynomial time relative to the domain size lies between the two-variable fragment ($\text{FO}^2$) and the three-variable fragment ($\text{FO}^3$). It is known that WFOMC for \FOthree{} is $\mathsf{\#P_1}$-hard while polynomial-time algorithms exist for computing WFOMC for $…

Asymptotic minimality of one-dimensional transition profiles in Aviles-Giga type models: an approach via 1-currents
Radu Ignat, Roger Moser
https://arxiv.org/abs/2508.13753 http…

Asymptotic minimality of one-dimensional transition profiles in Aviles-Giga type models: an approach via 1-currents
For vector fields on a two-dimensional domain, we study the asymptotic behaviour of Modica-Mortola (or Allen-Cahn) type functionals under the assumption that the divergence converges to $0$ at a certain rate, which effectively produces a model of Aviles-Giga type. This problem will typically give rise to transition layers, which degenerate into discontinuities in the limit. We analyse the energy concentration at these discontinuities and the corresponding transition profiles. We derive an est…

Excitation Gaps of Ground and Excited State Energy of the Fermi-Hubbard Model Using Variational Quantum Eigensolver
Mrinal Dev, Bikash K. Behera, Vivek Vyas, Prasanta K. Panigrahi
https://arxiv.org/abs/2508.12307

Excitation Gaps of Ground and Excited State Energy of the Fermi-Hubbard Model Using Variational Quantum Eigensolver
The Hubbard model is a challenging quantum many-body problem and serves as a benchmark for quantum computing research. Accurate computation of its ground and excited state energies is essential for understanding correlated electron systems. In this study, the ground, first, and second excited state energies of 4$\times$1 and 2$\times$2 Hubbard lattices are obtained using a newly designed ansatz circuit. The ansatz is constructed by combining concepts from the Hamiltonian Variational Ansatz (HVA…

Tight Bounds for Sparsifying Random CSPs
Joshua Brakensiek, Venkatesan Guruswami, Aaron Putterman
https://arxiv.org/abs/2508.13345 https://arxiv.org/pdf/25…

Tight Bounds for Sparsifying Random CSPs
The problem of CSP sparsification asks: for a given CSP instance, what is the sparsest possible reweighting such that for every possible assignment to the instance, the number of satisfied constraints is preserved up to a factor of $1 \pm ε$? We initiate the study of the sparsification of random CSPs. In particular, we consider two natural random models: the $r$-partite model and the uniform model. In the $r$-partite model, CSPs are formed by partitioning the variables into $r$ parts, with con…

$S$-units and period length of continued fractions of linear recursions
Veekesh Kumar, Vivek Singh, Johannes Sprang
https://arxiv.org/abs/2509.14599 https://

$S$-units and period length of continued fractions of linear recursions
Let $(A_n)_{n\in \mathbb{Z}}$ be a linear recurrence sequence with values in a real quadratic field. In this paper, we study the question whether the period length of the continued fraction of $A_n$ is bounded as $n$ varies. The case where $(A_n)_n$ is a linear recurrence of degree $1$ has previously been solved by Corvaja and Zannier. Their result settled a problem posed by Mendès France about the length of the periods of the continued fractions for $α^n$.

Real-Analyticity of the Density of States for Random Schr\"odinger operators with Point Interactions
Masahiro Kaminaga
https://arxiv.org/abs/2508.12664 https://

Real-Analyticity of the Density of States for Random Schrödinger operators with Point Interactions
We prove real-analyticity of the density of states (DOS) for random Schrödinger operators with lattice-supported point interactions in $\mathbb{R}^d$ ($d=1,2,3$) in the small-hopping regime. In the attractive case, Krein's resolvent formula reduces the problem to a lattice model, where a random-walk expansion and disorder averaging lead to single-site integrals with holomorphic single-site density $g$. Contour deformation in the coupling-constant plane under a uniform pole-gap condition ensure…

Faster Multi-Source Reachability and Approximate Distances via Shortcuts, Hopsets and Matrix Multiplication
Michael Elkin, Chhaya Trehan
https://arxiv.org/abs/2507.13470

Faster Multi-Source Reachability and Approximate Distances via Shortcuts, Hopsets and Matrix Multiplication
Given an $n$-vertex $m$-edge digraph $G = (V,E)$ and a subset $S \subseteq V$ of $|S| = n^σ$ (for some $0 \le σ\le 1$) designated sources, the $S \times V$ reachability problem is to compute the sets $\mathcal V_s$ of vertices reachable from $s$, for every $s \in S$. Naive centralized algorithms run BFS/DFS from each source in $O(m \cdot n^σ)$ time or compute $G$'s transitive closure in $\hat O(n^ω)$ time, where $ω\le 2.371552\ldots$ is the matrix multiplication exponent. Thus, t…

The maximum number of triangles in $K_{1,s,t}$-free graphs
Asier Calbet, Ritesh Goenka
https://arxiv.org/abs/2508.10611 https://arxiv.org/pdf/2508.10611

The maximum number of triangles in $K_{1,s,t}$-free graphs
We consider the following generalized Turán problem: For $2 \le s \le t$, what is the maximum number of triangles in a $K_{1,s,t}$-free graph on $n$ vertices? The previously best known lower and upper bounds are $Ω(n^2)$ and $o(n^{3-1/s})$, respectively. To the best of our knowledge, all known proofs of the upper bound use the triangle removal lemma. We give a new elementary proof that avoids the use of the triangle removal lemma and improves the upper bound to $O\left(n^{3-1/s}(\log n)^{-1+1…

Language models align with brain regions that represent concepts across modalities
Maria Ryskina, Greta Tuckute, Alexander Fung, Ashley Malkin, Evelina Fedorenko
https://arxiv.org/abs/2508.11536

Language models align with brain regions that represent concepts across modalities
Cognitive science and neuroscience have long faced the challenge of disentangling representations of language from representations of conceptual meaning. As the same problem arises in today's language models (LMs), we investigate the relationship between LM--brain alignment and two neural metrics: (1) the level of brain activation during processing of sentences, targeting linguistic processing, and (2) a novel measure of meaning consistency across input modalities, which quantifies how consiste…

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

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

Global well-posedness of the NLS hierarchy with nonzero boundary condition
Xian Liao, Robert Wegner
https://arxiv.org/abs/2508.14572 https://arxiv.org/pdf/…

Global well-posedness of the NLS hierarchy with nonzero boundary condition
We consider the NLS hierarchy with the nonzero boundary condition $q(t, x) \rightarrow q_\pm \in \mathbb{S}^1$ as $x \rightarrow \pm \infty$ and prove that it is global well-posedness for initial data of high regularity. Specifically, we prove well-posedness of the problem for the perturbation $p = q - q_\ast$ from a time-independent front $q_\ast$ connecting $q_-$ to $q_+$. The equations in the NLS hierarchy are defined using a recurrence relation derived from the expansion of the logarithmic …

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

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

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.

Bicentric configurations of pentagonal linkages
Ana Diakvnishvili
https://arxiv.org/abs/2508.11427 https://arxiv.org/pdf/2508.11427

Bicentric configurations of pentagonal linkages
Let $P$ be a planar $n$-gon with the sidelengths $a_1, \ldots, a_n$ and let us denote by $L=L(P)$ the corresponding planar polygonal linkage. We are concerned with the problem of finding conditions on the sidelengths $a_i$ which guarantee the existence of a bicentric configuration of $L$. Specifically, we present some related results on tangential and chordal polygons and characterize pentagonal linkages having bicentric configurations.

Falconer's problem for dot product on paraboloids
Chun-Kai Tseng
https://arxiv.org/abs/2509.11710 https://arxiv.org/pdf/2509.11710

Falconer's problem for dot product on paraboloids
We establish dimensional thresholds for dot product sets associated with compact subsets of translated paraboloids. Specifically, we prove that when the dimension of such a subset exceeds $ \frac{5}{4} = \frac{3}{2} - \frac{1}{4} $ in $\mathbb{R}^3$, and $ \frac{d}{2} - \frac{1}{4} - \frac{1}{8d - 4} $ in $\mathbb{R}^d$ for $d\geq 4$, its dot product set has positive Lebesgue measure. This result demonstrates that if a compact set in $ \mathbb{R}^d $ exhibits a paraboloidal structure, then th…

Crosslisted article(s) found for math.AP. https://arxiv.org/list/math.AP/new
[1/1]:
- The Gaussian Minkowski problem for epigraphs of convex functions
Xiao Li, Deping Ye

A generalised Ramsey--Tur\'an problem for matchings
Peter Keevash, Peleg Michaeli
https://arxiv.org/abs/2509.10679 https://arxiv.org/pdf/2509.10679

A generalised Ramsey--Turán problem for matchings
We prove a generalised Ramsey--Turán theorem for matchings, which (a) simultaneously generalises the Cockayne--Lorimer Theorem (Ramsey for matchings) and the Erdős--Gallai Theorem (Turán for matchings), and (b) is a generalised Turán theorem in the sense that we can optimise the count of any clique (Turán-type theorems optimise the count of edges). More precisely, for integers $q \ge 1$, $n \ge \ell \ge 2$, and $t_1,\dots,t_q \ge 1$ we determine the maximum number of $\ell$-vertex complete…

Streaming periodicity with mismatches, wildcards, and edits
Taha El Ghazi, Tatiana Starikovskaya
https://arxiv.org/abs/2509.14898 https://arxiv.org/pdf/250…

Streaming periodicity with mismatches, wildcards, and edits
In this work, we study the problem of detecting periodic trends in strings. While detecting exact periodicity has been studied extensively, real-world data is often noisy, where small deviations or mismatches occur between repetitions. This work focuses on a generalized approach to period detection that efficiently handles noise. Given a string $S$ of length $n$, the task is to identify integers $p$ such that the prefix and the suffix of $S$, each of length $n-p+1$, are similar under a given di…

Equivalence between solvability of the Dirichlet and Regularity problem under an $L^1$ Carleson condition on $\partial_t A$
Martin Ulmer
https://arxiv.org/abs/2509.10328 https:/…

Equivalence between solvability of the Dirichlet and Regularity problem under an $L^1$ Carleson condition on $\partial_t A$
We study an elliptic operator $L:=\mathrm{div}(A\nabla \cdot)$ on the upper half space. It is known that solvability of the Regularity problem in $\dot{W}^{1,p}$ implies solvability of the adjoint Dirichlet problem in $L^{p'}$. Previously, Shen (2007) established a partial reverse result. In our work, we show that if we assume an $L^1$-Carleson condition on only $|\partial_t A|$ the full reverse direction holds. As a result, we obtain equivalence between solvability of the Dirichlet p…

On Fixed-Parameter Tractability of Weighted 0-1 Timed Matching Problem on Temporal Graphs
Rinku Kumar, Bodhisatwa Mazumdar, Subhrangsu Mandal
https://arxiv.org/abs/2508.10562 ht…

On Fixed-Parameter Tractability of Weighted 0-1 Timed Matching Problem on Temporal Graphs
Temporal graphs are introduced to model systems where the relationships among the entities of the system evolve over time. In this paper, we consider the temporal graphs where the edge set changes with time and all the changes are known a priori. The underlying graph of a temporal graph is a static graph consisting of all the vertices and edges that exist for at least one timestep in the temporal graph. The concept of 0-1 timed matching in temporal graphs was introduced by Mandal and Gupta [DAM…

On the edge expansion of random polytopes
Asaf Ferber, Michael Krivelevich, Marcelo Sales, Wojciech Samotij
https://arxiv.org/abs/2509.09831 https://arxiv.…

On the edge expansion of random polytopes
A $0/1$-polytope in $\mathbb{R}^n$ is the convex hull of a subset of $\{0,1\}^n$. The graph of a polytope $P$ is the graph whose vertices are the zero-dimensional faces of $P$ and whose edges are the one-dimensional faces of $P$. A conjecture of Mihail and Vazirani states that the edge expansion of the graph of every $0/1$-polytope is at least one. We study a random version of the problem, where the polytope is generated by selecting vertices of $\{0,1\}^n$ independently at random with probabil…

Multiple sign-changing solutions for semilinear subelliptic Dirichlet problem
Hua Chen, Hong-Ge Chen, Jin-Ning Li, Xin Liao
https://arxiv.org/abs/2510.10120 https://

Multiple sign-changing solutions for semilinear subelliptic Dirichlet problem
We study the following perturbation from symmetry problem for the semilinear subelliptic equation \[ \left\{ \begin{array}{cc} -\triangle_{X} u=f(x,u)+g(x,u) & \mbox{in}~Ω, \\[2mm] u\in H_{X,0}^{1}(Ω),\hfill \end{array} \right. \] where $\triangle_{X}=-\sum_{i=1}^{m}X_{i}^{*}X_{i}$ is the self-adjoint sub-elliptic operator associated with Hörmander vector fields $X=(X_{1},X_{2},\ldots,X_{m})$, $Ω$ is an open bounded subset in $\mathbb{R}^n$, and $H_{X,0}^{1}(Ω)$ denotes the weigh…

Ill-posedness in $B^s_{p,\infty}$ of the Euler equations: Non-continuous dependence
Jinlu Li, Yanghai Yu
https://arxiv.org/abs/2509.12619 https://arxiv.org…

Ill-posedness in $B^s_{p,\infty}$ of the Euler equations: Non-continuous dependence
In this paper, we solve an open problem left in the monographs \cite[Bahouri-Chemin-Danchin, (2011)]{BCD}. Precisely speaking, it was obtained in \cite[Theorem 7.1 on pp293, (2011)]{BCD} the existence and uniqueness of $B^s_{p,\infty}$ solution for the Euler equations. We furthermore prove that the solution map of the Euler equation is not continuous in the Besov spaces from $B^s_{p,\infty}$ to $L_T^\infty B^s_{p,\infty}$ for $s>1+d/p$ with $1\leq p\leq \infty$ and in the Hölder spaces from $C…

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

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