Tootfinder

Interesting discussion thread on open science
https://neuromatch.social/@adredish/114942098283461507

Locating Extremal Periodic Orbits for the Planar Circular Restricted Three Body Problem using Polynomial Sum-of-Squares Optimization
Vinay Sharma, Sergei I Chernyshenko
https://arxiv.org/abs/2505.23430

Locating Extremal Periodic Orbits for the Planar Circular Restricted Three Body Problem using Polynomial Sum-of-Squares Optimization
With an increasing interest in the design of long and complex space missions, the search for orbits that require the least amount of fuel is of fundamental interest. This paper develops existing computational models for locating Unstable Periodic Orbits (UPOs) in polynomial dynamical systems using Sum-of-Squares (SOS) optimization technique and proposes a numerical framework to converge UPOs for the Planar Circular Restricted Three-Body Problem (PCR3BP) in astrodynamics. This is done by develop…

On finite $\beta$-expansions for the set of natural numbers
T\'ulio O. Carvalho, Catharina M. Moreira
https://arxiv.org/abs/2507.19604 https://arxiv.or…

On finite $β$-expansions for the set of natural numbers
We present a study of the problem of finiteness of the $β$-expansions for the set of natural numbers, condition $F_1$ in brief, for three families of Pisot numbers for which the $β$-expansion of 1 is not a non-decreasing sequence. We show a class of simple $β$-numbers which display a puzzling behaviour, in the sense that an infinite subset of such $β$ satisfy $F_1$, whereas a complementary infinite subset does not. This puzzle is organized by the residue class modulo 3 of an integer coeffic…

Inverse scattering without phase: Carleman convexification and phase retrieval via the Wentzel--Kramers--Brillouin approximation
Thuy T. Le, Phuong M. Nguyen, Loc H. Nguyen
https://arxiv.org/abs/2506.21699

Inverse scattering without phase: Carleman convexification and phase retrieval via the Wentzel--Kramers--Brillouin approximation
This paper addresses the challenging and interesting inverse problem of reconstructing the spatially varying dielectric constant of a medium from phaseless backscattering measurements generated by single-point illumination. The underlying mathematical model is governed by the three-dimensional Helmholtz equation, and the available data consist solely of the magnitude of the scattered wave field. To address the nonlinearity and severe ill-posedness of this phaseless inverse scattering problem, w…

from my link log —
Tiling with three polygons is undecidable.
https://arxiv.org/abs/2409.11582
saved 2024-11-21 https://dotat.at/…

Tiling with Three Polygons is Undecidable
We prove that the following problem is co-RE-complete and thus undecidable: given three simple polygons, is there a tiling of the plane where every tile is an isometry of one of the three polygons (either allowing or forbidding reflections)? This result improves on the best previous construction which requires five polygons.

Optimal Impulsive Control of Cislunar Relative Motion using Reachable Set Theory
Matthew Hunter, Walter J. Manuel, Simone D'Amico
https://arxiv.org/abs/2507.21425 https://…

Optimal Impulsive Control of Cislunar Relative Motion using Reachable Set Theory
This work presents the first application of the state-of-the-art Koenig-D'Amico reachable set theory solver to cislunar, chaotic relative motion in the Circular-Restricted Three-Body Problem (CR3BP). The relative motion dynamics of two spacecraft, a chief and a deputy, in the CR3BP are formulated as a Linear Time-Variant (LTV) system, allowing the solver to find an optimal impulsive control maneuver plan. This methodology demonstrates robust and accurate control performance for both small and l…

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Hybrid fluid-kinetic cylindrical equilibria with axial background magnetic field
D. A. Kaltsas, A. I. Kuiroukidis, G. N. Throumoulopoulos
https://arxiv.org/abs/2507.20248 https:…

Hybrid fluid-kinetic cylindrical equilibria with axial background magnetic field
Self-consistent, one-dimensional quasineutral screw-pinch equilibria are constructed within a hybrid model that couples fluid electrons with kinetic ions governed by the Vlasov equation. The equilibria depend on the radial coordinate perpendicular to the cylindrical axis and include an axial background magnetic field. Adopting a three-parameter ion distribution function depending on the energy and the canonical momenta conjugate to the two ignorable coordinates, the problem is reduced to a set …

Monolithic framework to simulate fluid-structure interaction problems using geometric volume-of-fluid method
Soham Prajapati (Department of Aerospace Engineering and Mechanics, University of Minnesota - Twin Cities, Minneapolis, Minnesota, USA), Ali Fakhreddine (Department of Aerospace Engineering and Mechanics, University of Minnesota - Twin Cities, Minneapolis, Minnesota, USA), Krishnan Mahesh (Department of Aerospace Engineering and Mechanics, University of Minnesota - Twin Cities, …

Monolithic framework to simulate fluid-structure interaction problems using geometric volume-of-fluid method
We develop a three-dimensional Eulerian framework to simulate fluid-structure interaction (FSI) problems on a fixed Cartesian grid using the geometric volume-of-fluid (VOF) method. The coupled problem involves incompressible flow and viscous hyperelastic solids. A VOF-based one-continuum formulation is used to describe the unified momentum conservation equations with incompressibility constraints that are solved using the finite volume method (FVM). In the geometric VOF interface-capturing (IC)…

rStar2-Agent: Agentic Reasoning Technical Report
Ning Shang, Yifei Liu, Yi Zhu, Li Lyna Zhang, Weijiang Xu, Xinyu Guan, Buze Zhang, Bingcheng Dong, Xudong Zhou, Bowen Zhang, Ying Xin, Ziming Miao, Scarlett Li, Fan Yang, Mao Yang
https://arxiv.org/abs/2508.20722

rStar2-Agent: Agentic Reasoning Technical Report
We introduce rStar2-Agent, a 14B math reasoning model trained with agentic reinforcement learning to achieve frontier-level performance. Beyond current long CoT, the model demonstrates advanced cognitive behaviors, such as thinking carefully before using Python coding tools and reflecting on code execution feedback to autonomously explore, verify, and refine intermediate steps in complex problem-solving. This capability is enabled through three key innovations that makes agentic RL effective at…

The Subset Sum Matching Problem
Yufei Wu, Manuel R. Torres, Parisa Zehtabi, Alberto Pozanco Lancho, Michael Cashmore, Daniel Borrajo, Manuela Veloso
https://arxiv.org/abs/2508.19218

The Subset Sum Matching Problem
This paper presents a new combinatorial optimisation task, the Subset Sum Matching Problem (SSMP), which is an abstraction of common financial applications such as trades reconciliation. We present three algorithms, two suboptimal and one optimal, to solve this problem. We also generate a benchmark to cover different instances of SSMP varying in complexity, and carry out an experimental evaluation to assess the performance of the approaches.

Ligand Pose Generation via QUBO-Based Hotspot Sampling and Geometric Triplet Matching
Pei-Kun Yang
https://arxiv.org/abs/2507.20304 https://arxiv.org/pdf/2…

Ligand Pose Generation via QUBO-Based Hotspot Sampling and Geometric Triplet Matching
We propose a framework based on Quadratic Unconstrained Binary Optimization (QUBO) for generating plausible ligand binding poses within protein pockets, enabling efficient structure-based virtual screening. The method discretizes the binding site into a grid and solves a QUBO problem to select spatially distributed, energetically favorable grid points. Each ligand is represented by a three-atom geometric contour, which is aligned to the selected grid points through rigid-body transformation, pr…

Hybrid Quantum-Classical Branch-and-Price Method for the Vertex Coloring Problem
Chiara Vercellino, M. Yassine Naghmouchi, Wesley Coelho, Giacomo Vitali, Alberto Scionti, Paolo Viviani, Olivier Terzo, Bartolomeo Montrucchio
https://arxiv.org/abs/2508.18887

Hybrid Quantum-Classical Branch-and-Price Method for the Vertex Coloring Problem
This paper introduces Quantum Classical Branch-and-Price (QCBP), a hybrid quantum-classical algorithm for the Vertex Coloring problem on neutral-atom Quantum Processing Units (QPUs). QCBP embeds quantum computation within the classical Branch-and-Price (BP) framework to address three bottlenecks in classical BP algorithms: the computational cost of Pricing Subproblems (PSPs), branching efficiency, and the quality of primal heuristics. It uses quantum-assisted Column Generation (CG) based on Qua…

Separation of Three or More Autonomous Mobile Models under Hierarchical Schedulers
Shota Naito, Tsukasa Ninomiya, Koichi Wada
https://arxiv.org/abs/2508.19805 https://

Separation of Three or More Autonomous Mobile Models under Hierarchical Schedulers
Understanding the computational power of mobile robot systems is a fundamental challenge in distributed computing. While prior work has focused on pairwise separations between models, we explore how robot capabilities, light observability, and scheduler synchrony interact in more complex ways. We first show that the Exponential Times Expansion (ETE) problem is solvable only in the strongest model -- fully-synchronous robots with full mutual lights ($\mathcal{LUMT}^F$). We then introduce the H…

Incorporating Pre-trained Diffusion Models in Solving the Schr\"odinger Bridge Problem
Zhicong Tang, Tiankai Hang, Shuyang Gu, Dong Chen, Baining Guo
https://arxiv.org/abs/2508.18095

Incorporating Pre-trained Diffusion Models in Solving the Schrödinger Bridge Problem
This paper aims to unify Score-based Generative Models (SGMs), also known as Diffusion models, and the Schrödinger Bridge (SB) problem through three reparameterization techniques: Iterative Proportional Mean-Matching (IPMM), Iterative Proportional Terminus-Matching (IPTM), and Iterative Proportional Flow-Matching (IPFM). These techniques significantly accelerate and stabilize the training of SB-based models. Furthermore, the paper introduces novel initialization strategies that use pre-trained…

A comparative study of finite element methods for a class of harmonic map heat flow problems
Nam Anh Nguyen, Arnold Reusken
https://arxiv.org/abs/2508.20590 https://

A comparative study of finite element methods for a class of harmonic map heat flow problems
In this paper, we review and systematically compare three finite element discretization methods for a harmonic map heat flow problem from the unit disk in $\mathbb{R}^2$ to the unit sphere in $\mathbb{R}^3$ in an unified framework. Numerical tests validate the convergence rates in a regime of smooth solutions and are used to compare the methods in terms of computational efficiency. For one of the methods a discrete inf-sup stability result is derived.

On the Parameterized Complexity of Grundy Domination and Zero Forcing Problems
Robert Scheffler
https://arxiv.org/abs/2508.18104 https://arxiv.org/pdf/2508…

On the Parameterized Complexity of Grundy Domination and Zero Forcing Problems
We consider two different problem families that deal with domination in graphs. On the one hand, we focus on dominating sequences. In such a sequence, every vertex dominates some vertex of the graph that was not dominated by any earlier vertex in the sequence. The problem of finding the longest dominating sequence is known as $\mathsf{Grundy~Domination}$. Depending on whether the closed or the open neighborhoods are used for domination, there are three other versions of this problem. We show th…

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

Three-point functions from integrability in $\mathcal{N}=2$ orbifold theories
Dennis le Plat, Torben Skrzypek
https://arxiv.org/abs/2506.21323 https://

Three-point functions from integrability in $\mathcal{N}=2$ orbifold theories
Besides solving the spectral problem of $\mathcal{N}=4$ Super-Yang-Mills (SYM) theory, integrability also provides us with tools to compute the structure constants of the theory, most prominently through the hexagon formalism. We show that, with minor modifications, this formalism can also be applied to orbifolds of $\mathcal{N}=4$ SYM theory, which are integrable theories in their own right. To substantiate this claim, we test our results against a direct gauge-theory calculation at tree-level…

Wild refitting for black box prediction
Martin J. Wainwright
https://arxiv.org/abs/2506.21460 https://arxiv.org/pdf/2506.21460…

Wild refitting for black box prediction
We describe and analyze a computionally efficient refitting procedure for computing high-probability upper bounds on the instance-wise mean-squared prediction error of penalized nonparametric estimates based on least-squares minimization. Requiring only a single dataset and black box access to the prediction method, it consists of three steps: computing suitable residuals, symmetrizing and scaling them with a pre-factor $ρ$, and using them to define and solve a modified prediction problem rece…

Horn's problem in PU$(n,1)$
Arielle Marc-Zwecker (IF)
https://arxiv.org/abs/2507.17362 https://arxiv.org/pdf/2507.17362

Horn's problem in PU$(n,1)$
The multiplicative Horn problem is the following question: given three conjugacy classes $\mathcal{C}_1, \mathcal{C}_2, \mathcal{C}_3$ in a Lie group $G$, do there exist elements $(A,B,C)\in\mathcal{C}_1\times\mathcal{C}_2\times\mathcal{C}_3$ such that $ABC=\operatorname{Id}$? In this paper, we study the multiplicative Horn problem restricted to the elliptic classes of the group $G={\rm PU}(n,1)$ for $n\geq 1$, which is the isometry group of the $n$-dimensional complex hyperbolic space. We show…

Distinguishing Filling Invariants Associated to Conjugacy in Groups
Conan Gillis, Timothy Riley
https://arxiv.org/abs/2506.19264 https://

Distinguishing Filling Invariants Associated to Conjugacy in Groups
Brick and Corson introduced annular Dehn functions in 1998 to quantify the conjugacy problem for finitely generated groups and gave the fundamental relationships between it, the Dehn function, and the conjugator length function. We furnish the theory with diverse examples groups. In particular, we show that these three invariants are independent -- no two of the three functions determine the other.

The problem of finding three numbers such that the sum or difference of any two of them is a square number
Seiji Tomita
https://arxiv.org/abs/2508.15781 https://

The problem of finding three numbers such that the sum or difference of any two of them is a square number
Euler explored the problem of finding three numbers such that the sum or difference of any two of them is a perfect square. He discovered a parametric solution represented by polynomials of degree 18 and identified the smallest of these solutions. Additionally, we derive two parametric solutions using the elliptic curve method and find all solutions within the range of $10^8$.

Triangle-free subsets of the Hypercube
Padmini Mukkamala
https://arxiv.org/abs/2506.18782 https://arxiv.org/pdf/2506.18782

Triangle-free subsets of the Hypercube
We study the problem of determining the largest subset of vertices of the $n$ dimensional hypercube without three vertices at a Hamming distance of exactly $r$ from each other. In particular, we provide a lower bound of $\frac{c2^n}{e^r2^{\frac r2} (\frac nr)^{\frac{3r}{4}}}$ and an upper bound of $O(\frac{r2^n}{n+1})$ when $2r \le n$. In particular, when $r$ is a constant, the lower bound is $\frac{c2^n}{n^{3r/4}}$, while the upper bound is $\frac{c'2^n}{n}$.

Making Graphs Irregular through Irregularising Walks
Julien Bensmail, Romain Bourneuf, Paul Colinot, Samuel Humeau, Timoth\'ee Martinod
https://arxiv.org/abs/2506.21254

Making Graphs Irregular through Irregularising Walks
The 1-2-3 Conjecture, introduced by Karoński, Łuczak, and Thomason in 2004, was recently solved by Keusch. This implies that, for any connected graph $G$ different from $K_2$, we can turn $G$ into a locally irregular multigraph $M(G)$, i.e., in which no two adjacent vertices have the same degree, by replacing some of its edges with at most three parallel edges. In this work, we introduce and study a restriction of this problem under the additional constraint that edges added to $G$ to reach $…

Disjunctions of Two Dependence Atoms
Nicolas Fr\"ohlich, Phokion G. Kolaitis, Arne Meier
https://arxiv.org/abs/2508.16146 https://arxiv.org/pdf/2508.1…

Disjunctions of Two Dependence Atoms
Dependence logic is a formalism that augments the syntax of first-order logic with dependence atoms asserting that the value of a variable is determined by the values of some other variables, i.e., dependence atoms express functional dependencies in relational databases. On finite structures, dependence logic captures NP, hence there are sentences of dependence logic whose model-checking problem is NP-complete. In fact, it is known that there are disjunctions of three dependence atoms whose mod…

On the Shape of the Symmetric Solution Set of a Linear Complementarity Problem with Interval Data
Uwe Sch\"afer
https://arxiv.org/abs/2508.16824 https://

On the Shape of the Symmetric Solution Set of a Linear Complementarity Problem with Interval Data
In this paper we give some two-dimensional and some three-dimensional examples for the shape of the symmetric solution set of a linear complementarity problem where the given data are not explicitly known but can only be enclosed in intervals.

Formation of vacuum state and delta-shock in the solution of two-dimensional Riemann problem for zero pressure gas dynamics
Anamika Pandey, T. Raja Sekhar
https://arxiv.org/abs/2507.17213

Formation of vacuum state and delta-shock in the solution of two-dimensional Riemann problem for zero pressure gas dynamics
In this article, we investigate the two-dimensional pressureless Euler equations with three constant Riemann initial data. Our primary focus is on the wave interactions involving contact discontinuities and delta shocks. A distinguishing feature of the solution is the emergence of a delta shock wave which is characterized by a Dirac delta function appearing in both the density and internal energy variables. By exploiting generalized characteristic analysis, nine topologically distinct solution …

Finite energy foliations in the restricted three-body problem
Lei Liu, Pedro A. S. Salom\~ao
https://arxiv.org/abs/2506.17867 https://

Finite energy foliations in the restricted three-body problem
This paper is about using pseudo-holomorphic curves to study the circular planar restricted three-body problem. The main result states that for mass ratios sufficiently close to $\frac{1}{2}$ and energies slightly above the first Lagrange value, the flow on the regularized component $\mathbb R P^3 \# \mathbb R P^3$ of the energy surface admits a finite energy foliation with three binding orbits, namely two retrograde orbits around the primaries and the Lyapunov orbit in the neck region about th…

Epstein shit and adjacent, Rural America, Poverty, Abuse
Everyone who's not a pedophile thinks pedophiles are bad, but there's this special obsessed hatred you'll find among poor rural Americans. The whole QAnon/Epstein obsession may not really make sense to folks raised in cities. Like, why do these people think *so much* about pedophiles? Why do they think that everyone in power is a pedophile? Why would the Pizzagate thing make sense to anyone? What is this unhinged shit? A lot of folks (who aren't anarchists) might be inclined to ask "why can't these people just let the cops take care of it?"
I was watching Legal Eagle's run down on the Trump Epstein thing earlier today and I woke up thinking about something I don't know if I've ever talked about. Now that I'm not in the US, I'm not at any risk of talking about it. I don't know how much I would have been before, but that's not something I'm gonna dig into right now. So let me tell you a story that might explain a few things.
I'm like 16, maybe 17. I have my license, so this girl I was dating/not dating/just friends with/whatever would regularly convince me to drive her and her friends around. I think she's like 15 at the time. Her friends are younger than her.
She tells me that there's a party we can go to where they have beer. She was told to invite her friends, so I can come too. We're going to pick her friends up (we regularly fill the VW Golf well beyond the legal limit and drive places) and head to the party.
So I take these girls, at least is 13 years old, down to this party. I'm already a bit sketched out bringing a 13 year old to a party. We drive out for a while. It's in the country. We drive down a long dark road. Three are some barrel fires and a shack. This is all a bit strange, but not too abnormal for this area. We're a little ways outside of a place called Mill City (in Oregon).
We park and walk towards the shack. This dude who looks like a rat comes up and offers us beer. He laughs and talks to the girl who invited me, "What's he doing here? You're supposed to bring your girl friends." She's like, "He's our ride." I don't remember if he offered me a beer or not.
We go over to this shed and everyone starts smoking, except me because I didn't smoke until I turned 18. The other girls start talking about the rat face dude, who's wandered over by the fire with some other guys. They're mainly teasing one of the 13 year old girls about having sex with him a bunch of times. They say he's like, 32 or something. The other girls joke about him only having sex with 13 year olds because he's too ugly to have sex with anyone closer to his own age.
Somewhere along the line it comes out that he's a cop. I never forgot that, it's absolutely seared in to my memory. I can picture his face perfectly still, decades later, and them talking about how he's a deputy, he was in his 30's, and he was having sex with a 13 year old girl. I was the only boy there, but there were a few older men. This was a chunk of the good ol' boys club of the town. I think there were a couple of cops besides the one deputy, and a judge or the mayor or some kind of big local VIP.
I kept trying to get my friend to leave, but she wanted to stay. Turns out under age drinking with cops seems like a great deal if you're a kid because you know you won't get busted. I left alone, creeped the fuck out.
I was told later that I wasn't invited and that I couldn't talk about it, I've always been good at compartmentalization, so I never did.
Decades later it occurred to me what was actually happening. I'm pretty sure that cop was giving meth he'd seized as evidence to these kids. This wasn't some one-off thing. It was regular. Who knows how many decades it went on after I left, or how many decades it had been going on before I found out. I knew this type of thing had happened at least a few times before because that's how that 13 year old girl and that 32 year old cop had hooked up in the first place.
Hearing about Epstein's MO, targeting these teenage girls from fucked up backgrounds, it's right there for me. I wouldn't be surprised if they were involved in sex trafficking of minors or some shit like that... but who would you call if you found out? Half the sheriff's department was there and the other half would cover for them.
You live in the city and shit like that doesn't happen, or at least you don't think it happens. But rural poor folks have this intuition about power and abuse. It's right there and you know it.
Trump is such a familiar character for me, because he's exactly that small town mayor or sheriff. He'll will talk about being tough on crime and hunting down pedophiles, while hanging out at a party that exists so people can fuck 8th graders.
The problem with the whole thing is that rural folks will never break the cognitive dissonance between "kill the peods" and "back the blue." They'll never go kill those cops. No, the pedos must be somewhere else. It must be the elites. It must be outsiders. It can't be the cops and good ol' boys everyone respects. It can't be the mayor who rigs the election to win every time. It can't be the "good upstanding" sheriff. Nah, it's the Clintons.
To be fair, it's probably also the Clitnons, a bunch of other politicians, billionaires, etc. Epstein was exactly who everyone thought he was, and he didn't get away with it for so long without a whole lot of really powerful help.
There are still powerful people who got away with involvement with #Epstein. #Trump is one of them, but I don't really believe that he's the only one.
#USPol #ACAB

Global lattice models of a rotating planet -- view on shake, rattle and roll
William E. Barnfield, Alessio Kandiah, Vladimir Frid, Igor B. Movchan, Alexander B. Movchan
https://arxiv.org/abs/2508.16630

Global lattice models of a rotating planet -- view on shake, rattle and roll
A new approach, based on the analysis of a spectral problem for a discrete gyroscopic system, to modelling earthquakes on a rotating planet is presented in this paper. The eigenmodes of gyroscopic three-dimensional icosahedron-dodecahedron lattices are used for the discrete approximations of Earth's vibrations. Related model of the gyroscopic centred icosahedron lattice reveals new results about the motion of Earth's core. The vibrations of the tectonic plate boundaries, inducing shear and long…

Democrats have an age problem
House Republicans managed to pass their draconian budget bill,
-- which promises to make massive cuts to Medicaid, Medicare, and food assistance,
-- early Thursday morning by a narrow one-vote margin
💥that was only possible due the deaths of three Democrats in this current Congress. 
The latest Democrat to pass away was 75-year-old Representative Gerry Connolly of Virginia, who died on Wednesday after battling esophageal cancer.

Republicans Pass Horrid Tax Bill Thanks to Democrats Dying in Office
Republicans passed their terrible tax bill by one vote. Guess how many Democrats died in office this year.

Experimental Evidence for the Propagation and Preservation of Machine Discoveries in Human Populations
Levin Brinkmann, Thomas F. Eisenmann, Anne-Marie Nussberger, Maxim Derex, Sara Bonati, Valerii Chirkov, Iyad Rahwan
https://arxiv.org/abs/2506.17741

Experimental Evidence for the Propagation and Preservation of Machine Discoveries in Human Populations
Intelligent machines with superhuman capabilities have the potential to uncover problem-solving strategies beyond human discovery. Emerging evidence from competitive gameplay, such as Go, demonstrates that AI systems are evolving from mere tools to sources of cultural innovation adopted by humans. However, the conditions under which intelligent machines transition from tools to drivers of persistent cultural change remain unclear. We identify three key conditions for machines to fundamentally i…

Minimal Banach-Tarski Decompositions
Cesare Straffelini, Kilian Zambanini
https://arxiv.org/abs/2507.17517 https://arxiv.org/pdf/2507.17517

Minimal Banach-Tarski Decompositions
We investigate the problem of finding the minimum number of pieces necessary for dividing a three-dimensional sphere or a ball and reassembling it to form $n$ congruent copies of the original object, generalising a known result by Raphael Robinson.

A predictor-corrector scheme for approximating signed distances using finite element methods
Amina El Bachari, Johann Rannou, Vladislav A. Yastrebov, Pierre Kerfriden, Susanne Claus
https://arxiv.org/abs/2506.17830

A predictor-corrector scheme for approximating signed distances using finite element methods
In this article, we introduce a finite element method designed for the robust computation of approximate signed distance functions to arbitrary boundaries in two and three dimensions. Our method employs a novel prediction-correction approach, involving first the solution of a linear diffusion-based prediction problem, followed by a nonlinear minimization-based correction problem associated with the Eikonal equation. The prediction step efficiently generates a suitable initial guess, significant…

Trion polaron problem in bulk and two-dimensional materials
V. Shahnazaryan, A. Kudlis, K. Varga, I. A. Shelykh, I. V. Tokatly
https://arxiv.org/abs/2508.14756 https://

Trion polaron problem in bulk and two-dimensional materials
We develop a microscopic theoryof the trion polaron: a bound state of two electrons and one hole, dressed by longitudinal optical (LO) phonons. Starting from the Frohlich Hamiltonian, which describes the interaction of charged particles with LO phonons in three-dimensional (bulk) and two-dimensional (monolayer) polar crystals, we adopt the intermediate coupling variational approximation of Lee, Low, and Pines, and generalize it for the three-body problem. This yields an effective three-particle…

Robotic Manipulation of a Rotating Chain with Bottom End Fixed
Qi Jing Chen, Shilin Shan, Quang-Cuong Pham
https://arxiv.org/abs/2506.18355 https://…

Robotic Manipulation of a Rotating Chain with Bottom End Fixed
This paper studies the problem of using a robot arm to manipulate a uniformly rotating chain with its bottom end fixed. Existing studies have investigated ideal rotational shapes for practical applications, yet they do not discuss how these shapes can be consistently achieved through manipulation planning. Our work presents a manipulation strategy for stable and consistent shape transitions. We find that the configuration space of such a chain is homeomorphic to a three-dimensional cube. Using …

Full non-LTE multi-level radiative transfer I. An atom with three bound infinitely sharp levels
Tristan Lagache, Fr\'ed\'eric Paletou, Malali Sampoorna
https://arxiv.org/abs/2506.15361

Full non-LTE multi-level radiative transfer I. An atom with three bound infinitely sharp levels
The standard nonlocal thermodynamic equilibrium (non-LTE) multi-level radiative transfer problem only takes into account the deviation of the radiation field and atomic populations from their equilibrium distribution. We aim to show how to solve for the full non-LTE (FNLTE) multi-level radiative transfer problem, also accounting for deviation of the velocity distribution of the massive particles from Maxwellian. We considered, as a first step, a three-level atom with zero natural broadening. In…

Triadic First-Order Logic Queries in Temporal Networks
Omkar Bhalerao, Yunjie Pan, C. Seshadhri, Nishil Talati
https://arxiv.org/abs/2507.17215 https://

Triadic First-Order Logic Queries in Temporal Networks
Motif counting is a fundamental problem in network analysis, and there is a rich literature of theoretical and applied algorithms for this problem. Given a large input network $G$, a motif $H$ is a small "pattern" graph indicative of special local structure. Motif/pattern mining involves finding all matches of this pattern in the input $G$. The simplest, yet challenging, case of motif counting is when $H$ has three vertices, often called a "triadic" query. Recent work has focused on "temporal g…

Going Beyond Twin-width? CSPs with Unbounded Domain and Few Variables
Peter Jonsson, Victor Lagerkvist, Jorke M. de Vlas, Magnus Wahlstr\"om
https://arxiv.org/abs/2508.16389

Going Beyond Twin-width? CSPs with Unbounded Domain and Few Variables
We study a model of constraint satisfaction problems geared towards instances with few variables but with domain of unbounded size (udCSP). Our model is inspired by recent work on FPT algorithms for MinCSP where frequently both upper and lower bounds on the parameterized complexity of a problem correspond to $k$-variable udCSPs; e.g., the FPT algorithms for Boolean MinCSP (Kim et al., SODA 2023) and Directed Multicut with three cut requests (Hatzel et al., SODA 2023) both reduce to k-variable u…

Understanding Distribution Structure on Calibrated Recommendation Systems
Diego Correa da Silva, Denis Robson Dantas Boaventura, Mayki dos Santos Oliveira, Eduardo Ferreira da Silva, Joel Machado Pires, Frederico Ara\'ujo Dur\~ao
https://arxiv.org/abs/2508.13568

Understanding Distribution Structure on Calibrated Recommendation Systems
Traditional recommender systems aim to generate a recommendation list comprising the most relevant or similar items to the user's profile. These approaches can create recommendation lists that omit item genres from the less prominent areas of a user's profile, thereby undermining the user's experience. To solve this problem, the calibrated recommendation system provides a guarantee of including less representative areas in the recommended list. The calibrated context works with three distributi…

Fermion mass ratios from the exceptional Jordan algebra
Tejinder P. Singh
https://arxiv.org/abs/2508.10131 https://arxiv.org/pdf/2508.10131

Fermion mass ratios from the exceptional Jordan algebra
We revisit the "three generations" problem and the pattern of charged-fermion masses from the vantage of octonionic and Clifford algebra structures. Working with the exceptional Jordan algebra J3(OC) (right-handed flavor) and the symmetric cube of SU(3) (left-handed charge frame), we show that a single minimal ladder in the symmetric cube, together with the Dynkin Z2 swap (the A2 diagram flip), leads to closed-form expressions for the square-root mass ratios of all three charged families. The u…

Supervised Extraction of the Thermal Sunyaev$-$Zel'dovich Effect with a Three-Dimensional Convolutional Neural Network
Cameron T. Pratt, Zhijie Qu, Joel N. Bregman
https://arxiv.org/abs/2507.13400

Supervised Extraction of the Thermal Sunyaev$-$Zel'dovich Effect with a Three-Dimensional Convolutional Neural Network
The thermal Sunyaev$-$Zel'dovich (SZ) effect offers a unique probe of the hot and diffuse universe that could help close the missing baryon problem. Traditional extractions of the SZ effect, however, exhibit systematic noise that may lead to unreliable results. In this work, we provide an alternative solution using a three-dimensional Attention Nested U-Net trained end-to-end with supervised learning. Our labeled data consists of simulated SZ signals injected into $\textit{Planck}$ frequency ma…

Recognizing Penny and Marble Graphs is Hard for Existential Theory of the Reals
Anna Lubiw, Marcus Schaefer
https://arxiv.org/abs/2508.10136 https://arxiv.…

Recognizing Penny and Marble Graphs is Hard for Existential Theory of the Reals
We show that the recognition problem for penny graphs (contact graphs of unit disks in the plane) is $\exists\mathbb{R}$-complete, that is, computationally as hard as the existential theory of the reals, even if a combinatorial plane embedding of the graph is given. The exact complexity of the penny graph recognition problem has been a long-standing open problem. We lift the penny graph result to three dimensions and show that the recognition problem for marble graphs (contact graphs of unit …

Probing EFX via PMMS: (Non-)Existence Results in Discrete Fair Division
Jaros{\l}aw Byrka, Franciszek Malinka, Tomasz Ponitka
https://arxiv.org/abs/2507.14957

Probing EFX via PMMS: (Non-)Existence Results in Discrete Fair Division
We study the fair division of indivisible items and provide new insights into the EFX problem, which is widely regarded as the central open question in fair division, and the PMMS problem, a strictly stronger variant of EFX. Our first result constructs a three-agent instance with two monotone valuations and one additive valuation in which no PMMS allocation exists. Since EFX allocations are known to exist under these assumptions, this establishes a formal separation between EFX and PMMS. We p…

On Reconstructing Training Data From Bayesian Posteriors and Trained Models
George Wynne
https://arxiv.org/abs/2507.18372 https://arxiv.org/pdf/2507.18372

On Reconstructing Training Data From Bayesian Posteriors and Trained Models
Publicly releasing the specification of a model with its trained parameters means an adversary can attempt to reconstruct information about the training data via training data reconstruction attacks, a major vulnerability of modern machine learning methods. This paper makes three primary contributions: establishing a mathematical framework to express the problem, characterising the features of the training data that are vulnerable via a maximum mean discrepancy equivalance and outlining a score…

Depression as a disorder of distributional coding
Matthew Botvinick, Zeb Kurth-Nelson, Timothy Muller, Will Dabney
https://arxiv.org/abs/2507.16598 https:/…

Depression as a disorder of distributional coding
Major depressive disorder persistently stands as a major public health problem. While some progress has been made toward effective treatments, the neural mechanisms that give rise to the disorder remain poorly understood. In this Perspective, we put forward a new theory of the pathophysiology of depression. More precisely, we spotlight three previously separate bodies of research, showing how they can be fit together into a previously overlooked larger picture. The first piece of the puzzle is …

Three-Dimensional Numerical Simulations of Magnetar Crust Quakes
Yuanhong Qu, Ashley Bransgrove
https://arxiv.org/abs/2508.12567 https://arxiv.org/pdf/2508…

Three-Dimensional Numerical Simulations of Magnetar Crust Quakes
Crust quakes are frequently invoked as a mechanism to trigger sudden transients in the magnetospheres of magnetars. In this picture, a mechanical failure of the crust excites seismic motions of the magnetar surface that launch force-free waves into the magnetosphere. We first investigate this problem analytically and then perform three-dimensional numerical simulations. Our simulations follow the propagation of high-frequency magneto-elastic waves in the entire crust, and include magnetic coupl…

The Hexablock: a domain associated with the $\mu$-synthesis in $M_2(\mathbb C)$
Indranil Biswas, Sourav Pal, Nitin Tomar
https://arxiv.org/abs/2506.15149 h…

The Hexablock: a domain associated with the $μ$-synthesis in $M_2(\mathbb C)$
We study a new domain in $\mathbb C^4$, namely the hexablock $\mathbb{H}$ that arises in connection with a special case of the $μ$-synthesis problem in $M_2(\mathbb C)$. Previous attempts to study a few instances of the $μ$-synthesis problem led to domains such as symmetrized bidisc $\mathbb G_2$, tetrablock $\mathbb E$ and pentablock $\mathbb P$. Throughout, the relations of $\mathbb{H}$ with these three domains are explored. Several characterizations of the hexablock are established. We det…

On the $PGL_2(q)$-orbits of lines of $PG(3,q)$ and binary quartic forms in characteristic three
Krishna Kaipa, Puspendu Pradhan
https://arxiv.org/abs/2508.11229 https://

On the $PGL_2(q)$-orbits of lines of $PG(3,q)$ and binary quartic forms in characteristic three
We consider the problem of classifying the lines of the projective $3$-space $PG(3,q)$ over a finite field $\mathbb{F}_q$ into orbits of the group $PGL_2(q)$ of linear symmetries of the twisted cubic $C$. The problem has been solved in literature in characteristic different from $3$, and in this work, we solve the problem in characteristic $3$. We reduce this problem to another problem, which is the classification of binary quartic forms into $PGL_2(q)$-orbits. We first solve the latter problem…

About three-quarters of fungi are “dark taxa” – species known only by their DNA sequence, as physical specimens have not been found.
https://www.theguardian.com/environment/2025/aug/15/biology-mycorrhizal-fungi-map-restoring-world-fore…

Exact Renormalization Relation and Binding Energies for Three Identical Bosons
Langxuan Chen, Pengfei Zhang
https://arxiv.org/abs/2506.12531 https://

Exact Renormalization Relation and Binding Energies for Three Identical Bosons
In the low-energy limit, non-relativistic particles with short-range interactions exhibit universal behavior that is largely independent of microscopic details. This universality is typically described by effective field theory, in which the two-body interaction is renormalized to a single parameter-the scattering length. For systems of identical bosons, the three-body problem reveals the Efimov effect, a novel phenomenon proposed that necessitates the introduction of an additional three-body p…

Series A, Episode 08 - Duel
JENNA: Deactivating.
BLAKE: Now, this is the pursuit ship that's done all the firing. That'll be low on power now, so it won't be a problem.
CALLY: So we can ignore it.
https://blake.torpidity.net/m/108/154 B7B3

Manifold Optics
Hongming Shen, Wen Xiao, Fei Fang Chuang, Huanyang Chen
https://arxiv.org/abs/2507.17437 https://arxiv.org/pdf/2507.17437

Manifold Optics
Transformation optics establishes an equivalence relationship between gradient media and curved space, unveiling intrinsic geometric properties of gradient media. However, this approach based on curved spaces is concentrated on two-dimensional manifolds, namely curved surfaces. In this Letter, we establish an intrinsic connection between three-dimensional manifolds and three-dimensional gradient media in transformation optics by leveraging the Yamabe problem and Ricci scalar curvature, a measur…

Sharp Boundary Growth Rate Estimate of the Singular Equation $-\Delta u=u^{-\gamma}$ in a Critical Cone
Leyun Wu, Chilin Zhang
https://arxiv.org/abs/2507.16319

Sharp Boundary Growth Rate Estimate of the Singular Equation $-Δu=u^{-γ}$ in a Critical Cone
For $γ>0$, we study the sharp boundary growth rate estimate of solutions to the Dirichlet problem of the singular Lane-Emden-Fowler equation \begin{equation*} -Δu=u^{-γ} \end{equation*} in a critical $C^{1,1}$ epigraphical cone $Cone_Σ$. We show that the growth rate estimate exhibits fundamentally different behaviors in the following three cases: $1<γ<2$, $γ=2$, and $γ>2$. Moreover, we obtain the sharp growth rate estimate near the origin for $γ>1$. As a consequence, we show that wh…

The SOS Rank of Biquadratic Forms
Liqun Qi, Chunfeng Cui, Yi Xu
https://arxiv.org/abs/2507.16399 https://arxiv.org/pdf/2507.16399

The SOS Rank of Biquadratic Forms
In 1973, Calderón proved that an $m \times 2$ positive semidefinite (psd) biquadratic form can always be expressed as the sum of squares (sos) of ${3m(m+1) \over 2}$ quadratic forms. Very recently, by applying Hilbert's theorem, we proved that a $2 \times 2$ psd biquadratic form can always be expressed as the sum of squares of three quadratic forms. This improved Calderón's result for $m=2$, and left the sos rank problem of $m \times 2$ biquadratic forms for $m \ge 3$ to further exploration. …

Low-order finite element complex with application to a fourth-order elliptic singular perturbation problem
Xuewei Cui, Xuehai Huang
https://arxiv.org/abs/2506.20240

Low-order finite element complex with application to a fourth-order elliptic singular perturbation problem
A low-order nonconforming finite element discretization of a smooth de Rham complex starting from the $H^2$ space in three dimensions is proposed, involving an $H^2$-nonconforming finite element space, a new tangentially continuous $H^1$-nonconforming vector-valued finite element space, the lowest-order Raviart-Thomas space, and piecewise constant functions. While nonconforming for the smooth complex, the discretization conforms to the classical de Rham complex. It is applied to develop a decou…

Quantum thermodynamics in a rotating BTZ black hole spacetime
Wenjing Chen, Yixuan Ma, Si-Wei Han, Zihao Wang, Jun Feng
https://arxiv.org/abs/2507.16787 ht…

Quantum thermodynamics in a rotating BTZ black hole spacetime
We address the problem of the thermalization process for an Unruh-DeWitt (UDW) detector outside a BTZ black hole, from a perspective of quantum thermodynamics. In the context of an open quantum system, we derive the complete dynamics of the detector, which encodes a complicated response to scalar background fields. Using various information theory tools, such as quantum relative entropy, quantum heat, coherence, quantum Fisher information, and quantum speed of evolution, we examined three quant…

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 shade plans, b…

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 $$…

Natura Urbana VII 🏡
城市自然 VII 🏡
📷 Nikon FE
🎞️Ilford FP4 Plus, expired 1995
buy me ☕️ ?/请我喝杯☕️？
#filmphotography

Yiding Cao Geld mit PayPal.Me senden
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Integrating Uncertainties for Koopman-Based Stabilization
Yicheng Lin, Bingxian Wu, Nan Bai, Zhiyong Sun, Yunxiao Ren, Chuanze Chen, Zhisheng Duan
https://arxiv.org/abs/2508.11533

Integrating Uncertainties for Koopman-Based Stabilization
Over the past decades, the Koopman operator has been widely applied in data-driven control, yet its theoretical foundations remain underexplored. This paper establishes a unified framework to address the robust stabilization problem in data-driven control via the Koopman operator, fully accounting for three uncertainties: projection error, estimation error, and process disturbance. It comprehensively investigates both direct and indirect data-driven control approaches, facilitating flexible met…

The Word Problem for Products of Symmetric Groups
Hans U. Simon
https://arxiv.org/abs/2506.13655 https://arxiv.org/pdf/2506.13655

The Word Problem for Products of Symmetric Groups
The word problem for products of symmetric groups (WPPSG) is a well-known NP-complete problem. An input instance of this problem consists of ``specification sets'' $X_1,\ldots,X_m \seq \{1,\ldots,n\}$ and a permutation $τ$ on $\{1,\ldots,n\}$. The sets $X_1,\ldots,X_m$ specify a subset of the symmetric group $\cS_n$ and the question is whether the given permutation $τ$ is a member of this subset. We discuss three subproblems of WPPSG and show that they can be solved efficiently. The subproble…

MOFCO: Mobility- and Migration-Aware Task Offloading in Three-Layer Fog Computing Environments
Soheil Mahdizadeh, Elyas Oustad, Mohsen Ansari
https://arxiv.org/abs/2507.12028

MOFCO: Mobility- and Migration-Aware Task Offloading in Three-Layer Fog Computing Environments
Task offloading in three-layer fog computing environments presents a critical challenge due to user equipment (UE) mobility, which frequently triggers costly service migrations and degrades overall system performance. This paper addresses this problem by proposing MOFCO, a novel Mobility- and Migration-aware Task Offloading algorithm for Fog Computing environments. The proposed method formulates task offloading and resource allocation as a Mixed-Integer Nonlinear Programming (MINLP) problem and…

Consecutive collision orbits in the restricted three-body problem above the first critical energy value
Jungsoo Kang, Kevin Ruck
https://arxiv.org/abs/2506.01735

Consecutive collision orbits in the restricted three-body problem above the first critical energy value
In this paper, we study the planar circular restricted three-body problem for energy levels slightly above the first critical value. We first observe that the energy hypersurfaces in the Birkhoff regularization corresponding to these energy levels are of contact type. Then, using a version of Rabinowitz Floer homology and an analytic continuation argument, we establish the existence of a symmetric consecutive collision orbit and, furthermore, prove the existence of infinitely many such orbits f…

Two out of three night trains on this trip has had our sleeper carriage cancelled or replaced last minute (causing 1hr delay).. I wonder if there's a bed bug problem in Europe at the moment

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 $…

Mixing of Gaussian Solute Plumes
Daniel Lester
https://arxiv.org/abs/2506.20387 https://arxiv.org/pdf/2506.20387

Mixing of Gaussian Solute Plumes
We consider the general problem of mixing of Gaussian solute plumes arising across a range of different flows ranging from two-dimensional (2D) to three-dimensional (3D), steady to unsteady, regular to chaotic, Stokes to turbulent. We consider a a range of infinitesimal injection protocols (point or line sources, continuous or pulsed) which generate solute points, lines and sheets and their finite-sized counterparts (blobs, tubes and slabs). We show that evolution of this broad family of Gaussi…

Partially rigid motions in the planar three-body problem
Richard Moeckel
https://arxiv.org/abs/2506.13570 https://arxiv.org/pdf/2506.…

Partially rigid motions in the planar three-body problem
A solution of the n-body problem in R^d is a relative equilibrium if all of the mutual distance between the bodies are constant. In other words, the bodies undergo a rigid motion. Here we investigate the possibility of partially rigid motions, where some but not all of the distances are constant. For the planar three-body problem with equal masses, we show that partially rigid motions are impossible -- if even one of the three mutual distances is constant, the motion must be a relative equilibr…

Non-invertible Symmetry as a Solution to the Strong CP Problem in a GUT-inspired Standard Model
Tatsuo Kobayashi, Hajime Otsuka, Tsutomu T. Yanagida
https://arxiv.org/abs/2508.12287

Non-invertible Symmetry as a Solution to the Strong CP Problem in a GUT-inspired Standard Model
We propose a three-zero texture for the down-quark mass matrix within a $SU(5)$ GUT-inspired Standard Model, enforced by a non-invertible selection rule originating from $\mathbb{Z}_2$ gauging of $\mathbb{Z}_N$ symmetries. Assuming CP invariance at the high-energy scale, our framework solves the strong CP problem while reproducing a realistic quark mass matrix. The CP symmetry is spontaneously broken down at an intermediate scale via complex vacuum expectation values of new scalar fields $η_i$…

Global existence and optimal time-decay rates of the compressible Navier-Stokes equations with density-dependent viscosities
Jie Fan, Xiangdi Huang, Anchun Ni
https://arxiv.org/abs/2507.16436

Global existence and optimal time-decay rates of the compressible Navier-Stokes equations with density-dependent viscosities
This paper is devoted to studying the Cauchy problem for the three-dimensional isentropic compressible Navier-Stokes equations with density-dependent viscosities given by $μ=ρ^α,λ=ρ^α(α>0)$. We establish the global existence and optimal decay rates of classical solutions under the assumptions of small initial data in $L^1(\mathbb{R}^3)\cap L^2(\mathbb{R}^3)$ and the viscosity constraint $|α-1|\ll 1$. The key idea of our proof lies in the combination of Green's function method,…

Simpler and Faster Contiguous Art Gallery
Sarita de Berg, Jacobus Conradi, Ivor van der Hoog, Frank Staals
https://arxiv.org/abs/2508.09734 https://arxiv.o…

Simpler and Faster Contiguous Art Gallery
The contiguous art gallery problem was introduced at SoCG'25 in a merged paper that combined three simultaneous results, each achieving a polynomial-time algorithm for the problem. This problem is a variant of the classical art gallery problem, first introduced by Klee in 1973. In the contiguous art gallery problem, we are given a polygon P and asked to determine the minimum number of guards needed, where each guard is assigned a contiguous portion of the boundary of P that it can see, such tha…

Conservative fusion of unbiased partial state estimates: CI is optimal
Jochen Trumpf, Behzad Zamani, Chris Manzie
https://arxiv.org/abs/2507.16216 https://…

Conservative fusion of unbiased partial state estimates: CI is optimal
We show that Covariance Intersection (CI) is optimal amongst all conservative unbiased linear fusion rules also in the general case of information fusion of two unbiased partial state estimates, significantly generalizing the known optimality result for fusion of full state estimates. In fact, we prove the much stronger result that three different optimization problems are equivalent, namely the abstract optimal conservative unbiased linear information fusion problem with respect to a strictly …

Nonexistence of Consecutive Powerful Triplets Around Cubes with Prime-Square Factors
Jialai She
https://arxiv.org/abs/2507.16828 https://

Nonexistence of Consecutive Powerful Triplets Around Cubes with Prime-Square Factors
The Erdős-Mollin-Walsh conjecture, asserting the nonexistence of three consecutive powerful integers, remains a celebrated open problem in number theory. A natural line of inquiry, following recent work by Chan (2025), is to investigate potential counterexamples centered around perfect cubes, which are themselves powerful. This paper establishes a new non-existence result for a family of such integer triplets with distinct structural constraints, combining techniques from modular arithmetic, $…

Data assimilation using a global Girsanov nudged particle filter
Maneesh Kumar Singh, Joshua Hope-Collins, Colin J. Cotter, Dan Crisan
https://arxiv.org/abs/2507.17685 https://

Data assimilation using a global Girsanov nudged particle filter
We present a particle filtering algorithm for stochastic models on infinite dimensional state space, making use of Girsanov perturbations to nudge the ensemble of particles into regions of higher likelihood. We argue that the optimal control problem needs to couple control variables for all of the particles to maintain an ensemble with good effective sample size (ESS). We provide an optimisation formulation that separates the problem into three stages, separating the nonlinearity in the ESS ter…

Almost and Approximate EFX for Few Types of Agents
Vishwa Prakash HV, Ruta Mehta, Prajakta Nimbhorkar
https://arxiv.org/abs/2508.15380 https://arxiv.org/pd…

Almost and Approximate EFX for Few Types of Agents
We study the problem of fair allocation of a set of indivisible goods among $n$ agents with $k$ distinct additive valuations, with the goal of achieving approximate envy-freeness up to any good ($α-\mathrm{EFX}$). It is known that EFX allocations exist for $n$ agents when there are at most three distinct valuations due to HV et al. Furthermore, Amanatidis et al. showed that a $\frac{2}{3}-\mathrm{EFX}$ allocation is guaranteed to exist when number of agents is at most seven. In this paper, w…

A Novel Feedforward Youla Parameterization Method for Avoiding Local Minima in Stereo Image Based Visual Servoing Control
Rongfei Li, Francis Assadian
https://arxiv.org/abs/2506.10252

A Novel Feedforward Youla Parameterization Method for Avoiding Local Minima in Stereo Image Based Visual Servoing Control
In robot navigation and manipulation, accurately determining the camera's pose relative to the environment is crucial for effective task execution. In this paper, we systematically prove that this problem corresponds to the Perspective-3-Point (P3P) formulation, where exactly three known 3D points and their corresponding 2D image projections are used to estimate the pose of a stereo camera. In image-based visual servoing (IBVS) control, the system becomes overdetermined, as the 6 degrees of fre…

Global well-posedness of the inviscid resistive isentropic compressible MHD system
Jinkai Li, Liening Qiao
https://arxiv.org/abs/2508.13627 https://arxiv.o…

Global well-posedness of the inviscid resistive isentropic compressible MHD system
Due to the absence of dissipation mechanism to the inviscid compressible systems, it is a challenging problem to prove their global solvability. In this paper, we are concerned with the initial-boundary value problem to the inviscid and resistive isentropic compressible magnetohydrodynamic (MHD) system on three dimensional torus $\mathbb T^3$. Global well-posedness and large time behavior of solutions are established in the first time for the isentropic setting, under the condition that the ini…

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

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

This https://arxiv.org/abs/2505.09708 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_…

The uncertainty of magnetic fields in 3D non-local thermodynamic equilibrium inversions
We describe our approach to solve the problem of ensuring the solenoidality of the magnetic field vector in three-dimensional (3D) inversions, as well as the estimation of the uncertainty in the inferred magnetic field. The solenoidality of the magnetic field vector is often disregarded in the inversion of spectropolarimetric data due to limitations in the traditional one-dimensional inversion techniques. We propose a method to ensure the solenoidal condition in 3D inversions based on our meshf…

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

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

Constructing characteristic initial data for three dimensional compressible Euler equations
Yuxuan Wang, Sifan Yu, Pin Yu
https://arxiv.org/abs/2508.15199 https://

Constructing characteristic initial data for three dimensional compressible Euler equations
This paper resolves the characteristic initial data problem for the three-dimensional compressible Euler equations - an open problem analogous to Christodoulou's characteristic initial value formulation for the vacuum Einstein field equations in general relativity. Within the framework of acoustical geometry, we prove that for any "initial cone" $C_0\subset \mathcal{D}=[0,T]\times\mathbb{R}^3$ with initial data $(\mathringρ,\mathring{v},\mathring{s})$ given at $S_{0,0}=C_0\cap Σ_0$, arbitrary…

Deciding the Value of Two-Clock Almost Non-Zeno Weighted Timed Games
Isa Vialard
https://arxiv.org/abs/2508.00014 https://arxiv.org/pdf/2508.00014

Deciding the Value of Two-Clock Almost Non-Zeno Weighted Timed Games
The Value Problem for weighted timed games (wtgs) consists in determining, given a two-player weighted timed game with a reachability objective and a rational threshold, whether or not the value of the game exceeds the threshold. When restrained to wtgs with non-negative weight, this problem is known to be undecidable for weighted timed games with three or more clocks, and decidable for one-clock wtgs. The Value Problem for two-clock non-negative wtgs, which remained stubbornly open for a decad…

Beyond Robustness: Learning Unknown Dynamic Load Adaptation for Quadruped Locomotion on Rough Terrain
Leixin Chang, Yuxuan Nai, Hua Chen, Liangjing Yang
https://arxiv.org/abs/2507.07825

Beyond Robustness: Learning Unknown Dynamic Load Adaptation for Quadruped Locomotion on Rough Terrain
Unknown dynamic load carrying is one important practical application for quadruped robots. Such a problem is non-trivial, posing three major challenges in quadruped locomotion control. First, how to model or represent the dynamics of the load in a generic manner. Second, how to make the robot capture the dynamics without any external sensing. Third, how to enable the robot to interact with load handling the mutual effect and stabilizing the load. In this work, we propose a general load modeling…

This https://arxiv.org/abs/2501.02529 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Prime Multiple Missing Graphs
The famous Goldbach conjecture remains open for nearly three centuries. Recently Goldbach graphs are introduced to relate the problem with the literature of Graph Theory. It is shown that the connectedness of the graphs is equivalent to the affirmative answer of the conjecture. Some modified version of the graphs, say, near Goldbach graphs are shown to be Hamiltonian for small number of vertices. In this context, we introduce a class of graphs, namely, prime multiple missing graphs such that ne…

An explicit computational approach for a three-dimensional system of nonlinear elastodynamic sine-Gordon problem
Eric Ngondiep
https://arxiv.org/abs/2506.14807

An explicit computational approach for a three-dimensional system of nonlinear elastodynamic sine-Gordon problem
This paper proposes an explicit computational method for solving a three-dimensional system of nonlinear elastodynamic sine-Gordon equations subject to appropriate initial and boundary conditions. The time derivative is approximated by interpolation technique whereas the finite element approach is used to approximate the space derivatives. The developed numerical scheme is so-called, high-order explicit computational technique. The new algorithm efficiently treats the time derivative term and p…

Data-Driven Stabilisation of Unstable Periodic Orbits of the Three-Body Problem
Owen M. Brook, Jason J. Bramburger, Davide Amato, Urban Fasel
https://arxiv.org/abs/2507.08630

Data-Driven Stabilisation of Unstable Periodic Orbits of the Three-Body Problem
Many different models of the physical world exhibit chaotic dynamics, from fluid flows and chemical reactions to celestial mechanics. The study of the three-body problem (3BP) and its many different families of unstable periodic orbits (UPOs) have provided fundamental insight into chaotic dynamics as far back as the 19th century. The 3BP, a conservative system, is inherently challenging to sample due to its volume-preservation property. In this paper we present an interpretable data-driven appr…

This https://arxiv.org/abs/2405.08485 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Doubly relaxed forward-Douglas--Rachford splitting for the sum of two nonconvex and a DC function
In this paper, we consider a class of structured nonconvex nonsmooth optimization problems whose objective function is the sum of three nonconvex functions, one of which is expressed in a difference-of-convex (DC) form. This problem class covers several important structures in the literature including the sum of three functions and the general DC program. We propose a splitting algorithm and prove the subsequential convergence to a stationary point of the problem. The full sequential convergenc…

Three-dimensional Navier-Stokes-Biot coupling via a moving reticular plate interface: existence of weak solutions
Felix Brandt, Sun\v{c}ica \v{C}ani\'c, Boris Muha
https://arxiv.org/abs/2508.14310 …

Three-dimensional Navier-Stokes-Biot coupling via a moving reticular plate interface: existence of weak solutions
We prove the existence of finite-energy weak solutions to a regularized three-dimensional fluid-structure interaction (FSI) problem involving an incompressible, viscous, Newtonian fluid and a multilayered poro(visco)elastic structure. The structure consists of a thick layer modeled by the Biot equations and a thin reticular plate with inertia and elastic energy, transparent to fluid flow. The coupling is nonlinear in the sense that it takes place on a moving interface that is not known a priori…

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.

A time-adaptive optimization approach for reconstructing immune response in a mathematical model of acute HIV infection using clinical data
L. Beilina, I. Gainova, G. Bocharov
https://arxiv.org/abs/2508.13123

A time-adaptive optimization approach for reconstructing immune response in a mathematical model of acute HIV infection using clinical data
The paper proposes a time-adaptive optimization approach for determining the time-dependent immune response function in a mathematical model of acute HIV infection, using clinical data from four untreated patients. We formulate the problem as a parameter identification problem for an immune response system of ODE which includes novel component integrated into the third equation of the classical three-equation HIV model. Tikhonov's regularization method, Lagrangian approach, from which we deri…

Nonlinear stochastic trajectory optimization
Thomas Caleb, Roberto Armellin, St\'ephanie Lizy-Destrez
https://arxiv.org/abs/2508.13677 https://arxiv.or…

Nonlinear stochastic trajectory optimization
Designing robust space trajectories in nonlinear dynamical environments, such as the Earth-Moon circular restricted three-body problem (CR3BP), poses significant challenges due to sensitivity to initial conditions and non-Gaussian uncertainty propagation. This work introduces a novel solver for discrete-time chance-constrained trajectory optimization under uncertainty, referred to as stochastic optimization with differential algebra (SODA). SODA combines differential algebra (DA) with adaptive …

A Stokes-Brinkman-type formulation for the eigenvalue problem in porous media
Felipe Lepe, Gonzalo Rivera, Jesus Vellojin
https://arxiv.org/abs/2507.08226 …

A Stokes-Brinkman-type formulation for the eigenvalue problem in porous media
In this paper we introduce and analyze, for two and three dimensions, a finite element method to approximate the natural frequencies of a flow system governed by the Stokes-Brinkman equations. Here, the fluid presents the capability of being within a porous media. Taking advantage of the Stokes regularity results for the solution, and considering inf-sup stable families of finite elements, we prove convergence together with a priori and a posteriori error estimates for the eigenvalues and eigen…

Global uniform regularity for the 3D incompressible MHD equations with slip boundary condition near a background magnetic field
Jincheng Gao, Lianyun Peng, Jiahong Wu, Zheng-an Yao
https://arxiv.org/abs/2508.09609

Global uniform regularity for the 3D incompressible MHD equations with slip boundary condition near a background magnetic field
This paper resolves the global regularity problem for the three-dimensional incompressible magnetohydrodynamics (MHD) equations in the upper half-space with slip boundary conditions, in the presence of a background magnetic field. Motivated by geophysical applications, we consider an anisotropic MHD system with weak dissipation in the $x_2$ and $x_3$ directions and small vertical magnetic diffusion. By exploiting the stabilizing effect induced by the background magnetic field and constructing a…

Comparison of three random field sampling methods for high-resolution Bayesian inversion with application to a plane stress problem
Pieter Vanmechelen, Geert Lombaert, Giovanni Samaey
https://arxiv.org/abs/2508.12876

Comparison of three random field sampling methods for high-resolution Bayesian inversion with application to a plane stress problem
Bayesian inversion aims to provide uncertainty quantification of posterior estimates conditional on observations. When the inferred parameter is a continuous spatial function, one common strategy is to model it as a random field. Several random field sampling strategies exist. In this article, we investigate three different approaches in terms of numerical efficiency and influence on the posterior distribution. These approaches are based on (i) Karhunen-Loeve and (ii) wavelet expansions, and (i…

The Riemann problem for three-phase foam flow in porous media
Luis Fernando Lozano, Grigori Chapiro, Dan Marchesin
https://arxiv.org/abs/2506.08152 https:/…

The Riemann problem for three-phase foam flow in porous media
Gas injection in the context of the three-phase flow in porous media appears in applications such as Enhanced Oil Recovery, aquifer remediation, and carbon capture, utilization, and storage (CCUS). In general, this technique suffers from a difficulty related to excessive gas mobility, which can be circumvented by using foam. This study addresses the non-linear system of differential equations describing the three-phase foam flow based on Corey relative permeability functions. A major obstacle i…

Weighted and unweighted enrichment strategies for solving the Poisson problem with Dirichlet boundary conditions
Francesco Dell'Accio, Luca Desiderio, Allal Guessab, Federico Nudo
https://arxiv.org/abs/2508.07238

Weighted and unweighted enrichment strategies for solving the Poisson problem with Dirichlet boundary conditions
In this paper, we propose weighted and unweighted enrichment strategies to enhance the accuracy of the linear lagrangian finite element for solving the Poisson problem with Dirichlet boundary conditions. We first recall key examples of admissible enrichment functions, specifically designed to overcome the limitations of the linear lagrangian finite element in capturing solution features such as sharp gradients and boundary-layer phenomena. We then introduce two novel three-parameter families of…

Three bound states with prescribed angular momentum to the cubic-quintic NLS equations in $\mathbb{R}^{3}$
Shuai Yao, Juntao Sun
https://arxiv.org/abs/2507.04057

Three bound states with prescribed angular momentum to the cubic-quintic NLS equations in $\mathbb{R}^{3}$
In this paper, we investigate bound states with prescribed angular momentum and mass for the nonlinear Schrödinger equations (NLS) with the cubic-quintic nonlinearity in dimensions three. We demonstrate that there exist three solutions for the double constrained problem: a local minimizer, a mountain pass type solution, and a global minimizer. Moreover, by means of the minimax method, we construct a new mountain pass path and further obtain the geometric link among the three solutions as well …

Structural stability of three dimensional steady Prandtl equation
Weiming Shen, Yue Wang, Tong Yang
https://arxiv.org/abs/2506.04578 https://

Structural stability of three dimensional steady Prandtl equation
The well-posedness of the three dimensional Prandtl equation is an outstanding open problem due to the appearance of the secondary flow even though there are studies on analytic and Gevrey function spaces. This problem is raised as the third open problem in the classical book by Oleinik and Samokhin [43]. This paper aims to address this open problem in the steady case by introducing a new approach to study the structural stability of background profile that includes the famous Blasius solutions…

On the uniqueness of strong solution to the nonhomogeneous incompressible Navier-Stokes-Cahn-Hilliard system
Lingxin Jiang, Jiahong Wu, Fuyi Xu
https://arxiv.org/abs/2508.09761 …

On the uniqueness of strong solution to the nonhomogeneous incompressible Navier-Stokes-Cahn-Hilliard system
This paper is mainly concerned with an initial-boundary value problem of the nonhomogeneous incompressible Navier-Stokes-Cahn-Hilliard system with the Landau potential in a two and three dimensions. Global existence of strong solutions with bounded and strictly positive density for this system was proven by Giorgini and Temam \cite{GT}; however, an additional smoothness assumption on the initial density was needed to prove uniqueness in \cite{GT1}. Whether uniqueness holds without this addition…

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

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