Tootfinder

BiLO: Bilevel Local Operator Learning for PDE Inverse Problems. Part II: Efficient Uncertainty Quantification with Low-Rank Adaptation
Ray Zirui Zhang, Christopher E. Miles, Xiaohui Xie, John S. Lowengrub
https://arxiv.org/abs/2507.17019

BiLO: Bilevel Local Operator Learning for PDE Inverse Problems. Part II: Efficient Uncertainty Quantification with Low-Rank Adaptation
Uncertainty quantification and inverse problems governed by partial differential equations (PDEs) are central to a wide range of scientific and engineering applications. In this second part of a two part series, we extend Bilevel Local Operator Learning (BiLO) for PDE-constrained optimization problems developed in Part 1 to the Bayesian inference framework. At the lower level, we train a network to approximate the local solution operator by minimizing the local operator loss with respect to the…

Regularization of Nonlinear Inverse Problems -- From Functional Analysis to Data-Driven Approaches
Clemens Kirisits, Bochra Mejri, Sergei Pereverzev, Otmar Scherzer, Cong Shi
https://arxiv.org/abs/2506.17465

Regularization of Nonlinear Inverse Problems -- From Functional Analysis to Data-Driven Approaches
The focus of this book is on the analysis of regularization methods for solving \emph{nonlinear inverse problems}. Specifically, we place a strong emphasis on techniques that incorporate supervised or unsupervised data derived from prior experiments. This approach enables the integration of data-driven insights into the solution of inverse problems governed by physical models. \emph{Inverse problems}, in general, aim to uncover the \emph{inner mechanisms} of an observed system based on indirect…

On the Power of Spatial Locality on Online Routing Problems
Swapnil Guragain, Gokarna Sharma
https://arxiv.org/abs/2506.17517 https://

On the Power of Spatial Locality on Online Routing Problems
We consider the online versions of two fundamental routing problems, traveling salesman (TSP) and dial-a-ride (DARP), which have a variety of relevant applications in logistics and robotics. The online versions of these problems concern with efficiently serving a sequence of requests presented in a real-time on-line fashion located at points of a metric space by servers (salesmen/vehicles/robots). In this paper, motivated from real-world applications, such as Uber/Lyft rides, where some limited…

Subtooting since people in the original thread wanted it to be over, but selfishly tagging @… and @… whose opinions I value...
I think that saying "we are not a supply chain" is exactly what open-source maintainers should be doing right now in response to "open source supply chain security" threads.
I can't claim to be an expert and don't maintain any important FOSS stuff, but I do release almost all of my code under open licenses, and I do use many open source libraries, and I have felt the pain of needing to replace an unmaintained library.
There's a certain small-to-mid-scale class of program, including many open-source libraries, which can be built/maintained by a single person, and which to my mind best operate on a "snake growth" model: incremental changes/fixes, punctuated by periodic "skin-shedding" phases where make rewrites or version updates happen. These projects aren't immortal either: as the whole tech landscape around them changes, they become unnecessary and/or people lose interest, so they go unmaintained and eventually break. Each time one of their dependencies breaks (or has a skin-shedding moment) there's a higher probability that they break or shed too, as maintenance needs shoot up at these junctures. Unless you're a company trying to make money from a single long-lived app, it's actually okay that software churns like this, and if you're a company trying to make money, your priorities absolutely should not factor into any decisions people making FOSS software make: we're trying (and to a huge extent succeeding) to make a better world (and/or just have fun with our own hobbies share that fun with others) that leaves behind the corrosive & planet-destroying plague which is capitalism, and you're trying to personally enrich yourself by embracing that plague. The fact that capitalism is *evil* is not an incidental thing in this discussion.
To make an imperfect analogy, imagine that the peasants of some domain have set up a really-free-market, where they provide each other with free stuff to help each other survive, sometimes doing some barter perhaps but mostly just everyone bringing their surplus. Now imagine the lord of the domain, who is the source of these peasants' immiseration, goes to this market secretly & takes some berries, which he uses as one ingredient in delicious tarts that he then sells for profit. But then the berry-bringer stops showing up to the free market, or starts bringing a different kind of fruit, or even ends up bringing rotten berries by accident. And the lord complains "I have a supply chain problem!" Like, fuck off dude! Your problem is that you *didn't* want to build a supply chain and instead thought you would build your profit-focused business in other people's free stuff. If you were paying the berry-picker, you'd have a supply chain problem, but you weren't, so you really have an "I want more free stuff" problem when you can't be arsed to give away your own stuff for free.
There can be all sorts of problems in the really-free-market, like maybe not enough people bring socks, so the peasants who can't afford socks are going barefoot, and having foot problems, and the peasants put their heads together and see if they can convince someone to start bringing socks, and maybe they can't and things are a bit sad, but the really-free-market was never supposed to solve everyone's problems 100% when they're all still being squeezed dry by their taxes: until they are able to get free of the lord & start building a lovely anarchist society, the really-free-market is a best-effort kind of deal that aims to make things better, and sometimes will fall short. When it becomes the main way goods in society are distributed, and when the people who contribute aren't constantly drained by the feudal yoke, at that point the availability of particular goods is a real problem that needs to be solved, but at that point, it's also much easier to solve. And at *no* point does someone coming into the market to take stuff only to turn around and sell it deserve anything from the market or those contributing to it. They are not a supply chain. They're trying to help each other out, but even then they're doing so freely and without obligation. They might discuss amongst themselves how to better coordinate their mutual aid, but they're not going to end up forcing anyone to bring anything or even expecting that a certain person contribute a certain amount, since the whole point is that the thing is voluntary & free, and they've all got changing life circumstances that affect their contributions. Celebrate whatever shows up at the market, express your desire for things that would be useful, but don't impose a burden on anyone else to bring a specific thing, because otherwise it's fair for them to oppose such a burden on you, and now you two are doing your own barter thing that's outside the parameters of the really-free-market.

Towards Understanding Decision Problems As a Goal of Visualization Design
Lena Cibulski, Stefan Bruckner
https://arxiv.org/abs/2507.18428 https://arxiv.org…

Towards Understanding Decision Problems As a Goal of Visualization Design
Decision-making is a central yet under-defined goal in visualization research. While existing task models address decision processes, they often neglect the conditions framing a decision. To better support decision-making tasks, we propose a characterization scheme that describes decision problems through key properties of the data, users, and task context. This scheme helps visualization researchers specify decision-support claims more precisely and informs the design of appropriate visual enc…

A $C^0$ weak Galerkin method with preconditioning for constrained optimal control problems with general tracking
SeongHee Jeong, Seulip Lee, Kening Wang
https://arxiv.org/abs/2506.17619

A $C^0$ weak Galerkin method with preconditioning for constrained optimal control problems with general tracking
This paper presents a $C^0$ weak Galerkin ($C^0$-WG) method combined with an additive Schwarz preconditioner for solving optimal control problems (OCPs) governed by partial differential equations with general tracking cost functionals and pointwise state constraints. These problems pose significant analytical and numerical challenges due to the presence of fourth-order variational inequalities and the reduced regularity of solutions. Our first contribution is the design of a $C^0$-WG method bas…

Comparative Evaluation of PyTorch, JAX, SciPy, and Neal for Solving QUBO Problems at Scale
Pei-Kun Yang
https://arxiv.org/abs/2507.17770 https://arxiv.org/…

Comparative Evaluation of PyTorch, JAX, SciPy, and Neal for Solving QUBO Problems at Scale
Quadratic Unconstrained Binary Optimization (QUBO) is a versatile framework for modeling combinatorial optimization problems. This study benchmarks five software-based QUBO solvers: Neal, PyTorch (CPU), PyTorch (GPU), JAX, and SciPy, on randomly generated QUBO matrices ranging from 1000x1000 to 45000x45000, under six convergence thresholds from 10^-1 to 10^-6. We evaluate their performance in terms of solution quality (energy) and computational time. Among the solvers tested, Neal achieved the …

Logarithmic convexity of evolution equations and application to inverse problems
S. E. Chorfi
https://arxiv.org/abs/2506.19954 https://

Logarithmic convexity of evolution equations and application to inverse problems
We review some results on the logarithmic convexity for evolution equations, a well-known method in inverse and ill-posed problems. We start with the classical case of self-adjoint operators. Then, we analyze the case of analytic semigroups. In this general case, we give an explicit estimate, which will be used to study inverse problems for initial data recovery. We illustrate our abstract result by an application to the Ornstein-Uhlenbeck equations. We discuss both analytic and non-analytic se…

130 unit tests passing; 90 regression tests passing… still choking on real-world content/end-to-end tests. FML.
(First world problems.)
(I’ll pick it up again tomorrow.)

Learning to Solve Parametric Mixed-Integer Optimal Control Problems via Differentiable Predictive Control
J\'an Boldock\'y, Shahriar Dadras Javan, Martin Gulan, Martin M\"onnigmann, J\'an Drgo\v{n}a
https://arxiv.org/abs/2506.19646

Learning to Solve Parametric Mixed-Integer Optimal Control Problems via Differentiable Predictive Control
We propose a novel approach to solving input- and state-constrained parametric mixed-integer optimal control problems using Differentiable Predictive Control (DPC). Our approach follows the differentiable programming paradigm by learning an explicit neural policy that maps control parameters to integer- and continuous-valued decision variables. This policy is optimized via stochastic gradient descent by differentiating the quadratic model predictive control objective through the closed-loop fin…

A US judge dismisses a lawsuit accusing Intel of defrauding shareholders by hiding problems in its foundry unit, news of which led to a $32B one-day stock fall (Jonathan Stempel/Reuters)
https://www.reuters.com/sustainability/boa

Spatial Regionalization: A Hybrid Quantum Computing Approach
Yunhan Chang, Amr Magdy, Federico M. Spedalieri, Ibrahim Sabek
https://arxiv.org/abs/2506.18799

Spatial Regionalization: A Hybrid Quantum Computing Approach
Quantum computing has shown significant potential to address complex optimization problems; however, its application remains confined to specific problems at limited scales. Spatial regionalization remains largely unexplored in quantum computing due to its complexity and large number of variables. In this paper, we introduce the first hybrid quantum-classical method to spatial regionalization by decomposing the problem into manageable subproblems, leveraging the strengths of both classical and …

Lean Meets Theoretical Computer Science: Scalable Synthesis of Theorem Proving Challenges in Formal-Informal Pairs
Terry Jingchen Zhang, Wenyuan Jiang, Rongchuan Liu, Yisong Wang, Junran Yang, Ning Wang, Nicole Ni, Yinya Huang, Mrinmaya Sachan
https://arxiv.org/abs/2508.15878

Lean Meets Theoretical Computer Science: Scalable Synthesis of Theorem Proving Challenges in Formal-Informal Pairs
Formal theorem proving (FTP) has emerged as a critical foundation for evaluating the reasoning capabilities of large language models, enabling automated verification of mathematical proofs at scale. However, progress has been constrained by limited datasets due to the high cost of manual curation and the scarcity of challenging problems with verified formal-informal correspondences. We propose leveraging theoretical computer science (TCS) as a scalable source of rigorous proof problems, where a…

Sequential Bayesian Design for Efficient Surrogate Construction in the Inversion of Darcy Flows
Hongji Wang, Hongqiao Wang, Jinyong Ying, Qingping Zhou
https://arxiv.org/abs/2507.17713

Sequential Bayesian Design for Efficient Surrogate Construction in the Inversion of Darcy Flows
Inverse problems governed by partial differential equations (PDEs) play a crucial role in various fields, including computational science, image processing, and engineering. Particularly, Darcy flow equation is a fundamental equation in fluid mechanics, which plays a crucial role in understanding fluid flow through porous media. Bayesian methods provide an effective approach for solving PDEs inverse problems, while their numerical implementation requires numerous evaluations of computationally …

Some of Vegas’ iconic casinos, convention centers and hotels
— and thousands of households across the city, too
— are using the sun to save money and better the planet’s odds at tackling climate change.
https://www.nytimes…

50 States, 50 Fixes
A series about local solutions, and the people behind them, to environmental problems.

Bin wieder hier! I'm back here!
All problems solved. Still glad to have a second home over at tldr.nettime.org. Mucho thanks to the people who do all the hosting work to make a comfy home for us here in the mastodon wilds!

"The Art of Solving Impossible Problems" @ Katina Magazine: https://katinamagazine.org/content/article/future-of-work/2025/the-art-of-solving-impossible-problems
"Sometimes the best way to solve a problem is by ad…

Hierarchical Finite-Element Analysis of Multiscale Electromagnetic Problems via Sparse Operator-Adapted Wavelet Decomposition
F. \c{S}{\i}k, F. L. Teixeira, B. Shanker
https://arxiv.org/abs/2507.17989 …

Hierarchical Finite-Element Analysis of Multiscale Electromagnetic Problems via Sparse Operator-Adapted Wavelet Decomposition
In this paper, we present a finite element method (FEM) framework enhanced by an operator-adapted wavelet decomposition algorithm designed for the efficient analysis of multiscale electromagnetic problems. Usual adaptive FEM approaches, while capable of achieving the desired accuracy without requiring a complete re-meshing of the computational domain, inherently couple different resolution levels. This coupling requires recomputation of coarser-level solutions whenever finer details are added t…

'The U.S. Cannot Solve All the World's Problems' (Nicholas Kristof/New York Times)
https://www.nytimes.com/2025/06/25/opinion/american-aid-africa.html
http://www.memeorandum.com/250626/p7#a250626p7

A comparison principle for variational problems : with an application to optimal transport
Flavien L\'eger, Maxime Sylvestre
https://arxiv.org/abs/2506.18884

A comparison principle for variational problems : with an application to optimal transport
We study variational problems on Banach spaces which involve submodular energies. We extend the notion of exchangeability to this infinite dimensional setting and show that it is in duality with submodularity. These two notions allow us to derive comparison principle in an abstract fashion. We apply our results to the optimal transport and entropic optimal transport problems. We then derive comparison principles on the Kantorovich and Schrödinger potentials. We also prove comparison principles…

Some interesting number theory problems
Wenpeng Zhang
https://arxiv.org/abs/2506.17235 https://arxiv.org/pdf/2506.17235

Some interesting number theory problems
The main purpose of this paper is to propose some interesting number theory problems related to the Legendre's symbol and the two-term exponential sums.

"Solar panels in space ‘could provide 80% of Europe’s renewable energy by 2050’"
#SolarPower #energy #Renewables

I for one welcome our new nose-robot overlords 🤖 🤧
https://www.theguardian.com/science/2025/jun/25/swarms-of-tiny-nose-robots-could-clear-infected-sinuses-researchers-say

Efficient Neural Network Verification via Order Leading Exploration of Branch-and-Bound Trees
Guanqin Zhang, Kota Fukuda, Zhenya Zhang, H. M. N. Dilum Bandara, Shiping Chen, Jianjun Zhao, Yulei Sui
https://arxiv.org/abs/2507.17453

Efficient Neural Network Verification via Order Leading Exploration of Branch-and-Bound Trees
The vulnerability of neural networks to adversarial perturbations has necessitated formal verification techniques that can rigorously certify the quality of neural networks. As the state-of-the-art, branch and bound (BaB) is a "divide-and-conquer" strategy that applies off-the-shelf verifiers to sub-problems for which they perform better. While BaB can identify the sub-problems that are necessary to be split, it explores the space of these sub-problems in a naive "first-come-first-serve" manner…

We have long had problems with slumlords in the US.
And we have long had codes related to habitability standards in residential buildings.
What #MayorLurie could do is direct the Dept of Public Health and Dept of building inspection to review these codes, and perhaps even more importantly what the penalties are for non-compliance, and work with the departments and if needed state …

Mayor Lurie makes marathon visits to S.F. low-income housing. But what can he do?
Mayor Lurie visited two neighborhoods and six subsidized housing complexes over the past month. Tenants are hoping for change.

We have long had problems with slumlords in the US.
And we have long had codes related to habitability standards in residential buildings.
What #MayorLurie could do is direct the Dept of Public Health and Dept of building inspection to review these codes, and perhaps even more importantly what the penalties are for non-compliance, and work with the departments and if needed state …

Mayor Lurie makes marathon visits to S.F. low-income housing. But what can he do?
Mayor Lurie visited two neighborhoods and six subsidized housing complexes over the past month. Tenants are hoping for change.

Was the almost endless protection of "exercise of religion" and the now almost dead "establishment of religion" clauses in our First Amendment a mistake?
I think it is.
We have seen and are seeing the extremes of fundamentalist religion: Al Queda, ISIS, MAGA, etc
Israel has its own fundamentalist problems too. (Link below).
It has been said "never let a good crisis go to waste". Well, we certainly have several good crises going on.

As Other Israelis Die in War, Ultra-Orthodox Resist Call to Fight
Ultra-Orthodox Israelis, exempt for decades from military service, are now being drafted. Their rage is dividing Israel and threatening Prime Minister Benjamin Netanyahu’s coalition.

Polynomial-Time Approximation Schemes via Utility Alignment: Unit-Demand Pricing and More
Robin Bowers, Marius Garbea, Emmanouil Pountourakis, Samuel Taggart
https://arxiv.org/abs/2506.20030

Polynomial-Time Approximation Schemes via Utility Alignment: Unit-Demand Pricing and More
This paper derives polynomial-time approximation schemes for several NP-hard stochastic optimization problems from the algorithmic mechanism design and operations research literatures. The problems we consider involve a principal or seller optimizing with respect to a subsequent choice by an agent or buyer. These include posted pricing for a unit-demand buyer with independent values (Chawla et al., 2007, Cai and Daskalakis, 2011), assortment optimization with independent utilities (Talluri and …

interesting, from around 10:00 there is large scale internet/mobile network connectivity problems in the netherlands: #nato

LeanGeo: Formalizing Competitional Geometry problems in Lean
Chendong Song, Zihan Wang, Frederick Pu, Haiming Wang, Xiaohan Lin, Junqi Liu, Jia Li, Zhengying Liu
https://arxiv.org/abs/2508.14644

LeanGeo: Formalizing Competitional Geometry problems in Lean
Geometry problems are a crucial testbed for AI reasoning capabilities. Most existing geometry solving systems cannot express problems within a unified framework, thus are difficult to integrate with other mathematical fields. Besides, since most geometric proofs rely on intuitive diagrams, verifying geometry problems is particularly challenging. To address these gaps, we introduce LeanGeo, a unified formal system for formalizing and solving competition-level geometry problems within the Lean 4 …

Solution to some conjectures on mobile position problems
Ethan Shallcross, James Tuite, Aoise Evans, Aditi Krishnakumar, Sumaiyah Boshar
https://arxiv.org/abs/2507.16622

Solution to some conjectures on mobile position problems
The general position problem for graphs asks for the largest number of vertices in a subset $S \subseteq V(G)$ of a graph $G$ such that for any $u,v \in S$ and any shortest $u,v$-path $P$ we have $S \cap V(P) = \{ u,v\} $, whereas the mutual visibility problem requires only that for any $u,v \in S$ there exists a shortest $u,v$-path with $S \cap V(P) = \{ u,v\} $. In the mobile versions of these problems, robots must move through the network in general position/mutual visibility such that every…

Physics-Driven Neural Network for Solving Electromagnetic Inverse Scattering Problems
Yutong Du, Zicheng Liu, Bazargul Matkerim, Changyou Li, Yali Zong, Bo Qi, Jingwei Kou
https://arxiv.org/abs/2507.16321

Physics-Driven Neural Network for Solving Electromagnetic Inverse Scattering Problems
In recent years, deep learning-based methods have been proposed for solving inverse scattering problems (ISPs), but most of them heavily rely on data and suffer from limited generalization capabilities. In this paper, a new solving scheme is proposed where the solution is iteratively updated following the updating of the physics-driven neural network (PDNN), the hyperparameters of which are optimized by minimizing the loss function which incorporates the constraints from the collected scattered…

Has anyone else come across the #BT outage? We need to ring the hospital to cancel an appt but the lines are down and now this.

Generalized Eshelby's inclusion and inhomogeneity problems for transient heat transfer
Chunlin Wu, Zhenhua Wei, Huiming Yin
https://arxiv.org/abs/2506.16498

Generalized Eshelby's inclusion and inhomogeneity problems for transient heat transfer
Eshelby's problems have been generalized to arbitrary shape of polygonal, polyhedral, and ellipsoidal inclusions embedded in an infinite isotropic domain under transient heat transfer, and Eshelby's tensors have been analytically derived to evaluate disturbed thermal fields caused by inclusions with a polynomial-form eigen-fields. Transformed coordinates are applied to arbitrarily shaped inclusions for domain integrals of transient fundamental solutions. This formulation is for general transien…

Smoothed Analysis of Online Metric Problems
Christian Coester, Jack Umenberger
https://arxiv.org/abs/2507.17834 https://arxiv.org/pdf/2507.17834

Smoothed Analysis of Online Metric Problems
We study three classical online problems -- $k$-server, $k$-taxi, and chasing size $k$ sets -- through a lens of smoothed analysis. Our setting allows request locations to be adversarial up to small perturbations, interpolating between worst-case and average-case models. Specifically, we show that if the metric space is contained in a ball in any normed space and requests are drawn from distributions whose density functions are upper bounded by $1/σ$ times the uniform density over the ball, th…

( \(2^{nd}\) announcement)
The #Springer Problem Book for the Indiana College Mathematics Competition (2001-2023) is now available in a (slightly less expensive) softcover format! This book, edited by me, J. Gash, R. Gillman, and @… , can be used by stu…

The Indiana College Mathematics Competition (2001⁠–2023)
This book gathers problems based on over twenty years of the Indiana College Mathematics Competition, a contest for teams of undergraduates.

When I send #Wordle my guesses, I’m not sending my best. They’re guesses that have lots of problems. They’re bringing weird letters. They’re bringing awkward phonemes. They’re statistically terrible. And some, I assume, are good guesses.
#Wordle1466 5/6*
⬜⬜🟨⬜🟨
🟨🟨⬜🟨⬜
⬜⬜🟩🟩🟩
🟩⬜🟩🟩🟩

Solution of Least Squares Problems with Randomized Preconditioned Normal Equations
Ilse C. F. Ipsen
https://arxiv.org/abs/2507.18466 https://arxiv.org/pdf/…

Solution of Least Squares Problems with Randomized Preconditioned Normal Equations
We consider the solution of full column-rank least squares problems by means of normal equations that are preconditioned, symmetrically or non-symmetrically, with a randomized preconditioner. With an effective preconditioner, the solutions from the preconditioned normal equations are almost as accurate as those from the QR-based Matlab backslash (mldivide) command -- even for highly illconditioned matrices. This means the accuracy of the preconditioned normal equations depends on the residual o…

A Common Pool of Privacy Problems: Legal and Technical Lessons from a Large-Scale Web-Scraped Machine Learning Dataset
Rachel Hong, Jevan Hutson, William Agnew, Imaad Huda, Tadayoshi Kohno, Jamie Morgenstern
https://arxiv.org/abs/2506.17185

A Common Pool of Privacy Problems: Legal and Technical Lessons from a Large-Scale Web-Scraped Machine Learning Dataset
We investigate the contents of web-scraped data for training AI systems, at sizes where human dataset curators and compilers no longer manually annotate every sample. Building off of prior privacy concerns in machine learning models, we ask: What are the legal privacy implications of web-scraped machine learning datasets? In an empirical study of a popular training dataset, we find significant presence of personally identifiable information despite sanitization efforts. Our audit provides concr…

FTIO: Frequent Temporally Integrated Objects
Mohammad Mohammadzadeh Kalati, Farhad Maleki, Ian McQuillan
https://arxiv.org/abs/2508.16183 https://arxiv.org…

FTIO: Frequent Temporally Integrated Objects
Predicting and tracking objects in real-world scenarios is a critical challenge in Video Object Segmentation (VOS) tasks. Unsupervised VOS (UVOS) has the additional challenge of finding an initial segmentation of salient objects, which affects the entire process and keeps a permanent uncertainty about the object proposals. Moreover, deformation and fast motion can lead to temporal inconsistencies. To address these problems, we propose Frequent Temporally Integrated Objects (FTIO), a post-proces…

Synthesizing DSLs for Few-Shot Learning
Paul Krogmeier, P. Madhusudan
https://arxiv.org/abs/2508.16063 https://arxiv.org/pdf/2508.16063

Synthesizing DSLs for Few-Shot Learning
We study the problem of synthesizing domain-specific languages (DSLs) for few-shot learning in symbolic domains. Given a base language and instances of few-shot learning problems, where each instance is split into training and testing samples, the DSL synthesis problem asks for a grammar over the base language that guarantees that small expressions solving training samples also solve corresponding testing samples. We prove that the problem is decidable for a class of languages whose semantics o…

Yes, I know it's a shit-hole.
But in the last days I found a solution to 2 pretty challenging problems. One, how to get to a samba share from within VoidLinux (no, the standard ones didn't work, and I run a wm).
Most importantly: looks like the 'open an application on a specific tag and switch focus to that on River wm' issue has been finally cracked!
Both solutions I found on Reddit.
Yes, Reddit, that cesspool of nonsense.
Imagine how good it coul…

Convergent Proximal Multiblock ADMM for Nonconvex Dynamics-Constrained Optimization
Bowen Li, Ya-xiang Yuan
https://arxiv.org/abs/2506.17405 https://

Convergent Proximal Multiblock ADMM for Nonconvex Dynamics-Constrained Optimization
This paper proposes a provably convergent multiblock ADMM for nonconvex optimization with nonlinear dynamics constraints, overcoming the divergence issue in classical extensions. We consider a class of optimization problems that arise from discretization of dynamics-constrained variational problems that are optimization problems for a functional constrained by time-dependent ODEs or PDEs. This is a family of $n$-sum nonconvex optimization problems with nonlinear constraints. We study the conver…

Open problems in ageing science: A roadmap for biogerontology
Angelo Talay, Aleksey V. Belikov, Paul Ka Po To, Hamid H. Alfatemi, Uri Alon, Joris Deelen, Collin Y. Ewald, David Gems, Vera Gorbunova, Jan Gruber, Sara H\"agg, John Hemming, Steve Horvath, Alaattin Kaya, Caitlin J. Lewis, Andrea Maier, Maria B Marinova, Graham Pawelec, Shahaf Peleg, Suresh Rattan, Morten Scheibye-Knudsen, Tomas Schmauck-Medina, Vardan Saroyan, Andrei Seluanov, Alexandra Stolzing, Emma Teeling, Robert …

Open problems in ageing science: A roadmap for biogerontology
The field of ageing science has gone through remarkable progress in recent decades, yet many fundamental questions remain unanswered or unexplored. Here we present a curated list of 100 open problems in ageing and longevity science. These questions were collected through community engagement and further analysed using Natural Language Processing to assess their prevalence in the literature and to identify both well-established and emerging research gaps. The final list is categorized into diffe…

Lost in Translation? Converting RegExes for Log Parsing into Dynatrace Pattern Language
Julian Fragner, Christian Macho, Bernhard Dieber, Martin Pinzger
https://arxiv.org/abs/2506.19539

Lost in Translation? Converting RegExes for Log Parsing into Dynatrace Pattern Language
Log files provide valuable information for detecting and diagnosing problems in enterprise software applications and data centers. Several log analytics tools and platforms were developed to help filter and extract information from logs, typically using regular expressions (RegExes). Recent commercial log analytics platforms provide domain-specific languages specifically designed for log parsing, such as Grok or the Dynatrace Pattern Language (DPL). However, users who want to migrate to these p…

Integrating Maneuverable Planning and Adaptive Control for Robot Cart-Pushing under Disturbances
Zhe Zhang, Peijia Xie, Zhirui Sun, Bingyi Xia, Bi-Ke Zhu, Jiankun Wang
https://arxiv.org/abs/2506.18410

Integrating Maneuverable Planning and Adaptive Control for Robot Cart-Pushing under Disturbances
Precise and flexible cart-pushing is a challenging task for mobile robots. The motion constraints during cart-pushing and the robot's redundancy lead to complex motion planning problems, while variable payloads and disturbances present complicated dynamics. In this work, we propose a novel planning and control framework for flexible whole-body coordination and robust adaptive control. Our motion planning method employs a local coordinate representation and a novel kinematic model to solve a non…

Contact loci of semihomogeneous singularities
Eduardo de Lorenzo Poza, Jiahui Huang
https://arxiv.org/abs/2506.18805 https://arxiv.or…

Contact loci of semihomogeneous singularities
Two of the main open problems in the theory of contact loci are the arc-Floer conjecture, which states that the compactly supported cohomology of the restricted $m$-contact locus and the fixed-point Floer cohomology of the $m$-th iterate of the Milnor monodromy are isomorphic up to a shift; and the embedded Nash problem, which asks for a description of the irreducible components of the unrestricted $m$-contact locus in terms of an embedded resolution of singularities. In this paper we study the…

Gauging practical computational advantage using a classical, threshold-based Gaussian boson sampler
Sarvesh Raghuraman, Aditya Patwardhan, Brian La Cour
https://arxiv.org/abs/2507.17567

Gauging practical computational advantage using a classical, threshold-based Gaussian boson sampler
We describe an efficient, scalable Gaussian boson sampler based on a classical description of squeezed quantum light and a deterministic model of single-photon detectors that click when the incident amplitude falls above a given threshold. Using this model, we map several NP-Complete graph theoretic problems to equivalent Gaussian boson sampling problems and numerically explore the practical efficacy of our approach. Specifically, for a given weighted, undirected graph we examined finding the d…

Diophantine approximation on abelian varieties; a conjecture of M. Waldschmidt
Lior Fishman, David Lambert, Keith Merrill, David Simmons
https://arxiv.org/abs/2506.19060

Diophantine approximation on abelian varieties; a conjecture of M. Waldschmidt
Following the work of Waldschmidt, we investigate problems in Diophantine approximation on abelian varieties. First we show that a conjecture of Waldschmidt for a given simple abelian variety is equivalent to a well-known Diophantine condition holding for a certain matrix related to that variety. We then posit a related but weaker conjecture, and establish the upper bound direction of that conjecture in full generality. For rank 1 elliptic curves defined over a number field $K \subset \mathbb{R…

"Ultra fast fashion could be taxed to oblivion in France. Could Australia follow suit?"
#FastFashion #Textiles #Clothes

Ultra fast fashion could be taxed to oblivion in France. Could Australia follow suit?
Ultra-fast fashion comes with a host of environmental problems. Australia’s response to the deluge of cheap low quality clothes hasn’t led to change.

A kernel-free boundary integral method for elliptic interface problems on surfaces
Pengsong Yin, Wenjun YIng, Yulin Zhang, Han Zhou
https://arxiv.org/abs/2508.16061 https://

A kernel-free boundary integral method for elliptic interface problems on surfaces
This work presents a generalized boundary integral method for elliptic equations on surfaces, encompassing both boundary value and interface problems. The method is kernel-free, implying that the explicit analytical expression of the kernel function is not required when solving the boundary integral equations. The numerical integration of single- and double-layer potentials or volume integrals at the boundary is replaced by interpolation of the solution to an equivalent interface problem, which…

Quality control in sublinear time: a case study via random graphs
Cassandra Marcussen, Ronitt Rubinfeld, Madhu Sudan
https://arxiv.org/abs/2508.16531 https://

Quality control in sublinear time: a case study via random graphs
Many algorithms are designed to work well on average over inputs. When running such an algorithm on an arbitrary input, we must ask: Can we trust the algorithm on this input? We identify a new class of algorithmic problems addressing this, which we call "Quality Control Problems." These problems are specified by a (positive, real-valued) "quality function" $ρ$ and a distribution $D$ such that, with high probability, a sample drawn from $D$ is "high quality," meaning its $ρ$-value is near $1$.…

Carleman estimate with piecewise weight and applications to inverse problems for first-order transport equations
P. Cannarsa, G. Floridia, M. Yamamoto
https://arxiv.org/abs/2507.17675

Carleman estimate with piecewise weight and applications to inverse problems for first-order transport equations
We consider a first-order transport equation $\ppp_tu(x,t) + (H(x)\cdot\nabla u(x,t)) + p(x)u(x,t) = F(x,t)$ for $x \in \OOO \subset \R^d$, where $\OOO$ is a bounded domain and $0

General Proximal Quasi-Newton Methods based on model functions for nonsmooth nonconvex problems
Xiaoxi Jia, Peter Ochs
https://arxiv.org/abs/2507.18363 https://

General Proximal Quasi-Newton Methods based on model functions for nonsmooth nonconvex problems
In this manuscript, we propose a general proximal quasi-Newton method tailored for nonconvex and nonsmooth optimization problems, where we do not require the sequence of the variable metric (or Hessian approximation) to be uniformly bounded as a prerequisite, instead, the variable metric is updated by a continuous matrix generator. From the respective of the algorithm, the objective function is approximated by the so-called local model function and subproblems aim to exploit the proximal point(…

Novel Multi-Agent Action Masked Deep Reinforcement Learning for General Industrial Assembly Lines Balancing Problems
Ali Mohamed Ali, Luca Tirel, Hashim A. Hashim
https://arxiv.org/abs/2507.16635

Novel Multi-Agent Action Masked Deep Reinforcement Learning for General Industrial Assembly Lines Balancing Problems
Efficient planning of activities is essential for modern industrial assembly lines to uphold manufacturing standards, prevent project constraint violations, and achieve cost-effective operations. While exact solutions to such challenges can be obtained through Integer Programming (IP), the dependence of the search space on input parameters often makes IP computationally infeasible for large-scale scenarios. Heuristic methods, such as Genetic Algorithms, can also be applied, but they frequently …

$\ell_{1}^{2}-\eta\ell_{2}^{2}$ sparsity regularization for nonlinear ill-posed problems
Long Li, Liang Ding
https://arxiv.org/abs/2508.16163 https://arxiv…

$\ell_{1}^{2}-η\ell_{2}^{2}$ sparsity regularization for nonlinear ill-posed problems
In this study, we investigate the $\left\|\cdot\right\|_{\ell_{1}}^{2}-η\left\|\cdot\right\|_{\ell_{2}}^{2}$ sparsity regularization with $0< η\leq 1$, in the context of nonlinear ill-posed inverse problems. We focus on the examination of the well-posedness associated with this regularization approach. Notably, the case where $η=1$ presents weaker theoretical outcomes than $0< η<1$, primarily due to the absence of coercivity and the Radon-Riesz property associated with t…

Partitioning to solve Bin Packing Problems
Angshuman Robin Goswami
https://arxiv.org/abs/2508.15780 https://arxiv.org/pdf/2508.15780

Partitioning to solve Bin Packing Problems
The Bin Packing Problem involves efficiently packing items into a limited number of bins without exceeding their capacity. In this paper, we try to answer a specific question in this field. Mathematically the combinatorial optimization problem of this classical Bin Packing can be formulated as follows "Will it be possible to distribute $n$ items with sizes $a_1, \cdots ,a_n$ in total $k$ numbers of bins such that each of the bins consists of exactly $\ell$ number of items whose combined item …

Structural Optimal Jacobian Accumulation and Minimum Edge Count are NP-Complete Under Vertex Elimination
Matthias Bentert, Alex Crane, P{\aa}l Gr{\o}n{\aa}s Drange, Yosuke Mizutani, Blair D. Sullivan
https://arxiv.org/abs/2506.17521

Structural Optimal Jacobian Accumulation and Minimum Edge Count are NP-Complete Under Vertex Elimination
We study graph-theoretic formulations of two fundamental problems in algorithmic differentiation. The first (Structural Optimal Jacobian Accumulation) is that of computing a Jacobian while minimizing multiplications. The second (Minimum Edge Count) is to find a minimum-size computational graph. For both problems, we consider the vertex elimination operation. Our main contribution is to show that both problems are NP-complete, thus resolving longstanding open questions. In contrast to prior work…

On using AI for EEG-based BCI applications: problems, current challenges and future trends
Thomas Barbera, Jacopo Burger, Alessandro D'Amelio, Simone Zini, Simone Bianco, Raffaella Lanzarotti, Paolo Napoletano, Giuseppe Boccignone, Jose Luis Contreras-Vidal
https://arxiv.org/abs/2506.16168

On using AI for EEG-based BCI applications: problems, current challenges and future trends
Imagine unlocking the power of the mind to communicate, create, and even interact with the world around us. Recent breakthroughs in Artificial Intelligence (AI), especially in how machines "see" and "understand" language, are now fueling exciting progress in decoding brain signals from scalp electroencephalography (EEG). Prima facie, this opens the door to revolutionary brain-computer interfaces (BCIs) designed for real life, moving beyond traditional uses to envision Brain-to-Speech, Brain-to-…

On Tur\'{a}n problems for Berge forests
Junpeng Zhou, D\'aniel Gerbner, Xiying Yuan
https://arxiv.org/abs/2506.16140 https://…

On Turán problems for Berge forests
For a graph $F$, an $r$-uniform hypergraph $H$ is a Berge-$F$ if there is a bijection $ϕ:E(F)\rightarrow E(H)$ such that $e\subseteq ϕ(e)$ for each $e\in E(F)$. Given a family $\mathcal{F}$ of $r$-uniform hypergraphs, an $r$-uniform hypergraph is $\mathcal{F}$-free if it does not contain any member in $\mathcal{F}$ as a subhypergraph. The Turán number of $\mathcal{F}$ is the maximum number of hyperedges in an $\mathcal{F}$-free $r$-uniform hypergraph on $n$ vertices. In this paper, some exac…

On circumcentered direct methods for monotone variational inequality problems
Roger Behling, Yunier Bello-Cruz, Alfredo Iusem, Di Liu, Luiz-Rafael Santos
https://arxiv.org/abs/2506.17814

On circumcentered direct methods for monotone variational inequality problems
The variational inequality problem (VIP) plays a central role in the theory and applications in continuous optimization. In particular, minimization problems and KKT systems can be regard as VIPs. In this work, we present the first methods using circumcenter iterations for solving VIPs. The circumcentered-reflection method (CRM) is a tool based on projections developed with the aim of finding a point in the intersection of finitely many closed convex sets. CRM has gone through enhancements and …

Uppaal Coshy: Automatic Synthesis of Compact Shields for Hybrid Systems
Asger Horn Brorholt, Andreas Holck H{\o}eg-Petersen, Peter Gj{\o}l Jensen, Kim Guldstrand Larsen, Marius Miku\v{c}ionis, Christian Schilling, Andrzej W\k{a}sowski
https://arxiv.org/abs/2508.16345

Uppaal Coshy: Automatic Synthesis of Compact Shields for Hybrid Systems
We present Uppaal Coshy, a tool for automatic synthesis of a safety strategy -- or shield -- for Markov decision processes over continuous state spaces and complex hybrid dynamics. The general methodology is to partition the state space and then solve a two-player safety game, which entails a number of algorithmically hard problems such as reachability for hybrid systems. The general philosophy of Uppaal Coshy is to approximate hard-to-obtain solutions using simulations. Our implementation is f…

Comparative Evaluation of PyTorch, JAX, SciPy, and Neal for Solving QUBO Problems at Scale
Pei-Kun Yang
https://arxiv.org/abs/2507.17770 https://arxiv.org/…

Comparative Analysis of UAV Path Planning Algorithms for Efficient Navigation in Urban 3D Environments
Hichem Cheriet, Khellat Kihel Badra, Chouraqui Samira
https://arxiv.org/abs/2508.16515

Comparative Analysis of UAV Path Planning Algorithms for Efficient Navigation in Urban 3D Environments
The most crucial challenges for UAVs are planning paths and avoiding obstacles in their way. In recent years, a wide variety of path-planning algorithms have been developed. These algorithms have successfully solved path-planning problems; however, they suffer from multiple challenges and limitations. To test the effectiveness and efficiency of three widely used algorithms, namely A*, RRT*, and Particle Swarm Optimization (PSO), this paper conducts extensive experiments in 3D urban city environ…

Spectral density estimates of surface-localized eigenmodes for transmission eigenvalue problems
Yan Jiang, Hongyu Liu, Kai Zhang, Haoran Zheng
https://arxiv.org/abs/2508.16203 h…

Spectral density estimates of surface-localized eigenmodes for transmission eigenvalue problems
This paper investigates a distinctive spectral pattern exhibited by transmission eigenfunctions in wave scattering theory. Building upon the discovery in [7, 8] that these eigenfunctions localize near the domain boundary, we derive sharp spectral density estimates--establishing both lower and upper bounds--to demonstrate that a significant proportion of transmission eigenfunctions manifest this surface-localizing behavior. Our analysis elucidates the connection between the geometric rigidity of…

How Do Code Smells Affect Skill Growth in Scratch Novice Programmers?
Ricardo Hidalgo Arag\'on, Jes\'us M. Gonz\'alez-Barahona, Gregorio Robles
https://arxiv.org/abs/2507.17314

How Do Code Smells Affect Skill Growth in Scratch Novice Programmers?
Context. Code smells, which are recurring anomalies in design or style, have been extensively researched in professional code. However, their significance in block-based projects created by novices is still largely unknown. Block-based environments such as Scratch offer a unique, data-rich setting to examine how emergent design problems intersect with the cultivation of computational-thinking (CT) skills. Objective. This research explores the connection between CT proficiency and design-level c…

Exact penalty functions and global saddle points of augmented Lagrangians for well-posed constrained optimization problems
M. V. Dolgopolik
https://arxiv.org/abs/2508.16462 http…

Exact penalty functions and global saddle points of augmented Lagrangians for well-posed constrained optimization problems
The goal of this article is to study necessary and sufficient conditions for the exactness of penalty functions and the existence of global saddle points of augmented Lagrangians for well-posed (in a suitable sense) constrained optimization problems in infinite dimensional spaces. To this end, we present a new version of extended well-posedness of a constrained optimization problem and analyse how it relates to the more well-known types of well-posedness, such as Tykhonov and Levitin-Polyak wel…

GLARE: Agentic Reasoning for Legal Judgment Prediction
Xinyu Yang, Chenlong Deng, Zhicheng Dou
https://arxiv.org/abs/2508.16383 https://arxiv.org/pdf/2508.…

GLARE: Agentic Reasoning for Legal Judgment Prediction
Legal judgment prediction (LJP) has become increasingly important in the legal field. In this paper, we identify that existing large language models (LLMs) have significant problems of insufficient reasoning due to a lack of legal knowledge. Therefore, we introduce GLARE, an agentic legal reasoning framework that dynamically acquires key legal knowledge by invoking different modules, thereby improving the breadth and depth of reasoning. Experiments conducted on the real-world dataset verify the…

ZORMS-LfD: Learning from Demonstrations with Zeroth-Order Random Matrix Search
Olivia Dry, Timothy L. Molloy, Wanxin Jin, Iman Shames
https://arxiv.org/abs/2507.17096

ZORMS-LfD: Learning from Demonstrations with Zeroth-Order Random Matrix Search
We propose Zeroth-Order Random Matrix Search for Learning from Demonstrations (ZORMS-LfD). ZORMS-LfD enables the costs, constraints, and dynamics of constrained optimal control problems, in both continuous and discrete time, to be learned from expert demonstrations without requiring smoothness of the learning-loss landscape. In contrast, existing state-of-the-art first-order methods require the existence and computation of gradients of the costs, constraints, dynamics, and learning loss with re…

A Computationally Efficient Method for Solving Mixed-Integer AC Optimal Power Flow Problems
Johannes Heid, Nils Bornhorst, Eric T\"onges, Philipp H\"artel, Denis Mende, Martin Braun
https://arxiv.org/abs/2506.18301

A Computationally Efficient Method for Solving Mixed-Integer AC Optimal Power Flow Problems
Stepwise controllable devices, such as switched capacitors or stepwise controllable loads and generators, transform the nonconvex AC optimal power flow (AC-OPF) problem into a nonconvex mixed-integer (MI) programming problem which is generally hard to solve optimally. Existing methods for solving MI-AC-OPF problems usually suffer from either limited accuracy or computational intractability, making them impractical for real-world applications. To address these challenges, we propose an efficient…

A Reduction of Input/Output Logics to SAT
Alexander Steen
https://arxiv.org/abs/2508.16242 https://arxiv.org/pdf/2508.16242

A Reduction of Input/Output Logics to SAT
Deontic logics are formalisms for reasoning over norms, obligations, permissions and prohibitions. Input/Output (I/O) Logics are a particular family of so-called norm-based deontic logics that formalize conditional norms outside of the underlying object logic language, where conditional norms do not carry a truth-value themselves. In this paper, an automation approach for I/O logics is presented that makes use of suitable reductions to (sequences of) propositional satisfiability problems. A pro…

Notes on sum-free sets in abelian groups
Nathana\"el Hassler, Andrew Treglown
https://arxiv.org/abs/2506.17401 https://arxiv.org…

Notes on sum-free sets in abelian groups
In this paper we highlight a few open problems concerning maximal sum-free sets in abelian groups. In addition, for most even order abelian groups $G$ we asymptotically determine the number of maximal distinct sum-free subsets in $G$. Our proof makes use of the container method.

Quantum-Enhanced Optimization by Warm Starts
Ieva \v{C}epait\.e, Niam Vaishnav, Leo Zhou, Ashley Montanaro
https://arxiv.org/abs/2508.16309 https://arxiv.o…

Quantum-Enhanced Optimization by Warm Starts
We present an approach, which we term quantum-enhanced optimization, to accelerate classical optimization algorithms by leveraging quantum sampling. Our method uses quantum-generated samples as warm starts to classical heuristics for solving challenging combinatorial problems like Max-Cut and Maximum Independent Set (MIS). To implement the method efficiently, we introduce novel parameter-setting strategies for the Quantum Approximate Optimization Algorithm (QAOA), qubit mapping and routing tech…

Implementation of the inverse scattering transform method for the nonlinear Schr\"odinger equation
Vladislav V. Kravchenko
https://arxiv.org/abs/2507.18586 https://

Implementation of the inverse scattering transform method for the nonlinear Schrödinger equation
We study the initial-value problem for the nonlinear Schrödinger equation. Application of the inverse scattering transform method involves solving direct and inverse scattering problems for the Zakharov-Shabat system with complex potentials. We solve these problems by using new series representations for the Jost solutions of the Zakharov-Shabat system. The representations have the form of power series with respect to a transformed spectral parameter. In terms of the representations, solution …

Scattered point measurement-based regularization for backward problems for fractional wave equations
Dakang Cen, Zhiyuan Li, Wenlong Zhang
https://arxiv.org/abs/2506.17575

Scattered point measurement-based regularization for backward problems for fractional wave equations
In this work, we are devoted to the reconstruction of an unknown initial value from the terminal data. The asymptotic and root-distribution properties of Mittag-Leffler functions are used to establish stability of the backward problem. Furthermore, we introduce a regularization method that effectively handles scattered point measurements contaminated with stochastic noise. Furthermore, we prove the stochastic convergence of our proposed regularization and provide an iterative algorithm to find …

AetherCode: Evaluating LLMs' Ability to Win In Premier Programming Competitions
Zihan Wang, Jiaze Chen, Zhicheng Liu, Markus Mak, Yidi Du, Geonsik Moon, Luoqi Xu, Aaron Tua, Kunshuo Peng, Jiayi Lu, Mingfei Xia, Boqian Zou, Chenyang Ran, Guang Tian, Shoutai Zhu, Yeheng Duan, Zhenghui Kang, Zhenxing Lin, Shangshu Li, Qiang Luo, Qingshen Long, Zhiyong Chen, Yihan Xiao, Yurong Wu, Daoguang Zan, Yuyi Fu, Mingxuan Wang, Ming Ding

AetherCode: Evaluating LLMs' Ability to Win In Premier Programming Competitions
Competitive programming has emerged as a critical benchmark for evaluating the reasoning and coding capabilities of Large Language Models (LLMs). Despite impressive progress on existing benchmarks, we argue that current evaluations overstate model proficiency, masking a substantial gap between LLMs and elite human programmers. This gap arises from two key limitations: insufficient difficulty and scope of benchmark problems, and evaluation bias from low-quality test cases. To address these short…

Computing Tree Structures in Anonymous Graphs via Mobile Agents
Prabhat Kumar Chand, Manish Kumar, Anisur Rahaman Molla
https://arxiv.org/abs/2506.19365 ht…

Computing Tree Structures in Anonymous Graphs via Mobile Agents
Minimum Spanning Tree (MST) and Breadth-First Search (BFS) tree constructions are classical problems in distributed computing, traditionally studied in the message-passing model, where static nodes communicate via messages. This paper investigates MST and BFS tree construction in an agent-based network, where mobile agents explore a graph and compute. Each node hosts one agent, and communication occurs when agents meet at a node. We consider $n$ agents initially dispersed (one per node) in an a…

TRIZ Agents: A Multi-Agent LLM Approach for TRIZ-Based Innovation
Kamil Szczepanik, Jaros{\l}aw A. Chudziak
https://arxiv.org/abs/2506.18783 https://

TRIZ Agents: A Multi-Agent LLM Approach for TRIZ-Based Innovation
TRIZ, the Theory of Inventive Problem Solving, is a structured, knowledge-based framework for innovation and abstracting problems to find inventive solutions. However, its application is often limited by the complexity and deep interdisciplinary knowledge required. Advancements in Large Language Models (LLMs) have revealed new possibilities for automating parts of this process. While previous studies have explored single LLMs in TRIZ applications, this paper introduces a multi-agent approach. W…

On Zero-Shot Reinforcement Learning
Scott Jeen
https://arxiv.org/abs/2508.16496 https://arxiv.org/pdf/2508.16496 …

On Zero-Shot Reinforcement Learning
Modern reinforcement learning (RL) systems capture deep truths about general, human problem-solving. In domains where new data can be simulated cheaply, these systems uncover sequential decision-making policies that far exceed the ability of any human. Society faces many problems whose solutions require this skill, but they are often in domains where new data cannot be cheaply simulated. In such scenarios, we can learn simulators from existing data, but these will only ever be approximately cor…

Numerical analysis of scattered point measurement-based regularization for backward problems for fractional wave equations
Dakang Cen, Zhiyuan Li, Wenlong Zhang
https://arxiv.org/abs/2506.18948

Numerical analysis of scattered point measurement-based regularization for backward problems for fractional wave equations
In this work, our aim is to reconstruct the unknown initial value from terminal data. We develop a numerical framework on nonuniform time grids for fractional wave equations under the lower regularity assumptions. Then, we introduce a regularization method that effectively handles scattered point measurements contaminated with stochastic noise. The optimal error estimates of stochastic convergence not only balance discretization errors, the noise, and the number of observation points, but also …

Enhanced Image Recognition Using Gaussian Boson Sampling
Si-Qiu Gong, Ming-Cheng Chen, Hua-Liang Liu, Hao Su, Yi-Chao Gu, Hao-Yang Tang, Meng-Hao Jia, Yu-Hao Deng, Qian Wei, Hui Wang, Han-Sen Zhong, Xiao Jiang, Li Li, Nai-Le Liu, Chao-Yang Lu, Jian-Wei Pan
https://arxiv.org/abs/2506.19707

Enhanced Image Recognition Using Gaussian Boson Sampling
Gaussian boson sampling (GBS) has emerged as a promising quantum computing paradigm, demonstrating its potential in various applications. However, most existing works focus on theoretical aspects or simple tasks, with limited exploration of its capabilities in solving real-world practical problems. In this work, we propose a novel GBS-based image recognition scheme inspired by extreme learning machine (ELM) to enhance the performance of perceptron and implement it using our latest GBS device, J…

Undecidability of Translational Tiling of the Plane with Four Tiles
Chao Yang, Zhujun Zhang
https://arxiv.org/abs/2506.19295 https://…

Undecidability of Translational Tiling of the Plane with Four Tiles
The translational tiling problem, dated back to Wang's domino problem in the 1960s, is one of the most representative undecidable problems in the field of discrete geometry and combinatorics. Ollinger initiated the study of the undecidability of translational tiling with a fixed number of tiles in 2009, and proved that translational tiling of the plane with a set of $11$ polyominoes is undecidable. The number of polyominoes needed to obtain undecidability was reduced from $11$ to $7$ by Yang an…

From Logic to Language: A Trust Index for Problem Solving with LLMs
Tehseen Rug, Felix B\"ohmer, Tessa Pfattheicher
https://arxiv.org/abs/2507.16028 h…

From Logic to Language: A Trust Index for Problem Solving with LLMs
Classical computation, grounded in formal, logical systems, has been the engine of technological progress for decades, excelling at problems that can be described with unambiguous rules. This paradigm, however, leaves a vast ocean of human problems -- those characterized by ambiguity, dynamic environments, and subjective context -- largely untouched. The advent of Large Language Models (LLMs) represents a fundamental shift, enabling computational systems to engage with this previously inaccessi…

Spectral Outer-Approximation Algorithms for Binary Semidefinite Problems
Daniel de Roux, Zedong Peng, David E. Bernal Neira
https://arxiv.org/abs/2506.18265

Spectral Outer-Approximation Algorithms for Binary Semidefinite Problems
Integer semidefinite programming (ISDP) has recently gained attention due to its connection to binary quadratically constrained quadratic programs (BQCQPs), which can be exactly reformulated as binary semidefinite programs (BSDPs). However, it remains unclear whether this reformulation effectively uses existing ISDP solvers to address BQCQPs. To the best of our knowledge, no specialized ISDP algorithms exploit the unique structure of BSDPs derived from BQCQPs. This paper proposes a novel spectr…

FLAMES: Improving LLM Math Reasoning via a Fine-Grained Analysis of the Data Synthesis Pipeline
Parker Seegmiller, Kartik Mehta, Soumya Saha, Chenyang Tao, Shereen Oraby, Arpit Gupta, Tagyoung Chung, Mohit Bansal, Nanyun Peng
https://arxiv.org/abs/2508.16514

FLAMES: Improving LLM Math Reasoning via a Fine-Grained Analysis of the Data Synthesis Pipeline
Recent works improving LLM math reasoning with synthetic data have used unique setups, making comparison of data synthesis strategies impractical. This leaves many unanswered questions about the roles of different factors in the synthetic data pipeline, such as the impact of filtering low-quality problems. To address this gap, we introduce FLAMES, a Framework for LLM Assessment of Math rEasoning Data Synthesis, and perform a systematic study of 10 existing data synthesis strategies and multiple…

AE-PINNs: Attention-enhanced physics-informed neural networks for solving elliptic interface problems
Jiachun Zheng, Yunqing Huang, Nianyu Yi
https://arxiv.org/abs/2506.18332

AE-PINNs: Attention-enhanced physics-informed neural networks for solving elliptic interface problems
Inspired by the attention mechanism, we develop an attention-enhanced physics-informed neural networks (AE-PINNs) for solving elliptic interface equations. In AE-PINNs, we decompose the solution into two complementary components: a continuous component and a component with discontinuities across the interface. The continuous component is approximated by a fully connected neural network in the whole domain, while the discontinuous component is approximated by an interface-attention neural networ…

Expert-Guided LLM Reasoning for Battery Discovery: From AI-Driven Hypothesis to Synthesis and Characterization
Shengchao Liu, Hannan Xu, Yan Ai, Huanxin Li, Yoshua Bengio, Harry Guo
https://arxiv.org/abs/2507.16110

Expert-Guided LLM Reasoning for Battery Discovery: From AI-Driven Hypothesis to Synthesis and Characterization
Large language models (LLMs) leverage chain-of-thought (CoT) techniques to tackle complex problems, representing a transformative breakthrough in artificial intelligence (AI). However, their reasoning capabilities have primarily been demonstrated in solving math and coding problems, leaving their potential for domain-specific applications-such as battery discovery-largely unexplored. Inspired by the idea that reasoning mirrors a form of guided search, we introduce ChatBattery, a novel agentic f…

Exact Hull Reformulation for Quadratically Constrained Generalized Disjunctive Programs
Sergey Gusev, David E. Bernal Neira
https://arxiv.org/abs/2508.16093 https://

Exact Hull Reformulation for Quadratically Constrained Generalized Disjunctive Programs
Generalized Disjunctive Programming (GDP) is a framework for optimization problems involving discrete decisions and nonlinear constraints. The widely used Hull Reformulation transforms GDPs into Mixed-Integer Nonlinear Programming (MINLP) problems with tighter continuous relaxations. However, it typically employs an epsilon approximation of the closure of the perspective function for nonlinear constraints, which can lead to numerical instability and a weaker continuous relaxation. We present …

Uncertainty Quantification for Linear Inverse Problems with Besov Prior: A Randomize-Then-Optimize Method
Andreas Horst, Babak Maboudi Afkham, Yiqiu Dong, Jakob Lemvig
https://arxiv.org/abs/2506.16888

Uncertainty Quantification for Linear Inverse Problems with Besov Prior: A Randomize-Then-Optimize Method
In this work, we investigate the use of Besov priors in the context of Bayesian inverse problems. The solution to Bayesian inverse problems is the posterior distribution which naturally enables us to interpret the uncertainties. Besov priors are discretization invariant and can promote sparsity in terms of wavelet coefficients. We propose the randomize-then-optimize method to draw samples from the posterior distribution with Besov priors under a general parameter setting and estimate the modes …

A Learning-based Domain Decomposition Method
Rui Wu, Nikola Kovachki, Burigede Liu
https://arxiv.org/abs/2507.17328 https://arxiv.org…

A Learning-based Domain Decomposition Method
Recent developments in mechanical, aerospace, and structural engineering have driven a growing need for efficient ways to model and analyse structures at much larger and more complex scales than before. While established numerical methods like the Finite Element Method remain reliable, they often struggle with computational cost and scalability when dealing with large and geometrically intricate problems. In recent years, neural network-based methods have shown promise because of their ability …

Nonconvex Nonsmooth Multicomposite Optimization and Its Applications to Recurrent Neural Networks
Lingzi Jin, Xiao Wang, Xiaojun Chen
https://arxiv.org/abs/2506.17884

Nonconvex Nonsmooth Multicomposite Optimization and Its Applications to Recurrent Neural Networks
We consider a class of nonconvex nonsmooth multicomposite optimization problems where the objective function consists of a Tikhonov regularizer and a composition of multiple nonconvex nonsmooth component functions. Such optimization problems arise from tangible applications in machine learning and beyond. To define and compute its first-order and second-order d(irectional)-stationary points effectively, we first derive the closed-form expression of the tangent cone for the feasible region of it…

Neural Network Acceleration of Iterative Methods for Nonlinear Schr\"odinger Eigenvalue Problems
Daniel Peterseim, Jan-F. Pietschmann, Jonas P\"uschel, Kilian Ruess
https://arxiv.org/abs/2507.16349

Neural Network Acceleration of Iterative Methods for Nonlinear Schrödinger Eigenvalue Problems
We present a novel approach to accelerate iterative methods to solve nonlinear Schrödinger eigenvalue problems using neural networks. Nonlinear eigenvector problems are fundamental in quantum mechanics and other fields, yet conventional solvers often suffer from slow convergence in extreme parameter regimes, as exemplified by the rotating Bose- Einstein condensate (BEC) problem. Our method uses a neural network to predict and refine solution trajectories, leveraging knowledge from previous sim…

Efficient Strategy Synthesis for MDPs via Hierarchical Block Decomposition
Alexandros Evangelidis, Gricel V\'azquez, Simos Gerasimou
https://arxiv.org/abs/2506.17792

Efficient Strategy Synthesis for MDPs via Hierarchical Block Decomposition
Software-intensive systems, such as software product lines and robotics, utilise Markov decision processes (MDPs) to capture uncertainty and analyse sequential decision-making problems. Despite the usefulness of conventional policy synthesis methods, they fail to scale to large state spaces. Our approach addresses this issue and accelerates policy synthesis in large MDPs by dynamically refining the MDP and iteratively selecting the most fragile MDP regions for refinement. This iterative procedu…

Mean-Field Generalisation Bounds for Learning Controls in Stochastic Environments
Boris Baros, Samuel N. Cohen, Christoph Reisinger
https://arxiv.org/abs/2508.16001 https://

Mean-Field Generalisation Bounds for Learning Controls in Stochastic Environments
We consider a data-driven formulation of the classical discrete-time stochastic control problem. Our approach exploits the natural structure of many such problems, in which significant portions of the system are uncontrolled. Employing the dynamic programming principle and the mean-field interpretation of single-hidden layer neural networks, we formulate the control problem as a series of infinite-dimensional minimisation problems. When regularised carefully, we provide practically verifiable a…

Using the Immersed Penalized Boundary Method with Splines to Solve PDE's on Curved Domains in 3D
Aussie Greene, Larry L. Schumaker
https://arxiv.org/abs/2508.16060 https://

Using the Immersed Penalized Boundary Method with Splines to Solve PDE's on Curved Domains in 3D
Second-order elliptic boundary-value problems defined on curved domains in 2D and 3D arise frequently in practice. A lot of work has gone into developing numerical methods for solving such problems. One of the newest and most promising methods is the $\textit{immersed penalized boundary method}$ (IPBM) introduced in [Schumaker, L. L., Solving elliptic PDE's on domains with curved boundaries with an immersed penalized boundary method, J. Sci. Comp. ${\bf 80(3)}$ (2019), 1369--1394]. For a compre…

Optimal Data Reduction under Information-Theoretic Criteria
Taotao He, Jun Luo, Junkai Zhao
https://arxiv.org/abs/2508.16123 https://arxiv.org/pdf/2508.161…

Optimal Data Reduction under Information-Theoretic Criteria
Selecting an optimal subset of features or instances under an information theoretic criterion has become an effective preprocessing strategy for reducing data complexity while preserving essential information. This study investigates two representative problems within this paradigm: feature selection based on the maximum relevance minimum redundancy criterion, and instance selection grounded in the Kullback Leibler divergence. To address the intrinsic nonconvexities of these problems, we develo…

KKT-based optimality conditions for neural network approximation
Vinesha Peiris, Nadezda Sukhorukova, Julien Ugon
https://arxiv.org/abs/2506.17305 https://…

KKT-based optimality conditions for neural network approximation
In this paper, we obtain necessary optimality conditions for neural network approximation. We consider neural networks in Manhattan ($l_1$ norm) and Chebyshev ($\max$ norm). The optimality conditions are based on neural networks with at most one hidden layer. We reformulate nonsmooth unconstrained optimisation problems as larger dimension constrained problems with smooth objective functions and constraints. Then we use KKT conditions to develop the necessary conditions and present the optimalit…

Comparison of substructured non-overlapping domain decomposition and overlapping additive Schwarz methods for large-scale Helmholtz problems with multiple sources
Boris Martin, Pierre Jolivet, Christophe Geuzaine
https://arxiv.org/abs/2506.16875

Comparison of substructured non-overlapping domain decomposition and overlapping additive Schwarz methods for large-scale Helmholtz problems with multiple sources
Solving large-scale Helmholtz problems discretized with high-order finite elements is notoriously difficult, especially in 3D where direct factorization of the system matrix is very expensive and memory demanding, and robust convergence of iterative methods is difficult to obtain. Domain decomposition methods (DDM) constitute one of the most promising strategy so far, by combining direct and iterative approaches: using direct solvers on overlapping or non-overlapping subdomains, as a preconditi…

Tikhonov regularized second-order dynamical systems with Hessian-driven damping for solving convex optimization problems
Xiangkai Sun, Guoxiang Tian, Huan Zhang
https://arxiv.org/abs/2506.15968

Tikhonov regularized second-order dynamical systems with Hessian-driven damping for solving convex optimization problems
This paper deals with a Tikhonov regularized second-order dynamical system that incorporates time scaling, asymptotically vanishing damping and Hessian-driven damping for solving convex optimization problems. Under appropriate setting of the parameters, we first obtain fast convergence results of the function value along the trajectory generated by the dynamical system. Then, we show that the trajectory generated by the dynamical system converges weakly to a minimizer of the convex optimization…

Infinite horizon discounted LQ optimal control problems for mean-field switching diffusions
Kai Ding, Xun Li, Siyu Lv, Zuo Quan Xu
https://arxiv.org/abs/2506.16033

Infinite horizon discounted LQ optimal control problems for mean-field switching diffusions
This paper investigates an infinite horizon discounted linear-quadratic (LQ) optimal control problem for stochastic differential equations (SDEs) incorporating regime switching and mean-field interactions. The regime switching is modeled by a finite-state Markov chain acting as common noise, while the mean-field interactions are characterized by the conditional expectation of the state process given the history of the Markov chain. To address system stability in the infinite horizon setting, a …