Tootfinder

Profinite groups with complemented closed subgroups
Gustavo A. Fern\'andez-Alcober, Giulia Sabatino
https://arxiv.org/abs/2507.20791 https://arxiv.org/…

Profinite groups with complemented closed subgroups
A group $G$ is said to be a $C$-group if every subgroup $H$ has a permutable complement, i.e. if there exists a subgroup $K$ of $G$ such that $G=HK$ and $H \cap K=1$. In this paper, we study the profinite counterpart of this concept. We say that a profinite group $G$ is profinite-$C$ if every closed subgroup admits a closed permutable complement. We first give some equivalent variants of this condition and then we determine the structure of profinite-$C$ groups: they are the semidirect products…

Bruce Hwy is closed again. It must be the end of the month. https://social.chinwag.org/@abc_bot/115109093034556410

The space of closed $G2$-structures. II. concavity and hypersymplectic structures
Kai Zheng
https://arxiv.org/abs/2507.20456 https://arxiv.org/pdf/2507.204…

The space of closed $G2$-structures. II. concavity and hypersymplectic structures
In the space of closed $G_2$-structures equipped with Bryant's Dirichlet-type metric, we continue to utilise the geodesic, constructed in our previous article, to show that, under a normalisation condition Hitchin's volume functional is geodesically concave and the $G_2$ Laplacian flow decreases the length. Furthermore, we also construct various examples of hyper-symplectic manifolds on geodesic concavity.

That is one tired mama...

Precision spectral estimation at sub-Hz frequencies: closed-form posteriors and Bayesian noise projection
Lorenzo Sala, Stefano Vitale
https://arxiv.org/abs/2507.20846 https://

Precision spectral estimation at sub-Hz frequencies: closed-form posteriors and Bayesian noise projection
We present a Bayesian method for estimating spectral quantities in multivariate Gaussian time series. The approach, based on periodograms and Wishart statistics, yields closed-form expressions at any given frequency for the marginal posterior distributions of the individual power spectral densities, the pairwise coherence, and the multiple coherence, as well as for the joint posterior distribution of the full cross-spectral density matrix. In the context of noise projection - where one series i…

This Anti-Corruption Tracker focuses on the erosion or dismantling of oversight and accountability systems within the United States Executive Branch
—watchdog offices closed,
enforcement units disbanded, oversight officials removed,
and transparency rules hollowed out.
These changes don’t always make headlines, but together, they create a more permissive environment for corruption and abuse of power to take root.

The Anti-Corruption Tracker: Mapping the Erosion of Oversight and Accountability
This Anti-Corruption Tracker focuses on the erosion or dismantling of oversight and accountability systems within the United States Executive Branch

Asymptotics of shortest filling closed multi-geodesics
Yue Gao, Zhongzi Wang, Yunhui Wu
https://arxiv.org/abs/2508.17566 https://arxiv.org/pdf/2508.17566…

Asymptotics of shortest filling closed multi-geodesics
In this paper, we investigate the asymptotics of shortest filling closed multi-geodesics of closed hyperbolic surfaces as systole $\to 0$ or as genus $\to \infty$. We first show that for a closed hyperbolic surface $X_g$ of genus $g$, the length of a shortest filling closed multi-geodesic of $X_g$ is uniformly comparable to $$\left(g+\sum\limits_{\textit{closed geodesic }γ\subset X_g, \ \ell(γ)<1}\log \left(\frac{1}{\ell(γ)}\right)\right).$$ As an application, we show that as $g\to \infty$, …

A Closed-form Approximation for Impulse Response of Fractionally Damped Oscillators
Shashank Pathak, Michael Ruzhansky, Karel Van Bockstal
https://arxiv.org/abs/2508.20497 https…

A Closed-form Approximation for Impulse Response of Fractionally Damped Oscillators
We consider a fractionally damped oscillator, where the damping term is expressed by the Caputo fractional derivative of order $β\in (0,1).$ The impulse response of this oscillator can be expressed in terms of the bivariate Mittag-Leffler function consisting of a double infinite series. Although this series is uniformly convergent, its numerical implementation suffers from computational instabilities. In this contribution, we propose an approximate closed-form solution that avoids these numeri…

We watched the #EngEsp #Euros final in a pub in Brecon, south Wales, and even the locals cheered when England won! (The gargoyles on a local church represent the mood when it went to penalties)

Nagumo-Type Characterization of Forward Invariance for Constrained Systems
Olayo Reynaud, Mohamed Maghenem, Adnane Saoud, Sadek Belamfedel Alaoui, Ahmad Hably
https://arxiv.org/abs/2508.20045

Nagumo-Type Characterization of Forward Invariance for Constrained Systems
This paper proposes a Nagumo-type invariance condition for differential inclusions defined on closed constraint sets. More specifically, given a closed set to render forward invariant, the proposed condition restricts the system's dynamics, assumed to be locally Lipschitz, on the boundary of the set restricted to the interior of the constraint set. In particular, when the boundary of the set is entirely within the interior of the constraint set, the proposed condition reduces to the well-known …

Selected topics in string field theory
Georg Stettinger
https://arxiv.org/abs/2508.19846 https://arxiv.org/pdf/2508.19846

Selected topics in string field theory
This thesis contains of two parts: The first part is a pedagogical introduction into the field of bosonic SFT. After discussing some general properties we expect, Witten's open SFT and Zwiebach's closed SFT are presented in detail. This means we set up the action, explain the algebraical and geometrical structure and mention physical applications. In the open case we review the most important analytic solutions including the necessary operator technology whileas in the closed case we focus on q…

I was late to pick my daughter up from camp because #NYCParks closed a huge portion of Corona-Meadows Flushing Park. Apparently for some kind of music festival. There was, of course, no bike detour. The area has highways running through it, and the bridges over the highways are cordoned off. How do you get to

Modelling the Closed Loop Dynamics Between a Social Media Recommender System and Users' Opinions
Ella C. Davidson, Mengbin Ye
https://arxiv.org/abs/2507.19792 https://

Modelling the Closed Loop Dynamics Between a Social Media Recommender System and Users' Opinions
This paper proposes a mathematical model to study the coupled dynamics of a Recommender System (RS) algorithm and content consumers (users). The model posits that a large population of users, each with an opinion, consumes personalised content recommended by the RS. The RS can select from a range of content to recommend, based on users' past engagement, while users can engage with the content (like, watch), and in doing so, users' opinions evolve. This occurs repeatedly to capture the endless c…

Typical #PolishPost:
18:40: "The parcel […] is waiting for you at […]"
The place was closed at 18:00.

Seattle Synth Store Patchwerks Has Closed
https://www.synthtopia.com/content/2025/07/18/seattle-synth-store-patchwerks-has-closed/?utm_source=flipboard&utm_content=m…

A closed formula for the Geil-Matsumoto bound on semigroups and curves with many points
Adler Marques, Erik Mendoza, Luciane Quoos, Guilherme Tizziotti
https://arxiv.org/abs/2508.17022

A closed formula for the Geil-Matsumoto bound on semigroups and curves with many points
The Geil-Matsumoto bound (GM bound) constrains the number of rational points on a curve over a finite field in terms of the Weierstrass semigroup of any of the points on the curve. For general numerical semigroups, the GM bound lacks a simple closed-form expression, making its computation a challenging problem. A closed formula has been obtained for the case when the semigroup is generated by two co-prime integers. In this work, for any numerical semigroup, we provide a closed formula for the G…

> I don’t mind the occasional yearly noise that inevitably comes with the organisation of such a huge multi-day show. But I can’t ignore the fact that each year the noise pollution becomes more and more apparent up to the point where we don’t sleep well those days, even with all windows closed.
https://

„Postgres continues to be widely used, and Postgres-derived closed source databases such as AlloyDB and AWS Aurora have gained popularity in recent years.“ At Berlin Buzzwords 2025, Celeste Horgan explored the architecture of these different systems, clarified what each company means by „Postgres-compatible“, and provided guidance on how to choose the right option for your needs.
Watch the full session: https://youtu.be/QUwbyqGbbOQ?si=38JTXOpCbpl_j8gQ

what a trip down memory lane; really happy I stumbled across this this morning. theres a lifetime of memories in this listicle
https://www.audiofemme.com/60-nyc-showspaces-that-closed-in-the-2010s/

I've used #Signal for months now, and I never noticed the AM/PM thing until recently. But today it was, like, hello OCD 😀
"en-BG" doesn't work either, and because "en-DE" or "en-DK", albeit harmless, feel weird, "en-GB" did the trick. ->
Timestamp format should match system time format · Issue #4252 · signalapp/Signal-Desktop…

Timestamp format should match system time format · Issue #4252 · signalapp/Signal-Desktop
I have searched open and closed issues for duplicates Description It would be nice if timestamps on messages matched the time format used by the system. Currently, timestamps appear in US format (t...

On Alperin's conjecture and functorial equivalence of blocks
Robert Boltje, Serge Bouc, Deniz Y{\i}lmaz
https://arxiv.org/abs/2507.20314 https://arxiv.…

On Alperin's conjecture and functorial equivalence of blocks
Let $k$ be an algebraically closed field of positive characteristic $p$ and let $\mathbb{F}$ be an algebraically closed field of characteristic 0. We consider Alperin's weight conjecture (over $k$) from the point of view of (stable) functorial equivalence of blocks over $\mathbb{F}$. We formulate a functorial version of Alperin's blockwise weight conjecture, and show that it is equivalent to the original one. We also show that this conjecture holds stably, i.e., in the category of stable diagon…

Representations of the Chekanov-Eliashberg algebra from closed exact Lagrangians I
Baptiste Chantraine, Georgios Dimitroglou Rizell, Paolo Ghiggini
https://arxiv.org/abs/2508.20964

Representations of the Chekanov-Eliashberg algebra from closed exact Lagrangians I
This is the first of a series of two articles aiming at relating the compact Fukaya category of a Weinstein manifold to the derived category of finite dimensional representations of the Chekanov-Eliashberg differential graded algebra of the attaching spheres of the critical handles. In this first article we associate a finite dimensional representation $V_L$ to any compact exact Lagrangian submanifold $L$ and prove that for two any such Lagrangian submanifolds $L_0$ and $L_1$ the isomorphism $$…

Closed-Form Input Design for Identification under Output Feedback with Perturbation Constraints
Jingwei Hu, Dave Zachariah, Torbj\"orn Wigren, Petre Stoica
https://arxiv.org/abs/2508.18813

Closed-Form Input Design for Identification under Output Feedback with Perturbation Constraints
In many applications, system identification experiments must be performed under output feedback to ensure safety or to maintain system operation. In this paper, we consider the online design of informative experiments for ARMAX models by applying a bounded perturbation to the input signal generated by a fixed output feedback controller. Specifically, the design constrains the resulting output perturbation within user-specified limits and can be efficiently computed in closed form. We demonstrat…

AOC's on the hook for $2,983.28 after the House Ethics panel closed its probe into her Met Gala appearance (Bryan Metzger/Business Insider)
https://www.businessinsider.com/aoc-house-ethics-probe-closed-met-gala-2025-7
http://www.memeorandum.com/250725/p61#a250725p61

GDS Agent: A Graph Algorithmic Reasoning Agent
Borun Shi, Ioannis Panagiotas
https://arxiv.org/abs/2508.20637 https://arxiv.org/pdf/2508.20637

GDS Agent: A Graph Algorithmic Reasoning Agent
Large language models (LLMs) have shown remarkable multimodal information processing and reasoning ability. When equipped with tools through function calling and enhanced with retrieval-augmented techniques, compound LLM-based systems can access closed data sources and answer questions about them. However, they still struggle to process and reason over large-scale graph-structure data. We introduce the GDS (Graph Data Science) agent in this technical report. The GDS agent introduces a comprehen…

Real-Time Model Checking for Closed-Loop Robot Reactive Planning
Christopher Chandler, Bernd Porr, Giulia Lafratta, Alice Miller
https://arxiv.org/abs/2508.19186 https://…

Real-Time Model Checking for Closed-Loop Robot Reactive Planning
We present a new application of model checking which achieves real-time multi-step planning and obstacle avoidance on a real autonomous robot. We have developed a small, purpose-built model checking algorithm which generates plans in situ based on "core" knowledge and attention as found in biological agents. This is achieved in real-time using no pre-computed data on a low-powered device. Our approach is based on chaining temporary control systems which are spawned to counteract disturbances in…

Does anyone know the origin of calling intermediate access servers "jump boxes" (eg for accessing ssh on a closed network). I've been told that it was maybe a Babylon 5 reference?

Behind Closed Doors
Great Australian Pods Podcast Directory: #GreatAusPods

Bayesian symbolic regression: Automated equation discovery from a physicists' perspective
Roger Guimera, Marta Sales-Pardo
https://arxiv.org/abs/2507.19540 https://

Bayesian symbolic regression: Automated equation discovery from a physicists' perspective
Symbolic regression automates the process of learning closed-form mathematical models from data. Standard approaches to symbolic regression, as well as newer deep learning approaches, rely on heuristic model selection criteria, heuristic regularization, and heuristic exploration of model space. Here, we discuss the probabilistic approach to symbolic regression, an alternative to such heuristic approaches with direct connections to information theory and statistical physics. We show how the prob…

Raining Sessions ☔️
雨 ☔️
📷 Pentax# MX
🎞️Fomapan 400 Action
buy me ☕️ ?/请我喝杯☕️？
#filmphotography

The variety of nilpotent pairs $(A,B)$ with $[A,B] = \lambda I$
Vlad Roman, Robert M. Guralnick
https://arxiv.org/abs/2508.20199 https://arxiv.org/pdf/2508…

The variety of nilpotent pairs $(A,B)$ with $[A,B] = λI$
Let $k$ be an algebraically closed field of characteristic $p >0$. We consider the variety of nilpotent pairs $(A,B)$ with $[A,B]=λI$, namely the set of pairs $ X = \{ (A,B) \in M_n(k) \times M_n(k) \mid A,B \text{ nilpotent}, [A,B]=λI, λ\in k \}$. We prove that if $n=pr$, then $X$ is irreducible of dimension $n^2$.

Apparently if you know the right folks to call you can just order up pubs by the TEU.

Closed Formulas for $\eta$-Corrections in the Once Punctured Torus
Nelson A. Colon Vargas
https://arxiv.org/abs/2508.18334 https://arxiv.org/pdf/2508.18334…

Closed Formulas for $η$-Corrections in the Once Punctured Torus
We study $η$-correction terms in the Kauffman bracket skein algebra of the once-punctured torus $K_t(Σ_{1,1})$. While the Frohman-Gelca product-to-sum rule is explicit on the closed torus, punctures introduce correction terms in the ideal $(η)$ whose structure has resisted systematic description beyond low-determinant cases. We give a closed form for the family $P_n=(1,0)\cdot T_n((1,2))$ (determinant $2$): the correction $ε_n$ has an explicit Chebyshev expansion with coefficients that fact…

Steady state representations for the harmonic process
Rouven Frassek
https://arxiv.org/abs/2507.20436 https://arxiv.org/pdf/2507.20436

Steady state representations for the harmonic process
In this note we discuss how the matrix product solution for the steady state of the harmonic process is obtained from the solutions already known in the literature, i.e. the closed-form expression derived in arXiv:2107.01720 and the nested integral form obtained in arXiv:2307.02793 and arXiv:2307.14975. Our results clarify the relation between the three representations of the steady state and provide the matrix product solution that has not been available for this model before.

Benoist-Hulin groups
Hideki Miyachi, Yannian Zhao
https://arxiv.org/abs/2507.19927 https://arxiv.org/pdf/2507.19927…

Benoist-Hulin groups
A Benoist-Hulin group is, by definition, a subgroup $Γ$ of ${\rm PSL}_2(\mathbb{C})$ such that any $Γ$-invariant closed set consisting of Jordan curves in the space of closed subsets of the Riemann sphere that are not singletons is composed of $K$-quasicircles for some $K \ge 1$. Y.Benoist and D.Hulin showed that the full group ${\rm PSL}_2(\mathbb{C})$ is a Benoist-Hulin group. In this paper, we develop the theory of Benoist-Hulin groups and show that both uniform lattices and parabolic subg…

The Coverage Depth Problem in DNA Storage Over Small Alphabets
Matteo Bertuzzo, Alberto Ravagnani, Eitan Yaakobi
https://arxiv.org/abs/2507.20639 https://a…

The Coverage Depth Problem in DNA Storage Over Small Alphabets
The coverage depth problem in DNA data storage is about minimizing the expected number of reads until all data is recovered. When they exist, MDS codes offer the best performance in this context. This paper focuses on the scenario where the base field is not large enough to allow the existence of MDS codes. We investigate the performance for the coverage depth problem of codes defined over a small finite field, providing closed formulas for the expected number of reads for various code families…

What's the point of installing an electronic timetable on a small train stop? Next to the paper one, of course. The kind that only displays the planned timetable, not the current departures. And of course the arrival platform is announced via loudspeakers after the barriers are closed.
#rail

After News Media Corporation announced the closure of 31 outlets in five states on August 6, a publishing group bought 8 papers in WY and another bought 4 in SD (Sarah Raza/Associated Press)
https://apnews.com/article/rural-newsp…

Closed newspapers in Wyoming and South Dakota are saved as buyers swoop in
A dozen newspapers in Wyoming and South Dakota are set to publish again after buyers stepped in to keep the communities from becoming news deserts where little or no local media remains. This quick action is notable in an industry where, according to a 2024 report from the Medill School of Journalism, more than two newspapers close each week. Illinois-based News Media Corporation had announced the closure of 31 outlets in five states. Within two weeks, new buyers in Wyoming and North Carolina p…

🇺🇦 #NowPlaying on KEXP's #MorningShow
Washed Out:
🎵 Eyes Be Closed
#WashedOut
https://washedout.bandcamp.com/track/eyes-be-closed
https://open.spotify.com/track/0AtMGGNifzEQuO3Lk7tRXe

Towards New Characterizations of Small Circuit Classes via Discrete Ordinary Differential Equations
Melissa Antonelli, Arnaud Durand, Juha Kontinen
https://arxiv.org/abs/2508.19392

Towards New Characterizations of Small Circuit Classes via Discrete Ordinary Differential Equations
Implicit computational complexity is a lively area of theoretical computer science, which aims to provide machine-independent characterizations of relevant complexity classes. % for uniformity with subsequent uses >> 1960s (but feel free to modify it) % One of the seminal works in this field appeared in the 1960s, when Cobham introduced a function algebra closed under bounded recursion on notation to capture polynomial time computable functions ($FP$). Later on, several complexity classes have …

Fermionic Love of Black Holes in General Relativity
Sumanta Chakraborty, Pierre Heidmann, Paolo Pani
https://arxiv.org/abs/2508.20155 https://arxiv.org/pdf…

Fermionic Love of Black Holes in General Relativity
Black holes in General Relativity exhibit a remarkable feature: their response to static scalar, electromagnetic, and gravitational perturbations -- as quantified by the so-called tidal Love numbers -- vanishes identically. We present the first exception to this rule: the Love numbers of a black hole perturbed by a fermionic field are nonzero. We derive a closed-form expression of these fermionic Love numbers for generic spin in the background of a Kerr black hole with arbitrary angular momentu…

Dammit. Why cant we have nice things? At least I did get an hour in today.
https://nyr.ruv.is/english/2025-08-18-vesturbaejarlaug-closed-again-due-to-paintwork-defect-451220/

Vesturbæjarlaug closed again due to paintwork defect - RÚV.is
Vesturbæjarlaug has been closed for the second time in a short period. The pool was closed for two months earlier this summer for maintenance but now closes unexpectedly again due to a fault in the paintwork.

Reinforcement Learning Increases Wind Farm Power Production by Enabling Closed-Loop Collaborative Control
Andrew Mole, Max Weissenbacher, Georgios Rigas, Sylvain Laizet
https://arxiv.org/abs/2506.20554

Reinforcement Learning Increases Wind Farm Power Production by Enabling Closed-Loop Collaborative Control
Traditional wind farm control operates each turbine independently to maximize individual power output. However, coordinated wake steering across the entire farm can substantially increase the combined wind farm energy production. Although dynamic closed-loop control has proven effective in flow control applications, wind farm optimization has relied primarily on static, low-fidelity simulators that ignore critical turbulent flow dynamics. In this work, we present the first reinforcement learnin…

It should be said, of course, that I can have the pleasure of experiencing this horror only because it’s OSS.
What lurks in the closed-source alternatives? We can only speculate.

Plug and Play Splitting Techniques for Poisson Image Restoration
Alessandro Benfenati
https://arxiv.org/abs/2507.19378 https://arxiv.org/pdf/2507.19378

Plug and Play Splitting Techniques for Poisson Image Restoration
Plug and Play (PnP) methods achieve remarkable results in the framework of image restoration problems for Gaussian data. Nonetheless, the theory available for the Gaussian case cannot be extended to the Poisson case, due to the non-Lipschitz gradient of the fidelity function, the Kullback-Leibler functional, or the absence of closed-form solution for the proximal operator of such term, leading to employ iterative solvers for the inner subproblem. In this work we extend the idea of PIDSplit+ alg…

Thermodynamics and stability of non-equilibrium steady states in open systems -- case study for compressible heat conducting fluid
V\'it Pr\r{u}\v{s}a
https://arxiv.org/abs/2508.19677

Thermodynamics and stability of non-equilibrium steady states in open systems -- case study for compressible heat conducting fluid
We carefully go through all the calculations necessary for the construction of a Lyapunov like functional for the nonlinear stability analysis of steady-states in thermodynamically closed/open systems composed of compressible heat conducting fluids.

Weak countability axioms on the quotient spaces of topological gyrogroups
Ying-Ying Jin, Yi-Ting Wang, Li-Hong Xie
https://arxiv.org/abs/2507.19506 https://

Weak countability axioms on the quotient spaces of topological gyrogroups
In this paper, we mainly prove that if $H$ is a closed strong subgyrogroup of a strongly topological gyrogroup $G$ and $H$ is neutral, then (1) \( G/H \) is biradial if and only if \( G/H \) is nested; (2) \( G/H \) is metrizable if and only if \( G/H \) is a biradial space with countable pseudocharacter; (3) \( G/H \) is metrizable if and only if \( G/H \) has countable $cn$-character, given that \( G/H \) has the Baire property.

"Turning closed coal mines into solar farms could power a country the size of Germany, report finds"
#Germany #CoalMine #SolarPower

Report reveals huge solar power potential of abandoned coal mines
“The same ground that powered the industrial era can help power the climate solutions we now urgently need,” analysts say of the 300 GW solution.

Controlling Topological Defects in Polar Fluids via Reinforcement Learning
Abhinav Singh, Petros Koumoutsakos
https://arxiv.org/abs/2507.19298 https://arxi…

Controlling Topological Defects in Polar Fluids via Reinforcement Learning
Topological defects in active polar fluids exhibit complex dynamics driven by internally generated stresses, reflecting the deep interplay between topology, flow, and non-equilibrium hydrodynamics. Feedback control offers a powerful means to guide such systems, enabling transitions between dynamic states. We investigated closed-loop steering of integer-charged defects in a confined active fluid by modulating the spatial profile of activity. Using a continuum hydrodynamic model, we show that loc…

$L^2$-Sobolev Theory for $\bar\partial$ on Domains in $\Bbb {CP}^n$
Mei-Chi Shaw
https://arxiv.org/abs/2507.19355 https://arxiv.org/pdf/2507.19355

$L^2$-Sobolev Theory for $\bar\partial$ on Domains in $\Bbb {CP}^n$
In this article, we study the range of the Cauchy-Riemann operator $\bar\partial$ on domains in the complex projective space $\Bbb{CP}^n$. In particular, we show that $\bar\partial$ does not have closed range in $L^2$ for (2,1)-forms on the Hartogs triangle in $\Bbb{CP}^2$. We also study the $\bar\partial$-Cauchy problem on pseudoconvex domains and use it to prove the Sobolev estimates for $\bar\partial$ on pseudoconcave domains in $\Bbb{CP}^n$.

Planar percolation and the loop O(n) model
Alexander Glazman, Matan Harel, Nathan Zelesko
https://arxiv.org/abs/2508.20917 https://arxiv.org/pdf/2508.20917…

Planar percolation and the loop O(n) model
We show that a large class of site percolation processes on any planar graph contains either zero or infinitely many infinite connected components. The assumptions that we require are: tail triviality, positive association (FKG) and that the set of open vertices is stochastically dominated by the set of closed ones. This covers the case of Bernoulli site percolation at parameter $p\leq 1/2$ and resolves Conjecture 8 from the work of Benjamini and Schramm from 1996. Our result also implies that …

Replaced article(s) found for cs.MA. https://arxiv.org/list/cs.MA/new
[1/1]:
- TrafficMCTS: A Closed-Loop Traffic Flow Generation Framework with Group-Based Monte Carlo Tree Se...
Ze Fu, Licheng Wen, Pinlong Cai, Daocheng Fu, Song Mao, Botian Shi

Dissipative Coupling in Photonic and Plasmonic Resonators
Tong Wu, Philippe Lalanne
https://arxiv.org/abs/2507.20132 https://arxiv.org/pdf/2507.20132

Dissipative Coupling in Photonic and Plasmonic Resonators
The rapid progress of nanophotonics demands theoretical frameworks capable of predicting the resonant behavior of complex systems comprising constituents of varying nature, operating beyond the weak-coupling, high-Q regime where classical temporal coupled-mode theory (CMT) is applicable. This work presents a coupled-quasinormal-mode (cQNM) framework for analyzing dissipative coupling with photonic and plasmonic resonators. The framework provides rigorous closed-form expressions for dissipative …

Deciding Robust Instances of an Escape Problem for Dynamical Systems in Euclidean Space
Eike Neumann
https://arxiv.org/abs/2506.21481 https://

Deciding Robust Instances of an Escape Problem for Dynamical Systems in Euclidean Space
We study the problem of deciding whether a point escapes a closed subset of $\mathbb{R}^d$ under the iteration of a continuous map $f \colon \mathbb{R}^d \to \mathbb{R}^d$ in the bit-model of real computation. We give a sound partial decision method for this problem which is complete in the sense that its halting set contains the halting set of all sound partial decision methods for the problem. Equivalently, our decision method terminates on all problem instances whose answer is robust under a…

Geometric Measures of Complexity for Open and Closed Quantum Systems
Alberto Acevedo, Antonio Falco
https://arxiv.org/abs/2507.18440 https://arxiv.org/pdf/…

Geometric Measures of Complexity for Open and Closed Quantum Systems
The unitary dynamics of quantum systems can be modeled as a trajectory on a Riemannian manifold. This theoretical framework naturally yields a purely geometric interpretation of computational complexity for quantum algorithms, a notion originally developed by Michael Nielsen (Circa, 2007). However, for nonunitary dynamics, it is unclear how one can recover a completely geometric characterization of Nielsen-like geometric complexity. The main obstacle to overcome is that nonunitary dynamics cann…

The Real Reasons Doug Ford Closed the Science Center
https://youtube.com/watch?v=Lw7TgM4nOpQ&si=xVCv0hpjf0y58r_2

So people are still fudding against open source.
(FUD = Fear, Uncertainty & Doubt)
All of this applies to closed source as well (or even worse):
https://www.xda-developers.com/drawbacks-open-source-software/
Let me make that clear:
The sole…

I can't ignore these 8 drawbacks to open-source software
I've found these drawbacks when using certain open-source tools.

Equi-bounded on order intervals families of semi-norms
Eduard Emelyanov
https://arxiv.org/abs/2507.18659 https://arxiv.org/pdf/2507.18659

Equi-bounded on order intervals families of semi-norms
It is proved that equi-bounded on order intervals families of semi-norms on an ordered Banach space with a closed generating cone are equi-continuous.

Replaced article(s) found for cs.PF. https://arxiv.org/list/cs.PF/new
[1/1]:
- TurboSpec: Closed-loop Speculation Control System for Optimizing LLM Serving Goodput
Liu, Park, Hu, Kwon, Li, Zhang, Du, Mo, You, Cheung, Deng, Stoica, Zhang

Homotopy classification of closed polygonal lines: results and problems
E. Alkin, O. Nikitenko, A. Skopenkov
https://arxiv.org/abs/2508.16287 https://arxiv…

Homotopy classification of closed polygonal lines: results and problems
In this text we expose (as a sequence of problems) basic cases of some fundamental ideas and methods of mathematics. Namely, of homotopy, degree, fundamental group, covering, Whitehead invariant, etc. This is done by considering the elementary example: closed polygonal lines in a subset of the plane. Although these ideas and methods are parts of topology, they are used in many other areas including computer science. This text is expository and is accessible to mathematicians not specialized in …

Closed-Form Decomposition for Simplicial Cones and PDBarv Algorithm for Lattice Point Counting
Sihao Tao, Guoce Xin, Zihao Zhang
https://arxiv.org/abs/2506.19322

Closed-Form Decomposition for Simplicial Cones and PDBarv Algorithm for Lattice Point Counting
Counting lattice points within a rational polytope is a foundational problem with applications across mathematics and computer science. A key approach is Barvinok's algorithm, which decomposes the lattice point generating function of cones to that of unimodular cones. However, standard implementations face difficulties: the original primal method struggles with points on cone boundaries, while the alternative dual method can be slow for certain cone types. This paper introduces two main contr…

Pic 6: Getting to know the new vets https://www.dallascowboys.com/news/pic-6-getting-to-know-the-new-vets-kenneth-murray

Geometric Superfluid Weight in Quasicrystals
Junsong Sun, Huaiming Guo, Bohm-Jung Yang
https://arxiv.org/abs/2507.20540 https://arxiv.org/pdf/2507.20540

Geometric Superfluid Weight in Quasicrystals
We study the geometric contribution to the superfluidity in quasicrystals in which the conventional momentum-space quantum geometric tensor cannot be defined due to the lack of translational invariance. Based on the correspondence between the momentum and magnetic flux, we introduce the flux-space quantum metric in finite-size closed systems and reveal its contribution to the superfluid weight in quasicrystalline superconductors. As a toy model, we study the attractive Hubbard model on the Fibo…

Open-Source LLMs Collaboration Beats Closed-Source LLMs: A Scalable Multi-Agent System
Shengji Tang, Jianjian Cao, Weihao Lin, Jiale Hong, Bo Zhang, Shuyue Hu, Lei Bai, Tao Chen, Wanli Ouyang, Peng Ye
https://arxiv.org/abs/2507.14200

Open-Source LLMs Collaboration Beats Closed-Source LLMs: A Scalable Multi-Agent System
This paper aims to demonstrate the potential and strengths of open-source collectives. It leads to a promising question: Can we harness multiple open-source LLMs to match or even beat the closed-source LLMs? To answer this, we propose SMACS, a scalable multi-agent collaboration system (MACS) framework with high performance. Specifically, for continuous integration of new LLMs and generalization to diverse questions, we first propose a Retrieval-based Prior Selection (RPS), which assigns a proxy…

Towards Open-Closed Categorical Enumerative Invariants: Circle-Action Formality Morphism
Jakob Ulmer
https://arxiv.org/abs/2507.15445 https://

Towards Open-Closed Categorical Enumerative Invariants: Circle-Action Formality Morphism
Categorical enumerative invariants of a Calabi-Yau category, encoded as the partition function of the associated closed string field theory (SFT), conjecturally equal Gromov-Witten invariants when applied to Fukaya categories. Part of this theory is a formality $L_\infty$ morphism which depends on a splitting of the non-commutative Hodge filtration. Our main result is providing an open-closed formality morphism; the algebraic structures involved conjecturallygive a home to open-closed GW invari…

Took the new #nightjet yesterday from Vienna > Amersfoort. Very new train, but still with a number of teething issues. An on-board technician tried to solve e.g. sliding doors that wouldn’t open. Some problems couldn’t be fixed (one cabin’s keycard didn’t work, person was moved to a free cabin, my neighbour’s cabin wouldn’t properly lock).
Huge delay (170 minutes) - that I partly expect…

Idefix-Closed Languages and Their Application in Contextual Grammars
Marvin K\"odding, Bianca Truthe
https://arxiv.org/abs/2507.15312 https://arxiv.or…

Idefix-Closed Languages and Their Application in Contextual Grammars
In this paper, we continue the research on the power of contextual grammars with selection languages from subfamilies of the family of regular languages. We investigate infix-, prefix-, and suffix-closed languages (referred to as idefix-closed languages) and compare such language families to some other subregular families of languages (finite, monoidal, nilpotent, combinational, (symmetric) definite, ordered, non-counting, power-separating, commutative, circular, union-free, star, and comet …

Replaced article(s) found for cs.RO. https://arxiv.org/list/cs.RO/new
[1/2]:
- TrafficMCTS: A Closed-Loop Traffic Flow Generation Framework with Group-Based Monte Carlo Tree Se...
Ze Fu, Licheng Wen, Pinlong Cai, Daocheng Fu, Song Mao, Botian Shi

Isolated $j$-invariants arising from the modular curve $X_0(n)$
Meghan Lee
https://arxiv.org/abs/2507.19462 https://arxiv.org/pdf/2507.19462

Isolated $j$-invariants arising from the modular curve $X_0(n)$
An isolated point of degree $d$ is a closed point on an algebraic curve which does not belong to an infinite family of degree $d$ points that can be parameterized by some geometric object. We provide an algorithm to test whether a rational, non-CM $j$-invariant gives rise to an isolated point on the modular curve $X_0(n)$, for any $n \in \mathbb{Z}^+$, using key results from Menendez and Zywina. This work is inspired by the prior algorithm of Bourdon et al. which tests whether a rational, non-C…

Resurgent structure of 2d Yang-Mills theory on a torus
Jiashen Chen, Jie Gu, Xin Wang
https://arxiv.org/abs/2507.19943 https://arxiv.org/pdf/2507.19943

Resurgent structure of 2d Yang-Mills theory on a torus
We study the resurgent structure of the topological string dual to 2d $U(N)$ Yang-Mills on torus. We find closed form formulas for instanton amplitudes up to arbitrarily high instanton orders, based on which we propose the non-perturbative partition function including contributions from all the real instantons, which is real for positive modulus and string coupling. We also explore complex instantons and find two infinite towers of them. We expect them to correspond to BPS states in type II str…

Rank one summands of Frobenius pushforwards of line bundles on G/P
Feliks R\k{a}czka
https://arxiv.org/abs/2507.20759 https://arxiv.org/pdf/2507.20759

Rank one summands of Frobenius pushforwards of line bundles on G/P
Let $X=G/P$ be a partial flag variety, where $G$ is a semi-simple, simply connected algebraic group defined over an algebraically closed field $K$ of positive characteristic. Let $\mathsf{F}\colon X\to X$ be the absolute Frobenius morphism. Given a line bundle $\mathscr{L}$ on $X$ and an integer $r\geq1$, we describe all line bundles that are direct summands of the pushforward $\mathsf{F}_{*}^{r}\mathscr{L}$. For $\mathscr{L}$ corresponding to a dominant weight, we also compute, for $r$ suffici…

Discounted LQR: stabilizing (near-)optimal state-feedback laws
Jonathan de Brusse, Jamal Daafouz, Mathieu Granzotto, Romain Postoyan, Dragan Nesic
https://arxiv.org/abs/2508.19599

Discounted LQR: stabilizing (near-)optimal state-feedback laws
We study deterministic, discrete linear time-invariant systems with infinite-horizon discounted quadratic cost. It is well-known that standard stabilizability and detectability properties are not enough in general to conclude stability properties for the system in closed-loop with the optimal controller when the discount factor is small. In this context, we first review some of the stability conditions based on the optimal value function found in the learning and control literature and highligh…

Area Rigidity for the Regular Representation of Surface Groups
Riccardo Caniato, Xingzhe Li, Antoine Song
https://arxiv.org/abs/2508.19480 https://arxiv.or…

Area Rigidity for the Regular Representation of Surface Groups
Let $\tildeΣ$ be the universal cover of a closed surface $Σ$ of genus at least $2$. We characterize all equivariantly area-minimizing maps from $\tildeΣ$ to a Hilbert sphere, which are equivariant with respect to an isometric action of $π_1(Σ)$ weakly equivalent to the regular representation. As part of our proof, we classify all minimal surfaces in Hilbert spheres with constant negative Gaussian curvature. This builds on earlier results of E. Calabi, K. Kenmotsu, R. Bryant.

Relatively closed subgroups of permutation groups with a cyclic regular normal subgroup
Alexander Buturlakin, Andrey V. Vasil'ev
https://arxiv.org/abs/2508.17664 https://

Relatively closed subgroups of permutation groups with a cyclic regular normal subgroup
Motivated by some known problems concerning combinatorial structures associated with finite one-dimensional affine permutation groups, we study subgroups which are closed in $\operatorname{Γ{L}}_1(q)$. This brings us to a description of the relatively closed subgroups of permutation groups with a cyclic regular normal subgroup. Our results, in particular, provide a classification of the minimal nontrivial one-dimensional affine association schemes which generalizes the recent Muzychuk classifi…

During a closed-door meeting of Republican senators on Tuesday, Sen. Mitch McConnell (R-Kentucky) tried to tamper down fears of voter blowback against the proposed cuts to Medicaid spending in the GOP’s budget reconciliation bill,
⭐️claiming that voters will ultimately “get over it.”
The former Republican Senate leader’s comments came after Sen. Thom Tillis (R-North Carolina), one of the most vulnerable Senate GOP incumbents in the 2026 midterm elections, expressed concern that

Voters Will “Get Over It,” McConnell Tells GOP Colleagues Scared That Medicaid Cuts Will Hurt Them in Midterms
Polling consistently shows that voters strongly object to the Medicaid cuts proposed in the GOP reconciliation package.

On the Irreducible Morphisms for Skew group algebras
Shantanu Sardar, Alfredo Gonzalez Chaio, Sonia Trepode
https://arxiv.org/abs/2507.20103 https://arxiv.…

On the Irreducible Morphisms for Skew group algebras
For an algebraically closed field K, let G be a finite abelian group of K-linear automorphisms of a finite-dimensional path algebra KQ of a quiver Q. Under certain assumptions on the action of G, we show the existence of a certain kind of covering that we call a Galois semi-covering functor, which becomes a Galois covering when the group action is free. We study the module category of its skew group algebra under this functor. As an application, we obtain a complete description of the irreducib…

Using Symbolic Regression to Emulate the Radial Fourier Transform of the S\'ersic profile for Fast, Accurate and Differentiable Galaxy Profile Fitting
Tim B. Miller, Imad Pasha
https://arxiv.org/abs/2508.20266

Using Symbolic Regression to Emulate the Radial Fourier Transform of the Sérsic profile for Fast, Accurate and Differentiable Galaxy Profile Fitting
Galaxy profile fitting is a ubiquitous technique that provides the backbone for photometric and morphological measurements in modern extragalactic surveys. A recent innovation in profile fitting algorithms is to render, or create, the model profile in Fourier space, which aims to provide faster and more accurate results. However, the most common parameterization, the Sérsic profile, has no closed form Fourier transform, requiring the use of computationally expensive approximations. In this pap…

Traverso's Isogeny Conjecture for Some Unitary p-Divisible Groups
Emerald Andrews, Deewang Bhamidipati, Maria Fox, Heidi Goodson, Steven R. Groen, Sandra Nair
https://arxiv.org/abs/2507.19708

Traverso's Isogeny Conjecture for Some Unitary p-Divisible Groups
The isogeny cutoff of a $p$-divisible group $X$ (defined over an algebraically closed field of characteristic $p$) measures the amount of $p$-torsion necessary to determine its isogeny class. The minimal height of $X$ measures its distance to the closest minimal $p$-divisible group (in the sense of Oort). In this paper, we study these invariants for supersingular unitary $p$-divisible groups of signature $(a,b)$. We provide a complete description of the possible minimal heights. As an applicati…

Hamiltonian torus actions and the unimodality of odd Betti numbers
Nicholas Lindsay
https://arxiv.org/abs/2507.19601 https://arxiv.org/pdf/2507.19601

Hamiltonian torus actions and the unimodality of odd Betti numbers
This paper is dedicated to the question: Is the sequence of odd and even Betti numbers of a closed symplectic manifold with a non-trivial Hamiltonian torus action unimodal? Recently, there was some progress on the question for the sequence of even Betti numbers by Cho-Kim and the author. The results of this paper give positive evidence in the case of odd Betti numbers, in dimensions $6,8$ and $10$ under progressively stronger symmetry assumptions.

Joint deformations of manifolds, coherent sheaves and sections
Donatella Iacono, Marco Manetti
https://arxiv.org/abs/2507.20276 https://arxiv.org/pdf/2507.…

Joint deformations of manifolds, coherent sheaves and sections
We describe a differential graded Lie algebra controlling infinitesimal deformations of triples $(X,\mathcal{F},σ)$, where $\mathcal{F}$ is a coherent sheaf on a smooth variety $X$ over an algebraically closed field of characteristic 0 and $σ\in H^0(X,\mathcal{F})$. Then, we apply this result to investigate deformations of pairs (variety, divisor).

Recurrent neural network-based robust control systems with closed-loop regional incremental ISS and application to MPC design
Daniele Ravasio, Marcello Farina, Alessio La Bella, Andrea Ballarino
https://arxiv.org/abs/2506.20334

Recurrent neural network-based robust control systems with closed-loop regional incremental ISS and application to MPC design
This paper investigates the design of output-feedback schemes for systems described by a class of recurrent neural networks. We propose a procedure based on linear matrix inequalities for designing an observer and a static state-feedback controller. The algorithm leverages global and regional incremental input-to-state stability (incremental ISS) and enables the tracking of constant setpoints, ensuring robustness to disturbances and state estimation uncertainty. To address the potential limitat…

Geometric considerations for energy minimization of topological links and chainmail networks
Alexander Klotz
https://arxiv.org/abs/2507.20903 https://arxiv…

Geometric considerations for energy minimization of topological links and chainmail networks
Knot and link energies can be computed from sets of closed curves in three dimensional space, and each type of knot or link has a minimum energy associated with it. Here, we consider embeddings of links that locally or globally minimize the Möbius and Minimum Distance energies. By describing these energies as functions of a small number of free parameters, we can find configurations that minimize the energies with respect to these parameters. It has previous been demonstrated that such minimiz…

We did a little promo video about the album for our Kickstarter campaign back then, and I think it’s pretty charming. The Kickstarter campaign is long since closed, but you can see see the video if you want to see the artists and get a little behind the scenes action:
https://www.kickstarter.com/projects/paul/the-river-inside-of-trees/

Orthocomplemented subspaces and partial projections on a Hilbert space
Iosif Petrakis
https://arxiv.org/abs/2508.15906 https://arxiv.org/pdf/2508.15906

Orthocomplemented subspaces and partial projections on a Hilbert space
We introduce the notion of an orthocomplemented subspace of a Hilbert space H, that is, a pair of orthogonal closed subspaces of H, as a two-dimensional counterpart to the one-dimensional notion of a closed subspace of H. Orthocomplemented subspaces are the Hilbert space-analogue to Bishop's complemented subsets. To complemented subsets correspond their characteristic functions, which are partial, Boolean-valued functions. Similarly, to orthocomplemented subspaces of H correspond partial projec…

Tietze extension does not always work in constructive mathematics if closed sets are defined as sequentially closed sets
Shun Ding, Yang Wan, Luofei Wang, Siqi Xiao
https://arxiv.org/abs/2508.11635

Tietze extension does not always work in constructive mathematics if closed sets are defined as sequentially closed sets
We prove that Tietze Extension does not always exist in constructive mathematics if closed sets on which the function we are extending are defined as sequentially closed sets. Firstly, we take a discrete metric space as our topological space. Now all sets open and sequentially closed. Then, we form an unextendible algorithmic function transforming positive integers to 0 and 1, looking at the preimages of these values as our sequentially closed sets. Then we show that if the Tietze theorem concl…

Open-closed 3d gravity as a random ensemble
Daniel L. Jafferis, Liza Rozenberg, Diandian Wang
https://arxiv.org/abs/2506.19817 https://

Open-closed 3d gravity as a random ensemble
We investigate an ensemble of boundary CFTs within the framework of a tensor model recently constructed to model 3d quantum gravity. The incorporation of CFT borders introduces new elements to the gravity theory. In particular, it leads to an open-closed extension of Virasoro TQFT, which in the classical limit gives rise to 3d gravity with tensionful end-of-the-world branes. It also provides predictions for off-shell manifolds with bordered asymptotic boundaries, such as the annulus wormhole. A…

Source: Fox has officially closed its upfront discussions, reaching $2B for core sports properties, excluding the World Cup, for the first time (Saleah Blancaflor/Adweek)
https://www.adweek.com/convergent-tv/fox-wraps-upfront-2-billion-sports-properties/…

Fox Wraps Upfront, Reaches $2 Billion for Core Sports Properties
Fox closed its upfront talks with double-digit volume growth across its portfolio.

A BBP-type formula for the remainder of the Madhava-Gregory-Leibniz series
Benoit Cloitre
https://arxiv.org/abs/2507.20428 https://arxiv.org/pdf/2507.20428…

A BBP-type formula for the remainder of the Madhava-Gregory-Leibniz series
We derive a BBP-type formula for the remainder of the Madhava-Gregory-Leibniz series for $π$. The result is a closed form in base-$16$ with Pochhammer denominators. The analogous formula for the alternating series for $\log 2$ is also presented.

Coadjoint orbits of low dimension for nilradicals of Borel subalgebras in classical types
Mikhail Ignatev, Alexey Petukhov
https://arxiv.org/abs/2507.20332 https://

Coadjoint orbits of low dimension for nilradicals of Borel subalgebras in classical types
Let $\mathfrak g$ be a classical simple Lie algebra over an algebraically closed field $\mathbb F$ of characteristic zero or large enough, and let $\mathfrak n$ be a maximal nilpotent subalgebra of $\mathfrak g$. The main tool in representation theory of $\mathfrak n$ is the orbit method, which classifies primitive ideals in the universal enveloping algebra ${\rm U}(\mathfrak n)$ and unitary representations of the unipotent group $N=\exp(\mathfrak n)$ in terms of coadjoint orbits on the dual sp…

Linear Dynamics meets Linear MDPs: Closed-Form Optimal Policies via Reinforcement Learning
Abed AlRahman Al Makdah, Oliver Kosut, Lalitha Sankar, Shaofeng Zou
https://arxiv.org/abs/2508.17185

Linear Dynamics meets Linear MDPs: Closed-Form Optimal Policies via Reinforcement Learning
Many applications -- including power systems, robotics, and economics -- involve a dynamical system interacting with a stochastic and hard-to-model environment. We adopt a reinforcement learning approach to control such systems. Specifically, we consider a deterministic, discrete-time, linear, time-invariant dynamical system coupled with a feature-based linear Markov process with an unknown transition kernel. The objective is to learn a control policy that optimizes a quadratic cost over the sy…

On algebraic vector bundles of rank $2$ over smooth affine fourfolds
Thomas Brazelton, Morgan Opie, Tariq Syed
https://arxiv.org/abs/2507.21029 https://arx…

On algebraic vector bundles of rank $2$ over smooth affine fourfolds
The classification of algebraic vector bundles of rank 2 over smooth affine fourfolds is a notoriously difficult problem. Isomorphism classes of such vector bundles are not uniquely determined by their Chern classes, in contrast to the situation in lower dimensions. Given a smooth affine fourfold over an algebraically closed field of characteristic not equal to $2$ or $3$, we study cohomological criteria for finiteness of the fibers of the Chern class map for rank $2$ bundles. As a consequence,…

Self-intersecting curves on a pair of pants and periodic orbits of Hamiltonian flows
Fernando Camacho-Cadena
https://arxiv.org/abs/2507.19191 https://arxiv…

Self-intersecting curves on a pair of pants and periodic orbits of Hamiltonian flows
The character variety $\mathscr{X}(S,G)$ associated to an oriented compact surface $S$ with boundary and a real reductive Lie group $G$ admits a Poisson structure and is foliated by symplectic leaves. When $G$ is a matrix group, any closed curve $c\inπ_1(S)$ induces a trace function $\mathsf{tr}_c\colon[ρ]\mapsto \mathsf{tr}(ρ(c))$ on $\mathscr{X}(S,G)$. In this article, we study the Hamiltonian flows of trace functions associated to self-intersecting curves. We prove that when $G=\mathsf{PS…

$C^0$-rigidity of the Hamiltonian diffeomorphism group of symplectic rational surfaces
Marcelo Atallah, Cheuk Yu Mak, Weiwei Wu
https://arxiv.org/abs/2508.20285 https://

$C^0$-rigidity of the Hamiltonian diffeomorphism group of symplectic rational surfaces
We investigate the $C^0$-topology of the group of symplectic diffeomorphisms of positive symplectic rational surfaces. For all but a few exceptions, we prove that the group of Hamiltonian diffeomorphisms forms a connected component in the $C^0$-topology. This provides the first nontrivial case in which the group of Hamiltonian diffeomorphisms is known to be $C^0$-closed inside the group of symplectic diffeomorphisms. The key to our approach is to build a bridge between techniques from symplec…

Finite generation of abelianizations of the genus 3 Johnson kernel and the commutator subgroup of the Torelli group for $\mathrm{Out}(F_3)$
Alexander A. Gaifullin
https://arxiv.org/abs/2507.20710

Finite generation of abelianizations of the genus 3 Johnson kernel and the commutator subgroup of the Torelli group for $\mathrm{Out}(F_3)$
Let $Σ_g^b$ be a compact oriented surface of genus $g$ with $b$ boundary components, where $b\in\{0,1\}$. The Johnson kernel $\mathcal{K}_g^b$ is the subgroup of the mapping class group $\mathrm{Mod}(Σ_g^b)$ generated by Dehn twists about separating simple closed curves. Let $F_n$ be a free group with $n$ generators. The Torelli group for $\mathrm{Out}(F_n)$ is the subgroup $\mathrm{IO}_n\subset\mathrm{Out}(F_n)$ consisting of all outer automorphisms that act trivially on the abelianization o…

A series involving a product of four consecutive harmonic numbers
Wilson J. Chen, Vincent Nguyen
https://arxiv.org/abs/2507.19502 https://arxiv.org/pdf/250…

A series involving a product of four consecutive harmonic numbers
In correspondence with Goldbach, Euler began investigating series of the form $\sum_{k \geq 1} k^{-m}\left(1 + 2^{-n} + \cdots + k^{-n}\right)$, which are known today as Euler sums. For the case where $n=1$ and $m \geq 2$, Euler was able to obtain a closed form in terms of zeta values. We use elementary techniques in the spirit of Euler to evaluate the series $\sum_{k \geq 1} \frac{H_k H_{k+1} H_{k+2} H_{k+3}}{k(k+1)(k+2)(k+3)},$ where $H_k := 1 + \frac{1}{2} + \cdots + \frac{1}{k}$ is the $k…

HuBE: Cross-Embodiment Human-like Behavior Execution for Humanoid Robots
Shipeng Lyu, Fangyuan Wang, Weiwei Lin, Luhao Zhu, David Navarro-Alarcon, Guodong Guo
https://arxiv.org/abs/2508.19002

HuBE: Cross-Embodiment Human-like Behavior Execution for Humanoid Robots
Achieving both behavioral similarity and appropriateness in human-like motion generation for humanoid robot remains an open challenge, further compounded by the lack of cross-embodiment adaptability. To address this problem, we propose HuBE, a bi-level closed-loop framework that integrates robot state, goal poses, and contextual situations to generate human-like behaviors, ensuring both behavioral similarity and appropriateness, and eliminating structural mismatches between motion generation an…

Aperiodic-sampled neural network controllers with closed-loop stability verifications (extended version)
Renjie Ma, Zhijian Hu, Rongni Yang, Ligang Wu
https://arxiv.org/abs/2506.18386

Aperiodic-sampled neural network controllers with closed-loop stability verifications (extended version)
In this paper, we synthesize two aperiodic-sampled deep neural network (DNN) control schemes, based on the closed-loop tracking stability guarantees. By means of the integral quadratic constraint coping with the input-output behaviour of system uncertainties/nonlinearities and the convex relaxations of nonlinear DNN activations leveraging their local sector-bounded attributes, we establish conditions to design the event- and self-triggered logics and to compute the ellipsoidal inner approximati…

STEP Planner: Constructing cross-hierarchical subgoal tree as an embodied long-horizon task planner
Zhou Tianxing, Wang Zhirui, Ao Haojia, Chen Guangyan, Xing Boyang, Cheng Jingwen, Yang Yi, Yue Yufeng
https://arxiv.org/abs/2506.21030

STEP Planner: Constructing cross-hierarchical subgoal tree as an embodied long-horizon task planner
The ability to perform reliable long-horizon task planning is crucial for deploying robots in real-world environments. However, directly employing Large Language Models (LLMs) as action sequence generators often results in low success rates due to their limited reasoning ability for long-horizon embodied tasks. In the STEP framework, we construct a subgoal tree through a pair of closed-loop models: a subgoal decomposition model and a leaf node termination model. Within this framework, we develo…

A note on the recursive computation of the bracket polynomial for closed 4-tangles
Franck Ramaharo
https://arxiv.org/abs/2508.17904 https://arxiv.org/pdf/2…

A note on the recursive computation of the bracket polynomial for closed 4-tangles
Given a 4-tangle shadow, we concatenate it with itself n times and form a knot by applying a closure operation that connects each top endpoint to the corresponding bottom endpoint on the same side without introducing any crossings. We then compute the Kauffman bracket polynomial for the resulting knot using a states matrix defined with respect to the basis of the Kauffman 4-strand diagram monoid.