Tootfinder

On elementary abelian 2-hypergroups
Yu Jiang
https://arxiv.org/abs/2506.05291 https://arxiv.org/pdf/2506.05291

On elementary abelian 2-hypergroups
A hypergroup is called an elementary abelian 2-hypergroup if it is a constrained direct product of the closed subsets of two elements. In this paper, the elementary abelian 2-hypergroups are studied. All closed subsets and all strongly normal closed subsets of the elementary abelian 2-hypergroups are determined. The numbers of all closed subsets and all strongly normal closed subsets of the elementary abelian 2-hypergroups are given. A criterion for the isomorphic closed subsets of the elementa…

This https://arxiv.org/abs/1804.08452 has been replaced.
link: https://scholar.google.com/scholar?q=a

Two closed geodesics on compact bumpy Finsler manifolds
In this paper, we prove there are at least two closed geodesics on any compact bumpy Finsler $n$-manifold with finite fundamental group and $n\ge 2$. Thus generically there are at least two closed geodesics on compact Finsler manifolds with finite fundamental group. Furthermore, there are at least two closed geodesics on any compact Finsler $2$-manifold, and this lower bound is achieved by the Katok 2-sphere $(S^2, F)$ and 2-real projective space $(S^2/\Z_2, F)$, cf. \cite{Kat}.

Boosting Open-Source LLMs for Program Repair via Reasoning Transfer and LLM-Guided Reinforcement Learning
Xunzhu Tang, Jacques Klein, Tegawend\'e F. Bissyand\'e
https://arxiv.org/abs/2506.03921

Boosting Open-Source LLMs for Program Repair via Reasoning Transfer and LLM-Guided Reinforcement Learning
Several closed-source LLMs have consistently outperformed open-source alternatives in program repair tasks, primarily due to their superior reasoning capabilities and extensive pre-training. This paper introduces Repairity, a novel three-stage methodology that significantly narrows this performance gap through reasoning extraction and reinforcement learning. Our approach: (1) systematically filters high-quality reasoning traces from closed-source models using correctness verification, (2) trans…

Ukraine's military intelligence agency (HUR) has gained access to sensitive data of Russia's strategic aircraft manufacturer Tupolev
Tupolev, a Soviet-era aerospace firm now fully integrated into Russia's defense-industrial complex, has been under international sanctions since 2022 for its role in Russia's war against Ukraine.
Its bombers have been widely used to launch long-range cruise missiles against Ukrainian cities and infrastructure.
According to the so…

'There is nothing secret left' — Ukraine hacks Russia's Tupolev aircraft manufacturer, source claims
HUR's cyber corps accessed over 4.4 gigabytes (GB) of internal data, including official correspondence, personnel files, home addresses, resumes, purchase records, and closed meeting minutes, a source claimed.

Stop saying "don't get distracted" and let us enjoy this one thing. It's been so long..

Fast Sampling for System Identification: Overcoming Noise, Offsets, and Closed-Loop Challenges with State Variable Filter
Ichiro Maruta, Toshiharu Sugie
https://arxiv.org/abs/2506.03650

Fast Sampling for System Identification: Overcoming Noise, Offsets, and Closed-Loop Challenges with State Variable Filter
This paper investigates the effects of setting the sampling frequency significantly higher than conventional guidelines in system identification. Although continuous-time identification methods resolve the numerical difficulties encountered in discrete-time approaches when employing fast sampling (e.g., the problems caused by all poles approaching unity), the potential benefits of using sampling frequencies that far exceed traditional rules like the "ten times the bandwidth" guideline remained …

On the robustness of Dirichlet-Neumann coupling schemes for fluid-structure-interaction problems with nearly-closed fluid domains
A. Aissa-Berraies, Ferdinando A. Auricchio, Gertjan van Zwieten, E. Harald van Brummelen
https://arxiv.org/abs/2506.04027

On the robustness of Dirichlet-Neumann coupling schemes for fluid-structure-interaction problems with nearly-closed fluid domains
Partitioned methods for fluid-structure interaction (FSI) involve solving the structural and flow problems sequentially. These methods allow for separate settings for the fluid and solid subsystems and thus modularity, enabling reuse of advanced commercial and open-source software. Most partitioned FSI schemes apply a Dirichlet-Neumann (DN) split of the interface conditions. The DN scheme is adequate in a wide range of applications, but it is sensitive to the added-mass effect, and it is suscep…

This https://arxiv.org/abs/2505.05098 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csRO_…

X-Driver: Explainable Autonomous Driving with Vision-Language Models
End-to-end autonomous driving has advanced significantly, offering benefits such as system simplicity and stronger driving performance in both open-loop and closed-loop settings than conventional pipelines. However, existing frameworks still suffer from low success rates in closed-loop evaluations, highlighting their limitations in real-world deployment. In this paper, we introduce X-Driver, a unified multi-modal large language models(MLLMs) framework designed for closed-loop autonomous driving…

I'm starting to become a #bandcamp fan...
Is there a better open source app, than the official closed one?
#opensource #music

This https://arxiv.org/abs/2403.05349 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Extended Sobolev scale for vector bundles, and its applications
We study an extended Sobolev scale for smooth vector bundles over a smooth closed manifold. This scale is built on the base of inner product distribution spaces of generalized smoothness given by an arbitrary positive function OR-varying at infinity. We show that this scale is obtained by the quadratic interpolation (with a function parameter) between inner product Sobolev spaces, is closed with respect to the quadratic interpolation, and consists of all Hilbert spaces that are interpolation sp…

This https://arxiv.org/abs/2401.00510 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Smoothness Estimation for Whittle-Matérn Processes on Closed Riemannian Manifolds
The family of Matérn kernels are often used in spatial statistics, function approximation and Gaussian process methods in machine learning. One reason for their popularity is the presence of a smoothness parameter that controls, for example, optimal error bounds for kriging and posterior contraction rates in Gaussian process regression. On closed Riemannian manifolds, we show that the smoothness parameter can be consistently estimated from the maximizer(s) of the Gaussian likelihood when the u…

Ben Johnson preparing his set of trick plays in Chicago: 'We've got some toys to work with' https://www.nfl.com/news/ben-johnson-preparing-trick-plays-chicago-some-toys-to-work-with

For Zotero users, the Android app is finally out of closed beta. It supports saving papers directly from the browser or other apps, which takes several steps out of my workflow for increasing my TBR pile.
https://www.zotero.org/blog/zotero-for-android/

This https://arxiv.org/abs/2505.24584 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLG_…

AutoChemSchematic AI: A Closed-Loop, Physics-Aware Agentic Framework for Auto-Generating Chemical Process and Instrumentation Diagrams
Recent advancements in generative AI have accelerated the discovery of novel chemicals and materials; however, transitioning these discoveries to industrial-scale production remains a critical bottleneck, as it requires the development of entirely new chemical manufacturing processes. Current AI methods cannot auto-generate PFDs or PIDs, despite their critical role in scaling chemical processes, while adhering to engineering constraints. We present a closed loop, physics aware framework for the…

Performed in an improv show in Shoreditch.
Good times.
Everyone seemed to think the show went well, and it featured repeated themes of fish taking over the entire world in a giant conspira-sea.
The venue downstairs at Shoreditch Balls is tight and dark and small but so were our audience. Thanks for coming everyone. 😆
Where does the group go from here? Dunno. Hard to find a venue for rehearsal in London really. Everywhere is either booked up or closed down. Makes you wonder why the closed down ones had to close given the apparent demand.
Fingers crossed we find somewhere 🤞
#london #improv #liveShow

Definable ranks of almost real closed fields
Lothar Sebastian Krapp, Salma Kuhlmann, Lasse Vogel
https://arxiv.org/abs/2506.00443 https://

Definable ranks of almost real closed fields
We introduce the notion of the definable rank of an ordered field, ordered abelian group and ordered set, respectively. We study the relation between the definable rank of an ordered field and the definable rank of the value group of its natural valuation. Similarly we compare the definable rank of an ordered abelian group and the value set of its natural valuation. We consider in particular the case of an almost real closed field and give conditions under which the definable ranks on the level…

Closed-form survival probabilities for biased random walks at arbitrary step number
Debendro Mookerjee, Sarah Kostinski
https://arxiv.org/abs/2505.24814 ht…

Closed-form survival probabilities for biased random walks at arbitrary step number
We present a closed-form expression for the survival probability of a biased random walker to first reach a target site on a 1D lattice. The expression holds for any step number $N$ and is computationally faster than non-closed-form results in the literature. Because our result is exact even in the intermediate step number range, it serves as a tool to study convergence to the large $N$ limit. We also obtain a closed-form expression for the probability of last passage. In contrast to prediction…

De Russen
Google Maps can’t explain why it falsely labeled German autobahns as closed - Ars Technica
https://arstechnica.com/tech-policy/2025/05/google-maps-cant-explain-why-it-falsely-labeled-german-aut…

Generalized Hardy's identity for the astroid-type p-circle lattice point problem
Masaya Kitajima
https://arxiv.org/abs/2506.03331 https://

Generalized Hardy's identity for the astroid-type p-circle lattice point problem
Let $r$ be a positive real number and $p$ satisfy $(2/p)\in\mathbb{N}$. Then, we consider the lattice point problem of the closed curves astroid-type $p$-circle $\{x\in\mathbb{R}^{2}|\ |x_{1}|^{p}+|x_{2}|^{p}=r^{p}\}$ which generalize the circle. In investigating the asymptotic behavior of the error term in the area approximation of the circle, G.H. Hardy conjectured an infimum for the evaluation in 1917. One of the grounds for this conjecture is the Hardy's identity, w…

There is a long abandoned industrial park that I go to to practice figure eights on the bike. It was closed and blocked off for a solid month. I finally got back to it and saw this at one of the entrances. I am slightly curious what DMV is.

This https://arxiv.org/abs/2205.00368 has been replaced.
link: https://scholar.google.com/scholar?q=a

Direct closed-loop identification of continuous-time systems using fixed-pole observer model
This paper provides a method for obtaining a continuous-time model of a target system in closed-loop from input-output data alone, in the case where no knowledge of the controllers nor excitation signals is available and I/O data may suffer from unknown offsets. The proposed method is based on a fixed-pole observer model, which is a reasonable continuous-time version corresponding to the innovation model in discrete-time and allows the identification of unstable target systems. Furthermore, it …

A robust approach to sigma point Kalman filtering
Shenglun Yi, Mattia Zorzi
https://arxiv.org/abs/2506.04815 https://arxiv.org/pdf/25…

A robust approach to sigma point Kalman filtering
In this paper, we address a robust nonlinear state estimation problem under model uncertainty by formulating a dynamic minimax game: one player designs the robust estimator, while the other selects the least favorable model from an ambiguity set of possible models centered around the nominal one. To characterize a closed-form expression for the conditional expectation characterizing the estimator, we approximate the center of this ambiguity set by means of a sigma point approximation. Furthermo…

Sensor Tower: daily US users of PDD Holdings' Temu fell by 58% in May; the US closed the "de minimis" loophole on May 2, and Temu then slashed its ad spending (Reuters)
https://www.reuters.com/business/retail-co

manchmal findet sich auch in sprachwissenschaftlichen werken was zu #openaccess:
https://doi.org/10.1515/9783110672633-036 [aber leider in closed access –

This https://arxiv.org/abs/2407.01203 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

An elementary proof of a criterion for subfunctors of Ext to be closed
Let $\mathcal{A}$ be an abelian category and let $F$ be a subbifunctor of the additive bifunctor $\text{Ext}_{\mathcal{A}}^{1}(-,-)\colon \mathcal{A}^{\text{op}}\times \mathcal{A}\to \mathsf{Ab}$. Buan proved in [4] that $F$ is closed if, and only if, $F$ has the $3\times 3$-lemma property, a certain diagrammatic property satisfied by the class of $F$-exact sequences. The proof of this result relies on the theory of exact categories and on the Freyd--Mitchell embedding theorem, a very well-know…

Vanishing arcs for isolated plane curve singularities
Hanwool Bae, Cheol-Hyun Cho, Dongwook Choa, Wonbo Jeong, Pablo Portilla Cuadrado
https://arxiv.org/abs/2506.04917

Vanishing arcs for isolated plane curve singularities
The variation operator associated with an isolated hypersurface singularity is a classical topological invariant that relates relative and absolute homologies of the Milnor fiber via a non trivial isomorphism. Here we work with a topological version of this operator that deals with proper arcs and closed curves instead of homology cycles. Building on the classical framework of geometric vanishing cycles, we introduce the concept of vanishing arcsets as their counterpart using this geometric var…

Efficient Gibbs Sampling in Cox Regression Models Using Composite Partial Likelihood and P\'olya-Gamma Augmentation
Shu Tamano, Yui Tomo
https://arxiv.org/abs/2506.04675

Efficient Gibbs Sampling in Cox Regression Models Using Composite Partial Likelihood and Pólya-Gamma Augmentation
The Cox regression model and its Bayesian extensions are widely used in survival analysis. However, standard Bayesian approaches require modeling of the baseline hazard, and their full conditional distributions lack closed-form expressions. Therefore, the Metropolis-Hastings sampling algorithm is typically employed, whose efficiency is highly sensitive to the choice of proposal distribution. To address these issues, we propose the GS4Cox, an efficient Gibbs sampling algorithm for the Cox regres…

This https://arxiv.org/abs/2104.07431 has been replaced.
link: https://scholar.google.com/scholar?q=a

One-ended spanning subforests and treeability of groups
We show that several new classes of groups are measure strongly treeable. In particular, finitely generated groups admitting planar Cayley graphs, elementarily free groups, and the group of isometries of the hyperbolic plane and all its closed subgroups. This provides the first examples of one-ended nonamenable groups which are measure strongly treeable. In higher dimensions, we also prove a dichotomy that the fundamental group of a closed aspherical $3$-manifold is either amenable or has stron…

StARS DCM: A Sleep Stage-Decoding Forehead EEG Patch for Real-time Modulation of Sleep Physiology
William G. Coon, Preston Peranich, Griffin Milsap
https://arxiv.org/abs/2506.03442

StARS DCM: A Sleep Stage-Decoding Forehead EEG Patch for Real-time Modulation of Sleep Physiology
The System to Augment Restorative Sleep (StARS) is a modular hardware/software platform designed for real-time sleep monitoring and intervention. Utilizing the compact DCM biosignal device, StARS captures electrophysiological signals (EEG, EMG, EOG) and synchronizes sensor data using the ezmsg real-time software framework. StARS supports interventions such as closed-loop auditory stimulation and dynamic thermal modulation guided by sleep-stage decoding via advanced neural network models and tra…

Gravitational Collapse: Generalizing Oppenheimer-Snyder and a Conjecture on Horizon Formation Time
H. Khodabakhshi, H. Lu, F. Shojai
https://arxiv.org/abs/2506.03702

Gravitational Collapse: Generalizing Oppenheimer-Snyder and a Conjecture on Horizon Formation Time
We generalize the Oppenheimer-Snyder model of gravitational collapse by considering a broader class of static, spherically symmetric exterior spacetimes, with an interior geometry described by a Friedmann-Lemaitre-Robertson-Walker (FLRW) geometry. Using Painleve-Gullstrand (PG) coordinates for the spatially flat interior geometry (k=0) and a Novikov-like coordinate system for the spatially closed geometry (k=1), we ensured a smooth transition between the interior and exterior of the collapsing …

Interlinking internal and external magnetic fields of relativistically rotating neutron stars
D. Ntotsikas, K. N. Gourgouliatos
https://arxiv.org/abs/2506.04198

Interlinking internal and external magnetic fields of relativistically rotating neutron stars
This work presents a global solution for the internal and the external field of an axisymmetric rotating neutron star. It is shown that the twist of the internal field affects the external field, by increasing the number of open field lines and eventually the spin-down rate of the star. This effect is far more drastic if the toroidal field, and consequently the poloidal current flowing within the star, is allowed to populate the closed field lines of the magnetosphere, rather than if it remains…

This https://arxiv.org/abs/2504.17644 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Bounded diagonal orbits in homogeneous spaces over function fields
This paper is about topological rigidity of diagonal group actions on the homogeneous $\SL_4\big(\F(\!(t^{-1})\!)\big)/\SL_4(\F[t])$ where $\F$ is a finite field of characteristic $3$. We show that there is a non-closed relatively compact orbit of the diagonal group.

A Fast Unsupervised Scheme for Polygonal Approximation
Bimal Kumar Ray
https://arxiv.org/abs/2506.04664 https://arxiv.org/pdf/2506.04…

A Fast Unsupervised Scheme for Polygonal Approximation
This paper proposes a fast and unsupervised scheme for a polygonal approximation of a closed digital curve. It is demonstrated that the approximation scheme is faster than state-of-the-art approximation and is competitive with the same in Rosin's measure and in its aesthetic aspect. The scheme comprises of three phases: initial segmentation, iterative vertex insertion, and iterative merging, followed by vertex adjustment. The initial segmentation is used to detect sharp turnings - the vertices …

Topological Mixed States: Axiomatic Approaches and Phases of Matter
Tai-Hsuan Yang, Bowen Shi, Jong Yeon Lee
https://arxiv.org/abs/2506.04221 https://

Topological Mixed States: Axiomatic Approaches and Phases of Matter
For closed quantum systems, topological orders are understood through the equivalence classes of ground states of gapped local Hamiltonians. The generalization of this conceptual paradigm to open quantum systems, however, remains elusive, often relying on operational definitions without fundamental principles. Here, we fill this gap by proposing an approach based on three axioms: ($i$) local recoverability, ($ii$) absence of long-range correlations, and ($iii$) spatial uniformity. States that s…

Weak solutions of Stochastic Volterra Equations in convex domains with general kernels
Eduardo Abi Jaber, Aur\'elien Alfonsi, Guillaume Szulda
https://arxiv.org/abs/2506.04911

Weak solutions of Stochastic Volterra Equations in convex domains with general kernels
We establish new weak existence results for $d$-dimensional Stochastic Volterra Equations (SVEs) with continuous coefficients and possibly singular one-dimensional non-convolution kernels. These results are obtained by introducing an approximation scheme and showing its convergence. A particular emphasis is made on the stochastic invariance of the solution in a closed convex set. To do so, we extend the notion of kernels that preserve nonnegativity introduced in \cite{Alfonsi23} to non-convolut…

Hyperbolicity and GCD for n 1 divisors with non-empty intersection
Julie Tzu-Yueh Wang, Zheng Xiao
#toXiv_bot_toot

Thinking Beyond Visibility: A Near-Optimal Policy Framework for Locally Interdependent Multi-Agent MDPs
Alex DeWeese, Guannan Qu
https://arxiv.org/abs/2506.04215

Thinking Beyond Visibility: A Near-Optimal Policy Framework for Locally Interdependent Multi-Agent MDPs
Decentralized Partially Observable Markov Decision Processes (Dec-POMDPs) are known to be NEXP-Complete and intractable to solve. However, for problems such as cooperative navigation, obstacle avoidance, and formation control, basic assumptions can be made about local visibility and local dependencies. The work DeWeese and Qu 2024 formalized these assumptions in the construction of the Locally Interdependent Multi-Agent MDP. In this setting, it establishes three closed-form policies that are tr…

Pseudo-Simulation for Autonomous Driving
Wei Cao, Marcel Hallgarten, Tianyu Li, Daniel Dauner, Xunjiang Gu, Caojun Wang, Yakov Miron, Marco Aiello, Hongyang Li, Igor Gilitschenski, Boris Ivanovic, Marco Pavone, Andreas Geiger, Kashyap Chitta
https://arxiv.org/abs/2506.04218

Pseudo-Simulation for Autonomous Driving
Existing evaluation paradigms for Autonomous Vehicles (AVs) face critical limitations. Real-world evaluation is often challenging due to safety concerns and a lack of reproducibility, whereas closed-loop simulation can face insufficient realism or high computational costs. Open-loop evaluation, while being efficient and data-driven, relies on metrics that generally overlook compounding errors. In this paper, we propose pseudo-simulation, a novel paradigm that addresses these limitations. Pseudo…

This https://arxiv.org/abs/2308.01715 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

An equivariant compactification for adjoint reductive group schemes
Wonderful compactifications of adjoint reductive groups over an algebraically closed field play an important role in algebraic geometry and representation theory. In this paper, we construct an equivariant compactification for adjoint reductive groups over arbitrary base schemes. Our compactifications parameterize classical wonderful compactifications of De Concini and Procesi as geometric fibers. Our construction is based on a variant of the Artin-Weil method of birational group laws. In parti…

This https://arxiv.org/abs/2410.00399 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The HOMFLY Polynomial of a Forest Quiver
We define the HOMFLY polynomial of a forest quiver $Q$ using a recursive definition on the underlying graph of the quiver. We then show that this polynomial is equal to the HOMFLY polynomial of any plabic link which comes from a connected plabic graph whose quiver is $Q$. We also prove a closed-form expression for the HOMFLY polynomial of a forest quiver $Q$ in terms of the independent sets of $Q$.

On Strong Markushevich bases $\{t^{\lambda_n}\}_{n=1}^{\infty}$ in their closed span in $L^2 (0, 1)$ and characterizing a subspace of $H^2 (\mathbb{D})$
Elias Zikkos
https://arxiv.org/abs/2505.24761

On Strong Markushevich bases $\{t^{λ_n}\}_{n=1}^{\infty}$ in their closed span in $L^2 (0, 1)$ and characterizing a subspace of $H^2 (\mathbb{D})$
Let $Λ=\{λ_n\}_{n=1}^{\infty}$ be a strictly increasing sequence of positive real numbers such that $\sum_{n=1}^{\infty}\frac{1}{λ_n}<\infty$ and $\inf(λ_{n+1}-λ_n)>0$. We investigate properties of the closed span of the system $\{t^{λ_n}\}_{n=1}^{\infty}$ in $L^2 (0,1)$, denoted by $\overline{M_Λ}$, and of the unique biorthogonal family $\{r_n (t)\}_{n=1}^{\infty}$ to the system $\{t^{λ_n}\}_{n=1}^{\infty}$ in $\overline{M_Λ}$. We show that the system $\{t^{λ_n}\}_{n=1}^{\infty}$ is …

Close points on a modular hyperbola
Tsz Ho Chan
https://arxiv.org/abs/2506.04087 https://arxiv.org/pdf/2506.04087

Close points on a modular hyperbola
In this paper, we continue the study of small squares containing at least two points on a modular hyperbola $x y \equiv c \pmod{p}$. We deduce a lower bound for its side length. We also investigate what happens if the ``distances" between two such points are special type of numbers like prime numbers, squarefree numbers or smooth numbers as well as more general multiplicatively closed sets or almost dense sets.

This https://arxiv.org/abs/2312.00138 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Scalar curvature and volume entropy of hyperbolic 3-manifolds
We show that any closed hyperbolic 3-manifold M admits a Riemannian metric with scalar curvature at least -6, but with volume entropy strictly larger than 2. In particular, this construction gives counterexamples to a conjecture of I. Agol, P. Storm and W. Thurston.

Optimal Dynamic Fees in Automated Market Makers
Leonardo Baggiani, Martin Herdegen, Leandro S\'anchez-Betancourt
https://arxiv.org/abs/2506.02869 https…

Optimal Dynamic Fees in Automated Market Makers
Automated Market Makers (AMMs) are emerging as a popular decentralised trading platform. In this work, we determine the optimal dynamic fees in a constant function market maker. We find approximate closed-form solutions to the control problem and study the optimal fee structure. We find that there are two distinct fee regimes: one in which the AMM imposes higher fees to deter arbitrageurs, and another where fees are lowered to increase volatility and attract noise traders. Our results also show…

access:conditional=angels
Found in CPH hotel, Copenhagen.

Classification of exact structures using the Ziegler spectrum
Julia Sauter
https://arxiv.org/abs/2506.02304 https://arxiv.org/pdf/250…

Classification of exact structures using the Ziegler spectrum
Given an idempotent complete additive category, we show the there is an explicitly constructed topological space such that the lattice of exact substructures is anti-isomorphic to the lattice of closed subsets. In the special case that the additive category has weak cokernels, this topological space is an open subset of the Ziegler spectrum and this is a result of Kevin Schlegel. We also look at some module categories of rings where the Ziegler spectrum is known and calculate the global dimensi…

This https://arxiv.org/abs/2409.14156 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Computing the Proximal Operator of the $q$-th Power of the $\ell_{1,q}$-norm for Group Sparsity
In this note, we comprehensively characterize the proximal operator of the $q$-th power of the $\ell_{1,q}$-norm (denoted by $\ell_{1,q}^{q}$) with $0\!<\!q\!<\!1$ by exploiting the well-known proximal operator of $|\cdot|^q$ on the real line. In particular, much more explicit characterizations can be obtained whenever $q\!=\!1/2$ and $q\!=\!2/3$ due to the existence of closed-form expressions for the proximal operators of $|\cdot|^{1/2}$ and $|\cdot|^{2/3}$. Numer…

A Bi-Level Optimization Method for Redundant Dual-Arm Minimum Time Problems
Jonathan Fried, Santiago Paternain
https://arxiv.org/abs/2506.03982 https://

A Bi-Level Optimization Method for Redundant Dual-Arm Minimum Time Problems
In this work, we present a method for minimizing the time required for a redundant dual-arm robot to follow a desired relative Cartesian path at constant path speed by optimizing its joint trajectories, subject to position, velocity, and acceleration limits. The problem is reformulated as a bi-level optimization whose lower level is a convex, closed-form subproblem that maximizes path speed for a fixed trajectory, while the upper level updates the trajectory using a single-chain kinematic formu…

This https://arxiv.org/abs/2505.07358 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Two-point tree-level string amplitudes as AdS transition amplitudes
We compute the two-point open string and closed string amplitudes at tree level and show that, in a 't Hooft-like limit, they take a form structurally analogous to boundary-to-boundary transition amplitudes of a scalar field in Euclidean AdS space. Interestingly, while both amplitudes yield equivalent expressions, the associated 't Hooft couplings are defined by different worldsheet curvatures-geodesic for the disk and Gaussian for the sphere-suggesting a possible geometric aspect of open/close…

On sums of $\mathscr{P}$-free forms under mis\`ere play
Alfie Davies, Sarah Miller, Rebecca Milley
https://arxiv.org/abs/2506.05257 https://

On sums of $\mathscr{P}$-free forms under misère play
Milley and Renault proved an interesting characterisation of invertible elements in the dead-ending universe: they are the games with no subpositions of outcome $\mathscr{P}$ (the '$\mathscr{P}$-free' games). We generalise their approach to obtain a stronger result and show in particular that the set of $\mathscr{P}$-free blocking games is closed under addition, which yields that every $\mathscr{P}$-free blocking game is invertible modulo the blocking universe. This has consequences for the inv…

Khintchine inequalities, trace monoids and Tur\'an-type problems
Patrick Oliveira Santos, Raghavendra Tripathi, Pierre Youssef
https://arxiv.org/abs/2506.02517

Khintchine inequalities, trace monoids and Turán-type problems
We prove scalar and operator-valued Khintchine inequalities for mixtures of free and tensor-independent semicircle variables, interpolating between classical and free Khintchine-type inequalities. Specifically, we characterize the norm of sums of $G$-independent semicircle variables in terms of the spectral radius of the Cayley graph associated with the trace monoid determined by the graph $G$. Our approach relies on a precise correspondence between closed paths in trace monoids and the norms o…

A fun glimpse on a North London street today.
#StreetArt
#PublicArt
#Astronaut
#London

This https://arxiv.org/abs/2505.24762 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Branched $α$-combinatorial Ricci flows on closed surfaces with Euler characteristic $χ\le 0$
This paper investigates branched $α$-flows on weighted triangulated closed surfaces with Euler characteristic \(χ\leq 0\), focusing on establishing their connections with topological (combinatorial) and geometric structures. In Euclidean (\(\mathbb{E}^2\)) and hyperbolic (\(\mathbb{H}^2\)) geometries, we define branched $α$-curvatures and corresponding branched $α$-flows. By introducing branched $α$-potentials, we prove the existence and uniqueness of constant branched $α$-metrics through…

High-Contrast Coronagraphy
Matthew A. Kenworthy, Sebastiaan Y. Haffert
#toXiv_bot_toot

Hyperbolic small knots in spherical manifolds
Kazuhiro Ichihara
https://arxiv.org/abs/2506.01041 https://arxiv.org/pdf/2506.01041

Hyperbolic small knots in spherical manifolds
It was conjectured by Lopez that every closed irreducible non-Haken 3-manifold contains a small knot. In this paper, we give explicit examples of hyperbolic small knots in most closed orientable spherical 3-manifolds other than prism manifolds.

This https://arxiv.org/abs/2501.09015 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Family-wise Error Rate Control with E-values
The closure principle is a standard tool for achieving strong family-wise error rate (FWER) control in multiple testing problems. We develop an e-value-based closed testing framework that inherits nice properties of e-values, which are common in settings of sequential hypothesis testing or universal inference for irregular parametric models. We prove that e-value-based closed testing strongly controls the post-hoc FWER in the static setting, and has stronger anytime-valid and always-valid FWER-…

This https://arxiv.org/abs/2411.03378 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Quasi-electrostatic eigenmode analysis of anisotropic particles
Anisotropic subwavelength particles combine the strong response and tunability of nanostructures with the exotic properties of anisotropic materials. Here we derive closed-form expressions for the quasielectrostatic eigenmodes and eigenpermittivity relations of uniaxial and biaxial spheres and ellipsoids. We show that such particles exhibit novel radiation patterns and axial-eigenpermittivity sum rules, resulting in resonance splitting and eigenvalue degeneracy. Finally, we analytically predict…

Understanding Physical Properties of Unseen Deformable Objects by Leveraging Large Language Models and Robot Actions
Changmin Park, Beomjoon Lee, Haechan Jung, Haejin Jung, Changjoo Nam
https://arxiv.org/abs/2506.03760

Understanding Physical Properties of Unseen Deformable Objects by Leveraging Large Language Models and Robot Actions
In this paper, we consider the problem of understanding the physical properties of unseen objects through interactions between the objects and a robot. Handling unseen objects with special properties such as deformability is challenging for traditional task and motion planning approaches as they are often with the closed world assumption. Recent results in Large Language Models (LLMs) based task planning have shown the ability to reason about unseen objects. However, most studies assume rigid o…

This https://arxiv.org/abs/2506.01226 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

React to Surprises: Stable-by-Design Neural Feedback Control and the Youla-REN
We study parameterizations of stabilizing nonlinear policies for learning-based control. We propose a structure based on a nonlinear version of the Youla-Kučera parameterization combined with robust neural networks such as the recurrent equilibrium network (REN). The resulting parameterizations are unconstrained, and hence can be searched over with first-order optimization methods, while always ensuring closed-loop stability by construction. We study the combination of (a) nonlinear dynamics, …

Toroidal embedding of Chevalley groups over $\mathbb{Z}$
Shang Li
https://arxiv.org/abs/2506.02638 https://arxiv.org/pdf/2506.02638…

Toroidal embedding of Chevalley groups over $\mathbb{Z}$
The classification of equivariant toroidal embeddings of a reductive group over an algebraically closed field is combinatorial and does not depend on the characteristic of the base field. This suggests that there should exist ``universal'' toroidal embeddings for a Chevalley group scheme over $\mathbb{Z}$ which specialize to classical toroidal embeddings via base change. In this paper, we establish the existence of ``universal'' equivariant toroidal embeddings for split reductive group schemes …

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Patioboater (@patioboater@mastodon.social)
Angehängt: 4 Bilder A visit to the Elephant Graveyard of West Bloomfield, Michigan: unsold Cybertrucks piling up in the parking lot of a closed Bed, Bath, & Beyond about a mile south of the Tesla dealer. May 30, 2025. #Tesla #Michigan #cybertruck

Information Geometry on the $\ell^2$-Simplex via the $q$-Root Transform
Levin Maier
https://arxiv.org/abs/2506.00485 https://arxiv.or…

Information Geometry on the $\ell^2$-Simplex via the $q$-Root Transform
In this paper, we introduce \emph{$\ell^p$-information geometry}, an infinite dimensional framework that shares key features with the geometry of the space of probability densities \( \mathrm{Dens}(M) \) on a closed manifold, while also incorporating aspects of measure-valued information geometry. We define the \emph{$\ell^2$-probability simplex} with a noncanonical differentiable structure induced via the \emph{$q$-root transform} from an open subset of the $\ell^p$-sphere. This structure rend…

I just closed my Amazon account.

An Open-source Capping Machine Suitable for Confined Spaces
Francisco Munguia-Galeano, Louis Longley, Satheeshkumar Veeramani, Zhengxue Zhou, Rob Clowes, Hatem Fakhruldeen, Andrew I. Cooper
https://arxiv.org/abs/2506.03743

An Open-source Capping Machine Suitable for Confined Spaces
In the context of self-driving laboratories (SDLs), ensuring automated and error-free capping is crucial, as it is a ubiquitous step in sample preparation. Automated capping in SDLs can occur in both large and small workspaces (e.g., inside a fume hood). However, most commercial capping machines are designed primarily for large spaces and are often too bulky for confined environments. Moreover, many commercial products are closed-source, which can make their integration into fully autonomous wo…

On the geometry of synthetic null hypersurfaces
Fabio Cavalletti, Davide Manini, Andrea Mondino
https://arxiv.org/abs/2506.04934 https://

On the geometry of synthetic null hypersurfaces
This paper develops a synthetic framework for the geometric and analytic study of null (lightlike) hypersurfaces in non-smooth spacetimes. Drawing from optimal transport and recent advances in Lorentzian geometry and causality theory, we define a synthetic null hypersurface as a triple $(H, G, \mathfrak{m})$: $H$ is a closed achronal set in a topological causal space, $G$ is a gauge function encoding affine parametrizations along null generators, and $\mathfrak{m}$ is a Radon measure serving as…

This https://arxiv.org/abs/2403.10529 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Closed Form for Half-Area Overlap Offset of 2 Unit Disks
The separation between the centers of two unit circles such that their overlapping area is exactly half of each's area is known to be around $0.8079455\dots$ (OEIS A133741). However, no closed form of this number is known. Here, we determine its closed form representation in terms of the inverse regularized beta function.

Rescaled topological entropy
E. Rego, C. Rojas, X. Wen
https://arxiv.org/abs/2506.02383 https://arxiv.org/pdf/2506.02383

Rescaled topological entropy
We prove that to any smooth vector field of a closed manifold it can be assigned a nonnegative number called {\em rescaled topological entropy} satisfying the following properties: it is an upper bound for both the topological entropy and the rescaled metric entropy \cite{ww}; coincides with the topological entropy for nonsingular vector fields; is positive for certain surface vector fields (in contrast to the topological entropy); is invariant under rescaled topological conjugacy; and serves a…

As I've seen a good number of people here post about "Worktree.ca" as a "Canadian-owned" alternative to GitHub: it's a closed-source fork of Gitea which "one day" (maybe, if the company doesn't change its mind) will be open core. It also runs on AWS…
Not that it's any of my business, but migrating there feels like the code-equivalent of leaving Twitter for Bluesky: Moving from one company-owned walled garden to the next, without having learned a lesson. All painted in a nationalist cash grab. 🤷‍♂️

Modeling the Optical Properties of Biological Structures using Symbolic Regression
Julian Sierra-Velez, Alexandre Vial, Marina Inchaussandague, Diana Skigin, Demetrio Mac\'ias
https://arxiv.org/abs/2506.01862

Modeling the Optical Properties of Biological Structures using Symbolic Regression
We present a Machine Learning approach based on Symbolic Regression to derive, from either numerically generated or experimentally measured spectral data, closed-form expressions that model the optical properties of biological materials. To evaluate the performance of our approach, we consider three case studies with the aim of retrieving the refractive index of the materials that constitute the biological structures considered. The results obtained show that, in addition to retrieving readable…

This https://arxiv.org/abs/2411.16855 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Analytic Solution for the Motion of Spinning Particles in Kerr Space-Time
The equations of motion of massive test particles near Kerr black holes are separable in Boyer-Lindquist coordinates, as established by Carter. This separability, however, is lost when the particles are endowed with classical spin. We show that separability of the equations of motion can be recovered to linear order in spin by a shift of the worldline derived with the use of the hidden symmetry of Kerr space-time. Consequently, the closed-form solution of the motion is expressed in a way closel…

Regular genus of $\mathbb{S}^2 \times \mathbb{S}^1 \times \mathbb{S}^1$, $4$-torus, and small covers over $\Delta^2 \times \Delta^2$
Anshu Agarwal, Biplab Basak
https://arxiv.org/abs/2506.01315

Regular genus of $\mathbb{S}^2 \times \mathbb{S}^1 \times \mathbb{S}^1$, $4$-torus, and small covers over $Δ^2 \times Δ^2$
A crystallization of a PL manifold is an edge-colored graph encoding a contracted triangulation of the manifold. The concept of regular genus generalizes the notions of surface genus and Heegaard genus for 3-manifolds to higher-dimensional closed PL manifolds. The regular genus of a PL manifold is a PL invariant. Determining the regular genus of a closed PL $n$-manifold remains a fundamental challenge in combinatorial topology. In this article, we first resolve a conjecture by proving that the …

Period matrices and homological quasi-trees on discrete Riemann surfaces
Wai Yeung Lam, On-Hei Solomon Lo, Chi Ho Yuen
https://arxiv.org/abs/2506.02317 htt…

Period matrices and homological quasi-trees on discrete Riemann surfaces
We study discrete period matrices associated with graphs cellularly embedded on closed surfaces, resembling classical period matrices of Riemann surfaces. Defined via integrals of discrete harmonic 1-forms, these period matrices are known to encode discrete conformal structure in the sense of circle patterns. We obtain a combinatorial interpretation of the discrete period matrix, where its minors correspond to weighted sums over certain spanning subgraphs, which we call homological quasi-trees.…

The tight length spectrum of large-genus random hyperbolic surfaces with many cusps
Timothy Budd, Tanguy Lions
https://arxiv.org/abs/2506.02611 https://

The tight length spectrum of large-genus random hyperbolic surfaces with many cusps
Since the work of Mirzakhani \& Petri \cite{Mirzakhani_petri_2019} on random hyperbolic surfaces of large genus, length statistics of closed geodesics have been studied extensively. We focus on the case of random hyperbolic surfaces with cusps, the number $n_g$ of which grows with the genus $g$. We prove that if $n_g$ grows fast enough and we restrict attention to special geodesics that are \emph{tight}, we recover upon proper normalization the same Poisson point process in the large-$g$ limit …

This https://arxiv.org/abs/2505.23387 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csSE_…

Afterburner: Reinforcement Learning Facilitates Self-Improving Code Efficiency Optimization
Large Language Models (LLMs) generate functionally correct solutions but often fall short in code efficiency, a critical bottleneck for real-world deployment. In this paper, we introduce a novel test-time iterative optimization framework to address this, employing a closed-loop system where LLMs iteratively refine code based on empirical performance feedback from an execution sandbox. We explore three training strategies: Supervised Fine-Tuning (SFT), Direct Preference Optimization (DPO), and G…

This https://arxiv.org/abs/2412.19753 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Divisibility classes of ultrafilters and their patterns
A divisibility relation on ultrafilters on the set $\mathbb{N}$ of natural numbers is defined as follows: ${\cal F}\hspace{1mm}\widetilde{\mid}\hspace{1mm}{\cal G}$ if and only if every set in $\cal F$ upward closed for divisibility also belongs to $\cal G$. Previously we isolated basic classes: powers of prime ultrafilters, and described the pattern of an ultrafilter, measuring the quantity of members of each basic class dividing a given ultrafilter. In this paper we define a topology on the s…

This https://arxiv.org/abs/2504.19364 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

A Perturbatively Stable Non-Supersymmetric String Model with AdS Vacuum
We present a construction of a perturbatively stable non-supersymmetric type II closed string model in four dimensions. It is based on a freely acting Scherk-Schwarz Z2-deformation of a supersymmetric construction which is recovered in appropriate decompactification limits. The model exhibits also the so-called misaligned supersymmetry with alternating signs for the number difference between bosons and fermions at successive mass levels. The tree-level spectrum is tachyon free for any value of …

Branched $\alpha$-combinatorial Ricci flows on closed surfaces with Euler characteristic $\chi\le 0$
Wenjun Li, Rongyuan Liu, Guohao Chen, Aijin Lin
https://arxiv.org/abs/2505.24762

Branched $α$-combinatorial Ricci flows on closed surfaces with Euler characteristic $χ\le 0$
This paper investigates branched $α$-flows on weighted triangulated closed surfaces with Euler characteristic \(χ\leq 0\), focusing on establishing their connections with topological (combinatorial) and geometric structures. In Euclidean (\(\mathbb{E}^2\)) and hyperbolic (\(\mathbb{H}^2\)) geometries, we define branched $α$-curvatures and corresponding branched $α$-flows. By introducing branched $α$-potentials, we prove the existence and uniqueness of constant branched $α$-metrics through…

Exploiting Pinching-Antenna Systems in Multicast Communications
Shan Shan, Chongjun Ouyang, Yong Li, Yuanwei Liu
https://arxiv.org/abs/2506.00616 https://

Exploiting Pinching-Antenna Systems in Multicast Communications
The pinching-antenna system (PASS) reconfigures wireless links through pinching beamforming, in which the activated locations of pinching antennas (PAs) along dielectric waveguides are optimized. This article investigates the application of PASS in multicast communication systems, where pinching beamforming is designed to maximize the multicast rate. i) In the single-waveguide scenario, a closed-form solution for the optimal activated location is derived under the assumption of a single PA and …

This https://arxiv.org/abs/2503.17274 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Composable Uncertainty in Symmetric Monoidal Categories for Design Problems
Applied category theory often studies symmetric monoidal categories (SMCs) whose morphisms represent open systems. These structures naturally accommodate complex wiring patterns, leveraging (co)monoidal structures for splitting and merging wires, or compact closed structures for feedback. A key example is the compact closed SMC of design problems (DP), which enables a compositional approach to co-design in engineering. However, in practice, the systems of interest may not be fully known. Recent…

Homomorphisms from ${\rm SL}(2, k)$ to ${\rm SL}(4, k)$ in positive characteristic
Ryuji Tanimoto
https://arxiv.org/abs/2506.00423 https://

Homomorphisms from ${\rm SL}(2, k)$ to ${\rm SL}(4, k)$ in positive characteristic
Let $k$ be an algebraically closed field of positive characteistic $p$ and let ${\rm SL}(n, k)$ denote the special linear algebraic group of degree $n$ over $k$. In this paper, we describe homomorphisms from ${\rm SL}(2, k)$ to ${\rm SL}(4, k)$. As by-products of this description, we give a classification of homomorphisms from ${\rm SL}(2, k)$ to ${\rm SL}(4, k)$ and describe the indecomposable decompositions of homomorphisms from ${\rm SL}(2, k)$ to ${\rm SL}(4, k)$.

Simplicial volume via foliated simplices and duality
Filippo Sarti
https://arxiv.org/abs/2506.02962 https://arxiv.org/pdf/2506.02962

Simplicial volume via foliated simplices and duality
Let $M$ be an aspherical oriented closed connected manifold with universal cover $\widetilde{M}\to M$ and let $Γ=π_1(M)\curvearrowright (X,μ)$ be a measure preserving action on a standard Borel probability space. We consider singular foliated simplices on the measured foliation $Γ\backslash(\widetilde{M}\times X)$ defined by Sauer and we compare the \emph{real singular foliated homology} with classic singular homology. We introduce a notion of \emph{foliated fundamental class} and we prove …

Neural Network-based Universal Formulas for Control
Pol Mestres, Jorge Cort\'es, Eduardo D. Sontag
https://arxiv.org/abs/2505.24744 https://

Neural Network-based Universal Formulas for Control
We study the problem of designing a controller that satisfies an arbitrary number of affine inequalities at every point in the state space. This is motivated by the use of guardrails in autonomous systems. Indeed, a variety of key control objectives, such as stability, safety, and input saturation, are guaranteed by closed-loop systems whose controllers satisfy such inequalities. Many works in the literature design such controllers as the solution to a state-dependent quadratic program (QP) who…

Equisingular lifting of semi-log canonical $F$-split $K$-trivial surfaces
Fabio Bernasconi, Quentin Posva
https://arxiv.org/abs/2506.01007 https://

Equisingular lifting of semi-log canonical $F$-split $K$-trivial surfaces
We show that a projective globally $F$-split semi-log canonical $K$-trivial surface over an algebraically closed field of characteristic $p>2$ admits an equisingular lifting over the ring of Witt vectors.

Gravitomagnetism from Temporal Dimensional Reduction
Mehran Z-Abyaneh, Mehrdad Farhoudi
https://arxiv.org/abs/2506.00525 https://arxi…

Gravitomagnetism from Temporal Dimensional Reduction
We propose that the Taub-NUT metric can be envisaged as a (3+1) dimensional analog of the Kaluza-Klein (4+1) dimensional metric. After dimensional reduction of the Taub-NUT metric to (3) spatial dimensions, by treating time as the extra curled dimension (since the closed time-like curves can exist in the Taub-NUT framework, such a dimensional reduction is justified), we end up with three dimensional Einstein field equations plus the Maxwell equations for the gravitomagnetic field, which also ac…

As I've seen a good number of people here post about "Worktree.ca" as a "Canadian-owned" alternative to GitHub: it's a closed-source fork of Gitea which "one day" (maybe, if the company doesn't change its mind) will be open core. It also runs on AWS…
Not that it's any of my business, but migrating there feels like the code-equivalent of leaving Twitter for Bluesky: Moving from one company-owned walled garden to the next, without having learned a lesson. All painted in a nationalist cash grab. 🤷‍♂️

Bounded cohomology of measure-preserving homeomorphism groups of non-orientable surfaces
Michael Brandenbursky, Lior Menashe
https://arxiv.org/abs/2506.02728

Bounded cohomology of measure-preserving homeomorphism groups of non-orientable surfaces
Let $N_g$ be a closed non-orientable surface of genus $g\geq 3$. Let $\operatorname{Homeo}_0(N_g,μ)$ be the identity component of the group of measure-preserving homeomorphisms of $N_g$. In this work we prove that the third bounded cohomology of $\operatorname{Homeo}_0(N_g,μ)$ is infinite dimensional.

Enabling Scalable Distributed Beamforming via Networked LEO Satellites Towards 6G
Yuchen Zhang Seungnyun Kim, Tareq Y. Al-Naffouri
https://arxiv.org/abs/2506.01382

Enabling Scalable Distributed Beamforming via Networked LEO Satellites Towards 6G
In this paper, we propose scalable distributed beamforming schemes over low Earth orbit (LEO) satellite networks that rely solely on statistical channel state information for downlink orthogonal frequency division multiplexing systems. We begin by introducing the system model and presenting a pragmatic yet effective analog beamformer and user-scheduling design. We then derive a closed-form lower bound on the ergodic sum rate, based on the hardening bound, for the digital beamformer design. Next…

This https://arxiv.org/abs/2310.19597 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Automorphism groups of $\mathbb{P}^1$-bundles over ruled surfaces
We classify the pairs $(X,π)$, where $π\colon X\to S$ is a $\mathbb{P}^1$-bundle over a non-rational ruled surface $S$ and $\mathrm{Aut}^\circ(X)$ is relatively maximal, i.e., maximal with respect to the inclusion in the group $\mathrm{Bir}(X/S)$. The results hold over any algebraically closed field of characteristic zero.

This https://arxiv.org/abs/2505.08280 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Extremising eigenvalues of the GJMS operators in a fixed conformal class
Let $(M,g)$ be a closed Riemannian manifold of dimension $n\geq 3$. If $s$ is a positive integer satisfying $2s

This https://arxiv.org/abs/2501.10302 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Martingale Approach to Gambler's Ruin Problem for Correlated Random Walks
The gambler's ruin problem for correlated random walks (CRW), both with and without delays, is addressed using the Optional Stopping Theorem for martingales. We derive closed-form expressions for the ruin probabilities and the expected game duration for CRW with increments $\{1,-1\}$ and for symmetric CRW with increments $\{1,0,-1\}$ (CRW with delays). Additionally, a martingale technique is developed for general CRW with delays. The gambler's ruin probability for a game involving bets on two a…

Nakano-Griffiths inequality, holomorphic Morse inequalities, and extension theorems for $q$-concave domains
Bingxiao Liu, George Marinescu, Huan Wang
https://arxiv.org/abs/2506.00879

Nakano-Griffiths inequality, holomorphic Morse inequalities, and extension theorems for $q$-concave domains
We consider a compact $n$-dimensional complex manifold endowed with a holomorphic line bundle that is semi-positive everywhere and positive at least at one point. Additionally, we have a smooth domain of this manifold whose Levi form has at least $n-q$ negative eigenvalues ($1\leq q\leq n-1$) on the boundary. We prove that every $\overline{\partial}_b$-closed $(0,\ell)$-form on the boundary with values in a holomorphic vector bundle admits a meromorphic extension for all $q\leq \ell\leq n-1$. T…

React to Surprises: Stable-by-Design Neural Feedback Control and the Youla-REN
Nicholas H. Barbara, Ruigang Wang, Alexandre Megretski, Ian R. Manchester
https://arxiv.org/abs/2506.01226

React to Surprises: Stable-by-Design Neural Feedback Control and the Youla-REN
We study parameterizations of stabilizing nonlinear policies for learning-based control. We propose a structure based on a nonlinear version of the Youla-Kučera parameterization combined with robust neural networks such as the recurrent equilibrium network (REN). The resulting parameterizations are unconstrained, and hence can be searched over with first-order optimization methods, while always ensuring closed-loop stability by construction. We study the combination of (a) nonlinear dynamics, …

Using Diffusion Ensembles to Estimate Uncertainty for End-to-End Autonomous Driving
Florian Wintel, Sigmund H. H{\o}eg, Gabriel Kiss, Frank Lindseth
https://arxiv.org/abs/2506.00560

Using Diffusion Ensembles to Estimate Uncertainty for End-to-End Autonomous Driving
End-to-end planning systems for autonomous driving are improving rapidly, especially in closed-loop simulation environments like CARLA. Many such driving systems either do not consider uncertainty as part of the plan itself, or obtain it by using specialized representations that do not generalize. In this paper, we propose EnDfuser, an end-to-end driving system that uses a diffusion model as the trajectory planner. EnDfuser effectively leverages complex perception information like fused camera …

This https://arxiv.org/abs/2110.15035 has been replaced.
link: https://scholar.google.com/scholar?q=a

Varieties with ample Frobenius-trace kernel
In the search of a projective analog of Kunz's theorem and a Frobenius-theoretic analog of Mori--Hartshorne's theorem, we investigate the positivity of the kernel of the Frobenius trace (equivalently, the negativity of the cokernel of the Frobenius endomorphism) on a smooth projective variety over an algebraically closed field of positive characteristic. For instance, such kernel is ample for projective spaces. Conversely, we show that for curves, surfaces, and threefolds the Frobenius trace ke…

IAE Optimized PID Tuning with Phase Margin and Crossover Frequency Constraints
Senol Gulgonul
https://arxiv.org/abs/2506.00923 https://

IAE Optimized PID Tuning with Phase Margin and Crossover Frequency Constraints
This paper presents PMwc-Tune, a novel PID tuning method that uniquely combines frequency-domain robustness constraints with time-domain performance optimization through constrained nonlinear programming. The key contribution is a unified formulation that simultaneously enforces phase margin and crossover frequency requirements (via nonlinear equality constraints) while minimizing the Integral Absolute Error (IAE) of the closed-loop response. The algorithm employs Sequential Quadratic Programmi…

This https://arxiv.org/abs/2410.08902 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Residual finiteness of some automorphism groups of high dimensional manifolds
We show that for a smooth, closed 2-connected manifold $M$ of dimension $d \geq 6$, the topological mapping class group $π_0 \mathrm{Homeo}(M)$ is residually finite, in contrast to the situation for the smooth mapping class group $π_0 \mathrm{Diff}(M)$. Combined with a result of Sullivan, this implies that $π_0 \mathrm{Homeo}(M)$ is an arithmetic group. The proof uses embedding calculus, and is of independent interest: we show that the $T_k$-mapping class group, $π_0 T_k \mathrm{Diff}(M)$, …

This https://arxiv.org/abs/2504.15962 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csRO_…

Blimp-based Crime Scene Analysis
Crime is a critical problem -- which often takes place behind closed doors, posing additional difficulties for investigators. To bring hidden truths to light, evidence at indoor crime scenes must be documented before any contamination or degradation occurs. Here, we address this challenge from the perspective of artificial intelligence (AI), computer vision, and robotics: Specifically, we explore the use of a blimp as a "floating camera" to drift over and record evidence with minimal disturbanc…

This https://arxiv.org/abs/2311.07309 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Non-singular extensions of circle-valued Morse functions
In this paper, we consider the non-singular extension problem for circle-valued Morse functions on closed orientable surfaces. The problem asks, given a circle-valued Morse function $f\colon M\to S^{1}$ on a closed orientable surface $M$, under what condition there exist a compact orientable 3-dimensional manifold $N$ with $\partial N = M$ and a submersion $G\colon N \to S^{1}$ such that $G|_{\partial N}=f$. We provide necessary and sufficient conditions for the existence of a non-singular…

Systolic lattice extensions of classical Schottky groups
Junzhi Huang, Matthew Zevenbergen
https://arxiv.org/abs/2505.24118 https://a…

Systolic lattice extensions of classical Schottky groups
We produce lattice extensions of a dense family of classical Schottky subgroups of the isometry group of $d$-dimensional hyperbolic space. The extensions produced are said to be systolic, since all loxodromic elements with short translation length are conjugate into the Schottky groups. Various corollaries are obtained, in particular showing that for all $d\geq3$, the set of complex translation lengths realized by systoles of closed hyperbolic $d$-manifolds is dense inside the set of all possib…