Tootfinder

Intersections of Schubert varieties and smooth $T$-stable subvarieties of flag varieties
Jaehyun Hong, Eunjeong Lee, Seonjeong Park
https://arxiv.org/abs/2506.21180

Intersections of Schubert varieties and smooth $T$-stable subvarieties of flag varieties
A smooth projective variety with an action of a torus admits a cell decomposition, called the Bialynicki-Birula decomposition. Singularities of the closures of these cells are not well-known. One of the examples of such closures is a Schubert variety in a flag variety G/B, and there are several criteria for the smoothness of Schubert varieties. In this paper, we focus on the closures of Bialynicki-Birula cells in regular semisimple Hessenberg varieties Hess(s,h), called Hessenberg Schubert vari…

A positive mass theorem for non-smooth metrics on asymptotically flat manifolds with non-compact boundary
Sergio Almaraz, Shaodong Wang
https://arxiv.org/abs/2506.20453

A positive mass theorem for non-smooth metrics on asymptotically flat manifolds with non-compact boundary
On a smooth asymptotically flat Riemannian manifold with non-compact boundary, we prove a positive mass theorem for metrics which are only continuous across a compact hypersurface. As an application, we obtain a positive mass theorem on manifolds with non-compact corners.

Compact Cauchy horizons admit constant surface gravity
Raymond A. Hounnonkpe, Ettore Minguzzi
https://arxiv.org/abs/2506.20004 https://

Compact Cauchy horizons admit constant surface gravity
We prove that in any spacetime dimension and under the dominant energy condition, every totally geodesic connected smooth compact null hypersurface (hence every compact Cauchy horizon) admits a smooth lightlike tangent vector field of constant surface gravity. That is, we solve the open degenerate case by showing that, if there is a complete generator, then there exists a smooth future-directed geodesic lightlike tangent field. The result can be stated as an existence result for a particular co…

Asymptotic Analysis of Boundary Layer Solutions to Poisson-Boltzmann Type Equations in General Bounded Smooth Domains
Jhih-Hong Lyu, Tai-Chia Lin
https://arxiv.org/abs/2506.20953 …

Asymptotic Analysis of Boundary Layer Solutions to Poisson-Boltzmann Type Equations in General Bounded Smooth Domains
We study the boundary layer solution to singular perturbation problems involving Poisson-Boltzmann (PB) type equations with a small parameter $ε$ in general bounded smooth domains (including multiply connected domains) under the Robin boundary condition. The PB type equations include the classical PB, modified PB and charge-conserving PB (CCPB) equations, which are mathematical models for the electric potential and ion distributions. The CCPB equations present particular analytical challenges …

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

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

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Missy Misdemeanor Elliott:
🎵 Smooth Chick
#MissyMisdemeanorElliott
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Sphericity and Analyticity of a strictly pdeusoconvex hypersurface in low regularity I
Ilya Kossovskiy, Dmitri Zaitsev
https://arxiv.org/abs/2506.20177 htt…

Sphericity and Analyticity of a strictly pdeusoconvex hypersurface in low regularity I
In our earlier work \cite{KZ}, we introduced an analytic regularizability theory for smooth strictly pseudoconvex hypersurfaces in complex space. That is, we found a necessary and sufficient condition for a hypersurface to be CR-equivalent to an analytic target. The condition amount to the holomorphic extension property for a smooth function on a totally real submanifold, both the function and the submanifold being uniquely associated with the given hypersurface. In the present paper, we deve…

#Wordle 1,469 3/6*
⬜🟨🟨⬜⬜ <1% of 219,671 (80)
⬜🟨🟩🟩🟨 0 of 22 (1)
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WordleBot
Skill 99/99
Luck 70/99
Happy to have a quick smooth wordle day after the last few

This https://arxiv.org/abs/2504.21000 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Well-posed Self-Similarity in Incompressible Standard Flows
This article reviews the properties of the self-similar solutions of the Navier-Stokes equation for incompressible fluids. Since any smooth solution can be embedded into a self-similar solution at the identity scale, it follows that under standard flow conditions, the initial solution will remain smooth for all time as long as the self-similar solution is selected to have certain isobaric weight.

AALC: Large Language Model Efficient Reasoning via Adaptive Accuracy-Length Control
Ruosen Li, Ziming Luo, Quan Zhang, Ruochen Li, Ben Zhou, Ali Payani, Xinya Du
https://arxiv.org/abs/2506.20160

AALC: Large Language Model Efficient Reasoning via Adaptive Accuracy-Length Control
Large reasoning models (LRMs) achieve impressive reasoning capabilities by generating lengthy chain-of-thoughts, but this "overthinking" incurs high latency and cost without commensurate accuracy gains. In this work, we introduce AALC, a lightweight, accuracy-aware length reward integrated into reinforcement learning that dynamically balances correctness and brevity during training. By incorporating validation accuracy into the reward and employing a smooth, dynamically scheduled length penalty…

Simple smooth modules over the Lie algebras of polynomial vector fields
Zhiqiang Li, Cunguang Cheng, Shiyuan Liu, Rencai Lu, Kaiming Zhao, Yueqiang Zhao
https://arxiv.org/abs/2506.18262

Simple smooth modules over the Lie algebras of polynomial vector fields
Let $\mathfrak{g}:={\rm Der}(\mathbb{C}[t_1, t_2,\cdots, t_n])$ and $\mathcal{L}:={\rm Der}(\mathbb{C}[[t_1, t_2,\cdots, t_n]])$ be the Witt Lie algebras. Clearly, $\mathfrak{g}$ is a proper subalegbra of $\mathcal{L}$. Surprisingly, we prove that simple smooth modules over $\mathfrak{g}$ are exactly the simple modules over $\mathcal{L}$ studied by Rodakov (no need to take completion). Then we find an easy and elementary way to classify all simple smooth modules over $\mathfrak{g}$. When the …

On nonorientable $4$--manifolds
R. \.Inan\c{c} Baykur, Porter Morgan
https://arxiv.org/abs/2506.20950 https://arxiv.org/pdf/2506.2095…

On nonorientable $4$--manifolds
We present several structural results on closed, nonorientable, smooth $4$--manifolds, extending analogous results and machinery for the orientable case. We prove the existence of simplified broken Lefschetz fibrations and simplified trisections on nonorientable $4$--manifolds, yielding descriptions of them via factorizations in mapping class groups of nonorientable surfaces. With these tools in hand, we classify low genera simplified broken Lefschetz fibrations on nonorientable $4$--manifolds.…

A generalization of Deodhar's defect statistic for Iwahori--Hecke algebras of type $BC$
Gavin Hobbs, Tommy Parisi, Mark Skandera, Jiayuan Wang
https://arxiv.org/abs/2506.20099

A generalization of Deodhar's defect statistic for Iwahori--Hecke algebras of type $BC$
Let $H$ be the Iwahori--Hecke algebra corresponding to any Coxeter group. Deodhar's defect statistic [Geom. Dedicata 36, (1990) pp.95--119] allows one to expand products of simple Kazhdan--Lusztig basis elements of $H$ in the natural basis of $H$. Clearwater and the third author gave a type-$A$ extension [Ann. Comb. 25, no. 3 (2021) pp.757--787] of this formula which combinatorially describes the natural expansion of products of Kazhdan--Lusztig basis elements indexed by smooth elements of the …

This https://arxiv.org/abs/2409.18947 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Smooth geometry of skew PBW extensions over commutative polynomial rings I
In this paper, we investigate the differential smoothness of skew PBW extensions over commutative polynomial rings on one and two indeterminates.

Selection of functional predictors and smooth coefficient estimation for scalar-on-function regression models
Hedayat Fathi, Marzia A. Cremona, Federico Severino
https://arxiv.org/abs/2506.17773

Selection of functional predictors and smooth coefficient estimation for scalar-on-function regression models
In the framework of scalar-on-function regression models, in which several functional variables are employed to predict a scalar response, we propose a methodology for selecting relevant functional predictors while simultaneously providing accurate smooth (or, more generally, regular) estimates of the functional coefficients. We suppose that the functional predictors belong to a real separable Hilbert space, while the functional coefficients belong to a specific subspace of this Hilbert space. …

Smooth linearization of contractive random dynamical systems in continuous time
Iryna Vasylieva
https://arxiv.org/abs/2506.19034 https://

Smooth linearization of contractive random dynamical systems in continuous time
We establish that uniformly exponentially stable random dynamical systems on the half line have equivalent dynamics through a $C^m-$ conjugacy. This result was obtained for random differential equations as well as for random dynamical systems with a uniformly exponentially stable linear part.

Time and covariance smoothing for restoration of bivariate signals
Yusuf Yigit Pilavci (CRIStAL), Pierre Palud (LERMA), Julien Flamant (CRAN), Pierre-Antoine Thouvenin (CRIStAL), J\'er\'emie Boulanger (CRIStAL), Pierre Chainais (CRIStAL)
https://arxiv.org/abs/2506.20237

Time and covariance smoothing for restoration of bivariate signals
In many applications and physical phenomena, bivariate signals are polarized, i.e. they trace an elliptical trajectory over time when viewed in the 2D planes of their two components. The smooth evolution of this elliptical trajectory, called polarization ellipse, is highly informative to solve ill-posed inverse problems involving bivariate signals where the signal is collected through indirect, noisy or incomplete measurements. This work proposes a novel formulation and an efficient algorithm f…

Basal layer of granular flow down smooth and rough inclines: kinematics, slip laws and rheology
Teng Wang, Lu Jing, Fiona C. Y. Kwok, Yuri D. Sobral, Thomas Weinhart, Anthony R. Thornton
https://arxiv.org/abs/2506.17920

Basal layer of granular flow down smooth and rough inclines: kinematics, slip laws and rheology
Granular flow down an inclined plane is ubiquitous in geophysical and industrial applications. On rough inclines, the flow exhibits Bagnold's velocity profile and follows the so-called $μ(I)$ local rheology. On insufficiently rough or smooth inclines, however, velocity slip occurs at the bottom and a basal layer with strong agitation emerges below the bulk, which is not predicted by the local rheology. Here, we use discrete element method simulations to study detailed dynamics of the basal lay…

Existence of smooth solutions of the Navier-Stokes equations in three-dimensional Euclidean space
Genqian Liu
https://arxiv.org/abs/2507.18063 https://arxi…

Existence of smooth solutions of the Navier-Stokes equations in three-dimensional Euclidean space
Based on the essential connection of the parabolic inertia Lamé equations and Navier-Stokes equations, we prove the existence of smooth solutions of the incompressible Navier-Stokes equations in three-dimensional Euclidean space $\mathbb{R}^3$ by showing the existence and uniqueness of smooth solutions of the parabolic inertia Lamé equations and by letting a Lamé constant $λ$ tends to infinity (the other Lamé constant $μ>0$ is fixed).

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Pete Rock & C.L. Smooth:
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Buchsbaumness, Macaulayfication and Castelnuovo-Mumford regularity of monomial curves
Biplab Dawn, Kumari Saloni
https://arxiv.org/abs/2506.20473 https://

Buchsbaumness, Macaulayfication and Castelnuovo-Mumford regularity of monomial curves
Projective monomial curves are associated with rings generated by monomials of equal degree in two variables. In this paper, we give an infinite class of non-smooth, non Cohen-Macaulay $k$-Buchsbaum projective monomial curves for any $k\geq 1$ and find the monomial generators for the respective Macaulayfication. More generally, we demonstrate a method to find the Macaulayfication of a $k$-Buchsbaum monomial curve for any $k\geq 1$. We also discuss Castelnuovo-Mumford regularity of certain curve…

HathiTrust was founded in 2008 as a not-for-profit collaborative of academic and research libraries now preserving 18 million digitized items in the HathiTrust Digital Library. We offer reading access to the fullest extent allowable by U.S. and international copyright law, text and data mining tools for the entire corpus, and other emerging services based on the combined collection.

Worst-case convergence analysis of relatively inexact gradient descent on smooth convex functions
Pierre Vernimmen, Fran\c{c}ois Glineur
https://arxiv.org/abs/2506.17145

Worst-case convergence analysis of relatively inexact gradient descent on smooth convex functions
We consider the classical gradient descent algorithm with constant stepsizes, where some error is introduced in the computation of each gradient. More specifically, we assume some relative bound on the inexactness, in the sense that the norm of the difference between the true gradient and its approximate value is bounded by a certain fraction of the gradient norm. This paper presents a worst-case convergence analysis of this so-called relatively inexact gradient descent on smooth convex functio…

Smooth Operators: LLMs Translating Imperfect Hints into Disfluency-Rich Transcripts
Duygu Altinok
https://arxiv.org/abs/2506.18510 https://

Smooth Operators: LLMs Translating Imperfect Hints into Disfluency-Rich Transcripts
Accurate detection of disfluencies in spoken language is crucial for enhancing the performance of automatic speech and language processing systems, as well as fostering the development of more inclusive speech and language technologies. Leveraging the growing trend of large language models (LLMs) as versatile learners capable of processing both lexical and non-lexical inputs (e.g., audio and video), we propose a novel approach to transcribing disfluencies as explicit tokens with timestamps, ena…

Cosmological perturbations for smooth sign-switching dark energy models
Mariam Bouhmadi-L\'opez, Be\~nat Ibarra-Uriondo
https://arxiv.org/abs/2506.18992

Cosmological perturbations for smooth sign-switching dark energy models
In this work, we carry out a comprehensive perturbative analysis of four cosmological models featuring a sign-switching cosmological constant. Among these, we include the well-known $Λ_{\rm s}$CDM model, characterised by an abrupt transition from a negative to a positive cosmological constant. We also consider the L$Λ$CDM model, which exhibits a generalised ladder-step evolution, as well as the SSCDM and ECDM models, both of which undergo a smooth sign change at comparable redshifts. We solve…

General-domain FC-based shock-dynamics solver II: Non-smooth domains, accuracy and parallel performance
Daniel V. Leibovici, Oscar P. Bruno
https://arxiv.org/abs/2506.19370

General-domain FC-based shock-dynamics solver II: Non-smooth domains, accuracy and parallel performance
This contribution Part II of a two-part series, extends the general-domain FC-SDNN (Fourier Continuation Shock-Detecting Neural Network) introduces in Part I to enable treatment of non-smooth domains, it introduces a parallel implementation of the scheme with high-quality weak and strong scalability properties, and it illustrates the overall methodology for a variety of tests for the 2D Euler equations--including supersonic and hypersonic flows and shocks past obstacles with corners. The result…

Affine invariant interacting Langevin dynamics in Markov chain importance sampling for rare event estimation
Jason Beh, J\'er\^ome Morio, Florian Simatos, Simon Weissmann
https://arxiv.org/abs/2506.20185

Affine invariant interacting Langevin dynamics in Markov chain importance sampling for rare event estimation
This work considers the framework of Markov chain importance sampling~(MCIS), in which one employs a Markov chain Monte Carlo~(MCMC) scheme to sample particles approaching the optimal distribution for importance sampling, prior to estimating the quantity of interest through importance sampling. In rare event estimation, the optimal distribution admits a non-differentiable log-density, thus gradient-based MCMC can only target a smooth approximation of the optimal density. We propose a new gradie…

VHU-Net: Variational Hadamard U-Net for Body MRI Bias Field Correction
Xin Zhu
https://arxiv.org/abs/2506.19181 https://arxiv.org/pdf…

VHU-Net: Variational Hadamard U-Net for Body MRI Bias Field Correction
Bias field artifacts in magnetic resonance imaging (MRI) scans introduce spatially smooth intensity inhomogeneities that degrade image quality and hinder downstream analysis. To address this challenge, we propose a novel variational Hadamard U-Net (VHU-Net) for effective body MRI bias field correction. The encoder comprises multiple convolutional Hadamard transform blocks (ConvHTBlocks), each integrating convolutional layers with a Hadamard transform (HT) layer. Specifically, the HT layer perfo…

Tails from the Bulk: Gravitational Decay in AdS$_5$
John R. V. Crump, Jorge E. Santos
https://arxiv.org/abs/2506.18991 https://arxiv.…

Tails from the Bulk: Gravitational Decay in AdS$_5$
We study gravitational perturbations of Schwarzschild-AdS black holes in $d = 5$ and identify a regime of late-time power-law decay for smooth initial data. Based on an analysis of the quasinormal mode spectrum, we predict and characterise this decay behaviour. We perform fully nonlinear numerical evolutions with long integration times that support the prediction and exhibit no signs of instability. Remarkably, the decay is modulated by a universal oscillatory pattern, consistent with subleadin…

On Bott's residue formula for toric complete intersections
Miguel Rodr\'iguez Pe\~na
https://arxiv.org/abs/2506.19790 https://

On Bott's residue formula for toric complete intersections
We determine the number of singularities - counted whit multiplicities - of generic distributions of dimension and codimension one on smooth complete intersections in compact toric orbifolds with isolated singularities. We also present some applications of this results. First, we analyze the case of regular distributions. A a second application, we establish a Poincaré-type inequality that relates the multidegree of a foliation to the multidegrees of an invariant smooth complete intersection c…

Supercyclic weighted composition operators on the space of smooth functions
J. Bes, C. Foster
https://arxiv.org/abs/2507.16425 https://

Supercyclic weighted composition operators on the space of smooth functions
A weighted composition operator on the space of scalar-valued smooth functions on an open set of d-dimensional Euclidean space is supercyclic if and only if it is weakly mixing, and it is strongly supercyclic if and only if it is mixing. Every mixing such operator is chaotic. In the one-dimensional case, it is supercyclic if and only if it is mixing and if and only if it is chaotic.

An Analytic Prime Indicator Based on the Fejer Kernel
Sebastian Fuchs
https://arxiv.org/abs/2506.18933 https://arxiv.org/pdf/2506.189…

An Analytic Prime Indicator Based on the Fejer Kernel
This note introduces an analytic prime indicator, constructed by smoothing a trigonometric analogue of trial division. First, a function P: R -> R of class C1 is presented, whose zeros for x > 2 correspond precisely to the odd primes. Its second derivative exhibits jump discontinuities at integer squares. Subsequently, it is shown how this construction can be modified via an infinite series to yield a globally smooth function, P_phi, of class C-inf that preserves this prime-zero property. As a …

Confidence Optimization for Probabilistic Encoding
Pengjiu Xia, Yidian Huang, Wenchao Wei, Yuwen Tan
https://arxiv.org/abs/2507.16881 https://

Confidence Optimization for Probabilistic Encoding
Probabilistic encoding introduces Gaussian noise into neural networks, enabling a smooth transition from deterministic to uncertain states and enhancing generalization ability. However, the randomness of Gaussian noise distorts point-based distance measurements in classification tasks. To mitigate this issue, we propose a confidence optimization probabilistic encoding (CPE) method that improves distance reliability and enhances representation learning. Specifically, we refine probabilistic enco…

Sharp lower bounds for the first eigenvalue of Steklov-type eigenvalue problems on a compact surface
Gunhee Cho, Keomkyo Seo
https://arxiv.org/abs/2506.21376

Sharp lower bounds for the first eigenvalue of Steklov-type eigenvalue problems on a compact surface
Let $Ω$ be a compact surface with smooth boundary and the geodesic curvature $k_g \ge {c > 0}$ along $\partial Ω$ for some constant $c \in \mathbb{R}$. We prove that, if the Gaussian curvature satisfies $K \ge -α$ for a constant $α\ge 0$, then the first eigenvalue $σ_1$ of the Steklov-type eigenvalue problem satisfies \[ σ_1 + \fracα{σ_1} \ge c. \] Moreover, equality holds if and only if $Ω$ is a Euclidean disk of radius $\frac{1}{c}$ and $α= 0$. Furthermore, we obtain a sharp lower b…

Koopman Operator Based Time-Delay Embeddings and State History Augmented LQR for Periodic Hybrid Systems: Bouncing Pendulum and Bipedal Walking
Chun-Ming Yang, Pranav A. Bhounsule
https://arxiv.org/abs/2507.14455

Koopman Operator Based Time-Delay Embeddings and State History Augmented LQR for Periodic Hybrid Systems: Bouncing Pendulum and Bipedal Walking
Time-delay embedding is a technique that uses snapshots of state history over time to build a linear state space model of a nonlinear smooth system. We demonstrate that periodic non-smooth or hybrid system can also be modeled as a linear state space system using this approach as long as its behavior is consistent in modes and timings. We extended time-delay embeddings to generate a linear model of two periodic hybrid systems: the bouncing pendulum and the simplest walker with control inputs. Th…

Fictional depiction of mild self-harm, blood.
#WritersCoffeeClub July 23: Share a description you're proud of.
I've been writing a vampire novel lately. Here's a description from the scene when the vampire character proves to the human protagonist that he's been telling the truth:
—
"It's okay, Ada," he gave me a reassuring close-mouthed smile. "Just watch."
He slashed across his wrist in a motion that made the matching scars on my left arm hum. I covered them with my right hand, as if to calm my skin that I wasn't hurting it like that anymore. That we were merely watching someone else.
The cut on Theodore's arm turned red and angry, as expected. And then, just before the wound pooled up enough to bleed, it closed. I watched time run backwards as it disappeared, the skin stitching itself together to leave no trace of the violence imposed on it by the blade.
"What?" I walked up to him as he handed his wrist to me for inspection. I ran the tips of my fingers over the spot where the cut was mere moments before - but Theodore's skin, cold as always, was smooth and unharmed.
—

Canard cycles of non-linearly regularized piecewise smooth vector fields
Peter De Maesschalck, Renato Huzak, Otavio Henrique Perez
https://arxiv.org/abs/2506.18099

Canard cycles of non-linearly regularized piecewise smooth vector fields
The main purpose of this paper is to study limit cycles in non-linear regularizations of planar piecewise smooth systems with fold points (or more degenerate tangency points) and crossing regions. We deal with a slow fast Hopf point after non-linear regularization and blow-up. We give a simple criterion for upper bounds and the existence of limit cycles of canard type, expressed in terms of zeros of the slow divergence integral. Using the criterion we can construct a quadratic regularization of…

Smooth Games of Configuration in the Linear-Quadratic Setting
Jesse Milzman, Jeffrey Mao, Giuseppe Loianno
https://arxiv.org/abs/2507.16611 https://…

Smooth Games of Configuration in the Linear-Quadratic Setting
Dynamic game theory offers a toolbox for formalizing and solving for both cooperative and non-cooperative strategies in multi-agent scenarios. However, the optimal configuration of such games remains largely unexplored. While there is existing literature on the parametrization of dynamic games, little research examines this parametrization from a strategic perspective where each agent's configuration choice is influenced by the decisions of others. In this work, we introduce the concept of a ga…

🎮 Feeling like #N64 or #PlayStation but don't have a console? #RetroArch on Apple TV or other TV-Box is a real game-changer! Runs super smooth and brings nostalgia st…

How to Record a Smooth Multi-Person Panel Video Using Just Two Phones
https://josvelasco.com/how-to-record-a-smooth-multi-person-panel-video-using-just-two-phones/

🇺🇦 #NowPlaying on KEXP's #Expansions
Calibre:
🎵 Smooth Baby
#Calibre
https://criticalmusic.bandcamp.com/album/piano-bizness-smooth-baby

Human Traces 👤
人类的踪迹 👤
📷 Pentax MX
🎞️Ilford FP4 Plus, expired 1995
buy me ☕️ ?/请我喝杯☕️？
#filmphotography

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Folgen Sie dem Link PayPal.Me/dingsterdingster und geben Sie den Betrag ein. Es ist bequem und sicher. Sie haben noch kein PayPal-Konto? Kein Problem.

Does anyone have some practical advice how do visualize/summarize factor level smooth/slope differences for a #GAM fitted with sz? #gratia is only partially supporting it and especially difference_smooth() does not seem to work with sz.
Any pointers for packages, tutorials etc appreciated!
#rstats

On Bergman type projection in some new analytic function spaces in bounded strongly pseudoconvex domains
R. F. Shamoyan, E. B. Tomashevskaya
https://arxiv.org/abs/2506.20913

On Bergman type projection in some new analytic function spaces in bounded strongly pseudoconvex domains
We prove the boundedness of Bergman type projections in two different analytic function spaces in bounded strongly pseudoconvex domains with the smooth boundary. Our results were previously well-known in the case of the unit disk.

Optimal differentially private kernel learning with random projection
Bonwoo Lee, Cheolwoo Park, Jeongyoun Ahn
https://arxiv.org/abs/2507.17544 https://

Optimal differentially private kernel learning with random projection
Differential privacy has become a cornerstone in the development of privacy-preserving learning algorithms. This work addresses optimizing differentially private kernel learning within the empirical risk minimization (ERM) framework. We propose a novel differentially private kernel ERM algorithm based on random projection in the reproducing kernel Hilbert space using Gaussian processes. Our method achieves minimax-optimal excess risk for both the squared loss and Lipschitz-smooth convex loss fu…

I'm switching away from LibreNMS to Zabbix and while there were a couple of inaccuracies in the documentation/video, the set-up was smooth sailing.
I even got a Discord webhook set up, so that will help!
Tested by adding a server, and it came up with an issue right away, so I know that works!

Scalable DC Optimization via Adaptive Frank-Wolfe Algorithms
Sebastian Pokutta
https://arxiv.org/abs/2507.17545 https://arxiv.org/pdf/2507.17545

Scalable DC Optimization via Adaptive Frank-Wolfe Algorithms
We consider the problem of minimizing a difference of (smooth) convex functions over a compact convex feasible region $P$, i.e., $\min_{x \in P} f(x) - g(x)$, with smooth $f$ and Lipschitz continuous $g$. This computational study builds upon and complements the framework of Maskan et al. [2025] by integrating advanced Frank-Wolfe variants to reduce computational overhead. We empirically show that constrained DC problems can be efficiently solved using a combination of the Blended Pairwise Condi…

Protocols for Verifying Smooth Strategies in Bandits and Games
Miranda Christ, Daniel Reichman, Jonathan Shafer
https://arxiv.org/abs/2507.10567 https://…

Protocols for Verifying Smooth Strategies in Bandits and Games
We study protocols for verifying approximate optimality of strategies in multi-armed bandits and normal-form games. As the number of actions available to each player is often large, we seek protocols where the number of queries to the utility oracle is sublinear in the number of actions. We prove that such verification is possible for sufficiently smooth strategies that do not put too much probability mass on any specific action. We provide protocols for verifying that a smooth policy for a mul…

ChatAR: Conversation Support using Large Language Model and Augmented Reality
Yuichiro Fujimoto
https://arxiv.org/abs/2506.16008 https://

ChatAR: Conversation Support using Large Language Model and Augmented Reality
Engaging in smooth conversations with others is a crucial social skill. However, differences in knowledge between conversation participants can sometimes hinder effective communication. To tackle this issue, this study proposes a real-time support system that integrates head-mounted display (HMD)-based augmented reality (AR) technology with large language models (LLMs). This system facilitates conversation by recognizing keywords during dialogue, generating relevant information using the LLM, r…

The determinant of \(\lll\)-smooth semigroups
M. H. Shahzamanian
https://arxiv.org/abs/2506.13700 https://arxiv.org/pdf/2506.13700

The determinant of \(\lll\)-smooth semigroups
This paper continues the investigation of non-zero determinants associated with finite semigroups containing a pair of non-commuting idempotents, as initiated in~\cite{Sha-Det2}. We focus on a class of semigroups, called \( \lll \)-smooth semigroups, that allow meaningful structural analysis despite the absence of \( \ll \)-transitivity. Within this framework, we develop a method for computing contracted semigroup determinants, building on and extending the approach carried over from~\cite{Sha-…

Essential Self-Adjointness of the Geometric Deformation Operator on a Compact Interval
Anton Alexa
https://arxiv.org/abs/2506.18914 https://

Essential Self-Adjointness of the Geometric Deformation Operator on a Compact Interval
We define a second-order differential operator $\hat{C}$ on the Hilbert space $L^2([-v_c, v_c])$, constructed from a smooth deformation function $C(v)$. The operator is considered on the Sobolev domain $H^2([-v_c, v_c]) \cap H^1_0([-v_c, v_c])$ with Dirichlet boundary conditions. We prove that $\hat{C}$ is essentially self-adjoint by verifying its symmetry and computing von Neumann deficiency indices, which vanish. All steps are carried out explicitly. This result ensures the mathematical consi…

On Uniform Weighted Deep Polynomial approximation
Kingsley Yeon, Steven B. Damelin
https://arxiv.org/abs/2506.21306 https://arxiv.org…

On Uniform Weighted Deep Polynomial approximation
It is a classical result in rational approximation theory that certain non-smooth or singular functions, such as $|x|$ and $x^{1/p}$, can be efficiently approximated using rational functions with root-exponential convergence in terms of degrees of freedom \cite{Sta, GN}. In contrast, polynomial approximations admit only algebraic convergence by Jackson's theorem \cite{Lub2}. Recent work shows that composite polynomial architectures can recover exponential approximation rates even with…

Hilbert scheme and Hilbert functions of smooth curves of degrees at most $15$ in $\mathbb{P}^5$
Edoardo Ballico, Changho Keem
https://arxiv.org/abs/2507.16547

Hilbert scheme and Hilbert functions of smooth curves of degrees at most $15$ in $\mathbb{P}^5$
Denoting $\mathcal{H}_{d,g,5}$ by the Hilbert scheme of smooth curves of degree $d$ and genus $g$ in $\mathbb{P}^5$, let $\mathcal{H}$ be an irreducible component of $\mathcal{H}_{d,g,5}$. We study the Hilbert function $h_X:\mathbb{N}\longrightarrow\mathbb{N}$, $h_X(t):= h^0(\mathcal{I}_X(t))$ of a general member $X\in\mathcal{H}$, especially when the degree of the curve is low; $d\le 15$. We also determine the irreducibility of $\mathcal{H}_{d,g,5}$ for $d\le 14$ and study the natural functori…

Long-time existence for the 2D ideal Boussinesq and the 2D density-dependent Euler equations
Hantaek Bae, Milton Lopes Filho, Anna Mazzucato, Helena Nussenzveig Lopes
https://arxiv.org/abs/2507.18244

Long-time existence for the 2D ideal Boussinesq and the 2D density-dependent Euler equations
We establish long-time existence of smooth solutions to the 2D ideal Boussinesq equations and to the 2D non-homogeneous incompressible Euler equations for initial data consisting of small temperature perturbations, or small density perturbations, of smooth initial flows which are not necessarily small. Both results are known (see Danchin and Fanelli 2013, Danchin 2011 in the references) but the technique we develop to prove them is at the same time elementary and has broad potential applicabili…

Holomorphic parabolic geometries on smooth projective varieties
Benjamin McKay
https://arxiv.org/abs/2507.15691 https://arxiv.org/pdf…

Holomorphic parabolic geometries on smooth projective varieties
We classify the holomorphic parabolic geometries on compact complex manifolds of general type. We accomplish this by bounding the numerical dimension of any smooth projective variety in terms of geometric invariants of the flag variety model of any holomorphic parabolic geometry on that variety. Along the way, we uncover foliations and fibrations on smooth projective varieties that admit holomorphic parabolic geometries.

NAADA: A Noise-Aware Attention Denoising Autoencoder for Dental Panoramic Radiographs
Khuram Naveed, Bruna Neves de Freitas, Ruben Pauwels
https://arxiv.org/abs/2506.19387

NAADA: A Noise-Aware Attention Denoising Autoencoder for Dental Panoramic Radiographs
Convolutional denoising autoencoders (DAEs) are powerful tools for image restoration. However, they inherit a key limitation of convolutional neural networks (CNNs): they tend to recover low-frequency features, such as smooth regions, more effectively than high-frequency details. This leads to the loss of fine details, which is particularly problematic in dental radiographs where preserving subtle anatomical structures is crucial. While self-attention mechanisms can help mitigate this issue by …

New examples of CR submanifolds for the $2$-jet determination problem
Florian Bertrand, Martin Kol\'a\v{r}, Francine Meylan
https://arxiv.org/abs/2506.21221

New examples of CR submanifolds for the $2$-jet determination problem
This paper addresses two questions related to mapping problems. In the first part of the paper, we discuss some recent results regarding the $2$-jet determination for biholomorphisms between smooth (weakly) pseudoconvex hypersurfaces; in light of those, we formulate a general problem and illustrate it with examples. In the second part of the paper, we provide a new example of a real submanifold of codimension $7$ in $\mathbb{C}^{10}$ that is not strictly pseudoconvex and for which its germs of …

Dual Thurston norm of Euler classes of foliations on negative curvature 3-Manifolds
Dmitry V. Bolotov
https://arxiv.org/abs/2506.19098 https://

Dual Thurston norm of Euler classes of foliations on negative curvature 3-Manifolds
In this paper we give an upper bound estimate on the dual Thurston norm of the Euler class of an arbitrary smooth foliation $\mathcal{F}$ of dimension one defined on a closed three-dimensional orientable manifold $M^3$ of negative curvature, which depends on the constants bounded the injectivity radius $inj(M^3)$, the volume $Vol(M^3)$, sectional curvature of the manifold $M^3$ and the mean curvature modulus of the leaves of the foliation $\mathcal{F}$.

From a collapsing radiating star to an evaporating black hole: A smooth transition from classical to quantum entropy
Sarbari Guha, Shamima Khan, Rituparno Goswami
https://arxiv.org/abs/2507.16485

From a collapsing radiating star to an evaporating black hole: A smooth transition from classical to quantum entropy
We present a robust mechanism where the geometrical free-gravitational entropy of an isolated astrophysical radiating star undergoing continual gravitational collapse, as measured by an external observer, makes a smooth transition to the Bekenstein-Hawking entropy at the onset of the horizon formation and in the late times of black hole evaporation. It is interesting to note that both in the classical regime and the semi classical evaporating black hole regime, the matter is radiated via the Va…

Robust and Smooth Estimation of the Extreme Tail Index via Weighted Minimum Density Power Divergence
Saida Mancer, Abdelhakim Necir, Djamel Meraghni
https://arxiv.org/abs/2507.15744

Robust and Smooth Estimation of the Extreme Tail Index via Weighted Minimum Density Power Divergence
By introducing a weight function into the density power divergence, we develop a new class of robust and smooth estimators for the tail index of Pareto-type distributions, offering improved efficiency in the presence of outliers. These estimators can be viewed as a robust generalization of both weighted least squares and kernel-based tail index estimators. We establish the consistency and asymptotic normality of the proposed class. A simulation study is conducted to assess their finite-sample p…

ReLCP: Scalable Complementarity-Based Collision Resolution for Smooth Rigid Bodies
Bryce Palmer, Hasan Metin Aktulga, Tong Gao
https://arxiv.org/abs/2506.14097

ReLCP: Scalable Complementarity-Based Collision Resolution for Smooth Rigid Bodies
We present a complementarity-based collision resolution algorithm for smooth, non-spherical, rigid bodies. Unlike discrete surface representation approaches, which approximate surfaces using discrete elements (e.g., tessellations or sub-spheres) with constraints between nearby faces, edges, nodes, or sub-objects, our algorithm solves a recursively generated linear complementarity problem (ReLCP) to adaptively identify potential collision locations during the collision resolution procedure. Desp…

A parametric tensor ROM for the shallow water dam break problem
Md Rezwan Bin Mizan, Maxim Olshanskii, Ilya Timofeyev
https://arxiv.org/abs/2506.20007 http…

A parametric tensor ROM for the shallow water dam break problem
We develop a variant of a tensor reduced-order model (tROM) for the parameterized shallow-water dam-break problem. This hyperbolic system presents multiple challenges for model reduction, including a slow decay of the Kolmogorov $N$-width of the solution manifold, shock formation, and the loss of smooth solution dependence on parameters. These issues limit the performance of traditional Proper Orthogonal Decomposition based ROMs. Our tROM approach, based on a low-rank tensor decomposition, buil…

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Shape sensitivity analysis of the heat equation and the Dirichlet-to-Neumann map
Matteo Dalla Riva, Paolo Luzzini, Paolo Musolino
https://arxiv.org/abs/2506.21196

Shape sensitivity analysis of the heat equation and the Dirichlet-to-Neumann map
We study a Dirichlet problem for the heat equation in a domain containing an interior hole. The domain has a fixed outer boundary and a variable inner boundary determined by a diffeomorphism $ϕ$. We analyze the maps that assign to the infinite-dimensional shape parameter $ϕ$ the corresponding solution and its normal derivative, and we prove that both are smooth. Motivated by an application to an inverse problem, we then compute the differential with respect to $ϕ$ of the normal derivative of…

Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems
Guillaume Garrigos, Daniel Cortild, Lucas Ketels, Juan Peypouquet
https://arxiv.org/abs/2507.14122

Last-Iterate Complexity of SGD for Convex and Smooth Stochastic Problems
Most results on Stochastic Gradient Descent (SGD) in the convex and smooth setting are presented under the form of bounds on the ergodic function value gap. It is an open question whether bounds can be derived directly on the last iterate of SGD in this context. Recent advances suggest that it should be possible. For instance, it can be achieved by making the additional, yet unverifiable, assumption that the variance of the stochastic gradients is uniformly bounded. In this paper, we show that …

An integral comparison of crystalline and de Rham cohomology
Abhinandan, Alex Youcis
https://arxiv.org/abs/2507.17631 https://arxiv.o…

An integral comparison of crystalline and de Rham cohomology
Let $\mathcal{O}_K$ be a mixed characteristic complete DVR with perfect residue field $k$ and fraction field $K$. It is a celebrated result of Berthelot and Ogus that for a smooth proper formal scheme $X/\mathcal{O}_K$ there exists a comparison between the de Rham cohomology groups $\mathrm{H}^i_\mathrm{dR}(X/\mathcal{O}_K)$ and the crystalline cohomology groups $\mathrm{H}^i_\mathrm{crys}(X_k/W(k))$ of the special fibre, after tensoring with $K$. In this article, we use the stacky perspective …

A new construction for Melnikov chaos in piecewise-smooth planar systems
Alessandro Calamai, Matteo Franca, Michal Pospisil
https://arxiv.org/abs/2507.15543

A new construction for Melnikov chaos in piecewise-smooth planar systems
In this paper we consider a piecewise smooth $2$-dimensional system \[ \dot{\vec{x}}=\vec{g} (\vec{x})+\varepsilon\vec{g}(t,\vec{x},\varepsilon) \] where $\varepsilon>0$ is a small parameter and $\vec{f}$ is discontinuous along a curve $Ω^0$. We assume that $\vec{0}$ is a critical point for any $\varepsilon \geq 0$, and that for $\varepsilon=0$ the system admits a trajectory $\vecγ(t)$ homoclinic to $\vec{0}$ and crossing transversely $Ω^0$ in $\vecγ(0)$. In a previous paper we have shown…

Generalized Mittag-Leffler functions, Borel-Laplace multitransforms, and quantum differential equations of Fano varieties
Giordano Cotti
https://arxiv.org/abs/2506.18033

Generalized Mittag-Leffler functions, Borel-Laplace multitransforms, and quantum differential equations of Fano varieties
This paper addresses the integration problem for the isomonodromic system of quantum differential equations associated with smooth projective Fano varieties. We begin by introducing a class of multivariable, multivalued analytic functions of Mittag-Leffler type. We study their analytic properties and provide explicit Mellin-Barnes integral representations. For any smooth Fano toric variety, we prove that suitable integral linear combinations of these generalized Mittag-Leffler functions and the…

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Well-posed Self-Similarity in Incompressible Standard Flows
This article reviews the properties of the self-similar solutions of the Navier-Stokes equation for incompressible fluids. Since any smooth solution can be embedded into a self-similar solution at the identity scale, it follows that under standard flow conditions, the initial solution will remain smooth for all time as long as the self-similar solution is selected to have certain isobaric weight.

The Mixed-Sparse-Smooth-Model Toolbox (MSSM): Efficient Estimation and Selection of Large Multi-Level Statistical Models
Joshua Krause, Jelmer P. Borst, Jacolien van Rij
https://arxiv.org/abs/2506.13132

The Mixed-Sparse-Smooth-Model Toolbox (MSSM): Efficient Estimation and Selection of Large Multi-Level Statistical Models
Additive smooth models, such as Generalized additive models (GAMs) of location, scale, and shape (GAMLSS), are a popular choice for modeling experimental data. However, software available to fit such models is usually not tailored specifically to the estimation of mixed models. As a result, estimation can slow down as the number of random effects increases. Additionally, users often have to provide a substantial amount of problem-specific information in case they are interested in more general …

Regret Minimization in Population Network Games: Vanishing Heterogeneity and Convergence to Equilibria
Die Hu, Shuyue Hu, Chunjiang Mu, Shiqi Fan, Chen Chu, Jinzhuo Liu, Zhen Wang
https://arxiv.org/abs/2507.17183

Regret Minimization in Population Network Games: Vanishing Heterogeneity and Convergence to Equilibria
Understanding and predicting the behavior of large-scale multi-agents in games remains a fundamental challenge in multi-agent systems. This paper examines the role of heterogeneity in equilibrium formation by analyzing how smooth regret-matching drives a large number of heterogeneous agents with diverse initial policies toward unified behavior. By modeling the system state as a probability distribution of regrets and analyzing its evolution through the continuity equation, we uncover a key phen…

Spike layered solutions for elliptic systems on Riemannian Manifolds
Anusree R Kannoth, Bhakti Bhusan Manna
https://arxiv.org/abs/2506.20300 https://

Spike layered solutions for elliptic systems on Riemannian Manifolds
In this article, we study the following Hamiltonian system: \begin{equation*} \begin{cases} \begin{aligned} &-\varepsilon^{2}Δ_{g} u +u = |v|^{q-1}v, &-\varepsilon^{2}Δ_{g} v +v = |u|^{p-1}u && \text{ in } \mathcal{M}, & \quad u,v >0 && \text{ in } \mathcal{M}, \end{aligned} \end{cases} \end{equation*} where $\mathcal{M}$ is a smooth, compact and connected Riemannian manifold of dimension $N\geq 3$ without boundary. The exponents $p,q>1$ are assumed to lie be…

On the Worst-Case Analysis of Cyclic Block Coordinate Descent type Algorithms
Yassine Kamri, Fran\c{c}ois Glineur, Julien M. Hendrickx, Ion Necoara
https://arxiv.org/abs/2507.16675

On the Worst-Case Analysis of Cyclic Block Coordinate Descent type Algorithms
We study the worst-case behavior of Block Coordinate Descent (BCD) type algorithms for unconstrained minimization of coordinate-wise smooth convex functions. This behavior is indeed not completely understood, and the practical success of these algorithms is not fully explained by current convergence analyses. We extend the recently proposed Performance Estimation Problem (PEP) approach to convex coordinate-wise smooth functions by proposing necessary interpolation conditions. We then exploit th…

The fundamental theorem of the local theory for non-smooth curves
Domenico Mucci, Alberto Saracco
https://arxiv.org/abs/2506.12564 https://

The fundamental theorem of the local theory for non-smooth curves
We extend the classical fundamental theorem of the local theory of smooth curves to a wider class of non-smooth data. Curvature and torsion are prescribed in terms of the distributional derivative measures of two given functions of bounded variation. The essentially unique non-smooth curve solution has both finite total curvature and total absolute torsion. In case of continuous data, we preliminarly discuss a more general problem involving a linear system of distributional derivative equations.

K-rings of smooth toric varieties via piecewise-exponential functions
Melody Chan, Emily Clader, Caroline Klivans, Dustin Ross
https://arxiv.org/abs/2507.13610

K-rings of smooth toric varieties via piecewise-exponential functions
We describe an explicit presentation of the ring of integral piecewise-exponential functions on a unimodular fan as a quotient of the Stanley-Reisner ring of the fan. This gives rise to a presentation of K-rings of smooth toric varieties that is parallel to the well-known presentation of integral Chow rings as quotients of Stanley-Reisner rings.

Smoothing topological pseudo-isotopies of 4-manifolds
Patrick Orson, Mark Powell, Oscar Randal-Williams
https://arxiv.org/abs/2507.16984 https://arxiv.org/…

Smoothing topological pseudo-isotopies of 4-manifolds
Given a closed, smooth 4-manifold $X$ and self-diffeomorphism $f$ that is topologically pseudo-isotopic to the identity, we study the question of whether $f$ is moreover smoothly pseudo-isotopic to the identity. If the fundamental group of $X$ lies in a certain class, which includes trivial, free, and finite groups of odd order, we show the answer is always affirmative. On the other hand, we produce the first examples of manifolds $X$ and diffeomorphisms $f$ where the answer is negative. Our in…

On the Dynamical System Generated by the M\"obius Transformation at Smooth Times
L\'aszl\'o M\'erai, Igor E. Shparlinski
https://arxiv.org/abs/2507.12160

On the Dynamical System Generated by the Möbius Transformation at Smooth Times
We study the distribution of the sequence of the first $N$ elements of the discrete dynamical system generated by the Möbius transformation $x \mapsto (αx + β)/(γx + δ)$ over a finite field of $p$ elements at the moments of time that correspond to $Q$-smooth numbers, that is, to numbers composed out of primes up to $Q$. In particular, we obtain nontrivial estimates of exponential sums with such sequences.

Normal forms of piecewise-smooth systems with a monodromic singular point
Jiahao Li, Xingwu Chen, Weinian Zhang
https://arxiv.org/abs/2506.13200 https://…

Normal forms of piecewise-smooth systems with a monodromic singular point
Normal form theory is developed deeply for planar smooth systems but has few results for piecewise-smooth systems because difficulties arise from continuity of the near-identity transformation, which is constructed piecewise. In this paper, we overcome the difficulties to study normal forms for piecewise-smooth systems with FF, FP, or PP equilibrium and obtain explicit any-order normal forms by finding piecewise-analytic homeomorphisms and deriving a new normal form for analytic syste…

Smooth binary evolution from wide resonances in boson clouds
Giovanni Maria Tomaselli
https://arxiv.org/abs/2507.15110 https://arxiv.…

Smooth binary evolution from wide resonances in boson clouds
Ultralight scalars can form superradiant clouds around rotating black holes. These may alter the dynamics of compact binaries and the ensuing waveform through orbital resonances and cloud ionization. We re-examine resonances involving states with nonzero decay width, deriving an effective treatment for resonances that are wider than the binary's frequency chirp. We demonstrate the utility of this approach by calculating an upper bound for the cloud's mass surviving up to the latest stages of th…

MCM: Mamba-based Cardiac Motion Tracking using Sequential Images in MRI
Jiahui Yin, Xinxing Cheng, Jinming Duan, Yan Pang, Declan O'Regan, Hadrien Reynaud, Qingjie Meng
https://arxiv.org/abs/2507.17678

MCM: Mamba-based Cardiac Motion Tracking using Sequential Images in MRI
Myocardial motion tracking is important for assessing cardiac function and diagnosing cardiovascular diseases, for which cine cardiac magnetic resonance (CMR) has been established as the gold standard imaging modality. Many existing methods learn motion from single image pairs consisting of a reference frame and a randomly selected target frame from the cardiac cycle. However, these methods overlook the continuous nature of cardiac motion and often yield inconsistent and non-smooth motion estim…

Non-smooth stochastic gradient descent using smoothing functions
Tommaso Giovannelli, Jingfu Tan, Luis Nunes Vicente
https://arxiv.org/abs/2507.10901 https…

Non-smooth stochastic gradient descent using smoothing functions
In this paper, we address stochastic optimization problems involving a composition of a non-smooth outer function and a smooth inner function, a formulation frequently encountered in machine learning and operations research. To deal with the non-differentiability of the outer function, we approximate the original non-smooth function using smoothing functions, which are continuously differentiable and approach the original function as a smoothing parameter goes to zero (at the price of increasin…

Segre forms of singular metrics on vector bundles and Lelong numbers
Mats Andersson, Richard L\"ark\"ang
https://arxiv.org/abs/2506.15473 https:/…

Segre forms of singular metrics on vector bundles and Lelong numbers
Let $E\to X$ be a holomorphic vector bundle with a singular Griffiths negative Hermitian metric $h$ with analytic singularities. One can define, given a smooth reference metric $h_0$, a current $s(E,h,h_0)$ that is called the associated Segre form, which defines the expected Bott-Chern class and coincides with the usual Segre form of $h$ where it is smooth. We prove that $s(E,h,h_0)$ is the limit of the Segre forms of a sequence of smooth metrics if the metric is smooth outside the unbounded lo…

A Piecewise Smooth $\lambda$-Lemma
Claudio A. Buzzi, Paulo Santana, Luan V. M. F. Silva
https://arxiv.org/abs/2507.10896 https://arxi…

A Piecewise Smooth $λ$-Lemma
In this paper we provide extensions of the $λ$-Lemma (also known as Inclination Lemma) for piecewise smooth vector fields and maps. In order to achieve our main result, we investigate the regularity of time-T-maps of piecewise smooth vector fields defined at crossing orbits. We prove that these maps are homeomorphisms and also piecewise smooth diffeomorphisms.

The $\sigma_k$-Loewner-Nirenberg problem on Riemannian manifolds for $k=\frac{n}{2}$ and beyond
Jonah A. J. Duncan, Luc Nguyen
https://arxiv.org/abs/2507.16394

The $σ_k$-Loewner-Nirenberg problem on Riemannian manifolds for $k=\frac{n}{2}$ and beyond
Let $(M^n,g_0)$ be a smooth compact Riemannian manifold of dimension $n\geq 3$ with smooth non-empty boundary $\partial M$. Let $Γ\subset\mathbb{R}^n$ be a symmetric convex cone and $f$ a symmetric defining function for $Γ$ satisfying standard assumptions. Denoting by $A_{g_u}$ the Schouten tensor of a conformal metric $g_u = u^{-2}g_0$, we show that the associated fully nonlinear Loewner-Nirenberg problem \begin{align*} \begin{cases} f(λ(-g_u^{-1}A_{g_u})) = \frac{1}{2}, \quad λ(-g_u…

Efficient evaluation of forward and inverse energy-based magnetic hysteresis operators
Herbert Egger, Felix Engertsberger, Andreas Schafelner
https://arxiv.org/abs/2507.15289

Efficient evaluation of forward and inverse energy-based magnetic hysteresis operators
The energy-based vector hysteresis model of Francois-Lavet et al. establishes an implicit relation between magnetic fields and fluxes via internal magnetic polarizations which are determined by convex but non-smooth minimization problems. The systematic solution of these problems for every material point is a key ingredient for the efficient implementation of the model into standard magnetic field solvers. We propose to approximate the non-smooth terms via regularization which allows to employ …

On a theorem of Narasimhan and Ramanan on deformations
V. Balaji, Y. Pandey
https://arxiv.org/abs/2506.17574 https://arxiv.org/pdf/25…

On a theorem of Narasimhan and Ramanan on deformations
Let $X$ be a smooth projective curve genus at least $3$, over an algebraically closed field $k$ of arbitrary characteristics. Let $\cM$ denote the moduli stack $\cM_X(\cH)$ of $\cH$-torsors on $X$, when $\cH$ {\em quasi-split absolutely simple, simply connected connected group scheme}. Using the theory of parahoric torsors and Hecke correspondences, we describe the cohomology groups $\text{H}^i(\cM, \cT_{_{\cM}}), i = 0,1,2$ and $\text{H}^i(\cM, Ω_{_{\cM}}), i = 0,1,2$ in terms of the curve $X…

Quaternionic Analysis of Conformal Maps and the Willmore Functional
Ross Ogilvie, Martin Ulrich Schmidt
https://arxiv.org/abs/2506.17723 https://

Quaternionic Analysis of Conformal Maps and the Willmore Functional
Quaternionic analysis, which describes conformal maps from Riemann surfaces into $\mathbb{R}^3$ or $\mathbb{R}^4$, is extended to weakly conformal maps. As a consequence we present a new proof that on any compact Riemann surface $X$ the Willmore functional, the integral of the square of the mean curvature, attains a minimum on the space of smooth conformal maps from $X$ to $\mathbb{R}^3$ or $\mathbb{R}^4$. This was first proven by Kuwert and Schätzle under the assumption that the infimum of th…

Boundary layer profiles of positive solutions for logistic equation with sublinear nonlinearity on the boundary
Kenichiro Umezu
https://arxiv.org/abs/2506.19237

Boundary layer profiles of positive solutions for logistic equation with sublinear nonlinearity on the boundary
In this paper, we consider the logistic elliptic equation $-Δu = u- u^{p}$ in a smooth bounded domain $Ω\subset \mathbb{R}^{N}$, $N\geq2$, equipped with the sublinear Neumann boundary condition $\frac{\partial u}{\partial ν} = μu^{q}$ on $\partial Ω$, where $0

Conformal blocks, parahoric torsors and Borel-Weil-Bott
V. Balaji, Y. Pandey
https://arxiv.org/abs/2506.17573 https://arxiv.org/pdf/2…

Conformal blocks, parahoric torsors and Borel-Weil-Bott
Let $X$ be a smooth projective curve over an algebraically closed field $k$. Let $\mathcal{G}$ be a parahoric group scheme on $X$ as in \cite{pr}. Via the principle of Hecke correspondences, we set-up relationships between the cohomology of lines bundles on various moduli stacks of torsors. This approach gives a proof of \cite[Conjecture 3.7]{pr} for group schemes $\mathcal G$ as above in characteristic zero. This further gives as a consequence, the principle of propagation of vacua. We give a …

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

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

Formation and construction of large variational shock waves for 1-D $n\times n$ quasilinear hyperbolic conservation systems
Huicheng Yin, Wanqing Zhu
https://arxiv.org/abs/2506.19313

Formation and construction of large variational shock waves for 1-D $n\times n$ quasilinear hyperbolic conservation systems
In the paper [Li Jun, Xu Gang, Yin Huicheng, On the blowup mechanism of smooth solutions to 1D quasilinear strictly hyperbolic systems with large variational initial data, Nonlinearity 38 (2025), No.2, 025016], for the 1-D $n\times n$ ($n\geqslant 3$) strictly hyperbolic system $\partial_tv+F(v)\partial_xv=0$ with some classes of large variational initial data $v(x, 0)$, the geometric blowup mechanism and the detailed singularity behaviours of $\partial_{x,t}v$ near the blowup point are studied…

Moment-like maps and real algebraic functions with prescribed preimages
Naoki Kitazawa
https://arxiv.org/abs/2506.17791 https://arxiv…

Moment-like maps and real algebraic functions with prescribed preimages
We discuss a problem on singularity theory of differentiable (smooth) or real algebraic maps which is different from knowing existence and has been difficult: constructing explcit real algebraic functions. We discuss construction of real algebraic functions with exactly one singular value, the singular points being of definite type, and prescribed preimages of single points. We discuss generalizations of the canonical projection of the unit sphere around the pole and the Morse-Bott functions …

An improvement toward global boundedness in a fully parabolic chemotaxis with singular sensitivity in any dimension
Minh Le
https://arxiv.org/abs/2506.19318

An improvement toward global boundedness in a fully parabolic chemotaxis with singular sensitivity in any dimension
We are concerned with the following chemotaxis system \begin{equation*} \begin{cases} u_t = Δu -χ\nabla \cdot \left ( \frac{u}{v} \nabla v\right ), v_t = Δv -u+ v, \end{cases} \end{equation*} in an open bounded domain with smooth boundary $Ω\subset \mathbb{R}^n$ with $n \geq 3$. It is known that solutions are globally bounded when $0<χ< \sqrt{ \frac{2}{n}}$. In this paper, by considering the following energy functional \begin{align*} F_λ(u,v)= \int_Ω\frac{u^p}{v^r} + λ\int_Ω\…

Automorphisms of prime power order of weighted hypersurfaces
Alvaro Liendo, Ana Julisa Palomino
https://arxiv.org/abs/2507.13538 https://

Automorphisms of prime power order of weighted hypersurfaces
We study automorphisms of quasi-smooth hypersurfaces in weighted projective spaces, extending classical results for smooth hypersurfaces in projective space to the weighted setting. We establish effective criteria for when a power of a prime number can occur as the order of an automorphism, and we derive explicit bounds on the possible prime orders. A key role is played by a weighted analogue of the classical Klein hypersurface, which we show realizes the maximal prime order of an automorphism …

$H^s_x$ regularity of solutions to the stationary Boltzmann equation with the incoming boundary condition
Daisuke Kawagoe
https://arxiv.org/abs/2507.18211 https://

$H^s_x$ regularity of solutions to the stationary Boltzmann equation with the incoming boundary condition
We consider the stationary Boltzmann equation with the cross section of the form $B(|v - \tilde{v}, θ|) = B_0 |v - \tilde{v}|^γ\cos θ\sin θ$ for $-3 < γ\leq 1$ in a bounded convex domain under the incoming boundary condition. In this article, we shall show the existence of a solution in a weighted $L^\infty$ space with fractional Sobolev regularity without assuming the positivity of the Gaussian curvature on the boundary. For boundary data sufficiently smooth and close …

Positive cones of the projectivization of a parabolic bundle over a curve
Ashima Bansal, Indranil Biswas, Souradeep Majumder
https://arxiv.org/abs/2506.17594

Positive cones of the projectivization of a parabolic bundle over a curve
We study the positivity properties of the projectivization of a parabolic bundle over a smooth complex projective curve. The generators of its Néron--Severi group are computed, and the positive cone is determined. In particular, we compute explicitly the generators for the higher nef cones and the pseudoeffective cones. As an application, we deduce a necessary and sufficient condition for the semistability of a parabolic bundle.

On the volume of K-semistable Fano manifolds
Chi Li, Minghao Miao
https://arxiv.org/abs/2506.17420 https://arxiv.org/pdf/2506.17420…

On the volume of K-semistable Fano manifolds
We prove that the volume of an $n$-dimensional K-semistable Fano manifold that is not $\mathbb{P}^n$ is at most $2n^n$. Moreover, the equality holds only if $X\cong \mathbb{P}^1\times \mathbb{P}^{n-1}$ or $X$ is a smooth quadric hypersurface $Q\subset \mathbb{P}^{n+1}$. Our proof is based on a new connection between K-semistability and minimal rational curves. More generally, we show that the volume of a K-semistable Fano manifold with a minimal rational curve of degree $d$ is bounded above by …

On the algebraic $K$-theory of smooth schemes over truncated Witt vectors
Xiaowen Hu
https://arxiv.org/abs/2507.12458 https://arxiv.o…

On the algebraic $K$-theory of smooth schemes over truncated Witt vectors
Using Brun's theorem relating the relative algebraic $K$-theory and the relative cyclic homology, we compute certain relative algebraic $K$-groups of a $p$-adic smooth scheme over $W_n(k)$, where $k$ is a perfect field of characteristic $p$. Inspired by this result and the work of Bloch, Esnault, and Kerz, we define the infinitesimal motivic complexes, and then show a relative Chern character isomorphism with integral coefficients in a range. This has a direct consequence on infinitesimal defor…