Tootfinder

A converse to Cartan's Theorem B: The extension property for real analytic and Nash sets
Jos\'e F. Fernando, Riccardo Ghiloni
https://arxiv.org/abs/2506.18347

A converse to Cartan's Theorem B: The extension property for real analytic and Nash sets
In 1957 Cartan proved his celebrated Theorem B and deduced that if $Ω\subset{\mathbb R}^n$ is an open set and $X$ is a coherent real analytic subset of $Ω$, then $X$ has the analytic extension property, that is, each real analytic function on $X$ extends to a real analytic function on $Ω$. The converse implication in its full generality remains unproven. In the literature only special cases of non-coherent real analytic sets $X\subsetΩ$ without the extension property appear, some of them du…

On the Exceptional Sets of Transcendental Analytic Functions in Several Variables with Integer Coefficients
Jean Lelis, Bruno De Paula Miranda, Carlos Gustavo Moreira
https://arxiv.org/abs/2506.15914

On the Exceptional Sets of Transcendental Analytic Functions in Several Variables with Integer Coefficients
In 2020, Marques and Moreira proved that every subset of $\overline{\mathbb{Q}} \cap B(0,1)$, which is closed under complex conjugation and contains $0$, is the exceptional set of uncountably many transcendental analytic functions with integer coefficients. In this paper, we extend this result to transcendental analytic functions in several variables. In particular, we show that every subset of $\overline{\mathbb{Q}}^m$ contained in the unit polydisc $Δ(0;1)$, closed under complex conjugation …

Analytic Full Potential Adjoint Solution for Two-dimensional Subcritical Flows
Carlos Lozano, Jorge Ponsin
https://arxiv.org/abs/2506.16886 https://…

Analytic Full Potential Adjoint Solution for Two-dimensional Subcritical Flows
We investigate the analytic adjoint solution of the two-dimensional (2D) full potential equation for subcritical flows for a cost function measuring aerodynamic force by the Green's function approach and by the connection of the adjoint full potential and compressible Euler equations. The solution for aerodynamic lift is written in terms of two unknown functions encoding the effect of perturbations to the Kutta condition. We analyze the properties of these functions from an analytic viewpoint a…

On embedding theorems in analytic and harmonic function spaces of several complex variables in some domains in $C^n$
R. F. Shamoyan, M. G. Bashmakova
https://arxiv.org/abs/2507.16980

On embedding theorems in analytic and harmonic function spaces of several complex variables in some domains in $C^n$
In this survey we collect some recent advances concerning embedding theorems in analytic and harmonic function spaces of several complex variables in various domains in $C^n$. The paper is based mainly only on recent results in this research area of the first author, but some recent new interesting nice, results of other authors will also be added in this survey in addition. Some rather short, but valuable discussions of related to this area of research problems in analytic and harmonic functio…

Analytic Theory on the Space of Blaschke Products: Simultaneous Uniformization and Pressure Metric
Yan Mary He, Homin Lee, Insung Park
https://arxiv.org/abs/2507.17077 https://

Analytic Theory on the Space of Blaschke Products: Simultaneous Uniformization and Pressure Metric
In this paper, we study complex analytic aspects of the moduli space $\Bcal_d^{fm}$ of degree $d\ge2$ fixed-point-marked Blaschke products. We define a complex structure on $\Bcal_d^{fm}$ and prove the simultaneous uniformization theorem for fixed-point-marked quasi-Blaschke products. As an application, we show that the pressure semi-norms on the space of Blaschke products are non-degenerate outside of the super-attracting locus $\mathcal{SA}^{fm}_d$, which is a codimension-1 subspace of $\Bcal…

An analytic formalism to describe the $N_{\rm eff}(\rm H)$-$n_{\rm H}$ relationship in molecular clouds
Brandt A. L. Gaches
https://arxiv.org/abs/2507.16931

An analytic formalism to describe the $N_{\rm eff}(\rm H)$-$n_{\rm H}$ relationship in molecular clouds
Context. Astrochemical modeling requires, as input, the effective column density of gas (or extinction) that attenuates an external, isotropic, far-ultraviolet radiation field. In three-dimensional simulations, this can be calculated through ray-tracing schemes, while in 0D chemical models it is often treated as a free parameter. Aims. We aim to produce an analytic, physically motivated formalism to predict the average relationship between the effective hydrogen-nuclei column density, $N_{\rm e…

Saddle-point method for resummed form factors in QCD
Ugo Giuseppe Aglietti, Giancarlo Ferrera, Wan-Li Ju
https://arxiv.org/abs/2506.18707 https://

Saddle-point method for resummed form factors in QCD
We consider the form factor appearing in QCD resummation formalism for event shape distributions in the two-jet (or Sudakov) region. We present an analytic formula for the inverse transform of the form factor, namely from the conjugate moment space to the (physical) momentum space, based on the saddle-point method. The saddle-point itself is determined by means of an analytic recursion method as well as by standard numerical methods. The results we have found are in very good agreement with the…

Hypercomplex analytic spaces and schemes
Roger Bielawski
https://arxiv.org/abs/2507.16452 https://arxiv.org/pdf/2507.16452

Hypercomplex analytic spaces and schemes
We propose definitions of hypercomplex analytic spaces and hypercomplex schemes. We show that such a hypercomplex space is canonically associated to the quotient of a hypercomplex manifold by a finite group action.

Analysis on fibred cusp spaces
Daniel Grieser, \'Alvaro S\'anchez-Hern\'andez, Boris Vertman
https://arxiv.org/abs/2507.15467 https://

Analysis on fibred cusp spaces
We give a survey of a number of analytic and geometric results on `fibred cusp spaces'. These results cover topics in spectral geometry, in particular analytic torsion and index theory, and boundary value problems. The underlying tools include a careful microlocal analysis of the resolvent and the heat kernel. We include an exposition of the geometric and analytic foundations and sketch the ideas of the proofs of the main theorems.

A Semi-analytic but Biased Uncertainty Assessment Method using Sample Extensions, Analysed for Nonlinear Travel Time Tomography
Xuebin Zhao, Andrew Curtis
https://arxiv.org/abs/2507.16353

A Semi-analytic but Biased Uncertainty Assessment Method using Sample Extensions, Analysed for Nonlinear Travel Time Tomography
Many geophysical problems can be cast as inverse problems that estimate a set of parameter values from observed data. Within a Bayesian framework, solutions to such problems are described probabilistically by the so-called posterior probability distribution functions (pdf's). To obtain robust inference results often requires millions of model parameter value samples to be drawn, and their simulation to be performed; this is a computationally expensive procedure. We investigate the concept of sa…

Bayesian Analysis and Analytic Continuation of Scattering Amplitudes from Lattice QCD
Miguel Salg, Fernando Romero-L\'opez, William I. Jay
https://arxiv.org/abs/2506.16161

Bayesian Analysis and Analytic Continuation of Scattering Amplitudes from Lattice QCD
We present a novel procedure for analyzing the lattice-QCD spectrum via the finite-volume formalism to obtain constraints on multi-hadron scattering amplitudes at both real and complex energies. This approach combines a Bayesian reconstruction of the scattering amplitude on the real axis with Nevanlinna interpolation for analytic continuation to complex-valued energies. The method is non-parametric, inherently accounting for parametrization dependence within the uncertainty. We demonstrate the …

Scattering from analytic and piecewise analytic inhomogeneities
Narek Hovsepyan, Michael S. Vogelius
https://arxiv.org/abs/2507.13986 https://

Scattering from analytic and piecewise analytic inhomogeneities
We study scattering for the linear Helmholtz operator in two dimensions and develop a technique, which can be used to ascertain scattering of a given incident wave from very regular inhomogeneities. This technique is then applied to a number of interesting examples.

Approximation of polynomial hulls by analytic varieties: A counterexample
Tobias Harz
https://arxiv.org/abs/2507.16338 https://arxiv.…

Approximation of polynomial hulls by analytic varieties: A counterexample
We construct a connected, compact set $K \subset \mathbb{C}^2$ with the following property: there exist points $p \in \hat{K} \setminus K$ such that there does not exist a sequence $\{A_ν\}$ of analytic sets $A_ν\subset\subset \mathbb{C}^2$ with boundary satisfying $p \in A_ν$ for every $ν\in \mathbb{N}$ and $\lim_{ν\to\infty} bA_ν\subset K$. For every point in $\hat{K} \setminus K$, we explicitly construct a sequence of Poletsky discs, and we compute the weak limit of the pushforwards of…

Observational Constraints on Scalar Field--Matter Interaction in Weyl Integrable Spacetime
Andronikos Paliathanasis
https://arxiv.org/abs/2506.16223 https:…

Observational Constraints on Scalar Field--Matter Interaction in Weyl Integrable Spacetime
We test an analytic cosmological solution within the framework of Weyl Integrable Spacetime using current observational data. In this model, dark energy is described by a pressureless fluid, while a scalar field arises naturally through the definition of the connection. This gravitational theory reveals a Chameleon Mechanism leading to a nonzero interaction between the scalar field and the matter sector. This model extends the standard $Λ$CDM cosmology by introducing one additional degree of f…

A unified spin-harmonic framework for correlating pulsar timing, astrometric deflection, and shimmering gravitational wave observations
Giorgio Mentasti, Carlo R. Contaldi
https://arxiv.org/abs/2507.16906

A unified spin-harmonic framework for correlating pulsar timing, astrometric deflection, and shimmering gravitational wave observations
We present a unified spin-weighted harmonic framework that delivers analytic, diagonal expressions for the overlap (correlation) functions of three low frequency gravitational wave observables-pulsar timing redshifts, astrometric deflections, and time-dependent image distortions (``shimmering''). Writing each response in spin-$s$ spherical harmonics and rotating to a basis in which the wave tensor has definite helicity, we obtain compact closed-form series for every auto- and cross-correlation,…

Generalized Spectral Statistics in the Kicked Ising model
Divij Gupta, Brian Swingle
https://arxiv.org/abs/2506.15816 https://arxiv.o…

Generalized Spectral Statistics in the Kicked Ising model
The kicked Ising model has been studied extensively as a model of quantum chaos. Bertini, Kos, and Prosen studied the system in the thermodynamic limit, finding an analytic expression for the spectral form factor, $K(t)$, at the self-dual point with periodic boundary conditions. The spectral form factor is the 2nd moment of the trace of the time evolution operator, and we study the higher moments of this random variable in the kicked Ising model. A previous study of these higher moments by Flac…

Projected Normal Distribution: Moment Approximations and Generalizations
Daniel Herrera-Esposito, Johannes Burge
https://arxiv.org/abs/2506.17461 https://

Projected Normal Distribution: Moment Approximations and Generalizations
The projected normal distribution, also known as the angular Gaussian distribution, is obtained by dividing a multivariate normal random variable $\mathbf{x}$ by its norm $\sqrt{\mathbf{x}^T \mathbf{x}}$. The resulting random variable follows a distribution on the unit sphere. No closed-form formulas for the moments of the projected normal distribution are known, which can limit its use in some applications. In this work, we derive analytic approximations to the first and second moments of the …

Crowned Lie groups and nets of real subspaces
Daniel Beltita, Karl-Hermann Neeb
https://arxiv.org/abs/2506.16422 https://arxiv.org/pd…

Crowned Lie groups and nets of real subspaces
We introduce the notion of a complex crown domain for a connected Lie group $G$, and we use analytic extensions of orbit maps of antiunitary representations to these domains to construct nets of real subspaces on $G$ that are isotone, covariant and satisfy the Reeh--Schlieder and Bisognano--Wichmann conditions from Algebraic Quantum Field Theory. This provides a unifying perspective on various constructions of such nets.The representation theoretic properties of different crowns are discussed i…

Univariate amenable functions
Carlos Beltr\'an
https://arxiv.org/abs/2507.17404 https://arxiv.org/pdf/2507.17404

Univariate amenable functions
The concepts of amenable and compatible functions have been introduced in a recent work, in order to state precise mathematical theorems that guarantee that a backward stable algorithm is also forward stable, and that the composition of two stable algorithms results in an stable algorithm. In this work, we elaborate in this theory for univariate real analytic functions, providing simple tests for both concepts and producing tables for a number of elementary functions which are or fail to be ame…

Rate estimates for weighted total variation norm in terms of Wasserstein distances
Iv\'an Ivkovic, Mikl\'os R\'asonyi
https://arxiv.org/abs/2506.16088

Rate estimates for weighted total variation norm in terms of Wasserstein distances
We study the weighted total variation distance between probability measures. Using Fourier-analytic tools, we present estimates in terms of Wasserstein distances between the respective probabilities, under appropriate smoothness and moment conditions. We apply our results to convergence of functionals in Malliavin calculus.

Darboux's Theorem in $p$-adic symplectic geometry
Luis Crespo, \'Alvaro Pelayo
https://arxiv.org/abs/2508.15443 https://arxiv.org/pdf/2508.15443

Darboux's Theorem in $p$-adic symplectic geometry
Let $p$ be a prime number. We derive an analog of Moser's Path Method for $p$-adic analytic manifolds and use it to prove a $p$-adic analog of Darboux's Theorem. Hence, in the $p$-adic category there are also no local symplectic invariants other than the dimension, as it happens in the real case: locally near any point, a $2n$-dimensional $p$-adic analytic symplectic manifold is symplectomorphic to $((\mathbb{Q}_p)^{2n},\sum_{i=1}^n\mathrm{d} x_1\wedge\mathrm{d} y_i)$. We also prove a $p$-adic …

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…

Quasi-Contact Forces with Resonant Range Control in Rydberg Atoms
Mohammadsadegh Khazali
https://arxiv.org/abs/2507.17361 https://arxiv.org/pdf/2507.17361 https://arxiv.org/html/2507.17361
arXiv:2507.17361v1 Announce Type: new
Abstract: We introduce a novel method to engineer sharply peaked, distance-selective interactions between neutral atoms by exploiting interaction-induced resonances within a resonantly driven Rydberg ladder system. By tuning laser parameters, a subsystem eigenstate twist rapidly and brought into degeneracy with the atomic ground state at precisely defined interatomic separations, resulting in an effective potential sharply localized around this resonance distance. Unlike previous off-resonant macrodimer-based schemes, our approach significantly enhances interaction sharpness and strength, reaching MHz scales, and provides straightforward experimental tunability without requiring sub-wavelength positional control. Analytic expressions, validated through comprehensive master-equation simulations, detail the interaction profile's amplitude, width, and resonant distance. This precise control facilitates parallel entangling gates crucial for measurement-based quantum computing and enables simulation of complex lattice Hamiltonians with customizable connectivity. Additionally, our scheme opens possibilities for novel studies in molecular physics through micrometer-scale bond-length diatomic molecules.
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Analytic Schur multipliers
Aleksei Aleksandrov, Vladimir Peller
https://arxiv.org/abs/2506.15173 https://arxiv.org/pdf/2506.15173

Analytic Schur multipliers
We study in this paper analytic Schur multipliers on ${\Bbb C}_+^2$ and ${\Bbb D}^2$, i.e. Schur multipliers on ${\Bbb R}^2$ and ${\Bbb T}^2$ that are boundary-value functions of functions analytic in ${\Bbb C}_+^2$ and ${\Bbb D}^2$. Such Schur multipliers are important when studying properties of functions of maximal dissipative operators and contractions under perturbation. We show that if the boundary-value function of a Schur multiplier has certain regularity properties, then it can be repr…

The higher order partial derivatives of Okamoto's function with respect to the parameter
Pieter Allaart, Nathan Dalaklis, Kiko Kawamura, Matthew Ortiz, Jiajie Zheng
https://arxiv.org/abs/2506.17737

The higher order partial derivatives of Okamoto's function with respect to the parameter
Let $\{F_a: a\in(0,1)\}$ be Okamoto's family of continuous self-affine functions, introduced in [{\em Proc. Japan Acad. Ser. A Math. Sci.} {\bf 81} (2005), no. 3, 47--50]. This family includes well-known ``pathological" examples such as Cantor's devil's staircase and Perkins' continuous but nowhere differentiable function. It is well known that $F_a(x)$ is real analytic in $a$ for every $x\in[0,1]$. We introduce the functions \[ M_{k,a}(x):=\frac{\partial^k}{\partial a^k}F_a(x), \qquad k\in\mat…

Anomalous diffusion for mass transport phenomena I: Analytic solutions to time fractional diffusion
Nathaniel G. Hermann, M. Shane Hutson
https://arxiv.org/abs/2506.14043

Anomalous diffusion for mass transport phenomena I: Analytic solutions to time fractional diffusion
Mass transport problems are ubiquitous in diverse fields of physics and engineering. With the development of fractional calculus, many have taken to studying problems of fractional mass transport either through numerical simulations or through complex mathematical structures (e.g. Fox-H functions). Here, we present a set of analytic solutions to common time fractional diffusion problems, written in terms of Mittag-Leffler and M-Wright functions, as well as generalized fractional error and compl…

APFL: Analytic Personalized Federated Learning via Dual-Stream Least Squares
Kejia Fan, Jianheng Tang, Zhirui Yang, Feijiang Han, Jiaxu Li, Run He, Yajiang Huang, Anfeng Liu, Houbing Herbert Song, Yunhuai Liu, Huiping Zhuang
https://arxiv.org/abs/2508.10732

APFL: Analytic Personalized Federated Learning via Dual-Stream Least Squares
Personalized Federated Learning (PFL) has presented a significant challenge to deliver personalized models to individual clients through collaborative training. Existing PFL methods are often vulnerable to non-IID data, which severely hinders collective generalization and then compromises the subsequent personalization efforts. In this paper, to address this non-IID issue in PFL, we propose an Analytic Personalized Federated Learning (APFL) approach via dual-stream least squares. In our APFL, w…

FEWSim: A Visual Analytic Framework for Exploring the Nexus of Food-Energy-Water Simulations
Fan Lei, David A. Sampson, Jiayi Hong, Yuxin Ma, Giuseppe Mascaro, Dave White, Rimjhim Agarwal, Ross Maciejewski
https://arxiv.org/abs/2506.14056

FEWSim: A Visual Analytic Framework for Exploring the Nexus of Food-Energy-Water Simulations
The interdependencies of food, energy, and water (FEW) systems create a nexus opportunity to explore the strengths and vulnerabilities of individual and cross-sector interactions within FEW systems. However, the variables quantifying nexus interactions are hard to observe, which hinders the cross-sector analysis. To overcome such challenges, we present FEWSim, a visual analytics framework designed to support domain experts in exploring and interpreting simulation results from a coupled FEW mode…

Quasi-normal modes and shadows of scale-dependent regular black holes
Benjamin Koch, Gonzalo J. Olmo, Ali Riahinia, \'Angel Rinc\'on, Diego Rubiera-Garcia
https://arxiv.org/abs/2506.15944

Quasi-normal modes and shadows of scale-dependent regular black holes
In this paper we investigate how a regular scale-dependent black hole, characterized by a single extra parameter $ε$, behaves under perturbations by a test field (quasi-normal modes) and under light imaging (shadows) in a four-dimensional space-time background. On the quasi-normal modes side, we study how it responds to scalar and Dirac perturbations. To do this, we implement the well known WKB semi-analytic method of 6th order for obtaining the quasi-normal frequencies. We discuss the behavio…

Semi-analytic studies of accretion disk and magnetic field geometry in M87*
Saurabh, Maciek Wielgus, Arman Tursunov, Andrei P. Lobanov, Razieh Emami
https://arxiv.org/abs/2508.11760

Semi-analytic studies of accretion disk and magnetic field geometry in M87*
Context: Magnetic fields play a pivotal role in dynamics of black hole accretion flows and formation of relativistic jets. Observations by the Event Horizon Telescope (EHT) provided unprecedented insights into accretion structures near black holes. Interpreting these observations requires a theoretical framework linking polarized emission to underlying system properties and magnetic field geometries. Aims: We investigate how system properties, particularly magnetic field geometry in the event h…

Analytic mappings of the unit disk with bounded compression
Oleg Ivrii, Artur Nicolau
https://arxiv.org/abs/2507.15200 https://arxiv.…

Analytic mappings of the unit disk with bounded compression
In this paper, we study analytic self-maps of the unit disk for which the hyperbolic diameters of the images of hyperbolic balls of radius 1 are uniformly bounded below. We give several characterizations of such maps involving the behaviour along geodesic rays, Aleksandrov-Clark measures, zero sets and critical sets.

MrMARTIAN: A Multi-resolution Mass Reconstruction Algorithm Combining Free-form and Analytic Components
Sangjun Cha, M. James Jee
https://arxiv.org/abs/2508.13262 https://

MrMARTIAN: A Multi-resolution Mass Reconstruction Algorithm Combining Free-form and Analytic Components
We present ${\tt MrMARTIAN}$ (Multi-resolution MAximum-entropy Reconstruction Technique Integrating Analytic Node), a new hybrid strong lensing (SL) modeling algorithm. By incorporating physically motivated analytic nodes into the free-form method ${\tt MARS}$, ${\tt MrMARTIAN}$ enables stable and flexible mass reconstructions while mitigating oversmoothing in the inner mass profile. Its multi-resolution framework increases the degrees of freedom in regions with denser strong lensing constraint…

Chirally Frustrated Superradiant Phases in a Jaynes-Cummings Trimer
Lin-Lin Jiang, Xuan Xie, Lin Tian, Jin-Feng Huang
https://arxiv.org/abs/2507.13800 http…

Chirally Frustrated Superradiant Phases in a Jaynes-Cummings Trimer
We investigate the emergence of frustrated quantum phases in a Jaynes-Cummings (JC) trimer with complex hopping amplitudes between the cavities, which represents the smallest frustrated unit in light-matter systems. The complex hopping amplitudes that can be engineered via synthetic gauge fields introduce chiral effects and geometric frustration into the system.We obtain analytic solutions in the semiclassical limit and map out the phase diagram of this model, featuring one normal and three dis…

The dependency digraph for irreducible finite-range random walk in free groups
Chevalier Guillaume (IMB)
https://arxiv.org/abs/2507.15902 https://

The dependency digraph for irreducible finite-range random walk in free groups
This article is one of a triptych composed with [Che25a] and [Che25b], that aims at proving an asymptotic expansion to any order of the passage probability of an irreducible equivariant finite range random walk on a tree. In this text we study the analytic and geometric properties of the objects introduced in [Che25b]. To do so we introduce the definition of a ''flooded cavern tree'' enabling a precise study of some dependency digraph associated with a given irreducible finite-range random walk…

On the analytic rank of the twin prime elliptic curve $y^2=x(x-2)(x-p)$
Kirti Joshi
https://arxiv.org/abs/2508.12340 https://arxiv.org/pdf/2508.12340

On the analytic rank of the twin prime elliptic curve $y^2=x(x-2)(x-p)$
Let $p\geq 7$ and suppose $(p,p-2)$ are twin prime numbers, in [Hatley, 2009], the elliptic curve $E_p:y^2=x(x-2)(x-p)$ was considered in the context of a conjecture by Jason Beers about the Mordell-Weil ranks of $E_p/\mathbb{Q}$. I show that for $p\equiv 3,5\bmod 8$, the analytic rank of $E_p$ is at least one (Theorem 1.1.2) in line with Beers' predictions. This is done by finding a formula (Theorem 4.1.1) for the global root number of $E_p$ for all twin prime pairs. I also show that Beers' co…

Spiral renormalization group flow and universal entanglement spectrum of the non-Hermitian 5-state Potts model
Vic Vander Linden, Boris De Vos, Kevin Vervoort, Frank Verstraete, Atsushi Ueda
https://arxiv.org/abs/2507.14732

Spiral renormalization group flow and universal entanglement spectrum of the non-Hermitian 5-state Potts model
The quantum $5$-state Potts model is known to possess a perturbative description using complex conformal field theory (CCFT), the analytic continuation of ``theory space" to a complex plane. To study the corresponding complex fixed point on the lattice, the model must be deformed by an additional non-Hermitian term due to its complex coefficient $λ$. Although the variational principle breaks down in this case, we demonstrate that tensor network algorithms are still capable of simulating these …

Who Gets the Mic? Investigating Gender Bias in the Speaker Assignment of a Speech-LLM
Dariia Puhach, Amir H. Payberah, \'Eva Sz\'ekely
https://arxiv.org/abs/2508.13603 h…

Who Gets the Mic? Investigating Gender Bias in the Speaker Assignment of a Speech-LLM
Similar to text-based Large Language Models (LLMs), Speech-LLMs exhibit emergent abilities and context awareness. However, whether these similarities extend to gender bias remains an open question. This study proposes a methodology leveraging speaker assignment as an analytic tool for bias investigation. Unlike text-based models, which encode gendered associations implicitly, Speech-LLMs must produce a gendered voice, making speaker selection an explicit bias cue. We evaluate Bark, a Text-to-Sp…

Vector valued weighted analogue of converse of Wiener-L\'evy theorem and applications to modulation spaces
Divyang G. Bhimani, Karishman B. Solanki
https://arxiv.org/abs/2507.16516

Vector valued weighted analogue of converse of Wiener-Lévy theorem and applications to modulation spaces
We shall prove a strong converse of the Wiener-Lévy theorem in weighted setting for Banach algebra valued functions. In fact, it is shown that if $ω$ is a weight on a discrete abelian group $G$, $\mathcal X$ is a unital commutative Banach algebra and if $F$ is a $\mathcal X-$valued function defined on $\mathbb C$ such that $T_F(f)=F\circ f \in A^q(Γ,\mathcal X)$ for all $f\in A^1_ω(Γ,\mathcal X)$, then $F$ must be real analytic. Its multivariate analogue and analogue for locally compact ab…

Duality pairings with the analytic structure group
Christopher Wulff, Rudolf Zeidler
https://arxiv.org/abs/2506.13703 https://arxiv.o…

Duality pairings with the analytic structure group
We construct a slant product $\mathrm{S}^{G\times H}_p(X\times Y)\otimes \mathrm{K}_{-q}(\bar{\mathfrak{c}}^{\mathrm{red}} Y\rtimes H)\to \mathrm{K}_{p-q}(\mathrm{C}^\ast_G X)$ on the analytic structure group of Higson and Roe and the K-theory of the stable Higson compactification taking values in the (equivariant) Roe algebra. This complements the slant products constructed in earlier work of Engel and the authors ( arXiv:1909.03777 [math.KT] ). The distinguishing feature of our new slant prod…

On Random Fields Associated with Analytic Wavelet Transform
Gi-Ren Liu, Yuan-Chung Sheu, Hau-Tieng Wu
https://arxiv.org/abs/2508.10495 https://arxiv.org/pd…

On Random Fields Associated with Analytic Wavelet Transform
Despite the broad application of the analytic wavelet transform (AWT), a systematic statistical characterization of its magnitude and phase as inhomogeneous random fields on the time-frequency domain when the input is a random process remains underexplored. In this work, we study the magnitude and phase of the AWT as random fields on the time-frequency domain when the observed signal is a deterministic function plus additive stationary Gaussian noise. We derive their marginal and joint distribu…

An equation of motion for unsteady frictional slip pulses
Eran Bouchbinder
https://arxiv.org/abs/2506.16097 https://arxiv.org/pdf/250…

An equation of motion for unsteady frictional slip pulses
Frictional sliding, e.g., earthquakes along geological faults, are mediated either by frictional crack-like ruptures, where interfacial (fault) slip is accumulated during the entire sliding event, or by frictional pulse-like ruptures, featuring a finite length over which slip is accumulated. Our basic understanding of slip pulses, which are believed to dominate most crustal earthquakes, is still incomplete. Here, building on recent progress, we present an analytic equation of motion for rate-an…

The Splitting Lemma in any Characteristic
Gert-Martin Greuel, Gerhard Pfister
https://arxiv.org/abs/2507.17078 https://arxiv.org/pdf/2507.17078

The Splitting Lemma in any Characteristic
We give a simple proof of the splitting lemma in singularity theory, also known as generalized Morse lemma, for formal power series over arbitrary fields. Our proof for the uniqueness of the residual part in any characteristic is new and was previously unknown in characteristic two. Beyond the formal case, we give proofs for algebraic power series and for convergent real and complex analytic power series, which are new for non-isolated singularities.

The analytic bootstrap at finite temperature
Julien Barrat, Deniz N. Bozkurt, Enrico Marchetto, Alessio Miscioscia, Elli Pomoni
https://arxiv.org/abs/2506.06422

The analytic bootstrap at finite temperature
We propose new universal formulae for thermal two-point functions of scalar operators based on their analytic structure, constructed to manifestly satisfy all the bootstrap conditions. We derive a dispersion relation in the complexified time plane, which fixes the correlator up to an additive constant and theory-dependent dynamical information. At non-zero spatial separation we introduce a formula for the thermal two-point function obtained by summing over images of the dispersion relation resu…

A proof of the reverse isoperimetric inequality using a geometric-analytic approach
Naman Kumar
https://arxiv.org/abs/2508.13235 https://arxiv.org/pdf/2508…

A proof of the reverse isoperimetric inequality using a geometric-analytic approach
We present the first proof of the reverse isoperimetric inequality for black holes in arbitrary dimension using a two-pronged geometric-analytic approach. The proof holds for compact Riemannian hypersurfaces in AdS space and seems to be a generic property of black holes in the extended phase space formalism. Using Euclidean gravitational action, we show that, among all hypersurfaces of given volume, the round sphere in the $D$-dimensional Anti-de Sitter space maximizes the area (and hence the e…

Analytic Task Scheduler: Recursive Least Squares Based Method for Continual Learning in Embodied Foundation Models
Lipei Xie, Yingxin Li, Huiping Zhuang
https://arxiv.org/abs/2506.09623

Analytic Task Scheduler: Recursive Least Squares Based Method for Continual Learning in Embodied Foundation Models
Embodied foundation models are crucial for Artificial Intelligence (AI) interacting with the physical world by integrating multi-modal inputs, such as proprioception, vision and language, to understand human intentions and generate actions to control robots. While these models demonstrate strong generalization and few-shot learning capabilities, they face significant challenges in continually acquiring new skills without forgetting previously learned skills, a problem known as catastrophic forg…

Analytic neutron wall loading from spin-polarized fusion in axisymmetric geometries
Jacob A. Schwartz
https://arxiv.org/abs/2507.11758 https://

Analytic neutron wall loading from spin-polarized fusion in axisymmetric geometries
Spin-polarized nuclei can be used to enhance the fusion reaction rate, preferentially direct neutrons and alpha particles, or do some combination of these. In this paper we present formulas for the neutron wall load (NWL) on the walls of an axisymmetric torus with a convex cross section from filamentary ring sources with arbitrary fuel polarizations and arbitrary local magnetic field directions. While the NWL does not include neutron scattering, which would require a more sophisticated treatmen…

Data-driven optimal approximation on Hardy spaces in simply connected domains
Alessandro Borghi, Tobias Breiten
https://arxiv.org/abs/2507.15837 https://…

Data-driven optimal approximation on Hardy spaces in simply connected domains
We consider optimal interpolation of functions analytic in simply connected domains in the complex plane. By choosing a specific structure for the approximant, we show that the resulting first order optimality conditions can be interpreted as optimal $\mathcal{H}_2$ interpolation conditions for discrete-time dynamical systems. Connections to the implicit Euler method, the midpoint method, and backward differentiation methods are also established. A data-driven algorithm is developed to compute …

Expressivity of bisimulation pseudometrics over analytic state spaces
Daniel Luckhardt, Harsh Beohar, Clemens Kupke
https://arxiv.org/abs/2505.23635 https:…

Expressivity of bisimulation pseudometrics over analytic state spaces
A Markov decision process (MDP) is a state-based dynamical system capable of describing probabilistic behaviour with rewards. In this paper, we view MDPs as coalgebras living in the category of analytic spaces, a very general class of measurable spaces. Note that analytic spaces were already studied in the literature on labelled Markov processes and bisimulation relations. Our results are twofold. First, we define bisimulation pseudometrics over such coalgebras using the framework of fibrations…

Locally analytic completed cohomology of Shimura varieties of Hodge type
Kensuke Aoki
https://arxiv.org/abs/2508.11099 https://arxiv.org/pdf/2508.11099

Locally analytic completed cohomology of Shimura varieties of Hodge type
For Shimura varieties of Hodge type, we show that there are natural isomorphisms between locally analytic complete cohomology groups and cohomology groups for flag varieties with coefficient which is given by their perfectoid covers. This result is a generalization of that of Pan for the modular curve and Qiu-Su for unitary Shimura curves.

On Steiner entire function
Maria Dospolova, Mikhail Germanskov, Dmitry Zaporozhets
https://arxiv.org/abs/2507.11626 https://arxiv.org…

On Steiner entire function
We introduce and study the Steiner entire function, an analytic generating function for the intrinsic volumes of a convex compact set in a Hilbert space. This function extends the classical Steiner polynomial to infinite dimensions and encodes key geometric information about the set. We establish fundamental results on its order, type, and canonical product representation, and show how its analytic growth properties characterize Gaussian continuity. In particular, we provide new criteria for th…

Galton-Watson processes, simple varieties of trees and Khinchin families
V\'ictor J. Maci\'a
https://arxiv.org/abs/2506.18370 https://

Galton-Watson processes, simple varieties of trees and Khinchin families
In this note, we introduce a unified analytic framework that connects simple varieties of trees, Bienayme-Galton-Watson processes and Khinchin families. Using Lagrange's inversion formula, we derive new coefficient-based expressions for extinction probabilities and reinterpret them as boundary phenomena tied to the domain of the inverse of the solution to Lagrange's equation. This perspective reveals a structural bridge between combinatorial and probabilistic models, simplifying classical argum…

Accuracy of analytic potentials for orbits of satellites around a Milky Way-like galaxy: comparison with $N$-body simulations
Rubens E. G. Machado, Giovanni C. Tauil, Nicholas Schweder-Souza
https://arxiv.org/abs/2506.13813

Accuracy of analytic potentials for orbits of satellites around a Milky Way-like galaxy: comparison with $N$-body simulations
To study the orbits of satellites, a galaxy could be modelled either by means of a static gravitational potential, or by live $N$-body particles. Analytic potentials allow for fast calculations, but are idealized and non-responsive. On the other hand, $N$-body simulations are more realistic, but demand higher computational cost. Our goal is to characterize the regimes in which analytic potentials provide a sufficient approximation, and those where $N$-bodies are necessary. We perform two sets o…

$\zeta$-functions via contour integrals and universal sum rules
Guglielmo Fucci, Mateusz Piorkowski, Jonathan Stanfill
https://arxiv.org/abs/2508.15699 https://

$ζ$-functions via contour integrals and universal sum rules
This work develops an analytic framework for the study of the $ζ$-function associated with general sequences of complex numbers. We show that a contour integral representation, commonly used when studying spectral $ζ$-functions associated with self-adjoint differential operators, can be extended far beyond its traditional setting. In contrast to representations utilizing integrals of $θ$-functions, our method applies to arbitrary sequences of complex numbers with minimal assumptions. This le…

Thermal Radiation from an Analytic Hydrodynamic Model with Hadronic and QGP Sources in Heavy-Ion Collisions
G\'abor L\'aszl\'o Kasza
https://arxiv.org/abs/2507.13240

Thermal Radiation from an Analytic Hydrodynamic Model with Hadronic and QGP Sources in Heavy-Ion Collisions
In high-energy heavy-ion collisions, a nearly perfect fluid is formed, known as the strongly coupled quark-gluon plasma (QGP). After a short thermalization period, the evolution of this medium can be described by the equations of relativistic hydrodynamics. As the system expands and cools, the QGP undergoes a transition into hadronic matter, marking the onset of quark confinement. Direct photons offer insights into an essential stage of evolution, spanning from the onset of thermalization to th…

Bias in Meta-Analytic Modeling of Surrogate Endpoints in Cancer Screening Trials
James P. Long, Abhishikta Roy, Ehsan Irajizad, Kim-Anh Do, Yu Shen
https://arxiv.org/abs/2508.04633

Bias in Meta-Analytic Modeling of Surrogate Endpoints in Cancer Screening Trials
In meta-analytic modeling, the functional relationship between a primary and surrogate endpoint is estimated using summary data from a set of completed clinical trials. Parameters in the meta-analytic model are used to assess the quality of the proposed surrogate. Recently, meta-analytic models have been employed to evaluate whether late-stage cancer incidence can serve as a surrogate for cancer mortality in cancer screening trials. A major challenge in meta-analytic models is that uncertainty …

Analytic Gravitational Wave Spectrum in Next-to-Minimal Bouncing Cosmology
Changhong Li
https://arxiv.org/abs/2507.12968 https://arxi…

Analytic Gravitational Wave Spectrum in Next-to-Minimal Bouncing Cosmology
Bouncing cosmology offers a singularity-free alternative to inflation, but its minimal realization-comprising only four cosmic phases-predicts a simple power-law stochastic gravitational-wave background (SGWB) with a narrow observational window. We introduce the next-to-minimal bouncing cosmology (NMBC), which adds an extra early contraction phase that imprints a broken power-law feature in the SGWB spectrum, enhancing detectability. Using our matrix-representation method grounded in an inequal…

Replaced article(s) found for math.CV. https://arxiv.org/list/math.CV/new
[1/1]:
- Automorphisms of subalgebras of bounded analytic functions
Kanha Behera, Rahul Maurya, P. Muthukumar

A Globally Optimal Analytic Solution for Semi-Nonnegative Matrix Factorization with Nonnegative or Mixed Inputs
Lu Chenggang
https://arxiv.org/abs/2508.07134 https://

A Globally Optimal Analytic Solution for Semi-Nonnegative Matrix Factorization with Nonnegative or Mixed Inputs
Semi-Nonnegative Matrix Factorization (semi-NMF) extends classical Nonnegative Matrix Factorization (NMF) by allowing the basis matrix to contain both positive and negative entries, making it suitable for decomposing data with mixed signs. However, most existing semi-NMF algorithms are iterative, non-convex, and prone to local minima. In this paper, we propose a novel method that yields a globally optimal solution to the semi-NMF problem under the Frobenius norm, through an orthogonal decomposi…

A State-Space Representation of Coupled Linear Multivariate PDEs and Stability Analysis using SDP
Declan S. Jagt, Matthew M. Peet
https://arxiv.org/abs/2508.14840 https://

A State-Space Representation of Coupled Linear Multivariate PDEs and Stability Analysis using SDP
Physical processes evolving in both time and space are often modeled using Partial Differential Equations (PDEs). Recently, it has been shown how stability analysis and control of coupled PDEs in a single spatial variable can be more conveniently performed using an equivalent Partial Integral Equation (PIE) representation. The construction of this PIE representation is based on an analytic expression for the inverse of the spatial differential operator, $\partial_s^{d}$, on the domain defined b…

Crosslisted article(s) found for math-ph. https://arxiv.org/list/math-ph/new
[1/1]:
- A proof of the reverse isoperimetric inequality using a geometric-analytic approach
Naman Kumar

HBAR entropy in causal diamond geometry: A near-horizon perspective
Nada Eissa, Carlos R. Ord\'o\~nez, Gustavo Valdivia-Mera
https://arxiv.org/abs/2508.13493 https://…

HBAR entropy in causal diamond geometry: A near-horizon perspective
In this article we extend the Horizon Brightened Acceleration Radiation (HBAR) framework to the causal diamond (CD) spacetime. We study a cloud of two-level atoms, injected at random times in the asymptotic past of the CD, freely falling toward its causal horizon and emitting scalar radiation via a weak dipole coupling to a quantum field. In the near-horizon region, an emergent conformal symmetry-captured by conformal quantum mechanics (CQM)-governs the field dynamics and allows analytic contro…

Belief-Conditioned One-Step Diffusion: Real-Time Trajectory Planning with Just-Enough Sensing
Gokul Puthumanaillam, Aditya Penumarti, Manav Vora, Paulo Padrao, Jose Fuentes, Leonardo Bobadilla, Jane Shin, Melkior Ornik
https://arxiv.org/abs/2508.12166

Belief-Conditioned One-Step Diffusion: Real-Time Trajectory Planning with Just-Enough Sensing
Robots equipped with rich sensor suites can localize reliably in partially-observable environments, but powering every sensor continuously is wasteful and often infeasible. Belief-space planners address this by propagating pose-belief covariance through analytic models and switching sensors heuristically--a brittle, runtime-expensive approach. Data-driven approaches--including diffusion models--learn multi-modal trajectories from demonstrations, but presuppose an accurate, always-on state estim…

Fractional Volterra-type operator induced by radial weight acting on Hardy space
Carlo Bellavita, \'Alvaro Miguel Moreno, Georgios Nikolaidis Jos\'e \'Angel Pel\'aez
https://arxiv.org/abs/2506.18122

Fractional Volterra-type operator induced by radial weight acting on Hardy space
Given a radial doubling weight $μ$ on the unit disc $\mathbb{D}$ of the complex plane and its odd moments $μ_{2n+1}=\int_0^1 s^{2n+1}μ(s)\, ds$, we consider the fractional derivative $$ D^μ(f)(z)=\sum_{n=0}^{\infty} \frac{\widehat{f}(n)}{μ_{2n+1}}z^n, $$ of a function $ f(z)=\sum_{n=0}^{\infty}\widehat{f}(n)z^n$ analytic in $\mathbb{D}$. We also consider the fractional integral operator $I^μ(f)(z)=\sum_{n=0}^{\infty} μ_{2n+1}\widehat{f}(n)z^n$, and the fractional Volterra-type op…

Equatorial light bending around a Hairy Kiselev Black Hole
Shrishti Kukreti, Shubham Kala, Hemwati Nandan, Faizuddin Ahmed, Saswati Roy
https://arxiv.org/abs/2507.15298

Equatorial light bending around a Hairy Kiselev Black Hole
We investigate the deflection angle of light rays confined to the equatorial plane of a Hairy Kiselev black hole. The analysis includes a thorough study of the horizon structure and critical parameters, leading to an analytic expression for the deflection angle in terms of elliptic integrals. Our results confirm that the deflection angle decreases with increasing impact parameter, in agreement with classical predictions of gravitational lensing. The influence of the scalar field, characterized …

Crosslisted article(s) found for math.DG. https://arxiv.org/list/math.DG/new
[1/1]:
- A proof of the reverse isoperimetric inequality using a geometric-analytic approach
Naman Kumar

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…

Combinatorics and Hodge theory of degenerations of abelian varieties: A survey of the Mumford construction
Philip Engel, Olivier de Gaay Fortman, Stefan Schreieder
https://arxiv.org/abs/2507.15695

Combinatorics and Hodge theory of degenerations of abelian varieties: A survey of the Mumford construction
We survey the Mumford construction of degenerating abelian varieties, with a focus on the analytic version of the construction, and its relation to toric geometry. Moreover, we study the geometry and Hodge theory of multivariable degenerations of abelian varieties associated to regular matroids, and extend some fundamental results of Clemens on 1-parameter semistable degenerations to the multivariable setting.

Analytic model for neutral penetration and plasma fueling
George J. Wilkie
https://arxiv.org/abs/2506.10906 https://arxiv.org/pdf/250…

Analytic model for neutral penetration and plasma fueling
Neutral atoms recycled from wall interaction interact with confined plasma, thereby refueling it, most strongly in the region closest to the wall. This occurs near the X-point in diverted configurations, or else near the wall itself in limited configurations. A progression of analytic models are developed for neutral density in the vicinity of a planar or linear source in an ionizing domain. First-principles neutral transport simulations with DEGAS2 are used throughout to test the validity and …

Optimal polynomial approximants and orthogonal polynomials on the unit circle. An electrostatic approach
Ram\'on Orive, Joaqu\'in S\'anchez-Lara, Daniel Seco
https://arxiv.org/abs/2507.15488

Optimal polynomial approximants and orthogonal polynomials on the unit circle. An electrostatic approach
We explore the connection between two seemingly distant fields: the set of cyclic functions $f$ in a Hilbert space of analytic functions over the unit disc $\D$, on the one hand, and the families of orthogonal polynomials for a weight on the unit circle $\T$ (OPUC), on the other. This link is established by so-called Optimal Polynomial Approximants (OPA) to $1/f$, that is, polynomials $p_n$ minimizing the norm of $1-p_nf$, among all polynomials $p_n$ of degree up to a given $n$. Here, we focu…

Sharp extensions of analytic function spaces in the unit disk and related domains
Romi F. Shamoyan, Nataliya M. Makhina
https://arxiv.org/abs/2506.12472 ht…

Sharp extensions of analytic function spaces in the unit disk and related domains
In this expository paper we collect many recent advances in analytic function spaces of several complex variables related with trace problem. We consider various function space of analytic functions of several variables in various domains in Cn and provide or complete descriptions of traces or estimates of traces of various analytic function spaces in various domains obtained in recent years, by various authors. The problem to find sharp estimates of Hardy analytic function spaces in the unit p…

Prospects for studying million-degree gas in the Milky Way halo using the forbidden optical [FeX] and [FeXIV] intersystem lines
P. Richter, F. Ruenger, N. Lehner, J. C. Howk, C. Peroux, N. Libeskind, M. Steinmetz, R. de Jong
https://arxiv.org/abs/2507.14279

Prospects for studying million-degree gas in the Milky Way halo using the forbidden optical [FeX] and [FeXIV] intersystem lines
The Milky Way is surrounded by large amounts of hot gas at temperatures T>10^6 K, which represents a major baryon reservoir. We here explore the prospects of studying the hot coronal gas in Milky Way halo by analyzing the highly forbidden optical coronal lines of [FeX] and [FeXIV] in absorption against bright extragalactic background sources. We use a semi-analytic model of the Milky Way's coronal gas distribution together wih HESTIA simulations of the Local Group and observational constraints …

Replaced article(s) found for cs.LG. https://arxiv.org/list/cs.LG/new
[7/7]:
- From Data-Driven to Purpose-Driven Artificial Intelligence: Systems Thinking for Data-Analytic Au...
Anadria, Dobbe, Giachanou, Kuiper, Bartels, van Amsterdam, de Troya, Z\"urcher, Oberski
…

On relative vertical compactification of weakly square complete adic spaces
Ronald Solodov
https://arxiv.org/abs/2508.15707 https://arxiv.org/pdf/2508.1570…

On relative vertical compactification of weakly square complete adic spaces
We prove for a morphism $f \colon X \rightarrow S$ locally of $^+$weakly finite type, separated and taut, where $X$ is a weakly square complete adic space and $S$ a square complete and stable adic space, there exists a universal vertical compactification $f' \colon X' \rightarrow S$. This provides a generalized version of Huber's proof of universal compactification of morphisms between analytic adic spaces. Notably, we will see that for the compactification, it is not necessary to assume that t…

The matrix weighted real-analytic double fibration transforms
Hiroyuki Chihara, Shubham R. Jathar, Jesse Railo
https://arxiv.org/abs/2506.24067 https://

The matrix weighted real-analytic double fibration transforms
We show that the real-analytic matrix-weighted double fibration transform determines the analytic wavefront set of a vector-valued function. We apply this result to show that the matrix weighted ray transform is injective on a two-dimensional, non-trapping, real-analytic Riemannian manifold with strictly convex boundary. Additionally, we show that a real-analytic Higgs field can be uniquely determined from the nonabelian ray transform on real-analytic Riemannian manifolds of any dimension with …

Analytic Dilogarithm Identities
Cetin Hakimoglu
https://arxiv.org/abs/2506.10206 https://arxiv.org/pdf/2506.10206

Analytic Dilogarithm Identities
By showing that the ratio of two beta-like integrals equals an integer, new Dilogarithm identities are derived, as well as analytic proofs to conjectured identities. New, non-trivial 2-term and ladder-like Dilogarithm identities are derived about ${Q}[\sqrt{2}]$, ${Q}[\sqrt{5}]$, ${Q}[\sqrt{-7}]$, and ${Q}[\sqrt{3}]$, . This also leads also to a connection between identities ${Q}[\sqrt{13}]$ and ${Q}[\sqrt{3}]$. Single-term and two-term complex Dilogarithm identities are derived, in addition to…

Learning the Analytic Geometry of Transformations to Achieve Efficient Computation
Pei-Chun Su, Ronald R. Coifman
https://arxiv.org/abs/2506.11990 https://…

Learning the Analytic Geometry of Transformations to Achieve Efficient Computation
We propose a novel framework for fast integral operations by uncovering hidden geometries in the row and column structures of the underlying operators. This is accomplished through an iterative procedure that constructs adaptive hierarchical partition trees, revealing latent multiscale organization and exposing local low-rank structures within the data. Guided by this geometry, we employ two complementary techniques: (1) the \emph{butterfly algorithm}, which exploits the learned hierarchical lo…

A converse of Cartan's Theorem B for Real Analytic Set
J\'anos Koll\'ar
https://arxiv.org/abs/2507.11679 https://arxiv.or…

A converse of Cartan's Theorem B for Real Analytic Set
In this lecture we prove a converse to Cartan's Theorem B for real analytic sets, due to Fernando and Ghiloni [arXiv:2506.18347].

syren-baryon: Analytic emulators for the impact of baryons on the matter power spectrum
Lukas Kammerer, Deaglan J. Bartlett, Gabriel Kronberger, Harry Desmond, Pedro G. Ferreira
https://arxiv.org/abs/2506.08783

syren-baryon: Analytic emulators for the impact of baryons on the matter power spectrum
Baryonic physics has a considerable impact on the distribution of matter in our Universe on scales probed by current and future cosmological surveys, acting as a key systematic in such analyses. We seek simple symbolic parametrisations for the impact of baryonic physics on the matter power spectrum for a range of physically motivated models, as a function of wavenumber, redshift, cosmology, and parameters controlling the baryonic feedback. We use symbolic regression to construct analytic approx…

On the analytic properties of the perturbing function in the PCR3Body Problem
Corrado Falcolini, Davide Zaccaria
https://arxiv.org/abs/2508.10621 https://a…

On the analytic properties of the perturbing function in the PCR3Body Problem
We provide a new expansion of the Fourier coefficient of the Perturbing function of the PCR3Body problem in terms of Hansen Coefficients. This gives us a precise asymptotic formula for the coefficient in the region of application of KAM theory (i.e small value of eccentricity and semi-major axis see e.g. \cite{Celletti-Chierchia}). Moreover, in the above region, we study the presence of zeros of the Fourier coefficient for coprime modes $(m,k) \in \Z^2$ and the presence of common zeros between …

Wick theorem for analytic functions of Gaussian fields
Fabio Coppini, Wioletta M. Ruszel, Dirk Schuricht
https://arxiv.org/abs/2507.05131 https://

Wick theorem for analytic functions of Gaussian fields
We compute the correlation of analytic functions of general Gaussian fields in terms of multigraphs and Feynman diagrams on the lattice Z^d. Then, we connect its scaling limit to tensors of the correlation functionals of Fock space fields. Afterwards, we investigate the relation with fermionic Gaussian field states for even functions. For instance, we characterize the correlation functionals of the exponential of a continuous Gaussian Free Field or general analytic functions of fractional Gauss…

Ces\`{a}ro-type operators acting on Dirichlet spaces
Petros Galanopoulos, Daniel Girela
https://arxiv.org/abs/2507.13502 https://arxi…

Cesàro-type operators acting on Dirichlet spaces
If $(η)=\{ η_n\} _{n=0}^\infty $ is a sequence of complex numbers, the Cesàro-type operator $\mathcal C_{(η)}$ is formally defined in the space of analytic funtions in the unit disc $\mathbb D$ as follows: If $f$ is an analytic function in $\mathbb D$, $f(z)=\sum_{n=0}^\infty a_nz^n$ ($z\in \mathbb D$), then $\mathcal C_{(η)}(f)$ is formally defined by $$\mathcal C_{(η)}(f)(z)=\mathcal C_{\{η_n\}}(f)(z)=\sum_{n=0}^\infty η_n\left (\sum_{k=0}^na_k\right )z^n.$$ The operator $\mathcal C_{…

Finite-Width Neural Tangent Kernels from Feynman Diagrams
Max Guillen, Philipp Misof, Jan E. Gerken
https://arxiv.org/abs/2508.11522 https://arxiv.org/pdf/…

Finite-Width Neural Tangent Kernels from Feynman Diagrams
Neural tangent kernels (NTKs) are a powerful tool for analyzing deep, non-linear neural networks. In the infinite-width limit, NTKs can easily be computed for most common architectures, yielding full analytic control over the training dynamics. However, at infinite width, important properties of training such as NTK evolution or feature learning are absent. Nevertheless, finite width effects can be included by computing corrections to the Gaussian statistics at infinite width. We introduce Feyn…

Classically psh and pluriharmonic functions on Berkovich spaces
Walter Gubler, Joseph Rabinoff
https://arxiv.org/abs/2506.13548 https://

Classically psh and pluriharmonic functions on Berkovich spaces
First we extend the theory of subharmonic functions on smooth strictly $k$-analytic curves from Thuillier's thesis to the case of possibly singular analytic curves over a non-archimedean field. Classically psh functions are then defined as in complex geometry by using pullbacks to analytic curves (and requiring compatibility with base change). We give various properties of classically psh functions including a local and a global maximum principle. As a consequence, we show that the space of plu…

The Weyl bound for triple product L-functions in the cubic level
Xinchen Miao, Huimin Zhang
https://arxiv.org/abs/2508.13746 https://arxiv.org/pdf/2508.137…

The Weyl bound for triple product L-functions in the cubic level
In this paper, we focus on the strong subconvexity bounds for triple product L-functions in the cubic level aspect. Our proof on the Weyl-type bound synthesizes techniques from classical analytic number theory with methods in automorphic forms and representation theory. The methods include the refined Petersson trace formula for the newforms of cubic level, classical Voronoi summation formula, Jutila's circle method, Kuznetsov trace formula and the spectral large sieve inequality.

On multipliers of some new analytic function spaces in polydisc of BMOA type
Romi F. Shamoyan
https://arxiv.org/abs/2506.12445 https://

On multipliers of some new analytic function spaces in polydisc of BMOA type
We define two new BMOA type analytic function spaces in polydisk. We provide several new results concerning coefficient multipliers of these two new BMOA analytic function spaces in polydisc. Our results extend previously known assertions.

Categorical K\"unneth formulas for analytic stacks
Youshua Kesting
https://arxiv.org/abs/2507.08566 https://arxiv.org/pdf/2507.0…

Categorical Künneth formulas for analytic stacks
In arXiv:0805.0157v5, the authors define a class of derived stacks, called "perfect stacks" and show that for this class the categories of quasi-coherent sheaves satisfy a categorical Künneth formula. Motivated to extend their results to the theory of analytic stacks as developed by Clausen-Scholze, we investigate categorical Künneth formulas for general $6$-functor formalisms. As applications we show a general Tannakian reconstruction result for analytic stacks and, following recent work of …

Crosslisted article(s) found for gr-qc. https://arxiv.org/list/gr-qc/new
[1/1]:
- Semi-analytic studies of accretion disk and magnetic field geometry in M87*
Saurabh, Maciek Wielgus, Arman Tursunov, Andrei P. Lobanov, Razieh Emami

An effective analytic recurrence for prime numbers: from asymptotics to explicit bounds
Benoit Cloitre
https://arxiv.org/abs/2508.02690 https://arxiv.org/p…

An effective analytic recurrence for prime numbers: from asymptotics to explicit bounds
We present an explicit and effective recurrence formula for prime numbers, bridging arithmetic and analytic approaches. Building upon foundational work by Gandhi (1971), Golomb (1976), and Keller (2007), we establish the effective bound $s_n \le 2p_n$ for all $n \ge 1$ within the Golomb-Keller analytic recurrence. This transforms their asymptotic formula into an explicit recurrence using twice the n-th prime as the exponent: $$ p_{n+1} = \left\lceil \left( -1 + ζ(2p_n) \prod_{j=1}^{n} \left(1 …

Evaluating the Accuracy of Reionization Prescriptions in Semi-analytic Models of the First Stars and Galaxies
Thomas Behling, Ryan Hazlett, Mihir Kulkarni, Eli Visbal
https://arxiv.org/abs/2508.04808

Evaluating the Accuracy of Reionization Prescriptions in Semi-analytic Models of the First Stars and Galaxies
Semi-analytic models are a valuable tool to study the first stars and galaxies. Their numerical efficiency makes it possible to survey broad regions of astrophysical parameter space across large volumes and redshift ranges. Following reionization in these models is necessary since star formation is suppressed in ionized regions due to photoheating of the gas. Here we evaluate the accuracy of three semi-analytic reionization prescriptions (two previously developed and one new model) by comparing…

Numerical conformal mapping
Lloyd N. Trefethen
https://arxiv.org/abs/2507.14872 https://arxiv.org/pdf/2507.14872

Numerical conformal mapping
Conformal mapping may be the best-known topic in complex analysis. Any simply connected nonempty domain $Ω$ in the complex plane ${\mathbb{C}}$ (assuming $Ω\ne {\mathbb{C}}$) can be mapped bijectively to the unit disk by an analytic function with nonvanishing derivative, as in Figure 1. If $Ω$ is doubly-connected, it can be mapped to a circular annulus $1<|z|

'Stealth' singularities from self-gravitating fermions
Peter E. D. Leith, Chris A. Hooley, Keith Horne, David G. Dritschel
https://arxiv.org/abs/2508.10604 https://

'Stealth' singularities from self-gravitating fermions
We present a new analytic solution to the Einstein-Dirac equations formulated by Finster, Smoller, and Yau [Phys. Rev. D 59, 104020 (1999)] to describe the stationary states of a pair of gravitationally interacting neutral fermions. The fermions' wavefunction in our analytic solution, as in their numerical ones, is both exponentially localized and normalizable. However, our solution differs from theirs in two key respects: it features a naked spacetime singularity at the origin, and the gravita…

Replaced article(s) found for math.AG. https://arxiv.org/list/math.AG/new
[1/1]:
- Arithmetic Properties Of $\ell$-adic \'Etale Cohomology and Nearby Cycles of Rigid-Analytic Spaces
David Hansen, Bogdan Zavyalov

The distance function and Lipschitz classes of mappings between metric spaces
Marijan Markovic
https://arxiv.org/abs/2507.14508 https://

The distance function and Lipschitz classes of mappings between metric spaces
We investigate when the local Lipschitz property of the real-valued function $g(z) = d_Y (f(z),A)$ implies the global Lipschitz property of the mapping $f:X\to Y$ between the metric spaces $(X,d_X)$ and $(Y,d_Y)$. Here, $d_Y(y,A)$ denotes the distance of $y\in Y$ from the non-empty set $\subseteq Y$. As a consequence, we find that an analytic function on a uniform domain of a normed space belongs to the Lipschitz class if and only if its modulus satisfies the same condition; in the case of the …

Congruences of $p$-adic $L$-functions of modular forms at non-ordinary primes
Raiza Corpuz, Antonio Lei
https://arxiv.org/abs/2508.09733 https://arxiv.org/…

Congruences of $p$-adic $L$-functions of modular forms at non-ordinary primes
We present an analogue of Greenberg-Vatsal's and Emerton-Pollack-Weston's results on congruences of $p$-adic $L$-functions for $p$-non-ordinary cuspidal eigenforms $f$ and $g$ of equal weight that are $p$-congruent. In particular, we prove that the Iwasawa invariants of the analytic and algebraic signed $p$-adic $L$-functions of $f$ and $g$ are related by explicit formulae under appropriate hypotheses. We also show under the same assumptions that provided the algebraic and analytic $μ$-invaria…

Relative Riemann-Hilbert and Newlander-Nirenberg Theorems for torsion-free analytic sheaves on maximal and homogeneous spaces
Thomas Kurbach
https://arxiv.org/abs/2506.05841

Relative Riemann-Hilbert and Newlander-Nirenberg Theorems for torsion-free analytic sheaves on maximal and homogeneous spaces
In this paper it is shown that for locally trivial complex analytic morphisms between some reduced spaces the Relative Riemann-Hilbert Theorem still holds up to torsion, i.e. tame flat relative connections on torsion-free sheaves are in 1-to-1 correspondence with torsion-free relative local systems. Subsequently, it is shown that generalised $\bar{\partial}$-operators on real analytic sheaves over complex analytic spaces can be viewed as relative complex analytic connections on the complexifica…

On some sharp estimates of Toeplitz operator in some spaces of Hardy-Lizorkin type of analytic functions in the polydisk
R. F. Shamoyan, E. B. Tomashevskaya
https://arxiv.org/abs/2507.10837

On some sharp estimates of Toeplitz operator in some spaces of Hardy-Lizorkin type of analytic functions in the polydisk
We provide some new sharp assertions on the action of Toeplitz $T_φ$ operator in new $F^{p,q}_α$ type spaces of analytic functions of several complex variables extending previously known assertions proved by various authors.

Decay of Fourier transforms and analytic continuation of power-constructible functions
Georges Comte, Dan J. Miller, Tamara Servi
https://arxiv.org/abs/2507.06142

Decay of Fourier transforms and analytic continuation of power-constructible functions
For a subfield K of C, we denote by C^K the category of algebras of functions defined on the globally subanalytic sets that are generated by all K-powers and logarithms of positively-valued globally subanalytic functions. For any function f in C^\K(R), we study links between holomorphic extensions of f and the decay of its Fourier transform F[f] by using tameness properties of the globally subanalytic functions from which f is constructed. We first prove a number of theorems about analytic cont…

Characteristic cycles for coadmissible D-modules on smooth rigid analytic curves
Raoul Hallopeau (IMJ-PRG)
https://arxiv.org/abs/2508.08348 https://arxiv.o…

Characteristic cycles for coadmissible D-modules on smooth rigid analytic curves
Let $\mathfrak{X}$ be a formal smooth curve over a complete discrete valuation ring of mixed characteristic and let $\mathfrak{X}_K$ be its generic fiber. We consider respectively over $\mathfrak{X}$ and $\mathfrak{X}_K$ the sheaves of differential operators $\mathcal{D}_{\mathfrak{X}, \infty}$ and $\overparen{\mathcal{D}}_{\mathfrak{X}_K}$ with a rapid convergence condition. In this article, we define a characteristic variety as a closed subset of the cotangent space $T^*\mathfrak{X}_K$ togeth…

Closed range of generalized integration operators on analytic tent spaces
Rong Yang, Xiangling Zhu
https://arxiv.org/abs/2506.10681 https://

Closed range of generalized integration operators on analytic tent spaces
In this paper, the necessary and sufficient conditions for the generalized integration operator $T_g^{n,k}$ to have closed ranges on the analytic tent spaces are investigated.

Derived analytic geometry: Derived K\"ahler space and Hodge theory
Eita Haibara
https://arxiv.org/abs/2506.19629 https://arxiv.o…

Derived analytic geometry: Derived Kähler space and Hodge theory
We introduce higher analytic geometry, a novel framework extending Lurie's derived complex analytic spaces. This theory generalizes classical complex analytic geometry, enabling the study of derived Kähler spaces with non-trivial higher homotopy groups. We develop derived de Rham and Dolbeault cohomologies, yielding a Hodge decomposition for compact derived Kähler spaces, and establish a derived Stokes' theorem, unifying classical results with homotopical structures.