Tootfinder

Compact Biconservative Hypersurfaces in Space Forms: Rigidity Without Scalar Curvature Assumptions
Aykut Kayhan
https://arxiv.org/abs/2506.05875 https://…

Compact Biconservative Hypersurfaces in Space Forms: Rigidity Without Scalar Curvature Assumptions
In this study, we investigate the intrinsic properties of compact biconservative hypersurfaces in space forms. In this framework, we establish rigidity results without imposing the assumption of constant scalar curvature. Furthermore, we present an additional result that does not require any assumptions on the sectional curvature. The key tool in our approach is the introduction of a novel divergence-free tensor, which enables us to derive these results without the usual curvature assumptions.

Single-cell metabolic flux analysis reveals coexisting optimal sub-groups, cross-feeding, and mixotrophy in a cyanobacterial population
Ari\'an Ferrero-Fern\'andez, Paula Prondzinsky, Lucia Gastoldi, David A. Fike, Harrison B. Smith, Daniele De Martino, Andrea De Martino, Shawn Erin McGlynn
https://arxiv.org/abs/2506.059…

Single-cell metabolic flux analysis reveals coexisting optimal sub-groups, cross-feeding, and mixotrophy in a cyanobacterial population
We derive a single-cell level understanding of metabolism in an isogenic cyanobacterial population by integrating secondary ion mass spectrometry (SIMS) derived multi-isotope uptake measurements of Synechocystis sp. PCC6803 with a statistical inference protocol based on Liebig's law of the minimum, the maximum entropy principle, and constraint-based modeling. We find the population is structured in two metabolically distinct clusters: cells optimizing carbon yield while excessively turning over…

This https://arxiv.org/abs/2505.12612 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCR_…

EPSpatial: Achieving Efficient and Private Statistical Analytics of Geospatial Data
Geospatial data statistics involve the aggregation and analysis of location data to derive the distribution of clients within geospatial. The need for privacy protection in geospatial data analysis has become paramount due to concerns over the misuse or unauthorized access of client location information. However, existing private geospatial data statistics mainly rely on privacy computing techniques such as cryptographic tools and differential privacy, which leads to significant overhead and in…

This https://arxiv.org/abs/2502.02070 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hepp…

Finite temperature QCD crossover at non-zero chemical potential: A Dyson-Schwinger approach
We study QCD at finite temperature and non-zero chemical potential to derive the critical temperature at the chiral phase transition (crossover). We solve a set of Dyson--Schwinger partial differential equations using the exact solution for the Yang--Mills quantum field theory based on elliptical functions. We derive a Nambu-Jona--Lasino (NJL) model of the quarks and obtain a very good agreement with recent lattice computations regarding the dependence of the critical temperature on the strong …

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The Hesse pencil of plane curves and osculating conics
Ewelina Nawara
https://arxiv.org/abs/2506.04662 https://arxiv.org/pdf/2506.046…

The Hesse pencil of plane curves and osculating conics
In this paper, we revisit the classical problem of determining osculating conics and sextactic points for a given algebraic curve. Our focus is on a particular family of plane cubic curves known as the Hesse pencil. By employing classical tools from projective differential geometry, we derive explicit coordinates for these special points. The resulting formulas not only clarify previous approaches but also lead to the construction of new families of free and nearly free curves, extending recent…

An emergence-oriented approach to cyclic pursuit
Zhaozhan Yao, Yuhua Yao, Xiaoming Hu
https://arxiv.org/abs/2506.05157 https://arxiv.…

An emergence-oriented approach to cyclic pursuit
In this paper, we explore the cyclic pursuit problem of unicycles and study circular formation from an emergence perspective. We first establish a systematic study on such formation and derive a necessary and sufficient condition for its existence. Building on this theoretical foundation, we design a distributed control law that enables the spontaneous formation of circular formations through only local interactions. Notably, key geometric features -- including the radius and agent spacing -- a…

This https://arxiv.org/abs/2502.14578 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

The massive BMS character in 3D quantum gravity
We derive the one-loop partition function for three-dimensional quantum gravity in a finite-radius thermal twisted flat space with a conical defect, reproducing the massive BMS$_3$ character. We perform the computation in both discrete and continuum geometry formulations, showing consistency between them. In the discrete case, we integrate out bulk degrees of freedom in a Regge gravity framework, while in the continuum, we construct a dual non-local boundary field theory encoding geodesic lengt…

This https://arxiv.org/abs/2501.00092 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Moments and saddles of heavy CFT correlators
We study the operator product expansion (OPE) of identical scalars in a conformal four-point correlator as a Stieltjes moment problem, and use Riemann-Liouville type fractional differential operators to generate classical moments from the correlation function. We use crossing symmetry to derive leading and subleading relations between moments in $Δ$ and $J_2 \equiv \ell(\ell+d-2)$ in the ``heavy" limit of large external scaling dimension, and combine them with constraints from unitarity to der…

Nonsmooth data error estimates for exponential Runge--Kutta methods and applications to split exponential integrators
Qiumei Huang, Alexander Ostermann, Gangfan Zhong
https://arxiv.org/abs/2506.02778

Nonsmooth data error estimates for exponential Runge--Kutta methods and applications to split exponential integrators
We derive error bounds for exponential Runge-Kutta discretizations of parabolic equations with nonsmooth initial data. Our analysis is carried out in a framework of abstract semilinear evolution equations with operators having non-dense domain. In particular, we investigate nonsmooth data error estimates for the Allen-Cahn and the Burgers' equation. As an application, we apply these nonsmooth data error estimates to split exponential integrators and derive a convergence result in terms of the d…

Optimization of the multiple sampling and signal extraction in non-destructive exposures
B. Kubik, R. Barbier, A. Castera, E. Chabanat, S. Ferriol, G. Smadja
https://arxiv.org/abs/2506.04904

Optimization of the multiple sampling and signal extraction in non-destructive exposures
We derive the full covariance matrix formulae are derived for proper treatment of correlations in signal fitting procedures, extending the results from previous publications. The straight line fits performed with these matrices demonstrate that a significantly higher signal to noise is obtained when the fluence exceeds 1 e/sec/pix in particular in long (several hundreds of seconds) spectroscopic exposures. The improvement arising from the covariance matrix is particularly strong for the initial…

Statistics of Non-Rayleigh Speckles Generated from Nonlinear Media
Deependra Singh Gaur, Akanksha Gautam, Rakesh Kumar Singh, Akhilesh Kumar Mishra
https://arxiv.org/abs/2506.04816

Statistics of Non-Rayleigh Speckles Generated from Nonlinear Media
We analytically derive an expression for a speckle field's intensity probability density function (PDF) in a nonlinear medium. The analytically driven results are in good agreement with the numerical outcomes. In a focusing nonlinear medium, the local intensity of the speckle is enhanced as manifested through the longer tail of the PDF. In contrast, the local intensity of speckle is reduced in the presence of a defocusing nonlinearity, and the tail of the probability density function also reduc…

Nonlinear projection for ballistic correlation functions: a formula in terms of minimal connected covers
Benjamin Doyon
https://arxiv.org/abs/2506.05266 ht…

Nonlinear projection for ballistic correlation functions: a formula in terms of minimal connected covers
In many-body systems, the dynamics is governed, at large scales of space and time, by the hydrodynamic principle of projection onto the conserved densities admitted by the model. This is formalised as local relaxation of fluctuations in the ballistic macroscopic fluctuation theory, a nonlinear Boltzmann-Gibbs principle. We use it to derive a projection formula, expressing n-point connected correlation functions (cumulants) of generic observables at different space-time points, in terms of those…

Large Deviations for Sequential Tests of Statistical Sequence Matching
Lin Zhou, Qianyun Wang, Yun Wei, Jingjing Wang
https://arxiv.org/abs/2506.03976 http…

Large Deviations for Sequential Tests of Statistical Sequence Matching
We revisit the problem of statistical sequence matching initiated by Unnikrishnan (TIT 2015) and derive theoretical performance guarantees for sequential tests that have bounded expected stopping times. Specifically, in this problem, one is given two databases of sequences and the task is to identify all matched pairs of sequences. In each database, each sequence is generated i.i.d. from a distinct distribution and a pair of sequences is said matched if they are generated from the same distribu…

Orthogonality of polar Legendre polynomials and approximation
Abdelhamid Rehouma
https://arxiv.org/abs/2506.04918 https://arxiv.org/p…

Orthogonality of polar Legendre polynomials and approximation
Let $\{Q_{n}(x)\}$ be a system of integral Legendre polynomials of degree exactly n,and let $\{P_{n}(x)\}$ be polar polynomials primitives of integral Legendre polynomials. We derive some identities and relations and extremal problems and minimization involving of polar integral Legendre polynomials.

This https://arxiv.org/abs/2503.14727 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csRO_…

Beacon-Based Feedback Control for Parking an Active-Joint Center-Articulated Mobile Robot
This paper presents an autonomous parking control strategy for an active-joint center-articulated mobile robot. We first derive a kinematic model of the robot, then propose a control law to stabilize the vehicle's configuration within a small neighborhood of the goal. The control law, designed using Lyapunov techniques, is based on the robot's polar coordinate equations. A beacon-based guidance system provides feedback on the target's position and orientation. Simulations demonstrate the robot'…

Inverse elastic obstacle scattering problems by monotonicity method
Mengjiao Bai, Huaian Diao, Weisheng Zhou
https://arxiv.org/abs/2506.04655 https://

Inverse elastic obstacle scattering problems by monotonicity method
We consider the elastic wave scattering problem involving rigid obstacles. This work addresses the inverse problem of reconstructing the position and shape of such obstacles using far-field measurements. A novel monotonicity-based approach is developed for this purpose. By factorizing the far-field operator and utilizing the existence of localized wave functions, we derive a shape characterization criterion for the obstacle boundary. The proposed method employs monotonicity tests to determine t…

The non-Hermitian magnetic moment
Bar Alon, Moshe Goldstein, Roni Ilan
https://arxiv.org/abs/2506.05206 https://arxiv.org/pdf/2506.05…

The non-Hermitian magnetic moment
We construct a semiclassical theory for electrons in a non-Hermitian periodic system subject to perturbations varying slowly in space and time. We derive the energy of the wavepacket to first order in the gradients of the perturbations. Applying the theory to the specific case of a uniform external magnetic field, we obtain an expression for the orbital magnetization energy. Using the principles of non-Hermitian dynamics, we define a physically meaningful non-Hermitian generalization of the ang…

How do Pre-Trained Models Support Software Engineering? An Empirical Study in Hugging Face
Alexandra Gonz\'alez, Xavier Franch, David Lo, Silverio Mart\'inez-Fern\'andez
https://arxiv.org/abs/2506.03013

How do Pre-Trained Models Support Software Engineering? An Empirical Study in Hugging Face
Open-Source Pre-Trained Models (PTMs) provide extensive resources for various Machine Learning (ML) tasks, yet these resources lack a classification tailored to Software Engineering (SE) needs. To address this gap, we derive a taxonomy encompassing 147 SE tasks and apply an SE-oriented classification to PTMs in a popular open-source ML repository, Hugging Face (HF). Our repository mining study began with a systematically gathered database of PTMs from the HF API, considering their model card de…

This https://arxiv.org/abs/2504.09029 has been replaced.
link: https://scholar.google.com/scholar?q=a

A Hierarchical Decomposition of Kullback-Leibler Divergence: Disentangling Marginal Mismatches from Statistical Dependencies
The Kullback-Leibler (KL) divergence is a foundational measure for comparing probability distributions. Yet in multivariate settings, its single value often obscures the underlying reasons for divergence, conflating mismatches in individual variable distributions (marginals) with effects arising from statistical dependencies. We derive an algebraically exact, additive, and hierarchical decomposition of the KL divergence between a joint distribution P(X1,...,Xn) and a standard product reference …

OntoRAG: Enhancing Question-Answering through Automated Ontology Derivation from Unstructured Knowledge Bases
Yash Tiwari, Owais Ahmad Lone, Mayukha Pal
https://arxiv.org/abs/2506.00664

OntoRAG: Enhancing Question-Answering through Automated Ontology Derivation from Unstructured Knowledge Bases
Ontologies are pivotal for structuring knowledge bases to enhance question answering (QA) systems powered by Large Language Models (LLMs). However, traditional ontology creation relies on manual efforts by domain experts, a process that is time intensive, error prone, and impractical for large, dynamic knowledge domains. This paper introduces OntoRAG, an automated pipeline designed to derive ontologies from unstructured knowledge bases, with a focus on electrical relay documents. OntoRAG integr…

This https://arxiv.org/abs/2209.10166 has been replaced.
link: https://scholar.google.com/scholar?q=a

Chaotic Hedging with Iterated Integrals and Neural Networks
In this paper, we derive an $L^p$-chaos expansion based on iterated Stratonovich integrals with respect to a given exponentially integrable continuous semimartingale. By omitting the orthogonality of the expansion, we show that every $p$-integrable functional, $p \in [1,\infty)$, can be approximated by a finite sum of iterated Stratonovich integrals. Using (possibly random) neural networks as integrands, we therefere obtain universal approximation results for $p$-integrable financial derivative…

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This https://arxiv.org/abs/2501.18787 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Quantitative Derivation of the Two-Component Gross--Pitaevskii Equation in the Hard-Core Limit with Uniform-in-Time Convergence Rate
We derive the time-dependent two-component Gross--Pitaevskii (GP) equation as an effective description of the dynamics of a dilute two-component Bose gas near its ground state, which exhibits a two-component Bose-Einstein condensate, in the GP limit. Our main result establishes a uniform-in-time bound on the convergence rate between the many-body dynamics and the effective description, explicitly quantified in terms of the particle number $N$, and also implies a uniform-in-time bound for the on…

Excited State Densities from Time-Dependent Density Functional Response Theory
Anna Baranova, Neepa T. Maitra
https://arxiv.org/abs/2506.05082 https://

Excited State Densities from Time-Dependent Density Functional Response Theory
While the variational principle for excited-state energies leads to a route to obtaining excited-state densities from time-dependent density functional theory, relatively little attention has been paid to the quality of the resulting densities in real space obtained with different exchange-correlation functional approximations, nor how non-adiabatic approximations developed for energies of states of double excitation character perform for their densities. Here we derive an expression directly i…

This https://arxiv.org/abs/2308.07803 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Misspecified Bernstein-Von Mises theorem for hierarchical models
We derive a Bernstein von-Mises theorem in the context of misspecified, non-i.i.d., hierarchical models parametrized by a finite-dimensional parameter of interest. We apply our results to hierarchical models containing non-linear operators, including the squared integral operator, and PDE-constrained inverse problems. More specifically, we consider the elliptic, time-independent Schrödinger equation with parametric boundary condition and general parabolic PDEs with parametric potential and bou…

The c-Entropy of non-dissipative L-systems
Sergey Belyi, Konstantin A. Makarov, Eduard Tsekanovskii
https://arxiv.org/abs/2506.05144 https://

The c-Entropy of non-dissipative L-systems
In this paper, we extend the definition of c-entropy to canonical L-systems with non-dissipative state-space operators. We also introduce the concepts of dissipation and accumulation coefficients for such systems. In addition, we examine the coupling of these L-systems and derive closed form expressions for the corresponding c-entropy.

Understanding synchronization between quantum self-sustained oscillators through coherence generation
Mohit Kumar, Bijay Kumar Agarwalla
https://arxiv.org/abs/2506.01703

Understanding synchronization between quantum self-sustained oscillators through coherence generation
Understanding the origin of phase synchronization between quantum self-sustained oscillators has garnered significant interest in recent years. In this work, we study phase synchronization in three settings: between two continuous-variable oscillators, between two arbitrary quantum spins, and within a hybrid setup involving a spin and an oscillator. We derive a simple and general condition on the elements of the joint density matrix that must be satisfied for them to contribute to the relative …

Refined Metrics, Sensing Limits, and Resource Allocation in OTFS-RSMA LEO ISAC
Bruno Felipe Costa, Taufik Abr\~ao
https://arxiv.org/abs/2506.02624 https://…

Refined Metrics, Sensing Limits, and Resource Allocation in OTFS-RSMA LEO ISAC
This paper develops an integrated OTFS-RSMA framework employing advanced SP techniques tailored for this demanding environment. We derive refined communication performance metrics, specifically SINR expressions capturing the practical effects of ICSI and ISIC. Moreover, fundamental sensing limits are established via CRB derivation incorporating parameter-dependent echo gain, linking waveform SP properties to estimation accuracy. The resource allocation is formulated as a non-convex optimization…

This https://arxiv.org/abs/2503.12700 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Schur Rank, Compatibility Degree, and Canonical Decomposition
The notion of denominator vectors can be extended to all generic basis elements of upper cluster algebras in a natural way. Under a weakened version of generic pairing assumption, we provide a representation-theoretic interpretation for this extended notion. We derive several consequences in this generality. We present a counterexample to the conjecture that distinct cluster monomials have distinct denominator vectors. Utilizing a new rank function called the Schur rank, we extend the notion of…

This https://arxiv.org/abs/2505.10229 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Strong and weak convergence rates for fully coupled multiscale stochastic differential equations driven by $α$-stable processes
We first establish strong convergence rates for multiscale systems driven by $α$-stable processes, with analyses constructed in two distinct scaling regimes. When addressing weak convergence rates of this system, we derive four averaged equations with respect to four scaling regimes. Notably, under sufficient Hölder regularity conditions on the time-dependent drifts of slow process, the strong convergence orders are related to the known optimal strong convergence order $1-\frac{1}α$, and the…

This https://arxiv.org/abs/2501.08718 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_…

Pixelization effects in cosmic shear angular power spectra
We conduct a comprehensive study into the impact of pixelization on cosmic shear, uncovering several sources of bias in standard pseudo-$C_\ell$ estimators based on discrete catalogues. We derive models that can bring residual biases to the percent level on small scales. We elucidate the impact of aliasing and the varying shape of HEALPix pixels on power spectra and show how the HEALPix pixel window function approximation is made in the discrete spin-2 setting. We propose several improvements t…

This https://arxiv.org/abs/2502.06381 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Revisiting Optimal Allocations for Binary Responses: Insights from Considering Type-I Error Rate Control
This work revisits optimal response-adaptive designs from a type-I error rate perspective, highlighting when and how much these allocations exacerbate type-I error rate inflation - an issue previously undocumented. We explore a range of approaches from the literature that can be applied to reduce type-I error rate inflation. However, we found that all of these approaches fail to give a robust solution to the problem. To address this, we derive two optimal allocation proportions, incorporating t…

Transient dynamics of associative memory models
David G. Clark
https://arxiv.org/abs/2506.05303 https://arxiv.org/pdf/2506.05303

Transient dynamics of associative memory models
Associative memory models such as the Hopfield network and its dense generalizations with higher-order interactions exhibit a "blackout catastrophe"--a discontinuous transition where stable memory states abruptly vanish when the number of stored patterns exceeds a critical capacity. This transition is often interpreted as rendering networks unusable beyond capacity limits. We argue that this interpretation is largely an artifact of the equilibrium perspective. We derive dynamical mean-field equ…

This https://arxiv.org/abs/2408.00810 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

p-adic Equiangular Lines and p-adic van Lint-Seidel Relative Bound
We introduce the notion of p-adic equiangular lines and derive the first fundamental relation between common angle, dimension of the space and the number of lines. More precisely, we show that if $\{τ_j\}_{j=1}^n$ is p-adic $γ$-equiangular lines in $\mathbb{Q}^d_p$, then \begin{align*} (1) \quad\quad \quad \quad |n|^2\leq |d|\max\{|n|, γ^2 \}. \end{align*} We call Inequality (1) as the p-adic van Lint-Seidel relative bound. We believe that this complements funda…

Phonon-Mediated Intrinsic Topological Superconductivity in Fermi Arcs
Kristian M{\ae}land, Masoud Bahari, Bj\"orn Trauzettel
https://arxiv.org/abs/2506.03250

Phonon-Mediated Intrinsic Topological Superconductivity in Fermi Arcs
We propose that phonons can mediate topological superconductivity on the surface of Weyl semimetals. Weyl semimetals are gapless topological materials with nondegenerate zero energy surface states known as Fermi arcs. We derive the phonon spectrum and electron-phonon coupling in an effective model of a Weyl semimetal and apply weak-coupling Bardeen-Cooper-Schrieffer theory of superconductivity. In a slab geometry, we demonstrate that surface superconductivity dominates over bulk superconductivi…

This https://arxiv.org/abs/2409.16757 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csNE_…

An Adaptive Re-evaluation Method for Evolution Strategy under Additive Noise
The Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES) is one of the most advanced algorithms in numerical black-box optimization. For noisy objective functions, several approaches were proposed to mitigate the noise, e.g., re-evaluations of the same solution or adapting the population size. In this paper, we devise a novel method to adaptively choose the optimal re-evaluation number for function values corrupted by additive Gaussian white noise. We derive a theoretical lower bound o…

This https://arxiv.org/abs/2410.13634 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Additional first order equation for infinitesimal bendings of smooth surfaces in the isothermal coordinates
The article contributes to the theory of infinitesimal bendings of smooth surfaces in Euclidean 3-space. We derive a linear differential equation of the first order, which previously did not appear in the literature and which is satisfied by any Darboux rotation field of a smooth surface. We show that, for some surfaces, this additional equation is functionally independent of the three standard equations that the Darboux rotation field satisfies (and by which it is determined). As a consequence…

Retrieval-Augmented Generation of Ontologies from Relational Databases
Mojtaba Nayyeri, Athish A Yogi, Nadeen Fathallah, Ratan Bahadur Thapa, Hans-Michael Tautenhahn, Anton Schnurpel, Steffen Staab
https://arxiv.org/abs/2506.01232

Retrieval-Augmented Generation of Ontologies from Relational Databases
Transforming relational databases into knowledge graphs with enriched ontologies enhances semantic interoperability and unlocks advanced graph-based learning and reasoning over data. However, previous approaches either demand significant manual effort to derive an ontology from a database schema or produce only a basic ontology. We present RIGOR, Retrieval-augmented Iterative Generation of RDB Ontologies, an LLM-driven approach that turns relational schemas into rich OWL ontologies with minimal…

This https://arxiv.org/abs/2501.03470 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Positivstellensätze for polynomial matrices with universal quantifiers
This paper investigates Positivstellensätze for polynomial matrices subject to universally quantified polynomial matrix inequality constraints. We first establish a matrix-valued Positivstellensatz under the Archimedean condition, incorporating universal quantifiers. For scalar-valued polynomial objectives, we further develop a sparse Positivstellensatz that leverages correlative sparsity patterns within these quantified constraints. Moving beyond the Archimedean framework, we then derive a se…

Conservation Laws and Boundedness for Linearised Einstein--Maxwell Equations on the Reissner--Nordstr\"om Black Hole
Marios A. Apetroaie, Sam C. Collingbourne, Elena Giorgi
https://arxiv.org/abs/2506.04812

Conservation Laws and Boundedness for Linearised Einstein--Maxwell Equations on the Reissner--Nordström Black Hole
We study the linearised Einstein--Maxwell equations on the Reissner--Nordström spacetime and derive the canonical energy conservation law in double null gauge. In the spirit of the work of Holzegel and the second author, we avoid any use of the hyperbolic nature of the Teukolsky equations and rely solely on the conservation law to establish control of energy fluxes for the gauge-invariant Teukolsky variables, previously identified by the third author, along all outgoing null hypersurfaces, for…

This https://arxiv.org/abs/2503.17228 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Mean value of cubic $L$-funcitons with fixed genus
We investigate the mean value of the first moment of primitive cubic $L$-functions over $\mathbb{F}_q(T)$ in the non-Kummer setting. Specifically, we study the sum \begin{equation*} \sum_{\substack{χ primitive\ cubic\\ genus(χ)=g}}L_q(\frac{1}{2}, χ), \end{equation*} where $L_q(s,χ)$ denotes the $L$-function associated with primitive cubic character $χ$. Using double Dirichlet series, we derive an error term of size $q^{(\frac{7}{8}+\varepsilon)g}$.

Classification of the real Painlev\'{e} I transcendents by zeros and connection problem: an asymptotic study
Yan Huang, Yu-Tian Li, Wen-Gao Long
https://arxiv.org/abs/2506.03648

Classification of the real Painlevé I transcendents by zeros and connection problem: an asymptotic study
In this paper, we study the asymptotic behavior and connection problem of Painlevé I (PI) equation through a detailed analysis of the Stokes multipliers associated with its solutions. Focusing on the regime where the derivative at the real zeros of the solution becomes large, we apply the complex WKB method to derive full asymptotic expansions of the Stokes multipliers. These expansions allow us to classify real solutions of PI according to their behavior at the zeros, distinguishing between o…

Dimension of Besicovitch-Eggleston sets for non-autonomous systems with countable symbolic dynamics
Jonny Imbierski, Charlene Kalle
https://arxiv.org/abs/2506.01803

Dimension of Besicovitch-Eggleston sets for non-autonomous systems with countable symbolic dynamics
In this article we derive a formula for the Hausdorff dimension of Besicovitch-Eggleston level sets associated with non-autonomous dynamics constructed from families of countable affine iterated function systems. The formula obtained shows that the universal-lower-bound phenomenon present in the autonomous case studied by Fan et al. (2010) persists in this non-autonomous setting.

This https://arxiv.org/abs/2505.18910 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Uncovering relationships between the electronic self-energy and coupled-cluster doubles theory
We derive the coupled-cluster doubles (CCD) amplitude equations by introduction of the particle-hole-time decoupled electronic self-energy. This leads to an alternative ground state correlation energy obtained from the Green's function formalism which is exactly of the form obtained in coupled-cluster doubles theory. We demonstrate the relationship to the ionization potential/electron affinity equation-of-motion coupled-cluster doubles (IP/EA-EOM-CCD) eigenvalue problem by coupling the reverse-…

Learning to optimize convex risk measures: The cases of utility-based shortfall risk and optimized certainty equivalent risk
Sumedh Gupte, Prashanth L. A., Sanjay P. Bhat
https://arxiv.org/abs/2506.01101

Learning to optimize convex risk measures: The cases of utility-based shortfall risk and optimized certainty equivalent risk
We consider the problems of estimation and optimization of two popular convex risk mea- sures: utility-based shortfall risk (UBSR) and Optimized Certainty Equivalent (OCE) risk. We extend these risk measures to cover possibly unbounded random variables. We cover prominent risk measures like the entropic risk, expectile risk, monotone mean-variance risk, Value-at-Risk, and Conditional Value-at-Risk as few special cases of either the UBSR or the OCE risk. In the context of estimation, we derive n…

Magnetic field dynamics in presence of Hall conductivity, and thermodiffusion
G. S. Bisnovatyi-Kogan, M. V. Glushikhina
https://arxiv.org/abs/2506.02202 ht…

Magnetic field dynamics in presence of Hall conductivity, and thermodiffusion
This anisotropy of kinetic coefficients in presence of a magnetic field is represented by so-called Hall currents, which appear in a collisional medium due to action of the Lorentz force on the charged particles between collisions. In many papers the Hall currents had been considered in different approximate approaches. We derive equations, describing dynamics of the magnetic field in presence of Hall currents, using a standard electrodynamic consideration. We consider collisional media, an…

The random $k$-SAT Gibbs uniqueness threshold revisited
Arnab Chatterjee, Amin Coja-Oghlan, Catherine Greenhill, Vincent Pfenninger, Maurice Rolvien, Pavel Zakharov, Kostas Zampetakis
https://arxiv.org/abs/2506.01359

The random $k$-SAT Gibbs uniqueness threshold revisited
We prove that for any $k\geq3$ for clause/variable ratios up to the Gibbs uniqueness threshold of the corresponding Galton-Watson tree, the number of satisfying assignments of random $k$-SAT formulas is given by the `replica symmetric solution' predicted by physics methods [Monasson, Zecchina: Phys. Rev. Lett. (1996)]. Furthermore, while the Gibbs uniqueness threshold is still not known precisely for any $k\geq3$, we derive new lower bounds on this threshold that improve over prior work [Montan…

This https://arxiv.org/abs/2411.19604 has been replaced.
initial toot: https://mastoxiv.page/@ar…

Continuous Approximation of the Ising Hamiltonian: Exact Ground States and Applications to Fidelity Assessment in Ising Machines
In this study, we present a novel analytical approach to solving large-scale Ising problems by reformulating the discrete Ising Hamiltonian into a continuous framework. This transformation enables us to derive exact solutions for a non-trivial class of fully connected Ising models. To validate our method, we conducted numerical experiments comparing our analytical solutions with those obtained from a quantum-inspired Ising algorithm and a quantum Ising machine. The results demonstrate that the …

This https://arxiv.org/abs/2505.15748 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Characterization of bi-parametric potentials and rate of convergence of truncated hypersingular integrals in the Dunkl setting
In this work, we introduce the $β$-semigroup for $β> 0$, which unifies and extends the classical Poisson (for $β=1$) and heat (for $β=2$) semigroups within the Dunkl analysis framework. Leveraging this semigroup, we derive an explicit representation for the inverse of the Dunkl-Riesz potential and characterize the image of the function space $L_k^p(\mathbb{R}^n)$ for $1 \leq p < \frac{n + 2γ}α$. We further define the bi-parametric potential of order $α$ by $$\mathfrak{S}_k^{(α,β)} = \l…

This https://arxiv.org/abs/2412.14844 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_…

Astrometry-Only Detection of Microlensing Events with Gaia
Astrometric microlensing events occur when a massive object passes between a distant source and the observer, causing a shift of the light centroid. The precise astrometric measurements of the Gaia mission provide an unprecedented opportunity to detect and analyze these events, revealing properties of lensing objects such as their mass and distance. We develop and test the Gaia Astrometric Microlensing Events (GAME) Filter, a software tool to identify astrometric microlensing events and derive …

Asymptotic behavior of complete conformal metric near singular boundary
Weiming Shen, Yue Wang
https://arxiv.org/abs/2506.04591 https://

Asymptotic behavior of complete conformal metric near singular boundary
The boundary behavior of the singular Yamabe problem has been extensively studied near sufficiently smooth boundaries, while less is known about the asymptotic behavior of solutions near singular boundaries. In this paper, we study the asymptotic behaviors of solutions to the singular Yamabe problem with negative constant scalar curvature near singular boundaries and derive the optimal estimates for the background metric which is not necessarily conformally flat. In particular, we prove that th…

A comparative study of focusing with scalar and vector beams in an active Raman gain system
Partha Das, Tarak Nath Dey
https://arxiv.org/abs/2506.05093 htt…

A comparative study of focusing with scalar and vector beams in an active Raman gain system
We investigate the focusing characteristics of scalar and vector beams within an atomic medium. An active-Raman-gain configuration is employed to achieve significant Kerr nonlinearity in a four-state atomic system. The probe beams can attain focusing within the medium through careful selection of input beam intensities and the spatial profile of the control field. We analytically derive the linear and third-order nonlinear susceptibilities for both scalar and vector probe beams. Our observation…

This https://arxiv.org/abs/2504.15462 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hepp…

Light front holographic QCD theory in the generalized uncertainty principle framework
In this article, we develop the framework of light-front holographic QCD in the presence of a minimal length scale by incorporating the Generalized Uncertainty Principle (GUP) into the QCD Lagrangian. From this modified theory, we derive a GUP-corrected light-front holographic QCD (LFH QCD) equation and obtain the corresponding hadronic mass spectrum. Our results show that the hadronic mass spectrum acquires an additional GUP-dependent term that increases the masses. This mass enhancement leads…

Geometric Bloch oscillations and transverse displacement in flat band systems
Jing-Xin Liu, Giandomenico Palumbo, Marco Di Liberto
https://arxiv.org/abs/2506.04314

Geometric Bloch oscillations and transverse displacement in flat band systems
We investigate transport phenomena and dynamical effects in flat bands where the band dispersion plays no role. We show that wavepackets in geometrically non-trivial flat bands can display dynamics when inhomogeneous electric fields are present. This dynamics is revealed both for the wavepacket trajectory and for its variance, for which we derive semiclassical equations extended to the non-Abelian case. Our findings are tested in flat band models in one- and two-dimensional lattices where the d…

This https://arxiv.org/abs/2505.20078 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Notes on Rindler wave packets in Minkowski spacetime
We consider wave packets of a massless scalar field that have well-localized Rindler energy, and examine how their energy appears to a Minkowski observer to see how the classical gravitational blue-shift formula is modified quantum mechanically. We derive, by using the saddle point approximation, an analytic expression for the Minkowski momentum distribution of such Rindler wave packets. We find a universal lower bound on the uncertainty of Minkowski momentum; the momentum distribution can neve…

This https://arxiv.org/abs/2503.03076 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Non-Affine Extensions of the Raychaudhuri Equation in the K-essence Framework
We present a new avenue of the Raychaudhuri Equation (RE) by introducing a non-affine parametrization within the k-essence framework. This modification accounts for non-geodesic flow curves, leading to emergent repulsive effects in cosmic evolution. Using a DBI-type k-essence Lagrangian, we derive a modified RE and demonstrate its ability to address the Hubble tension while predicting a natural emergence of a dynamical dark energy equation of state. Our Bayesian analysis, constrained by cosmolo…

Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow
Juanling Lu, Yu Zheng
https://arxiv.org/abs/2506.04937

Gradient estimates and parabolic frequency monotonicity for positive solutions of the heat equation under generalized Ricci flow
In this paper, we establish Li-Yau-type and Hamilton-type estimates for positive solutions to the heat equation associated with the generalized Ricci flow, under a less stringent curvature condition. Compared with [25] and [35], these estimates generalize the results in Ricci flow to this new flow under the weaker Ricci curvature bounded assumption. As an application, we derive the Harnack-type inequalities in spacetime and find the monotonicity of one parabolic frequency for positive solutions…

This https://arxiv.org/abs/2504.12885 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csIT_…

Optimizing Movable Antennas in Wideband Multi-User MIMO With Hardware Impairments
Movable antennas represent an emerging field in telecommunication research and a potential approach to achieving higher data rates in multiple-input multiple-output (MIMO) communications when the total number of antennas is limited. Most solutions and analyses to date have been limited to \emph{narrowband} setups. This work complements the prior studies by quantifying the benefit of using movable antennas in \emph{wideband} MIMO communication systems. First, we derive a novel uplink wideband sy…

This https://arxiv.org/abs/2401.12526 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Refined generalization analysis of the Deep Ritz Method and Physics-Informed Neural Networks
In this paper, we derive refined generalization bounds for the Deep Ritz Method (DRM) and Physics-Informed Neural Networks (PINNs). For the DRM, we focus on two prototype elliptic partial differential equations (PDEs): Poisson equation and static Schrödinger equation on the $d$-dimensional unit hypercube with the Neumann boundary condition. Furthermore, sharper generalization bounds are derived based on the localization techniques under the assumptions that the exact solutions of the PDEs lie …

A primal-dual price-optimization method for computing equilibrium prices in mean-field games models
Xu Wang, Samy Wu Fung, Levon Nurbekyan
https://arxiv.org/abs/2506.04169

A primal-dual price-optimization method for computing equilibrium prices in mean-field games models
We develop a simple yet efficient Lagrangian method for computing equilibrium prices in a mean-field game price-formation model. We prove that equilibrium prices are optimal in terms of a suitable criterion and derive a primal-dual gradient-based algorithm for computing them. One of the highlights of our computational framework is the efficient, simple, and flexible implementation of the algorithm using modern automatic differentiation techniques. Our implementation is modular and admits a seam…

The Cost of Restaking vs. Proof-of-Stake
Akaki Mamageishvili, Benny Sudakov
https://arxiv.org/abs/2505.24440 https://arxiv.org/pdf/25…

The Cost of Restaking vs. Proof-of-Stake
We compare the efficiency of restaking and Proof-of-Stake (PoS) protocols in terms of stake requirements. First, we consider the sufficient condition for the restaking graph to be secure. We show that the condition implies that it is always possible to transform such a restaking graph into secure PoS protocols. Next, we derive two main results, giving upper and lower bounds on required extra stakes that one needs to add to validators of the secure restaking graph to be able to transform it into…

Second-Order Characterization of Micro Doppler Radar Signatures of Drone Swarms
Anders Malthe Westerkam, Alba Spliid Damkj{\ae}r, Rasmus Erik Villadsen, Magnus {\O}rum Bastrup Poulsen, Troels Pedersen
https://arxiv.org/abs/2506.00497

Second-Order Characterization of Micro Doppler Radar Signatures of Drone Swarms
We investigate the second-order characteristics of the radar return signal from a swarm of rotor drones. We consider the case of a swarm of identical drones, with each a number of rotors comprised of a number of rotor blades. By considering the orientation and speed of each rotor as stochastic variables, we derive expressions for the autocorrelation function (ACF) and power spectral density (PSD). The ACF and PSD are in the form of an infinite series with coefficients that drop to zero at a pre…

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

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

The superspace coinvariant ring of type B
Sutanay Bhattacharya
https://arxiv.org/abs/2505.24122 https://arxiv.org/pdf/2505.24122

The superspace coinvariant ring of type B
Given the rank $n$ superspace $Ω_n$, the ring of polynomial-valued differential forms on $\mathbb C^n$, one can define an action of hyperoctahedral group $\mathfrak B_n$ on it. This leads to a superspace coinvariant ideal $SR_n^B$, defined as the quotient of $Ω_n$ by two-sided ideal generated by all $\mathfrak B_n$ invariants with vanishing constant terms. We derive the Hilbert series of $SR^B_n$ conjectured by Sagan and Swanson, and prove an operator theorem that yields a concrete descriptio…

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

This https://arxiv.org/abs/2405.11676 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The High-Dimensional Asymptotics of Principal Component Regression
We study principal components regression (PCR) in an asymptotic high-dimensional regression setting, where the number of data points is proportional to the dimension. We derive exact limiting formulas for the estimation and prediction risks, which depend in a complicated manner on the eigenvalues of the population covariance, the alignment between the population PCs and the true signal, and the number of selected PCs. A key challenge in the high-dimensional setting stems from the fact that the …

This https://arxiv.org/abs/2505.00761 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

What is a photon in de Sitter spacetime?
The states of a single photon in four-dimensional de Sitter (dS) spacetime form a Unitary Irreducible Representation (UIR) of SO(1,4), which we call the photon UIR. While in flat spacetime photons are intimately tied to gauge symmetry, we demonstrate that in de Sitter, photon states emerge generically in any quantum field theory, even without an underlying U(1) gauge field. We derive a Källén-Lehmann representation for antisymmetric tensor two-point functions and show that numerous composite …

General Numerical Radius for Products of Sectorial Matrices
Mohammad Alakhrass
https://arxiv.org/abs/2506.02042 https://arxiv.org/pdf…

General Numerical Radius for Products of Sectorial Matrices
In this paper, we investigate the generalized numerical radius $ω_N$, associated with a matrix norm $N$ defined by $ω_N(X) = \sup_{θ\in \mathbb{R}} N(\operatorname{Re}(e^{iθ}X))$. We focus on matrices whose numerical ranges are contained in sectors of the complex plane (sectorial matrices) and derive upper bounds for $ω_N(XY)$ and $ω_N(X \circ Y)$ for such matrices $X$ and $Y$. Our results generalize and refine well known numerical radius inequalities. Several known inequalities for $ω(X…

Graded representations of current Lie superalgebras $\mathfrak{sl}(1|2)[t]$
Shushma Rani, Divya Setia
https://arxiv.org/abs/2506.01134 https://

Graded representations of current Lie superalgebras $\mathfrak{sl}(1|2)[t]$
This paper is the study of finite-dimensional graded representations of current lie superalgebras $\mathfrak{sl}(1|2)[t]$. We define the notion of super POPs, a combinatorial tool to provide another parametrization of the basis of the local Weyl module given in [2]. We derive the graded character formula of local Weyl module for $\mathfrak{sl}(1|2)[t]$. Furthermore, we construct a short exact sequence of Chari-Venkatesh modules for $\mathfrak{sl}(1|2)[t]$. As a consequence, we pr…

Bernstein-Markov measures and Toeplitz theory
Siarhei Finski
https://arxiv.org/abs/2506.01610 https://arxiv.org/pdf/2506.01610…

Bernstein-Markov measures and Toeplitz theory
We prove that Toeplitz operators associated with a Bernstein-Markov measure on a compact complex manifold endowed with a big line bundle form an algebra under composition. As an application, we derive a Szegő-type spectral equidistribution result for this class of operators. A key component of our approach is the off-diagonal asymptotic analysis of the Bergman kernel, also known as the Christoffel-Darboux kernel.

This https://arxiv.org/abs/2208.11392 has been replaced.
link: https://scholar.google.com/scholar?q=a

Data-driven stabilization of switched and constrained linear systems
We consider the design of state feedback control laws for both the switching signal and the continuous input of an unknown switched linear system, given past noisy input-state trajectories measurements. Based on Lyapunov-Metzler inequalities, we derive data-dependent bilinear programs whose solution directly returns a provably stabilizing controller and ensures $\mathcal{H}_2$ or $\mathcal{H}_{\infty}$ performance. We further present relaxations that considerably reduce the computational cost, …

This https://arxiv.org/abs/2502.17573 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hepp…

Single pion resonant production in BSM scenarios: cross sections and amplitudes
We present a comprehensive theoretical framework describing single pion resonant production through inelastic dark fermion-nucleon interactions mediated by resonances in the GeV-scale regime. Building upon the Rein-Sehgal approach, we derive differential cross sections for processes in which an incoming dark fermion scatters off a nucleon, exciting a resonance that subsequently decays into a nucleon and a pion. Our formulation accommodates various mediator types-namely, dark photons with vector…

Investigating Strange Stars in Rastall Theory
Malick Sallah, M. Sharif
https://arxiv.org/abs/2506.03220 https://arxiv.org/pdf/2506.03…

Investigating Strange Stars in Rastall Theory
This study explores the structural formation of various spherically symmetric anisotropic stars within the framework of Rastall theory. To achieve this, we derive modified field equations which are then resolved using the Finch-Skea ansatz, which involve unknown parameters $(A_1,A_2,A_3)$. These parameters are found by using appropriate constraints given by the junction conditions, in addition to observational data from some selected stars. The $\mathbb{EOS}$ given by the $\mathbb{MIT}$ bag mod…

This https://arxiv.org/abs/2501.11443 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the hierarchy of plate models for a singularly perturbed multi-well nonlinear elastic energy
In the celebrated work of Friesecke, James and Müller '06 the authors derive a hierarchy of models for plates by carefully analyzing the $Γ$-convergence of the rescaled nonlinear elastic energy. The key ingredient of their proofs is the rigidity estimate proved in an earlier work of theirs. Here we consider the case in which the elastic energy has a multi-well structure: this type of functional arises, for example, in the study of solid-solid phase transitions. Since the rigidity estimate fai…

An adaptive delaminating Levin method in two dimensions
Shukui Chen, Kirill Serkh, James Bremer, Murdock Aubry
https://arxiv.org/abs/2506.02424 https://

An adaptive delaminating Levin method in two dimensions
We present an adaptive delaminating Levin method for evaluating bivariate oscillatory integrals over rectangular domains. Whereas previous analyses of Levin methods impose non-resonance conditions that exclude stationary and resonance points, we rigorously establish the existence of a slowly-varying, approximate solution to the Levin PDE across all frequency regimes, even when the non-resonance condition is violated. This allows us to derive error estimates for the numerical solution of the Lev…

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

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

Transverse Distance Estimation with Higher-Order Hermite-Gauss modes
Dilip Paneru, Alessio D'Errico, Ebrahim Karimi
https://arxiv.org/abs/2506.02926 ht…

Transverse Distance Estimation with Higher-Order Hermite-Gauss modes
We explore the use of higher-order Hermite-Gauss modes for sensing optically induced transverse displacements. In the small-displacement regime, we show that projective measurements onto the two neighboring spatial modes yield optimal Fisher information, linearly scaling with the mode order $m$. We further extend the analysis to arbitrary displacement values and derive general expressions for the Fisher information, demonstrating that higher-order modes continue to outperform the fundamental Ga…

Vulnerability Measures and Zagreb Indices of Graphs
Sanju Vaidya, Cheng Chang
https://arxiv.org/abs/2505.24707 https://arxiv.org/pdf/…

Vulnerability Measures and Zagreb Indices of Graphs
This paper establishes sharp bounds for the vulnerability measures of closeness and generalized closeness in graphs and identifies graphs that attain these bounds. It further develops bounds incorporating Zagreb indices for triangle- and quadrangle-free graphs, yielding formulas for closeness and generalized closeness in such graphs with diameter at most 3. Moreover, using Zagreb indices, we derive bounds for trees and connected graphs with girth at least 7, which are attained by graphs with di…

This https://arxiv.org/abs/2504.06686 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Quantitative Halmos-Savage theorems and robust large financial markets
We establish a quantitative version of the classical Halmos-Savage Theorem for convex sets of probability measures and its dual counterpart, generalizing previous quantitative versions. These results are then used to derive robust versions of the fundamental theorem of asset pricing (FTAP) in large financial markets in a one period setting, characterizing the absence of arbitrage under Knightian uncertainty. To this end, we consider robust formulations of no asymptotic arbitrage of first kind (…

Bounds on the Excess Minimum Risk via Generalized Information Divergence Measures
Ananya Omanwar, Fady Alajaji, Tam\'as Linder
https://arxiv.org/abs/2505.24117

Bounds on the Excess Minimum Risk via Generalized Information Divergence Measures
Given finite-dimensional random vectors $Y$, $X$, and $Z$ that form a Markov chain in that order (i.e., $Y \to X \to Z$), we derive upper bounds on the excess minimum risk using generalized information divergence measures. Here, $Y$ is a target vector to be estimated from an observed feature vector $X$ or its stochastically degraded version $Z$. The excess minimum risk is defined as the difference between the minimum expected loss in estimating $Y$ from $X$ and from $Z$. We present a family of …

This https://arxiv.org/abs/2412.04249 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Approach to the separatrix with eccentric orbits
Eccentric binary compact mergers are prime targets of current and future gravitational wave observatories. In the small mass ratio expansion, post-adiabatic inspirals have been modeled up to the separatrix, where first-principle modeling currently ends. In this paper, we derive the analytic late time solution to the adiabatic inspiral in terms of self-force coefficients at the separatrix. We identify the role of the Lambert $W_{-1}$ function as a key mathematical ingredient in the approach to t…

This https://arxiv.org/abs/2412.19480 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Inequalities between Dirichlet and Neumann Eigenvalues on Surfaces
For a bounded Lipschitz domain $Σ$ in a Riemannian surface $M$ satisfying certain curvature condition, we prove that $$μ_{3-β_1} \leq λ_{1},$$ where $μ_k$ ($λ_k$ resp.) is the $k$-th Neumann (Dirichlet resp.) Laplacian eigenvalue on $Σ$ and $β_1$ is the first Betti number of $Σ.$ If $Σ$ is smooth and simply connected, we can further derive the strict inequality $ μ_{3}< λ_{1}. $ This extends previous results on the Euclidean space to various curved surfaces, including the flat cylin…

This https://arxiv.org/abs/2501.14087 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hepp…

On the scalar sector of 2HDM: ring of basis invariants, syzygies, and six-loop renormalization-group equations
We consider a generating set of reparametrization invariants that can be constructed from the couplings and masses entering the scalar potential of the general Two-Higgs-Doublet Model (2HDM). Being independent of higgs-basis rotations, they generate a polynomial ring of basis invariants that represent the physical content of the model. Ignoring for the moment gauge and Yukawa interactions, we derive six-loop renormalization group equations (RGE) for all the invariants entering the set. We do no…

The near infrared airglow continuum conundrum. Constraints for ground-based faint object spectroscopy
J. K. M. Viuho (Cosmic Dawn Center, Niels Bohr Institute, University of Copenhagen, Jagtvej 155A, DK-2200, Copenhagen N, Denmark, Nordic Optical Telescope, Rambla Jose Ana Fernandez Perez 7, ES-38711 Brena Baja, Spain, Department of Physics and Astronomy, Aarhus University, Munkegade 120, DK-8000 Aarhus C, Denmark), J. P. U. Fynbo (Cosmic Dawn Center, Niels Bohr Institute, University of Copenhagen, Jagtvej 155A, DK-2200, Copenhagen N, Denmark), M. I. Andersen (Cosmic Dawn Center, Niels Bohr Institute, University of Copenhagen, Jagtvej 155A, DK-2200, Copenhagen N, Denmark)
#toXiv_bot_toot

This https://arxiv.org/abs/2502.16673 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the asymptotic validity of confidence sets for linear functionals of solutions to integral equations
This paper examines the construction of confidence sets for parameters defined as linear functionals of a function of W and X whose conditional mean given Z and X equals the conditional mean of another variable Y given Z and X. Many estimands of interest in causal inference can be expressed in this form, including the average treatment effect in proximal causal inference and treatment effect contrasts in instrumental variable models. We derive a necessary condition for a confidence set to be un…

Characterization of positive superharmonic functions in a half-space
Lorenzo D'Ambrosio, Enzo Mitidieri
https://arxiv.org/abs/2506.02305 https://

Characterization of positive superharmonic functions in a half-space
We prove a representation formula for superharmonic functions on the half-space $\mathbb{R}^N_+ := \mathbb{R}^{N-1}\times]0,+\infty[$. As a consequence, we derive some comparison principles and various positivity results.

This https://arxiv.org/abs/2503.21653 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

$α$-scaled strong convergence and stability of stochastic theta method for time-changed stochastic differential equations with local Lipschitz coefficients
We propose the first $α$-parameterized framework for solving time-changed stochastic differential equations (SDEs), explicitly linking convergence rates and key driving parameter of the underlying stochastic processes. Theoretically, we derive exact moment estimates and exponential moment estimate of inverse $α$-stable subordinator $E$ using Mittag-Leffler functions. The stochastic theta (ST) method is investigated for a class of SDEs driven by a time-changed Brownian motion, whose coefficien…

Parity violation in photon quasinormal modes of black holes
Sugumi Kanno, Jiro Soda, Akira Taniguchi
https://arxiv.org/abs/2506.04149 https://

Parity violation in photon quasinormal modes of black holes
Given that black holes are ubiquitous in the universe and axion-like scalar fields are potential candidates for dark energy and/or dark matter, it is natural to consider cosmological black holes endowed with axion hair. We investigate the photon quasinormal modes of a Schwarzschild black hole with axion hair where the electromagnetic field is coupled to the axion field via a Chern-Simons interaction. We derive the master equations for the electromagnetic field as a set of coupled equations for …

Sharp error bounds for approximate eigenvalues and singular values from subspace methods
Irina-Beatrice Haas, Yuji Nakatsukasa
https://arxiv.org/abs/2506.01207

Sharp error bounds for approximate eigenvalues and singular values from subspace methods
Subspace methods are commonly used for finding approximate eigenvalues and singular values of large-scale matrices. Once a subspace is found, the Rayleigh-Ritz method (for symmetric eigenvalue problems) and Petrov-Galerkin projection (for singular values) are the de facto method for extraction of eigenvalues and singular values. In this work we derive quadratic error bounds for approximate eigenvalues obtained via the Rayleigh-Ritz process. Our bounds take advantage of the fact that extremal ei…

This https://arxiv.org/abs/2502.09493 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Quantitative estimates for high-contrast random media
This paper studies quantitative homogenization of elliptic equations with random, uniformly elliptic coefficients that vanish in a union of random holes. Assuming an upper bound on the size of the holes and a separation condition between them, we derive optimal bounds for the regularity radius $r_*$ and suboptimal growth estimates for the corrector. These results are key ingredients for error analysis in stochastic homogenization and serve as crucial input for recent developments in the double-…

Axial quasi-normal modes of slowly rotating black holes in dynamical Chern-Simons gravity to second-order in spin and coupling
Tharaka Alapati (IIT Bombay), S. Shankaranarayanan (IIT Bombay)
https://arxiv.org/abs/2506.03600

Axial quasi-normal modes of slowly rotating black holes in dynamical Chern-Simons gravity to second-order in spin and coupling
We compute the quasi-normal mode (QNM) frequencies of slowly rotating black holes in dynamical Chern-Simons (dCS) gravity, including corrections up to second order in the black hole's dimensionless spin parameter ($χ$) and second order in the dCS coupling parameter ($α$). Due to the complexities of constructing a Newman-Penrose tetrad at this order, we employ a metric perturbation approach. We derive a system of coupled ordinary differential equations for the primary axial $l$-mode and the po…

This https://arxiv.org/abs/2503.14328 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Risk-Sensitive Model Predictive Control for Interaction-Aware Planning -- A Sequential Convexification Algorithm
This paper considers risk-sensitive model predictive control for stochastic systems with a decision-dependent distribution. This class of systems is commonly found in human-robot interaction scenarios. We derive computationally tractable convex upper bounds to both the objective function, and to frequently used penalty terms for collision avoidance, allowing us to efficiently solve the generally nonconvex optimal control problem as a sequence of convex problems. Simulations of a robot navigatin…

This https://arxiv.org/abs/2505.16961 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hepp…

Predicting the outcome of collisional neutrino flavor conversion
Collisional flavor instabilities, driven by differing neutrino and antineutrino reaction rates, are expected to occur in dense astrophysical environments like supernovae and neutron star mergers, but have yet to be incorporated in large-scale simulations. We derive, for the first time, analytical expressions for the asymptotic state resulting from a homogeneous and isotropic instability, and apply these predictions to two representative conditions from a neutron star merger simulation. We empha…

A Positivity-Preserving Finite Element Framework for Accurate Dose Computation in Proton Therapy
Ben S. Ashby, Abdalaziz Hamdan, Tristan Pryer
https://arxiv.org/abs/2506.01105

A Positivity-Preserving Finite Element Framework for Accurate Dose Computation in Proton Therapy
We present a stabilised finite element method for modelling proton transport in tissue, incorporating both inelastic energy loss and elastic angular scattering. A key innovation is a positivity-preserving formulation that guarantees non-negative fluence and dose, even on coarse meshes. This enables reliable computation of clinically relevant quantities for treatment planning. We derive a priori error estimates demonstrating optimal convergence rates and validate the method through numerical ben…

This https://arxiv.org/abs/2212.11928 has been replaced.
link: https://scholar.google.com/scholar?q=a

The Gauss formulas for Laplacians on submanifolds
There are several types of Laplacians of a vector field on a Riemannian manifold. These include the Bochner and the Hodge Laplacian. The Gauss formula for the Levi-Civita connection relates the extrinsic connection to the intrinsic connection. We extend the Gauss formula for the connection to formulas for the different types of Laplacians of a vector field on a submanifold of any codimension $k\geq 1$. In the process, we derive a Gauss formula for the Ricci operator, formulas for the divergence…

This https://arxiv.org/abs/2308.10270 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Stochastic Perturbations in the Fractional Nonlinear Schrödinger Equation: Well-posedness and Blow-up
This work investigates radial solutions for nonlinear fractional Schrödinger equations driven by multiplicative noise. Leveraging radial deterministic and stochastic Strichartz estimates, we establish local well-posedness in the energy-subcritical regime for the stochastic fractional nonlinear Schrödinger equation. Global existence is subsequently demonstrated through stochastic evolution of mass and energy. In focusing supercritical settings, we derive blow-up criteria via localized virial i…

Generalized Brans-Dicke theory from Verlinde's entropic gravity
Salih Kibaro\u{g}lu, Mustafa Senay
https://arxiv.org/abs/2506.02729 https://

Generalized Brans-Dicke theory from Verlinde's entropic gravity
In this work, we develop a q-deformed scalar-tensor theory of gravitation by combining Verlinde's entropic gravity paradigm with statistical deformation effects. The resulting model modifies the Brans-Dicke framework through a deformation function, treated as a constant rescaling factor for the effective gravitational coupling. We derive the corresponding q-deformed field equations and analyze their theoretical consistency including the recovery of standard gravitational models in specific limi…

`Translation invariant' black hole: autoparallels and complete integrability
Jens Boos
https://arxiv.org/abs/2506.02301 https://a…

`Translation invariant' black hole: autoparallels and complete integrability
We consider the autoparallel motion of test bodies in static, spherically symmetric spacetimes with torsion. We prove complete integrability of such motion for a wide range of off-shell geometries via four commuting autoparallel Killing vectors. Since these vectors reduce to translation generators in a certain limit, we refer to these geometries as `translation invariant.' Invoking the field equations of quadratic Poincaré gauge gravity we re-derive an exact Schwarzschild black hole solution e…

This https://arxiv.org/abs/2501.08161 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Cosmological model with Gong-Zong Parametrization in $f(R,L_m)$ gravity
We present the cosmic expansion scenarios in the $f(R, L_m)$ gravity studied by using the dark energy equation of state (EoS) parameters. We proceed with the specific form of $f(R, L_m)$ gravity termed as $f(R, L_m)=\frac{R}{2}+L_{m}^α$. We derive the expansion rate in terms of the red-shift for two different forms of EoS parameter. In first model, EoS parameter varies inversely with the redshift and in second model, it involves the exponential form with the redshift. By using the Bayesian met…