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arXiv:2601.18599v2 Announce Type: replace Abstract: The d'Arcais numbers are the triangular array $\{A(2,n,k)\, :\, n=0,1,\dots,\, k=0,\dots,n\}$, such that $\sum_{n=0}^{\infty} \sum_{k=0}^{n} A(2,n,k) x^k z^n/n! = ((z;z)_{\infty})^{-x}$....
arXiv:2108.09074v3 Announce Type: replace-cross Abstract: In the framework of Algebraic Quantum Field Theory, several operator algebraic notions of entanglement entropy can be associated with any...
arXiv:2209.10166v5 Announce Type: replace-cross Abstract: In this paper, we derive an $L^p$-chaos expansion based on iterated Stratonovich integrals with respect to a given exponentially integrable...
arXiv:2305.01984v3 Announce Type: replace-cross Abstract: A first-order formula is called primitive positive (pp) if it only admits the use of existential quantifiers and conjunction. Pp-formulas...
arXiv:2404.19222v2 Announce Type: replace-cross Abstract: In 1996, Reed, Robertson, Seymour and Thomas [Combinatorica 1996] proved Younger's Conjecture, which states that, for all directed graphs $D$,...
arXiv:2405.15132v4 Announce Type: replace-cross Abstract: The Intrinsic Dimension (ID) is a key concept in unsupervised learning and feature selection, as it is a lower bound...
arXiv:2407.02700v4 Announce Type: replace-cross Abstract: This paper presents a novel approach for the output range estimation problem in Deep Neural Networks (DNNs) by integrating a...
arXiv:2407.03903v2 Announce Type: replace-cross Abstract: We prove a nonlinear characteristic $C^k$-gluing theorem for vacuum gravitational fields in Bondi gauge for a class of characteristic hypersurfaces...
arXiv:2407.10070v3 Announce Type: replace-cross Abstract: Kernel ridge regression (KRR) is a fundamental computational tool, appearing in problems that range from computational chemistry to health analytics,...
arXiv:2409.05131v3 Announce Type: replace-cross Abstract: In this paper, we give a rigorous mathematical justification for the relaxation time approximation (RTA) model. We find that only...
arXiv:2409.11967v3 Announce Type: replace-cross Abstract: Causal inference problems often involve continuous treatments, such as dose, duration, or frequency. However, identifying and estimating standard dose-response estimands...
arXiv:2410.15244v2 Announce Type: replace-cross Abstract: The discrete cosine transform (DCT) is a central tool for image and video coding because it can be related to...
arXiv:2501.00677v2 Announce Type: replace-cross Abstract: Robust matrix completion (RMC) is a widely used machine learning tool that simultaneously tackles two critical issues in low-rank data...
arXiv:2504.02233v2 Announce Type: replace-cross Abstract: We propose new statistical tests, in high-dimensional settings, for testing the independence of two random vectors and their conditional independence...
arXiv:2506.00779v2 Announce Type: replace-cross Abstract: We propose a bootstrapping framework to quantify uncertainty in time-frequency representations (TFRs) generated by the short-time Fourier transform (STFT) and...
arXiv:2506.04775v3 Announce Type: replace-cross Abstract: We study stochastic linear bandits with heavy-tailed rewards, where the rewards have a finite $(1+\epsilon)$-absolute central moment bounded by $\upsilon$...
arXiv:2506.09298v4 Announce Type: replace-cross Abstract: We present an effective set of necessary and sufficient criteria for block-positivity of matrices of order $4$ over $\mathbb{C}$. The...
arXiv:2508.09506v3 Announce Type: replace-cross Abstract: Walking droplets -- millimetric oil droplets that self-propel across the surface of a vibrating fluid bath -- exhibit striking emergent...
arXiv:2509.06223v2 Announce Type: replace-cross Abstract: We present a statistically and computationally efficient spectral-domain maximum-likelihood procedure to solve for the structure of Gaussian spatial random fields...
arXiv:2509.22755v2 Announce Type: replace-cross Abstract: Concept Activation Vectors (CAVs) are a tool from explainable AI, offering a promising approach for understanding how human-understandable concepts are...
arXiv:2509.24639v3 Announce Type: replace-cross Abstract: This paper explores stability properties of periodic solutions of (nonlinear) fractional-order differential equations (FODEs). As classical Caputo-type FODEs do not...
arXiv:2509.25327v4 Announce Type: replace-cross Abstract: We establish the conditions under which a conservation law associated with a non-invertible operator may be realized as a symmetry...
arXiv:2511.10732v3 Announce Type: replace-cross Abstract: We study superconformal indices of four-dimensional $SU(N)$ gauge theories with $\mathcal{N}=1,2,4$ supersymmetry. The usual representation of a gauge theory index...
arXiv:2512.01912v2 Announce Type: replace-cross Abstract: We prove that the lonely runner conjecture holds for nine runners. Our proof is based on a couple of improvements...