Related papers: Rational approximations in Analytic QCD
For revDSD double hybrids, the G\"orling-Levy second-order perturbation theory component is an Achilles' Heel when applied to systems with significant near-degeneracy ("static") correlation. We have explored its replacement by the direct…
In classical density functional theory (DFT) the part of the Helmholtz free energy functional arising from attractive inter-particle interactions is often treated in a mean-field or van der Waals approximation. On the face of it, this is a…
Optimization on the Stiefel manifold or with orthogonality constraints is an important problem in many signal processing and data analysis applications such as Sparse Principal Component Analysis (SPCA). Algorithms such as the Riemannian…
Estimating linear, mean-square continuous functionals is a pivotal challenge in statistics. In high-dimensional contexts, this estimation is often performed under the assumption of exact model sparsity, meaning that only a small number of…
Finite 't Hooft coupling corrections to multiple physical observables in strongly coupled $N=4$ supersymmetric Yang-Mills plasma are examined, in an attempt to assess the stability of the expansion in inverse powers of the 't Hooft coupling…
We develop a Non-Crossing Approximation (NCA) for the effective cluster problem of the recently developed Dynamical Cluster Approximation (DCA). The DCA technique includes short-ranged correlations by mapping the lattice problem onto a…
Let $\Lambda$ be a uniformly discrete set and $S$ be a compact set in $R$. We prove that if there exists a bounded sequence of functions in Paley--Wiener space $PW_S$, which approximates $\delta-$functions on $\Lambda$ with $l^2-$error $d$,…
Evaluating the action of a matrix function on a vector, that is $x=f(\mathcal M)v$, is an ubiquitous task in applications. When $\mathcal M$ is large, one usually relies on Krylov projection methods. In this paper, we provide effective…
We investigate the relation between holographic calculations in 5D and the Migdal approach to correlation functions in large N theories. The latter employs Pade approximation to extrapolate short distance correlation functions to large…
Second order M{\o}ller-Plesset perturbation theory (MP2) approximates the exact Hartree-Fock (HF) adiabatic connection (AC) curve by a straight line. Thus by using the deviation of the exact curve from the linear behaviour, we construct an…
The properties of the new analytic running coupling are investigated at the higher loop levels. The expression for this invariant charge, independent of the normalization point, is obtained by invoking the asymptotic freedom condition. It…
The focus of this article is the approximation of functions which are analytic on a compact interval except at the endpoints. Typical numerical methods for approximating such functions depend upon the use of particular conformal maps from…
Solving the QCD renormalization group equation at the 2-loop and 3-loop orders we obtain explicit expressions for the coupling as a function of the scale in terms of the Lambert W function. We study the nature of the ``Landau…
We introduce a new stable mathematical model for locating and measuring the medial axis of geometric objects, called the quadratic multiscale medial axis map of scale $\lambda$, and prove a sharp regularity result for the squared-distance…
Random features (RFs) are a popular technique to scale up kernel methods in machine learning, replacing exact kernel evaluations with stochastic Monte Carlo estimates. They underpin models as diverse as efficient transformers (by…
Strongly contracting dynamical systems have numerous properties (e.g., incremental ISS), find widespread applications (e.g., in controls and learning), and their study is receiving increasing attention. This work starts with the simple…
Consider a Brownian motion on the circumference of the unit circle, which jumps to the opposite point of the circumference at incident times of an independent Poisson process of rate $\lambda$. We examine the problem of coupling two copies…
Movable Antenna (MA) technology is emerging as a promising advancement with the potential to significantly enhance the performance of future wireless communication and sensing systems. In this paper, we address two-dimensional (2D)…
We consider massive \lambda\phi^4 theory in de Sitter background. The mass of the scalar field \phi is chosen small enough, such that the amplification of superhorizon momentum modes leads to a significant enhancement of infrared…
Canonical correlation analysis (CCA) is a popular statistical technique for exploring relationships between datasets. In recent years, the estimation of sparse canonical vectors has emerged as an important but challenging variant of the CCA…