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We give new rounding schemes for the standard linear programming relaxation of the correlation clustering problem, achieving approximation factors almost matching the integrality gaps: - For complete graphs our appoximation is $2.06 -…
Several new developments in the calculation and interpretation of hadron density-density correlation functions are presented. The asymptotic behavior of correlation functions is determined from a tree diagram path integral. A method is…
Polyharmonic functions f of infinite order and type {\tau} on annular regions are systematically studied. The first main result states that the Fourier-Laplace coefficients f_{k,l}(r) of a polyharmonic function f of infinite order and type…
The main purpose of this note is to provide an algorithm for approximating the value of the balanced $p$-adic $L$-function, as constructed in [Hsi21], at the point $(2,1,1)$, which is lying outside of the interpolation region. The…
We examine the large-order behaviour of a recently proposed renormalization-group-improved expansion of the Adler function in perturbative QCD, which sums in an analytically closed form the leading logarithms accessible from…
We determine approximate next-to-next-to-leading order (NNLO) corrections to unpolarized and polarized semi-inclusive DIS. They are derived using the threshold resummation formalism, which we fully develop to next-to-next-to-leading…
An approximation, in the sense of $\Gamma$-convergence and in any dimension $d\geq1$, of Griffith-type functionals, with $p-$growth ($p>1$) in the symmetrized gradient, is provided by means of a sequence of non-local integral functionals…
We study two- and three-point correlation functions of chiral primary half-BPS operators in four-dimensional $\mathcal{N}=2$ superconformal circular, cyclic symmetric quiver theories. Using supersymmetric localization, these functions can…
Approximating periodic solutions to the coupled Duffing equations amounts to solving a system of polynomial equations. The number of complex solutions measures the algebraic complexity of this approximation problem. Using the theory of…
We derive semiclassical periodic orbit expansions for a correlation function of the Wigner time delay. We consider the Fourier transform of the two-point correlation function, the form factor $K(\tau,x,y,M)$, that depends on the number of…
We demonstrate $k+1$-term arithmetic progressions in certain subsets of the real line whose "higher-order Fourier dimension" is sufficiently close to 1. This Fourier dimension, introduced in previous work, is a higher-order (in the sense of…
Sleeve functions are generalizations of the well-established ridge functions that play a major role in the theory of partial differential equation, medical imaging, statistics, and neural networks. Where ridge functions are non-linear,…
A set of piecewise linear functions, called polylines, $P_1,\ldots,P_L$ each with at most $n$ vertices can be simplified into a polyline $M$ with $k$ vertices, such that the Fr\'echet distances $\epsilon_1,\ldots,\epsilon_L$ to each of…
Many functions of interest are in a high-dimensional space but exhibit low-dimensional structures. This paper studies regression of a $s$-H\"{o}lder function $f$ in $\mathbb{R}^D$ which varies along a central subspace of dimension $d$ while…
We consider the problem of approximating $[0,1]^{d}$-periodic functions by convolution with a scaled Gaussian kernel. We start by establishing convergence rates to functions from periodic Sobolev spaces and we show that the saturation rate…
This article pertains to interpolation of Sobolev functions at shrinking lattices $h\mathbb{Z}^d$ from $L_p$ shift-invariant spaces associated with cardinal functions related to general multiquadrics,…
We present a new $\texttt{python}$ package SARABANDE for measuring 3 & 4 Point Correlation Functions (3/4 PCFs) in $\mathcal{O}(N_{\rm g} \log N_{\rm g})$ time using Fast Fourier Transforms (FFTs), with $N_{\rm g}$ the number of grid points…
Many present lattice QCD approaches to calculate the parton distribution functions (PDFs) rely on a factorization formula or effective theory expansion of certain Euclidean matrix elements in boosted hadron states. In the quasi- and…
Differential (Ore) type polynomials with approximate polynomial coefficients are introduced. These provide a useful representation of approximate differential operators with a strong algebraic structure, which has been used successfully in…
We consider the singular behaviour of tree-level QCD amplitudes when the momenta of three partons become simultaneously parallel. We discuss the universal factorization formula that controls the singularities of the multiparton matrix…