Related papers: p-adic reconstruction of rational functions in mul…
We have derived the coefficients of the highest three 1/x-enhanced small-x logarithms of all timelike splitting functions and the coefficient functions for the transverse fragmentation function in one-particle inclusive e^+e^- annihilation…
The reconstruction of high-dimensional sparse signals is a challenging task in a wide range of applications. In order to deal with high-dimensional problems, efficient sparse fast Fourier transform algorithms are essential tools. The second…
The problem of estimating missing fragments of curves from a functional sample has been widely considered in the literature. However, a majority of the reconstruction methods rely on estimating the covariance matrix or the components of its…
We present a deep learning-based computational algorithm for inversion of circular Radon transforms in the partial radial setup, arising in photoacoustic tomography. We first demonstrate that the truncated singular value decomposition-based…
We present an algorithm to perform a simultaneous modular reduction of several residues. This algorithm is applied fast modular polynomial multiplication. The idea is to convert the $X$-adic representation of modular polynomials, with $X$…
Scattering amplitudes at loop level can be expressed in terms of Feynman integrals. The latter satisfy partial differential equations in the kinematical variables. We argue that a good choice of basis for (multi-)loop integrals can lead to…
An operator theoretic approach to orthogonal rational functions on the unit circle with poles in its exterior is presented in this paper. This approach is based on the identification of a suitable matrix representation of the multiplication…
We compute a complete set of independent leading-color two-loop five-parton amplitudes in QCD. These constitute a fundamental ingredient for the next-to-next-to-leading order QCD corrections to three-jet production at hadron colliders. We…
We give a detailed account of the phenomenology of all-order resummations of logarithmically enhanced contributions at small momentum fraction of the observed hadron in semi-inclusive electron-positron annihilation and the time-like scale…
In this paper, we construct a digraph structure on $p$-adic dynamical systems defined by rational functions. We study the conditions under which the functions are measure-preserving, invertible and isometric, ergodic, and minimal on…
One of the crucial generic techniques for quantum computation is amplitude encoding. Although several approaches have been proposed, each of them often requires exponential classical-computational cost or an oracle whose explicit…
We consider an inverse problem arising in thermo-/photo- acoustic tomography that amounts to reconstructing a function $f$ from its circular or spherical means with the centers lying on a given measurement surface. (Equivalently, these…
We present a simplified variant of the integrand reduction algorithm for multiloop scattering amplitudes in $d = 4 - 2\epsilon$ dimensions, which exploits the decomposition of the integration momenta in parallel and orthogonal subspaces,…
Recent progress in unitarity techniques for one-loop scattering amplitudes makes a numerical implementation of this method possible. We present a 4-dimensional unitarity method for calculating the cut-constructible part of amplitudes and…
With the availability of more powerful computers, iterative reconstruction algorithms are the subject of an ongoing work in the design of more efficient reconstruction algorithms for X-ray computed tomography. In this work, we show how two…
In these lectures, we discuss different types of renormalization problems in QCD and their non-perturbative solution in the framework of the lattice formulation. In particular the recursive finite size methods to compute the…
Two-loop corrections to scattering amplitudes are crucial theoretical input for collider physics. Recent years have seen tremendous advances in computing Feynman integrals, scattering amplitudes, and cross sections for five-particle…
In this paper the properties of R\'edei rational functions are used to derive rational approximations for square roots and both Newton and Pad\'e approximations are given as particular cases. As a consequence, such approximations can be…
The 4-loop QED mass and wave function renormalization constants $Z_2$ and $Z_m$ have been evaluated in the on-shell subtraction scheme with 1100 digits of precision. We also worked out the coefficients of the five color structures of the…
We propose a combined reconstruction-classification method for simultaneously recovering absorption and scattering in turbid media from images of absorbed optical energy. This method exploits knowledge that optical parameters are determined…