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Quantum simulations of many-body systems offer novel methods for probing the dynamics of the Standard Model and its constituent gauge theories. Extracting low-energy predictions from such simulations rely on formulating…
We propose a two step algorithm based on $\ell_1/\ell_0$ regularization for the detection and estimation of parameters of a high dimensional change point regression model and provide the corresponding rates of convergence for the change…
We solve a family of fractional Riccati differential equations with constant (possibly complex) coefficients. These equations arise, e.g., in fractional Heston stochastic volatility models, that have received great attention in the recent…
In this article, a numerical simulation of two dimensional nonlinear sine-Gordon equation with Neumann boundary condition is obtained by using a composite scheme referred to as a modified cubic B spline differential quadrature method. The…
Golden ratio primal-dual algorithm (GRPDA) is a new variant of the classical Arrow-Hurwicz method for solving structured convex optimization problem, in which the objective function consists of the sum of two closed proper convex functions,…
For the purposes of electric circuit simulation, we consider an iterative simulation model based on solving systems of linear equations by Gauss-Jordan elimination (GJE) for individual moments in time. To accelerate the simulation, we…
We study embedding a subset $K$ of the unit sphere to the Hamming cube $\{-1,+1\}^m$. We characterize the tradeoff between distortion and sample complexity $m$ in terms of the Gaussian width $\omega(K)$ of the set. For subspaces and several…
In this paper, we consider the Clenshaw-Curtis-Filon method for the highly oscillatory Bessel transform $\int_0^1x^\alpha (1-x)^\beta f(x) J_{\nu}(\omega x)dx$, where $f$ is a smooth function on $[0, 1]$, and $\nu\geq0.$ The method is based…
Single-spin quantum sensors, for example based on nitrogen-vacancy centres in diamond, provide nanoscale mapping of magnetic fields. In applications where the magnetic field may be changing rapidly, total sensing time is crucial and must be…
A new O(N) algorithm based on a recursion method, in which the computational effort is proportional to the number of atoms N, is presented for calculating the inverse of an overlap matrix which is needed in electronic structure calculations…
A scheme of simplified smooth hybrid inflation is realized in the framework of supersymmetric $SU(5)$. The smooth model of hybrid inflation provides a natural solution to the monopole problem that appears in the breaking of $SU(5)$ gauge…
We present a flexible approach to colour transfer inspired by techniques recently proposed for shape registration. Colour distributions of the palette and target images are modelled with Gaussian Mixture Models (GMMs) that are robustly…
We propose to take advantage of the common knowledge of the characteristic function of the swap rate process as modelled in the LIBOR Market Model with Stochastic Volatility and Displaced Diffusion (DDSVLMM) to derive analytical expressions…
Building upon the efficient implementation of hybrid density functionals (HDFs) for large-scale periodic systems within the framework of numerical atomic orbital bases using the localized resolution of identity (RI) technique, we have…
An efficient hybrid numerical method for multiple scattering calculations is proposed. We use the well established doubling--adding method to find the reflection function of the lowermost homogeneous slab comprising the atmosphere of our…
This article devotes to developing robust but simple correction techniques and efficient algorithms for a class of second-order time stepping methods, namely the shifted fractional trapezoidal rule (SFTR), for subdiffusion problems to…
In this paper, we first propose an unconditionally stable implicit difference scheme for solving generalized time-space fractional diffusion equations (GTSFDEs) with variable coefficients. The numerical scheme utilizes the $L1$-type formula…
We introduce a simple, efficient and accurate nonnegative preserving numerical scheme for simulating the square-root process. The novel idea is to simulate the integrated square-root process first instead of the square-root process itself.…
It was recently demonstrated that a simple Monte Carlo (MC) algorithm involving the swap of particle pairs dramatically accelerates the equilibrium sampling of simulated supercooled liquids. We propose two numerical schemes integrating the…
We propose new positive definite kernels for permutations. First we introduce a weighted version of the Kendall kernel, which allows to weight unequally the contributions of different item pairs in the permutations depending on their ranks.…