相关论文: Improved cutoff functions for short-range potentia…

We suggest a new optimization technique for minimizing the sum $\sum_{i=1}^n f_i(x)$ of $n$ non-convex real functions that satisfy a property that we call piecewise log-Lipschitz. This is by forging links between techniques in computational…

The complexity of Philip Wolfe's method for the minimum Euclidean-norm point problem over a convex polytope has remained unknown since he proposed the method in 1974. The method is important because it is used as a subroutine for one of the…

We study constraint effective potentials for various strongly interacting $\phi^4$ theories. Renormalization group (RG) equations for these quantities are discussed and a heuristic development of a commonly used RG approximation is…

The effects of a long range electronic potential on a one dimensional chain of spinless fermions are investigated by numerical techniques (Exact Diagonalisation of rings with up to 30 sites complemented by finite size analysis) and analytic…

For the Maxwellian molecules or hard potentials case, we verify the smoothing effect for the spatially inhomogeneous Boltzmann equation without angular cutoff. Given initial data with low regularity, we prove its solutions at any positive…

We demonstrate how to scalably solve a class of constrained self-concordant minimization problems using linear minimization oracles (LMO) over the constraint set. We prove that the number of LMO calls of our method is nearly the same as…

We introduce an approximation strategy for the discounted moments of a stochastic process that can, for a large class of problems, approximate the true moments. These moments appear in pricing formulas of financial products such as bonds…

We consider the spatially homogeneous Boltzmann equation for hard potentials with angular cutoff. This equation has a unique conservative weak solution $(f_t)_{t\geq 0}$, once the initial condition $f_0$ with finite mass and energy is…

We consider the minimization problem of a sum of a number of functions having Lipshitz $p$-th order derivatives with different Lipschitz constants. In this case, to accelerate optimization, we propose a general framework allowing to obtain…

Accurately estimating expectation values of quantum observables with as few measurements as possible is crucial to many quantum computing applications. We introduce a framework that covers many of existing measurement strategies and…

We consider the numerical approximation of $f({\cal A})b$ where $b\in{\mathbb R}^{N}$ and $\cal A$ is the sum of Kronecker products, that is ${\cal A}=M_2 \otimes I + I \otimes M_1\in{\mathbb R}^{N\times N}$. Here $f$ is a regular function…

We present a subtraction scheme for eliminating the ultraviolet, soft, and collinear divergences in the numerical calculation of an arbitrary one-loop QCD amplitude with an arbitrary number of external legs. The subtractions consist of…

Classical optimization is a cornerstone of the success of variational quantum algorithms, which often require determining the derivatives of the cost function relative to variational parameters. The computation of the cost function and its…

Projection-free optimization via different variants of the Frank-Wolfe (FW) method has become one of the cornerstones in large scale optimization for machine learning and computational statistics. Numerous applications within these fields…

The theme of the present paper is numerical integration of $C^r$ functions using randomized methods. We consider variance reduction methods that consist in two steps. First the initial interval is partitioned into subintervals and the…

We study methods to replace entangling operations with random local operations in a quantum computation, at the cost of increasing the number of required executions. First, we consider "space-like cuts" where an entangling unitary is…

We give a simple and natural method for computing approximately optimal solutions for minimizing a convex function $f$ over a convex set $K$ given by a separation oracle. Our method utilizes the Frank--Wolfe algorithm over the cone of valid…

We study the cut-off phenomenon for a family of stochastic small perturbations of a one dimensional dynamical system. We will focus in a semi-flow of a deterministic differential equation which is perturbed by adding to the dynamics a white…

Under a rescaling of longitudinal coordinates $x^{0,3}$ by a factor $\lambda$ which is taken to zero, the classical QCD action simplifies dramatically. This is the high-energy limit, as $\lambda$ is of order $s^{-1/2}$, where $s$ is the…

We present a simple and general formalism to compute efficiently the derivatives of a multi-determinant Jastrow-Slater wave function, the local energy, the interatomic forces, and similar quantities needed in quantum Monte Carlo. Through a…