相关论文: Improved cutoff functions for short-range potentia…
We consider the problem of minimizing the sum of submodular set functions assuming minimization oracles of each summand function. Most existing approaches reformulate the problem as the convex minimization of the sum of the corresponding…
We study the cut-off resolvent of semiclassical Schr{\"o}dinger operators on $\mathbb{R}^d$ with bounded compactly supported potentials $V$. We prove that for real energies $\lambda^2$ in a compact interval in $\mathbb{R}_+$ and for any…
The scattering problem for two particles interacting via the Coulomb potential is examined for the case where the potential has a sharp cut-off at some distance. The problem is solved for two complimentary situations, firstly when the…
For lambda phi^4 problems, convergent perturbative series can be obtained by cutting off the large field configurations. The modified series converge to values exponentially close to the exact ones. For lambda larger than some critical…
We propose a fast proximal Newton-type algorithm for minimizing regularized finite sums that returns an $\epsilon$-suboptimal point in $\tilde{\mathcal{O}}(d(n + \sqrt{\kappa d})\log(\frac{1}{\epsilon}))$ FLOPS, where $n$ is number of…
Fast Ewald summation efficiently evaluates Coulomb interactions and is widely used in molecular dynamics simulations. It is based on a split into a short-range and a long-range part, where evaluation of the latter is accelerated using the…
Recently the partial wave cutoff method was developed as a new calculational scheme for a functional determinant of quantum field theory in radial backgrounds. For the contribution given by an infinite sum of large partial waves, we derive…
We present the singular Euler--Maclaurin expansion, a new method for the efficient computation of large singular sums that appear in long-range interacting systems in condensed matter and quantum physics. In contrast to the traditional…
The Frank-Wolfe optimization algorithm has recently regained popularity for machine learning applications due to its projection-free property and its ability to handle structured constraints. However, in the stochastic learning setting, it…
The modern conformal bootstrap program often employs the method of linear functionals to derive the numerical or analytical bounds on the CFT data. These functionals must have a crucial "swapping" property, allowing to swap infinite…
We estimate short exponential sums weighted by the Fourier coefficients of a Maass form. This requires working out a certain transformation formula for non-linear exponential sums, which is of independent interest. We also discuss how the…
We discuss kinematical enhancements of cutoff effects at short and intermediate distances. Starting from a pedagogical example with periodic boundary conditions, we switch to the case of the Schroedinger Functional, where the theoretical…
The Frank-Wolfe (FW) method is a popular approach for solving optimization problems with structured constraints that arise in machine learning applications. In recent years, stochastic versions of FW have gained popularity, motivated by…
We argue that the sharp-cutoff Wilson renormalization group provides a powerful tool for the analysis of second-order and weakly first-order phase transitions. In particular, in a computation no harder than the calculation of the 1-loop…
We consider the classical Coulomb gas in two dimensions at the inverse temperature $\beta=2$, confined within a droplet of radius $R$ by a rotationally invariant potential $U(r)$. For $U(r)\sim r^2$ this describes the eigenvalues of the…
To minimise systematic errors in Monte Carlo simulations of charged particles, long range electrostatic interactions have to be calculated accurately and efficiently. Standard approaches, such as Ewald summation or the naive application of…
In recent papers it has been noted that the local potential approximation of the Legendre and Wilson-Polchinski flow equations give, within numerical error, identical results for a range of exponents and Wilson-Fisher fixed points in three…
Submodular functions are a fundamental object of study in combinatorial optimization, economics, machine learning, etc. and exhibit a rich combinatorial structure. Many subclasses of submodular functions have also been well studied and…
We propose a new analytical method to solve for nonexactly soluble Schrodinger equation via expansions through some existing quantum numbers. Successfully, it is applied to the rational non-polynomial oscillator potential. Moreover, a…
We consider random normal matrix and planar symplectic ensembles, which can be interpreted as two-dimensional Coulomb gases having determinantal and Pfaffian structures, respectively. For general radially symmetric potentials, we derive the…