Related papers: Time- and space-efficient evaluation of the comple…
We mainly study the M-estimation method for the high-dimensional linear regression model, and discuss the properties of M-estimator when the penalty term is the local linear approximation. In fact, M-estimation method is a framework, which…
We present a quantum algorithm for estimating the matrix determinant based on quantum spectral sampling. The algorithm estimates the logarithm of the determinant of an $n \times n$ positive sparse matrix to an accuracy $\epsilon$ in time…
We propose a method for efficient simulations in extended ensembles, useful, e.g., for the study of problems with complex energy landscapes and for free energy calculations. The main difficulty in such simulations is the estimation of the a…
We present an auxiliary space theory that provides a unified framework for analyzing various iterative methods for solving linear systems that may be semidefinite. By interpreting a given iterative method for the original system as an…
We develop an efficient algorithm for evaluating divergent perturbation expansions of field theories in the bare coupling constant g_B for which we possess a finite number L of expansion coefficients plus two more informations: The…
The anisotropic diffusion equation is imperative in understanding cosmic ray diffusion across the Galaxy, the heliosphere, and its interplay with the ambient magnetic field. This diffusion term contributes to the highly stiff nature of the…
We present an iterative algorithm for solving a class of \\nonlinear Laplacian system of equations in $\tilde{O}(k^2m \log(kn/\epsilon))$ iterations, where $k$ is a measure of nonlinearity, $n$ is the number of variables, $m$ is the number…
This paper developed a method called "modified exponential cubic B-Spline differential quadrature (mExp-DQM) for space discretization together with a time integration algorithm" for the numerical computation of hyperbolic telegraph equation…
This is a survey on the computational complexity of nonlinear mixed-integer optimization. It highlights a selection of important topics, ranging from incomputability results that arise from number theory and logic, to recently obtained…
Symbolic Regression (SR) algorithms attempt to learn analytic expressions which fit data accurately and in a highly interpretable manner. Conventional SR suffers from two fundamental issues which we address here. First, these methods search…
In this report the emphasis is on an alternative representation of the Magnus series by proper operator (matrix) exponential solutions to differential equations (systems), both linear and nonlinear ODEs and PDEs. The main idea here is in…
Various properties of the general two-center two-electron integral over the explicitly correlated exponential function are analyzed for the potential use in high precision calculations for diatomic molecules. A compact one dimensional…
Higher-Order Fixpoint Logic (HFL) is a hybrid of the simply typed \lambda-calculus and the modal \lambda-calculus. This makes it a highly expressive temporal logic that is capable of expressing various interesting correctness properties of…
We give an O(sqrt n log n)-query quantum algorithm for evaluating size-n AND-OR formulas. Its running time is poly-logarithmically greater after efficient preprocessing. Unlike previous approaches, the algorithm is based on a quantum walk…
Most current sampling algorithms for high-dimensional distributions are based on MCMC techniques and are approximate in the sense that they are valid only asymptotically. Rejection sampling, on the other hand, produces valid samples, but is…
We propose new algorithms for the computation of the first N terms of a vector (resp. a basis) of power series solutions of a linear system of differential equations at an ordinary point, using a number of arithmetic operations which is…
Error estimates for the numerical solution of the master equation are presented. Estimates are based on adjoint methods. We find that a good estimate can often be computed without spending computational effort on a dual problem. Estimates…
This paper presents an accelerated quadrature scheme for the evaluation of layer potentials in three dimensions. Our scheme combines a generic, high order quadrature method for singular kernels called Quadrature by Expansion (QBX) with a…
We develop a method to evaluate integrals of non-holomorphic modular functions over the fundamental domain of the torus with modular parameter $\tau$ analytically. It proceeds in two steps: first the integral is transformed to a Lorentzian…
We apply the derivative expansion of the effective action in the exact renormalization group equation up to fourth order to the $Z_2$ and $O(N)$ symmetric scalar models in $d=3$ Euclidean dimensions. We compute the critical exponents $\nu$,…