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We propose a computationally efficient method to solve the dynamics of operators of bosonic quantum systems coupled to their environments. The method maps the operator under interest to a set of complex-valued functions, and its adjoint…
Motivation: Stochastic reaction networks are a widespread model to describe biological systems where the presence of noise is relevant, such as in cell regulatory processes. Unfortu-nately, in all but simplest models the resulting discrete…
Large-scale optimization problems require algorithms both effective and efficient. One such popular and proven algorithm is Stochastic Gradient Descent which uses first-order gradient information to solve these problems. This paper studies…
We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…
The EM (Expectation-Maximization) algorithm is regarded as an MM (Majorization-Minimization) algorithm for maximum likelihood estimation of statistical models. Expanding this view, this paper demonstrates that by choosing an appropriate…
Stochastic approximation algorithm is a useful technique which has been exploited successfully in probability theory and statistics for a long time. The step sizes used in stochastic approximation are generally taken to be deterministic and…
We study the incremental knapsack problem, where one wishes to sequentially pack items into a knapsack whose capacity expands over a finite planning horizon, with the objective of maximizing time-averaged profits. While various…
We develop several efficient algorithms for the classical \emph{Matrix Scaling} problem, which is used in many diverse areas, from preconditioning linear systems to approximation of the permanent. On an input $n\times n$ matrix $A$, this…
We analyze and compare the computational complexity of different simulation strategies for Monte Carlo in the setting of classically scaled population processes. This allows a range of widely used competing strategies to be judged…
We study the efficiency of algorithms simulating a system evolving with Hamiltonian $H=\sum_{j=1}^m H_j$. We consider high order splitting methods that play a key role in quantum Hamiltonian simulation. We obtain upper bounds on the number…
The machine learning explosion has created a prominent trend in modern computer hardware towards low precision floating-point operations. In response, there have been growing efforts to use low and mixed precision in general scientific…
An exact and efficient new method to simulate dynamics in dissipative quantum systems is presented. A stochastic Liouville equation, deduced from Feynman and Vernon's path-integral expression of the reduced density matrix, is used to…
Recent applications of machine learning and statistical inference provide case studies demonstrating how such approaches can accelerate the discovery process in physical chemistry and related fields. Examples discussed in this review…
The Expectation-Maximization (EM) algorithm has been predominantly used to approximate the maximum likelihood estimation of the location-scale Gaussian mixtures. However, when the models are over-specified, namely, the chosen number of…
A stochastic model for a chemical reaction network is embedded in a one-parameter family of models with species numbers and rate constants scaled by powers of the parameter. A systematic approach is developed for determining appropriate…
The goal of this paper is to understand how exponential-time approximation algorithms can be obtained from existing polynomial-time approximation algorithms, existing parameterized exact algorithms, and existing parameterized approximation…
We present a novel and simple method to numerically calculate Fisher Information Matrices for stochastic chemical kinetics models. The linear noise approximation is used to derive model equations and a likelihood function which leads to an…
In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of…
The EM algorithm is one of many important tools in the field of statistics. While often used for imputing missing data, its widespread applications include other common statistical tasks, such as clustering. In clustering, the EM algorithm…
The aim of this work is to investigate the application of partial moment approximations to kinetic chemotaxis equations in one and two spatial dimensions. Starting with a kinetic equation for the cell densities we apply a…