Related papers: On converting any one-step method to a variational…
A stochastic control of the vibrational motion for a single trapped ion/atom is proposed. It is based on the possibility to continously monitor the motion through a light field meter. The output from the measurement process should be then…
Modular and reconfigurable robotic systems have been designed to provide a customized solution for the non-repetitive tasks to be performed in a constrained environment. Customized solutions are normally extracted from task-based…
We develop a one step matrix method in order to obtain approximate solutions of first order systems and non-linear ordinary differential equations, reducible to first order systems. We find a sequence of such solutions that converge to the…
In this paper, we propose a general algorithmic framework for first-order methods in optimization in a broad sense, including minimization problems, saddle-point problems, and variational inequalities. This framework allows obtaining many…
We propose a first-order method for stochastic strongly convex optimization that attains $O(1/n)$ rate of convergence, analysis show that the proposed method is simple, easily to implement, and in worst case, asymptotically four times…
Robotic systems are multi-dimensional entities, combining both hardware and software, that are heavily dependent on, and influenced by, interactions with the real world. They can be variously categorised as embedded, cyberphysical,…
The Adaptive Multilevel Splitting algorithm is a very powerful and versatile method to estimate rare events probabilities. It is an iterative procedure on an interacting particle system, where at each step, the $k$ less well-adapted…
Single molecular rotor is an important component for constructing bot-tom-up molecular mechanical machines and a window for shedding light on complex physical and chemical questions about motions of organic molecules on surfaces. Stability…
Reaction mechanisms are often presented as sequences of elementary steps, such as codified by arrow pushing. We propose an approach for representing such mechanisms using graph transformation. In this framework, each elementary step is a…
The precise description of quantum nuclear fluctuations in atomistic modelling is possible by employing path integral techniques, which involve a considerable computational overhead due to the need of simulating multiple replicas of the…
This article is concerned with a new filtered two-step variational integrator for solving the charged-particle dynamics in a mildly non-uniform moderate or strong magnetic field with a dimensionless parameter $\varepsilon$ inversely…
We propose new local error estimators for splitting and composition methods. They are based on the construction of lower order schemes obtained at each step as a linear combination of the intermediate stages of the integrator, so that the…
We consider convex-concave saddle-point problems where the objective functions may be split in many components, and extend recent stochastic variance reduction methods (such as SVRG or SAGA) to provide the first large-scale linearly…
We investigate the stochastic modified equation which plays an important role in the stochastic backward error analysis for explaining the mathematical mechanism of a numerical method. The contribution of this paper is threefold. First, we…
We report on a lattice based algorithm, completely vectorized for molecular dynamics simulations. Its algorithmic complexity is of the order $O(N)$, where $N$ is the number of particles. The algorithm works very effectively when the…
The implementation of multi-stage splitting integrators is essentially the same as the implementation of the familiar Strang/Verlet method. Therefore multi-stage formulas may be easily incorporated into software that now uses the…
We focus on the optimization problem with smooth, possibly nonconvex objectives and a convex constraint set for which the Euclidean projection operation is practically available. Focusing on this setting, we carry out a general convergence…
The concept of effective order is a popular methodology in the deterministic literature for the construction of efficient and accurate integrators for differential equations over long times. The idea is to enhance the accuracy of a…
We report on a lattice based algorithm, completely vectorized for molecular dynamics simulations. Its algorithmic complexity is of the order O(N), where $N$ is the number of particles. The algorithm works very effectively when the particles…
Functional group replacement is a pivotal approach in cheminformatics to enable the design of novel chemical compounds with tailored properties. Traditional methods for functional group removal and replacement often rely on rule-based…