We present a unified framework to analyze the global convergence of Langevin dynamics based algorithms for nonconvex finite-sum optimization with n component functions. At the core of our analysis is a direct analysis of the ergodicity of the numerical approximations to Langevin dynamics, which leads to faster convergence rates. Specifically, we show that gradient Langevin dynamics (GLD) and st...

Deterministic dynamical systems of Langevin type recently introduced by Beck & Roepsdorf Physica 145 A (1987) 1] generate Langevin dynamics in a suitable limit. We discuss the transition from chaos to randomness in these systems under the point of view of the attractor dimension and dynamical en-tropy and show that the limit of a stochastic process is reached via a shift of the deterministic pr...

The stochastic opening and closing of voltage-gated ion channels produce noise in neurons. The effect of this noise on the neuronal performance has been modeled using either an approximate or Langevin model based on stochastic differential equations or an exact model based on a Markov process model of channel gating. Yet whether the Langevin model accurately reproduces the channel noise produce...

Markov jump processes are widely used to model interacting species in circumstances where discreteness and stochasticity are relevant. Such models have been particularly successful in computational cell biology, and in this case, the interactions are typically first-order. The Chemical Langevin Equation is a stochastic differential equation that can be regarded as an approximation to the underl...

This paper presents a Lie–Trotter splitting for inertial Langevin equations (geometric Langevin algorithm) and analyzes its long-time statistical properties. The splitting is defined as a composition of a variational integrator with an Ornstein–Uhlenbeck flow. Assuming that the exact solution and the splitting are geometrically ergodic, the paper proves the discrete invariant measure of the spl...

Langevin noise leads to inhibition of the temporal synchronization of the pulse oscillations from a gain-switched multimode semiconductor laser, resulting in the power reduction in optical beat detection. In this paper, the degree of the temporal synchronization of the pulse oscillations was examined by numerically estimating the output energy in THz time-domain spectroscopy (THz-TDS) using mul...

The secondary structure of the member of the AKH/RPCH family has been studied by Molecular Dynamics and Langevin Dynamics methods. Molecular dynamics simulation were performed in vacuum, model aqueous solution and simulated membrane. Langevin dynamics simulation was performed using the friction factor y equal to 2 ps_1. Molecular dynamics as well as Langevin Dynamics simulation were conducted a...