We present a derivation of a coarse-grained description, in the form of a generalized Langevin equation, from the Langevin dynamics model that describes the dynamics of bio-molecules. The focus is placed on the form of the memory kernel function, the colored noise, and the second fluctuation-dissipation theorem that connects them. Also presented is a hierarchy of approximations for the memory a...

Telecommunication network topologies are changing nowadays. The core telecommunication networks are based on fiber optics infrastructure. WDM technology is used to transmit multiple flows of traffic over a single fiber. Virtual network topology (VNT) is used to route IP traffic over WDM networks. VNT control system must be adaptive to traffic changes and dynamically reconfigure VNT. Langevin eq...

We extend the Langevin approach to a class of driving noises whose generating processes have independent increments with super-heavy-tailed distributions. The time-dependent generalized Fokker–Planck equation that corresponds to the first-order Langevin equation driven by such a noise is derived and solved exactly. This noise generates two probabilistic states of the system, survived and absorb...

We derive the linear Langevin equation that describes the behavior of the fluctuations of the order parameter of the chiral phase transition above the critical temperature by applying the projection operator method to the Nambu-Jona-Lasinio model at finite temperature and density. The Langevin equation relaxes exhibiting oscillation, reveals thermalization and converges to the equilibrium state...

We directly extend Kurchans’ work on the fluctuation theorem to general finite state space Markov jump processes and general Langevin dynamics. All systems are treated in a unified manner and we show that this directly reproduces (and corrects) the results of Lebowitz and Spohn in the Langevin case. For the jump process the quantity, for which the fluctuation theorem holds, is different from th...

There has been a recent burst of activity in the atmosphere/ocean sciences community in utilizing stable linear Langevin stochastic models for the unresolved degree of freedom in stochastic climate prediction. Here several idealized models for stochastic climate modeling are introduced and analyzed through unambiguous mathematical theory. This analysis demonstrates the potential need for more s...

An efficient method is presented as a means of an approximate, analytic timedependent solution of the Fokker-Planck equation (FPE) for the linear Langevin model subjected to additive and multiplicative noise. We have assumed that the dynamical distribution has the same structure as the exact stationary one and that its parameters are expressed in terms of first and second moments, whose equatio...

Langevin equation is widely used to study the stochastic effects in molecular networks, as it often approximates well the underlying chemical master equation. However, frequently it is not clear when such an approximation is applicable and when it breaks down. Here we study the simple Schnakenberg model consisting of two molecular species whose concentrations vary and three reversible reactions...

In this paper, we propose a novel technique to implement stochastic gradient methods, which are beneficial for learning from large datasets, through accelerated stochastic dynamics. A stochastic gradient method is based on mini-batch learning for reducing the computational cost when the amount of data is large. The stochasticity of the gradient can be mitigated by the injection of Gaussian nois...