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The minute-by-minute move of the Hang Seng Index (HSI) data over a four-year period is analysed and shown to possess similar statistical features as those of other markets. Based on a mathematical theorem [S. B. Pope and E. S. C. Ching,…
Recently there has been remarkable progress in the complex Langevin method, which aims at solving the complex action problem by complexifying the dynamical variables in the original path integral. In particular, a new technique called the…
We investigate dynamical changes and its corresponding phase space complexity in a stochastic red blood cell system. The system is obtained by incorporating power noise with the associated sinusoidal flow. Both chaotic and non-chaotic…
We use a set of simplified non-linear Langevin equations to study the hydrodynamic excitations in a nematic liquid crystal. We calculate the one-loop self-energy corrections in the long wavelength limit.
Diffusion in nonhomogeneous media is described by a dynamical process driven by a general Levy noise and subordinated to a random time; the subordinator depends on the position. This problem is approximated by a multiplicative process…
We study the non-equilibrium dynamics of a symmetry restoring phase transition in a scalar field theory, the ``system'', linearly coupled to another scalar field taken as a ``heat bath''. The ``system'' is initially in an ordered low…
Stochastically switching force terms appear frequently in models of biological systems under the action of active agents such as proteins. The interaction of switching force and Brownian motion can create an "effective thermal equilibrium"…
The study of experimental data is a relevant task in several physical, chemical and biological applications. In particular, the analysis of chaotic dynamics in cardiac systems is crucial as it can be related to some pathological…
We present the implementation of an algorithm to generate Gaussian random noises with prescribed time correlations that can be either long or short ranged. Examples of Langevin dynamics with short and long range noises are presented and…
Networks of globally coupled, noise activated, bistable elements with connection time delays are considered. The dynamics of these systems is studied numerically using a Langevin description and analytically using (1) a Gaussian…
A theoretical analysis of the mechanisms underlying the dynamics of gallbladder and heart pulsation could clarify the question regarding the classification as chaotic of the associated behaviour, eventually related to a normal and healthy…
As an example of the nonlinear Fokker-Planck equation, the mean field Langevin dynamics recently attracts attention due to its connection to (noisy) gradient descent on infinitely wide neural networks in the mean field regime, and hence the…
A Langevin equation with a special type of additive random source is considered. This random force presents a fractional order derivative of white noise, and leads to a power-law time behavior of the mean square displacement of a particle,…
Fundamental understanding of complex dynamics in many-particle systems on the atomistic level is of utmost importance. Often the systems of interest are of macroscopic size but can be partitioned into few important degrees of freedom which…
A deep latent variable model is a powerful method for capturing complex distributions. These models assume that underlying structures, but unobserved, are present within the data. In this dissertation, we explore high-dimensional problems…
Current molecular dynamic simulations of biomolecules using multiple time steps to update the slowingly changing force are hampered by an instability occuring at time step equal to half the period of the fastest vibrating mode. This has…
A system-reservoir nonlinear coupling model has been proposed for a situation where the reservoir is nonlinearly driven by an external Gaussian stationary noise which exposes the system particles to a nonequilibrium environment. Apart from…
We investigate the nature of the effective dynamics and statistical forces obtained after integrating out nonequilibrium degrees of freedom. To be explicit, we consider the Rouse model for the conformational dynamics of an ideal polymer…
We study functionals, such as heat and work, along trajectories of a class of multi-dimensional generalized Langevin systems in various limiting situations that correspond to different level of homogenization. These are the situations where…
An ensemble of pulse-coupled phase-oscillators is thoroughly analysed in the presence of a mean-field coupling and a dispersion of their natural frequencies. In spite of the analogies with the Kuramoto setup, a much richer scenario is…