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The dynamics of a one-dimensional stochastic system of classical particles consisting of asymmetric death and branching processes is studied. The dynamical activity, defined as the number of configuration changes in a dynamical trajectory,…
In self-gravitating stars, two dimensional or geophysical flows and in plasmas, long range interactions imply a lack of additivity for the energy; as a consequence, the usual thermodynamic limit is not appropriate. However, by contrast with…
We present a theory of modified reduced dynamics in the presence of counting fields. Reduced dynamics techniques are useful for describing open quantum systems at long emergent timescales when the memory timescales are short. However, they…
Studying extreme events and how they evolve in a changing climate is one of the most important current scientific challenges. Starting from complex climate models, a key difficulty is to be able to run long enough simulations in order to…
A widely-used model for determining the long-term health impacts of public health interventions, often called a "multistate lifetable", requires estimates of incidence, case fatality, and sometimes also remission rates, for multiple…
In this paper we address the use of rare event computation techniques to estimate small over-threshold probabilities of observables in determin-istic dynamical systems. We demonstrate that the genealogical particle analysis algorithms can…
The fluctuations of turbulence intensity in a pipe flow around the critical Reynolds number is difficult to study but important because they are related to turbulent-laminar transitions. We here propose a rare-event sampling method to study…
We consider the problem of extinction processes on random networks with a given structure. For sufficiently large well-mixed populations, the process of extinction of one or more state variable components occurs in the tail of the…
How long does a trajectory take to reach a stable equilibrium point in the basin of attraction of a dynamical system? This is a question of quite general interest, and has stimulated a lot of activities in dynamical and stochastic systems…
Rate processes are simple and analytically tractable models for many dynamical systems which switch stochastically between a discrete set of quasi stationary states but they may also approximate continuous processes by coarse grained,…
Scaling analysis exploiting timescale separation has been one of the most important techniques in the quantitative analysis of nonlinear dynamical systems in mathematical and theoretical biology. In the case of enzyme catalyzed reactions,…
The efficient calculation of rare-event kinetics in complex dynamical systems, such as the rate and pathways of ligand dissociation from a protein, is a generally unsolved problem. Markov state models can systematically integrate ensembles…
Current statistics can be calculated in various ways. Event-based approaches use the statistics of the number of events occuring during a given time. Time-based approaches use the statistics of the time needed to reach a given number of…
Rare trajectories of stochastic systems are important to understand -- because of their potential impact. However, their properties are by definition difficult to sample directly. Population dynamics provides a numerical tool allowing their…
Complexity is an important metric for appropriate characterization of different classes of irregular signals, observed in the laboratory or in nature. The literature is already rich in the description of such measures using a variety of…
This paper extends the canonical model of epidemiology, the SIRD model, to allow for time-varying parameters for real-time measurement and prediction of the trajectory of the Covid-19 pandemic. Time variation in model parameters is captured…
When a chemical reaction is driven by an external field, the transition state that the system must pass through as it changes from reactant to product -for example, an energy barrier- becomes time-dependent. We show that for periodic…
Temporal networks are commonly used to represent dynamical complex systems like social networks, simultaneous firing of neurons, human mobility or public transportation. Their dynamics may evolve on multiple time scales characterising for…
Freidlin-Wentzell theory of large deviations can be used to compute the likelihood of extreme or rare events in stochastic dynamical systems via the solution of an optimization problem. The approach gives exponential estimates that often…
In this short note, we discuss the basic approach to computational modeling of dynamical systems. If a dynamical system contains multiple time scales, ranging from very fast to slow, computational solution of the dynamical system can be…