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In many complex systems studied in statistical physics, inter-arrival times between events such as solar flares, trades and neuron voltages follow a heavy-tailed distribution. The set of event times is fractal-like, being dense in some time…

We introduce a path sampling method for the computation of rate constants for systems with a highly diffusive character. Based on the recently developed algorithm of transition interface sampling (TIS) this procedure increases the…

We study the disruption process of hierarchical 3-body systems with bodies of comparable mass. Such systems have long survival times that vary by orders of magnitude depending on the initial conditions. By comparing with 3-body numerical…

We describe a method to extract from experimental data the important dynamical modes in spatio-temporal patterns in a system driven out of thermodynamic equilibrium. Using a novel optical technique for controlling fluid flow, we create an…

Complex systems can convert energy imparted by nonequilibrium forces to regulate how quickly they transition between long lived states. While such behavior is ubiquitous in natural and synthetic systems, currently there is no general…

Rare events are processes that occur upon the emergence of unlikely fluctuations. Unlike what their name suggests, rare events are fairly ubiquitous in nature, as the occurrence of many structural transformations in biology and material…

This paper is concerned with the study of the stability of dynamical systems evolving on time scales. We first {formalize the notion of matrix measures on time scales, prove some of their key properties and make use of this notion to study…

Transition State Theory is a central cornerstone in reaction dynamics. Its key step is the identification of a dividing surface that is crossed only once by all reactive trajectories. This assumption is often badly violated, especially when…

We estimate the initial conditions of a multivariable dynamical system from a scalar signal, using a modified Newton-Raphson method incorporating the time evolution. We can estimate initial conditions of periodic and chaotic systems and the…

We present a method to study rare nonadiabatic dynamics in open quantum systems using transition path sampling and quantum jump trajectories. As with applications of transition path sampling to classical dynamics, the method does not rely…

We present a new method, Non-Stationary Forward Flux Sampling, that allows efficient simulation of rare events in both stationary and non-stationary stochastic systems. The method uses stochastic branching and pruning to achieve uniform…

This work introduces a novel, simple, and flexible method to quantify irreversibility in generic high-dimensional time series based on the well-known mapping to a binary classification problem. Our approach utilizes gradient boosting for…

We consider the problem of probabilistic quantification of dynamical systems that have heavy-tailed characteristics. These heavy-tailed features are associated with rare transient responses due to the occurrence of internal instabilities.…

We propose a general methodology for performing statistical inference within a `rare-events regime' that was recently suggested by Wagner, Viswanath and Kulkarni. Our approach allows one to easily establish consistent estimators for a very…

It is well known that the addition of noise to a multistable dynamical system can induce random transitions from one stable state to another. For low noise, the times between transitions have an exponential tail and Kramers' formula gives…

Rare event simulation and estimation for systems in equilibrium are among the most challenging topics in molecular dynamics. As was shown by Jarzynski and others, nonequilibrium forcing can theoretically be used to obtain equilibrium rare…

Boundary conditions may change the phase diagram of non-equilibrium statistical systems like the one-dimensional asymmetric simple exclusion process with and without particle number conservation. Using the quantum Hamiltonian approach, the…

Risk assessment for rare events is essential for understanding systemic stability in complex systems. As rare events are typically highly correlated, it is important to study heavy-tailed multivariate distributions of the relevant…

Statistical models provide a powerful and useful class of approximations for calculating reaction rates by bypassing the need for detailed, and often difficult, dynamical considerations. Such approaches invariably invoke specific…

Catastrophic transitions, where a system shifts abruptly between alternate steady states, are a generic feature of many nonlinear systems. Recently these regime shift were suggested as the mechanism underlies many ecological catastrophes,…