Related papers: Simulation of large deviation functions using popu…
A class of random non-stationary signals termed timbre x dynamics is introduced and studied. These signals are obtained by non-linear transformations of sta-tionary random gaussian signals, in such a way that the transformation can be…
Epochal dynamics, in which long periods of stasis in population fitness are punctuated by sudden innovations, is a common behavior in both natural and artificial evolutionary processes. We use a recent quantitative mathematical analysis of…
Simulations play important and diverse roles in statistical workflows, for example, in model specification, checking, validation, and even directly in model inference. Over the past decades, the application areas and overall potential of…
Many biological systems are governed by difference equations and exhibit discrete-time dynamics. Examples include the size of a population when generations are non-overlapping, and the incidence of a disease when infections are recorded at…
We focus on variational inference in dynamical systems where the discrete time transition function (or evolution rule) is modelled by a Gaussian process. The dominant approach so far has been to use a factorised posterior distribution,…
We present a flexible data-driven method for dynamical system analysis that does not require explicit model discovery. The method is rooted in well-established techniques for approximating the Koopman operator from data and is implemented…
We consider compartmental models in epidemiology. For the study of the divergence of the stochastic model from its corresponding deterministic limit (i.e., the solution of an ODE) for long time horizon, a large deviations principle suggests…
We investigate the large deviation behaviour of a point process sequence based on a stationary symmetric stable non-Gaussian discrete-parameter random field using the framework of Hult and Samorodnitsky (2010). Depending on the ergodic…
Time-irreversible stochastic processes are frequently used in natural sciences to explain non-equilibrium phenomena and to design efficient stochastic algorithms. Our main goal in this thesis is to analyse their dynamics by means of large…
We show that two dynamical systems exhibiting very different deterministic behaviours possess very similar stationary distributions when stabilized by a multiplicative Gaussian white noise. We also discuss practical aspects of numerically…
Progress on modern scientific questions regularly depends on using large-scale datasets to understand complex dynamical systems. An especially challenging case that has grown to prominence with advances in single-cell sequencing…
One of the goals of climate science is to characterize the statistics of extreme and potentially dangerous events in the present and future climate. Extreme events like heat waves, droughts, or floods due to persisting rains are…
Mathematical models for systems of interacting agents using simple local rules have been proposed and shown to exhibit emergent swarming behavior. Most of these models are constructed by intuition or manual observations of real phenomena,…
We consider the problem of forecasting complex, nonlinear space-time processes when observations provide only partial information of on the system's state. We propose a natural data-driven framework, where the system's dynamics are modelled…
We present a Hamiltonian approach for the wellknown Eigen model of the Darwin selection dynamics. Hamiltonization is carried out by means of the embedding of the population variable space, describing behavior of the system, into the space…
Thermodynamics of trajectories promises to make possible the thorough analysis of the dynamical properties of an open quantum system, a sought-after goal in modern physics. Unfortunately, calculation of the relevant quantities presents…
In many stochastic models, the observables of interest are naturally encoded in double transforms (e.g., Laplace transforms) that couple spatial and temporal variables. Notably, the double transform often provides the only analytically…
We study classical stochastic systems with discrete states, coupled to switching external environments. For fast environmental processes we derive reduced dynamics for the system itself, focusing on corrections to the adiabatic limit of…
In analyzing big data for finite population inference, it is critical to adjust for the selection bias in the big data. In this paper, we propose two methods of reducing the selection bias associated with the big data sample. The first…
Modern recording technologies now enable simultaneous recording from large numbers of neurons. This has driven the development of new statistical models for analyzing and interpreting neural population activity. Here we provide a broad…