Related papers: Extremes and Recurrence in Dynamical Systems
In a wide variety of situations, anomalies in the behaviour of a complex system, whose health is monitored through the observation of a random vector X = (X1,. .. , X d) valued in R d , correspond to the simultaneous occurrence of extreme…
Dynamical systems with high intrinsic dimensionality are often characterized by extreme events having the form of rare transitions several standard deviations away from the mean. For such systems, order-reduction methods through projection…
We introduce a rigorous mathematical framework for Granger causality in extremes, designed to identify causal links from extreme events in time series. Granger causality plays a pivotal role in uncovering directional relationships among…
A general method to derive the master equations for extremal models is established. These systems are shown to develop a peculiar kind of correlations between elements related to the characterization of extremal dynamics as an information…
We study distributional robustness in the context of Extreme Value Theory (EVT). We provide a data-driven method for estimating extreme quantiles in a manner that is robust against incorrect model assumptions underlying the application of…
The broad concept of emergence is instrumental in various of the most challenging open scientific questions -- yet, few quantitative theories of what constitutes emergent phenomena have been proposed. This article introduces a formal theory…
We consider the basic features of complex dynamical and control systems. Special attention is paid to the problems of synthesis of dynamical models of complex systems, construction of efficient control models, and to the development of…
Simulation based or dynamic probabilistic risk assessment methodologies were primarily developed for proving a more realistic and complete representation of complex systems accident response. Such simulation based methodologies have proven…
Multivariate extreme-value analysis is concerned with the extremes in a multivariate random sample, that is, points of which at least some components have exceptionally large values. Mathematical theory suggests the use of max-stable models…
Ecological systems often exhibit complex nonlinear dynamics like oscillations, chaos, and regime shifts. Universal dynamic equations have shown promise in modeling complex dynamics by combining known functional forms with neural networks…
Deep Learning has received increased attention due to its unbeatable success in many fields, such as computer vision, natural language processing, recommendation systems, and most recently in simulating multiphysics problems and predicting…
We study the extreme events taking place on complex networks. The transport on networks is modelled using random walks and we compute the probability for the occurance and recurrence of extreme events on the network. We show that the nodes…
Abrupt and rapid high-amplitude changes in a dynamical system's states known as extreme event appear in many processes occurring in nature, such as drastic climate patterns, rogue waves, or avalanches. These events often entail catastrophic…
Emergence, the phenomena where a system's micro-scale dynamics facilitate the development of non-trivial, informative higher scales, has become a foundational concept in modern sciences, tying together fields as diverse as physics, biology,…
Extreme events generated by complex systems have been intensively studied in many fields due to their great impact on scientific research and our daily lives. However, their prediction is still a challenge in spite of the tremendous…
Noise-induced phase transitions are common in various complex systems, from physics to biology. In this article, we investigate the emergence of crucial events in noise-induced phase transition processes and their potential significance for…
Extreme weather events are increasing in frequency and intensity due to climate change. This, in turn, is exacting a significant toll in communities worldwide. While prediction skills are increasing with advances in numerical weather…
It is known that statistical model selection as well as identification of dynamical equations from available data are both very challenging tasks. Physical systems behave according to their underlying dynamical equations which, in turn, can…
Numerical climate models are complex and combine a large number of physical processes. They are key tools in quantifying the relative contribution of potential anthropogenic causes (e.g., the current increase in greenhouse gases) on high…
We discuss the relevance of studying ecology within the framework of Complexity Science from a statistical mechanics approach. Ecology is concerned with understanding how systems level properties emerge out of the multitude of interactions…