Related papers: Master equations for extremal models
Ordinary differential equation models have become a standard tool for the mechanistic description of biochemical processes. If parameters are inferred from experimental data, such mechanistic models can provide accurate predictions about…
We develop a master equation formalism to describe the evolution of the average density matrix of a closed quantum system driven by a stochastic Hamiltonian. The average over random processes generally results in decoherence effects in…
It is shown that a chain of closed systems of first order ordinary differential equations describing the evolution of moments can be constructed using the Jacobi equation. It is shown that Wronsky determinants for fundamental matrices of…
We propose a framework for studying predictability of extreme events in complex systems. Major conceptual elements -- direct cascading or fragmentation, spatial dynamics, and external driving -- are combined in a classical age-dependent…
During modeling of dynamical systems, often two or more model architectures are combined to obtain a more powerful or efficient model regarding a specific application area. This covers the combination of multiple machine learning…
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…
Ordinary differential equation models are nowadays widely used for the mechanistic description of biological processes and their temporal evolution. These models typically have many unknown and non-measurable parameters, which have to be…
Max-stable processes are a common choice for modelling spatial extreme data as they arise naturally as the infinite-dimensional generalisation of multivariate extreme value theory. Statistical inference for such models is complicated by the…
A trend across most areas where simulation-driven development is used is the ever increasing size and complexity of the systems under consideration, pushing established methods of modeling and simulation towards their limits. This paper…
The modeling of complex systems such as ecological or socio-economic systems can be very challenging. Although various modeling approaches exist, they are generally not compatible and mutually consistent, and empirical data often do not…
The master equation plays an important role in many scientific fields including physics, chemistry, systems biology, physical finance, and sociodynamics. We consider the master equation with periodic transition rates. This may represent an…
The estimation of conditional quantiles at extreme tails is of great interest in numerous applications. Various methods that integrate regression analysis with an extrapolation strategy derived from extreme value theory have been proposed…
Extreme events, such as rogue waves, earthquakes and stock market crashes, occur spontaneously in many dynamical systems. Because of their usually adverse consequences, quantification, prediction and mitigation of extreme events are highly…
Ensemble data assimilation is a problem in determining the most likely phase space trajectory of a model of an observed dynamical sys- tem as it receives inputs from measurements passing information to the model. Using methods developed in…
We describe a general-purpose method for finding high-quality solutions to hard optimization problems, inspired by self-organized critical models of co-evolution such as the Bak-Sneppen model. The method, called Extremal Optimization,…
When extreme weather events affect large areas, their regional to sub-continental spatial scale is important for their impacts. We propose a novel machine learning (ML) framework that integrates spatial extreme-value theory to model weather…
Complex biological processes are usually experimented along time among a collection of individuals. Longitudinal data are then available and the statistical challenge is to better understand the underlying biological mechanisms. The…
This paper shows how to build a formal analytical solution for a differential equation of arbitrary order and with variable coefficients. It proofs that the most known approximated solutions for such a problem can be derived from the…
We propose a general-purpose method for finding high-quality solutions to hard optimization problems, inspired by self-organizing processes often found in nature. The method, called Extremal Optimization, successively eliminates extremely…
I present a scheme of drawing causal diagrams based on physically motivated mathematical models expressed in terms of temporal differential equations. They provide a means of better understanding the processes and causal relationships…