1,863 research outputs found
Universal transient behavior in large dynamical systems on networks
We analyze how the transient dynamics of large dynamical systems in the
vicinity of a stationary point, modeled by a set of randomly coupled linear
differential equations, depends on the network topology. We characterize the
transient response of a system through the evolution in time of the squared
norm of the state vector, which is averaged over different realizations of the
initial perturbation. We develop a mathematical formalism that computes this
quantity for graphs that are locally tree-like. We show that for unidirectional
networks the theory simplifies and general analytical results can be derived.
For example, we derive analytical expressions for the average squared norm for
random directed graphs with a prescribed degree distribution. These analytical
results reveal that unidirectional systems exhibit a high degree of
universality in the sense that the average squared norm only depends on a
single parameter encoding the average interaction strength between the
individual constituents. In addition, we derive analytical expressions for the
average squared norm for unidirectional systems with fixed diagonal disorder
and with bimodal diagonal disorder. We illustrate these results with numerical
experiments on large random graphs and on real-world networks.Comment: 19 pages, 7 figures. Substantially enlarged version. Submitted to
Physical Review Researc
Curve boxplot: Generalization of boxplot for ensembles of curves
pre-printIn simulation science, computational scientists often study the behavior of their simulations by repeated solutions with variations in parameters and/or boundary values or initial conditions. Through such simulation ensembles, one can try to understand or quantify the variability or uncertainty in a solution as a function of the various inputs or model assumptions. In response to a growing interest in simulation ensembles, the visualization community has developed a suite of methods for allowing users to observe and understand the properties of these ensembles in an efficient and effective manner. An important aspect of visualizing simulations is the analysis of derived features, often represented as points, surfaces, or curves. In this paper, we present a novel, nonparametric method for summarizing ensembles of 2D and 3D curves. We propose an extension of a method from descriptive statistics, data depth, to curves. We also demonstrate a set of rendering and visualization strategies for showing rank statistics of an ensemble of curves, which is a generalization of traditional whisker plots or boxplots to multidimensional curves. Results are presented for applications in neuroimaging, hurricane forecasting and fluid dynamics
Ensemble Reinforcement Learning: A Survey
Reinforcement Learning (RL) has emerged as a highly effective technique for
addressing various scientific and applied problems. Despite its success,
certain complex tasks remain challenging to be addressed solely with a single
model and algorithm. In response, ensemble reinforcement learning (ERL), a
promising approach that combines the benefits of both RL and ensemble learning
(EL), has gained widespread popularity. ERL leverages multiple models or
training algorithms to comprehensively explore the problem space and possesses
strong generalization capabilities. In this study, we present a comprehensive
survey on ERL to provide readers with an overview of recent advances and
challenges in the field. First, we introduce the background and motivation for
ERL. Second, we analyze in detail the strategies that have been successfully
applied in ERL, including model averaging, model selection, and model
combination. Subsequently, we summarize the datasets and analyze algorithms
used in relevant studies. Finally, we outline several open questions and
discuss future research directions of ERL. By providing a guide for future
scientific research and engineering applications, this survey contributes to
the advancement of ERL.Comment: 42 page
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