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Editorial Comment on the Special Issue of "Information in Dynamical Systems and Complex Systems"
This special issue collects contributions from the participants of the
"Information in Dynamical Systems and Complex Systems" workshop, which cover a
wide range of important problems and new approaches that lie in the
intersection of information theory and dynamical systems. The contributions
include theoretical characterization and understanding of the different types
of information flow and causality in general stochastic processes, inference
and identification of coupling structure and parameters of system dynamics,
rigorous coarse-grain modeling of network dynamical systems, and exact
statistical testing of fundamental information-theoretic quantities such as the
mutual information. The collective efforts reported herein reflect a modern
perspective of the intimate connection between dynamical systems and
information flow, leading to the promise of better understanding and modeling
of natural complex systems and better/optimal design of engineering systems
Block-diagonal covariance selection for high-dimensional Gaussian graphical models
Gaussian graphical models are widely utilized to infer and visualize networks
of dependencies between continuous variables. However, inferring the graph is
difficult when the sample size is small compared to the number of variables. To
reduce the number of parameters to estimate in the model, we propose a
non-asymptotic model selection procedure supported by strong theoretical
guarantees based on an oracle inequality and a minimax lower bound. The
covariance matrix of the model is approximated by a block-diagonal matrix. The
structure of this matrix is detected by thresholding the sample covariance
matrix, where the threshold is selected using the slope heuristic. Based on the
block-diagonal structure of the covariance matrix, the estimation problem is
divided into several independent problems: subsequently, the network of
dependencies between variables is inferred using the graphical lasso algorithm
in each block. The performance of the procedure is illustrated on simulated
data. An application to a real gene expression dataset with a limited sample
size is also presented: the dimension reduction allows attention to be
objectively focused on interactions among smaller subsets of genes, leading to
a more parsimonious and interpretable modular network.Comment: Accepted in JAS
Predicting trend reversals using market instantaneous state
Collective behaviours taking place in financial markets reveal strongly
correlated states especially during a crisis period. A natural hypothesis is
that trend reversals are also driven by mutual influences between the different
stock exchanges. Using a maximum entropy approach, we find coordinated
behaviour during trend reversals dominated by the pairwise component. In
particular, these events are predicted with high significant accuracy by the
ensemble's instantaneous state.Comment: 18 pages, 15 figure
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