1,214 research outputs found
Hyperharmonic analysis for the study of high-order information-theoretic signals
Network representations often cannot fully account for the structural richness of complex systems spanning multiple levels of organisation. Recently proposed high-order information-theoretic signals are well-suited to capture synergistic phenomena that transcend pairwise interactions; however, the exponential-growth of their cardinality severely hinders their applicability. In this work, we combine methods from harmonic analysis and combinatorial topology to construct efficient representations of high-order information-theoretic signals. The core of our method is the diagonalisation of a discrete version of the Laplace–de Rham operator, that geometrically encodes structural properties of the system. We capitalise on these ideas by developing a complete workflow for the construction of hyperharmonic representations of high-order signals, which is applicable to a wide range of scenarios
Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package
We introduce the \texttt{pyunicorn} (Pythonic unified complex network and
recurrence analysis toolbox) open source software package for applying and
combining modern methods of data analysis and modeling from complex network
theory and nonlinear time series analysis. \texttt{pyunicorn} is a fully
object-oriented and easily parallelizable package written in the language
Python. It allows for the construction of functional networks such as climate
networks in climatology or functional brain networks in neuroscience
representing the structure of statistical interrelationships in large data sets
of time series and, subsequently, investigating this structure using advanced
methods of complex network theory such as measures and models for spatial
networks, networks of interacting networks, node-weighted statistics or network
surrogates. Additionally, \texttt{pyunicorn} provides insights into the
nonlinear dynamics of complex systems as recorded in uni- and multivariate time
series from a non-traditional perspective by means of recurrence quantification
analysis (RQA), recurrence networks, visibility graphs and construction of
surrogate time series. The range of possible applications of the library is
outlined, drawing on several examples mainly from the field of climatology.Comment: 28 pages, 17 figure
Quantifying dynamical high-order interdependencies from the O-information : an application to neural spiking dynamics
We address the problem of efficiently and informatively quantifying how multiplets of variables carry information about the future of the dynamical system they belong to. In particular we want to identify groups of variables carrying redundant or synergistic information, and track how the size and the composition of these multiplets changes as the collective behavior of the system evolves. In order to afford a parsimonious expansion of shared information, and at the same time control for lagged interactions and common effect, we develop a dynamical, conditioned version of the O-information, a framework recently proposed to quantify high-order interdependencies via multivariate extension of the mutual information. The dynamic O-information, here introduced, allows to separate multiplets of variables which influence synergistically the future of the system from redundant multiplets. We apply this framework to a dataset of spiking neurons from a monkey performing a perceptual discrimination task. The method identifies synergistic multiplets that include neurons previously categorized as containing little relevant information individually
Detecting and quantifying causal associations in large nonlinear time series datasets
Identifying causal relationships and quantifying their strength from observational time series data are key problems in disciplines dealing with complex dynamical systems such as the Earth system or the human body. Data-driven causal inference in such systems is challenging since datasets are often high dimensional and nonlinear with limited sample sizes. Here, we introduce a novel method that flexibly combines linear or nonlinear conditional independence tests with a causal discovery algorithm to estimate causal networks from large-scale time series datasets. We validate the method on time series of well-understood physical mechanisms in the climate system and the human heart and using large-scale synthetic datasets mimicking the typical properties of real-world data. The experiments demonstrate that our method outperforms state-of-the-art techniques in detection power, which opens up entirely new possibilities to discover and quantify causal networks from time series across a range of research fields
How complex climate networks complement eigen techniques for the statistical analysis of climatological data
Eigen techniques such as empirical orthogonal function (EOF) or coupled
pattern (CP) / maximum covariance analysis have been frequently used for
detecting patterns in multivariate climatological data sets. Recently,
statistical methods originating from the theory of complex networks have been
employed for the very same purpose of spatio-temporal analysis. This climate
network (CN) analysis is usually based on the same set of similarity matrices
as is used in classical EOF or CP analysis, e.g., the correlation matrix of a
single climatological field or the cross-correlation matrix between two
distinct climatological fields. In this study, formal relationships as well as
conceptual differences between both eigen and network approaches are derived
and illustrated using exemplary global precipitation, evaporation and surface
air temperature data sets. These results allow to pinpoint that CN analysis can
complement classical eigen techniques and provides additional information on
the higher-order structure of statistical interrelationships in climatological
data. Hence, CNs are a valuable supplement to the statistical toolbox of the
climatologist, particularly for making sense out of very large data sets such
as those generated by satellite observations and climate model intercomparison
exercises.Comment: 18 pages, 11 figure
Quantifying dynamical high-order interdependencies from the O-information: an application to neural spiking dynamics
We address the problem of efficiently and informatively quantifying how
multiplets of variables carry information about the future of the dynamical
system they belong to. In particular we want to identify groups of variables
carrying redundant or synergistic information, and track how the size and the
composition of these multiplets changes as the collective behavior of the
system evolves. In order to afford a parsimonious expansion of shared
information, and at the same time control for lagged interactions and common
effect, we develop a dynamical, conditioned version of the O-information, a
framework recently proposed to quantify high-order interdependencies via
multivariate extension of the mutual information. We thus obtain an expansion
of the transfer entropy in which synergistic and redundant effects are
separated. We apply this framework to a dataset of spiking neurons from a
monkey performing a perceptual discrimination task. The method identifies
synergistic multiplets that include neurons previously categorized as
containing little relevant information individually
Advances of high-order interactions in the human brain: Applications in aging and neurodegeneration.
82 p.The human brain generates a large repertoire of spatio-temporal patterns, which supporta wide variety of motor, cognitive, and behavioral functions. The most acceptedhypothesis in modern neuroscience is that each of these representations is encoded indifferent brain networks. From MRI, networks can be defined anatomically (¿structuralconnectivity¿-SC) or functionally (¿functional connectivity¿-FC). Interestingly, while SCis by definition pairwise (white matter fibers project from one region to another), FC isnot. In this thesis we have focused on the study of high-order interactions (HOI) that occur in functional networks, beyond the existing statistical relationships in pairs of regions.When evaluating the interacting n-plets, from triplets to order n, a novel type of statistical interdependencies appear, namely the synergistic and redundant interactions,which are inaccessible when evaluating interacting pairs. The study of these HOI inthe human brain in aging and neurodegeneration is the purpose of this thesis.Biocruces Bizkai
Aberrant High-Order Dependencies in Schizophrenia Resting-State Functional MRI Networks
The human brain has a complex, intricate functional architecture. While many
studies primarily emphasize pairwise interactions, delving into high-order
associations is crucial for a comprehensive understanding of how functional
brain networks intricately interact beyond simple pairwise connections.
Analyzing high-order statistics allows us to explore the nuanced and complex
relationships across the brain, unraveling the heterogeneity and uncovering
patterns of multilevel overlap on the psychosis continuum. Here, we employed
high-order independent component analysis (ICA) plus multivariate
information-theoretical metrics (-information and -information) to
estimate high-order interaction to examine schizophrenia using resting-state
fMRI. The results show that multiple brain regions networks may be altered in
schizophrenia, such as temporal, subcortical, and higher-cognitive brain
regions, and meanwhile, it also shows that revealed synergy gives more
information than redundancy in diagnosing schizophrenia. All in all, we showed
that high-order dependencies were altered in schizophrenia. Identification of
these aberrant patterns will give us a new window to diagnose schizophrenia.Comment: 7 pages, 4 figures, Accepted to InfoCog@NeurIPS 2023
(https://sites.google.com/view/infocog-neurips-2023/home
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