Network Analysis of Time Series: Novel Approaches to Network Neuroscience

Varley, Thomas F.; Sporns, Olaf

doi:10.3389/fnins.2021.787068

Cited by 22 publications

(24 citation statements)

References 151 publications

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“…Circuit analysis is unavoidable in electrical engineering for understanding and analysing electrical systems. The present work discovers the possibility of applying graph theory in circuit analysis, considering the most fundamental rectifier circuit as an https://www.indjst.org/ example as the methodology can be extended for analysing any signal (24)(25)(26)(27) . The output of full-wave and half-wave rectifiers without and with capacitor filters (0.22, 1, 10, 100, 1000 µF) recorded in the digital storage oscilloscope are shown in Figures 2 and 3 , respectively.…”

Section: Resultsmentioning

confidence: 99%

Markov Chain: A Novel Tool for Electronic Ripple Analysis

Vijesh¹,

Kumar²,

Swapna³

et al. 2022

IJST

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Objective: To delineate a novel surrogate approach to analyse the ripple component by constructing a complex network using the Markov model. Methods: Adjacency matrices (A) are constructed from the digital storage oscilloscope output signal of the Full-Wave (FWR) and Half-Wave Rectifiers (HWR) without and with a filter. The centrality measures -indegree, outdegree, in closeness, out closeness, Weighted Network Clustering Coefficient (WNCC) -are also computed for the Markov chain. Findings: With the increase of filter capacitance, more elements in the adjacency matrix become zero. Finally, only one matrix element corresponding to A 10,10 remains nonzero for FWR and A 20,20 for HWR, indicating the total rectification of the signal at 10 volts. The Markov chain analysis shows that as the ripple component decreases, the number of unconnected nodes increases and the self-loop of the last node increases. For the rectifier output without filtering, it is found that all the nodes are interconnected through edges. The greater the filtering efficiency, the greater the indegree and outdegree, and the lesser the incloseness, outcloseness and WNCC measures.

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Section: Resultsmentioning

confidence: 99%

Markov Chain: A Novel Tool for Electronic Ripple Analysis

Vijesh¹,

Kumar²,

Swapna³

et al. 2022

IJST

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“…We then correlated every TR against every other frame to construct a weighted, signed recurrence network [41], which we could then cluster using the MRCC algorithm [32] (Fig. 4G).…”

Section: Redundancy-synergy Gradient and Time-resolved Analysismentioning

confidence: 99%

Partial entropy decomposition reveals higher-order structures in human brain activity

Varley¹,

Pope²,

Puxeddu³

et al. 2023

Preprint

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The standard approach to modeling the human brain as a complex system is with a network, where the basic unit of interaction is a pairwise link between two brain regions. While powerful, this approach is limited by the inability to assess higher-order interactions involving three or more elements directly. In this work, we present a method for capturing higher-order dependencies in discrete data based on partial entropy decomposition (PED). Our approach decomposes the joint entropy of the whole system into a set of strictly non-negative partial entropy atoms that describe the redundant, unique, and synergistic interactions that compose the system's structure. We begin by showing how the PED can provide insights into the mathematical structure of both the FC network itself, as well as established measures of higher-order dependency such as the O-information. When applied to resting state fMRI data, we find robust evidence of higher-order synergies that are largely invisible to standard functional connectivity analyses. This synergistic structure is symmetrical across hemispheres, largely conserved across individual subjects, and is distinct from structural features based on redundancy that have previously dominated FC analyses. Our approach can also be localized in time, allowing a frame-by-frame analysis of how the distributions of redundancies and synergies change over the course of a recording. We find that different ensembles of regions can transiently change from being redundancy-dominated to synergy-dominated, and that the temporal pattern is structured in time. These results provide strong evidence that there exists a large space of unexplored structures in human brain data that have been largely missed by a focus on bivariate network connectivity models. This synergistic "shadow structures" is dynamic in time and, likely will illuminate new and interesting links between brain and behavior. Beyond brain-specific application, the PED provides a very general approach for understanding higher-order structures in a variety of complex systems.

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“…The relationship between dynamic graphs, spectral theory and TDA is examined further in Bronski and DeVille (2014) and in Xu et al (2020). Relationships with time series networks generated by TDA is treated in Varley and Sporns (2022).…”

Section: The Dynamic Casementioning

confidence: 99%

“…(2020). Relationships with time series networks generated by TDA is treated in Varley and Sporns (2022).…”

Section: Dynamic Graphsmentioning

confidence: 99%

Some recent trends in embeddings of time series and dynamic networks

Tjøstheim

Jullum

Løland

2023

Journal Time Series Analysis

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We give a review of some recent developments in embeddings of time series and dynamic networks. We start out with traditional principal components and then look at extensions to dynamic factor models for time series. Unlike principal components for time series, the literature on time‐varying nonlinear embedding is rather sparse. The most promising approaches in the literature is neural network based, and has recently performed well in forecasting competitions. We also touch on different forms of dynamics in topological data analysis (TDA). The last part of the article deals with embedding of dynamic networks, where we believe there is a gap between available theory and the behavior of most real world networks. We illustrate our review with two simulated examples. Throughout the review, we highlight differences between the static and dynamic case, and point to several open problems in the dynamic case.

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Network Analysis of Time Series: Novel Approaches to Network Neuroscience

Cited by 22 publications

References 151 publications

Markov Chain: A Novel Tool for Electronic Ripple Analysis

Markov Chain: A Novel Tool for Electronic Ripple Analysis

Partial entropy decomposition reveals higher-order structures in human brain activity

Some recent trends in embeddings of time series and dynamic networks

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