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Title: Network theory approaches for the analysis of ordered data
Author: Flanagan, Ryan
ISNI:       0000 0004 9355 4255
Awarding Body: Queen Mary University of London
Current Institution: Queen Mary, University of London
Date of Award: 2020
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Graphs are mathematical structures comprised of a set of nodes connected by edges, and network science is the application of graph theory to real world data. Networks are used as a model to analyse how entities, either individual actors, or complex systems, interact with one another. The research here will consist of extracting networks (we will use the terms \graph" and \network" interchangeably) from ordered series, which we will focus on series ordered by time. We will either do this with the aid of the visibility graph, which is a method, based on visibility, for mapping a time series in to a graph, or through estimating the wavelet correlation, a more conventional method used in neuroscience. The aim is to describe the structure of time series and their underlying dynamical properties in graphtheoretical terms, and then using this motivation to analyse large data sets spanning several disciplines. We will describe a method, using the visibility graph, for quantifying reversibility of non-stationary processes and apply this method to a large nancial data set, with the intent of ranking companies based on their irreversibility. We also use the visibility graph to develop a method which e ciently quanti es the asymmetries between minima and maxima in time series, and we then apply the method to a variety of data sets. Continuing with the theme of visibility, we study the spectral properties of visibility graphs extracted from trajectories of the logistic map undergoing a period-doubling route to chaos (known as the Feigenbaum scenario). Finally, we will use wavelet correlation to construct networks from fMRI time series, and examine community structure with the aim of di erentiating between brain networks of patients with schizophrenia from control subjects. The general format throughout this thesis will start with theory, followed by extensive numerical simulations, which we can then apply the methods to real data sets.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available