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The module "Time Series Networks" constitutes part of the course "Statistical Analysis of Networks" of the postgraduate program "Web Science" organized by the Department of Mathematics of AUTh.
Syllabus, suggested literature
The module is about the construction of networks from multivariate time-series, where each time-series defines the node, and the association of two time-series determines the link between the respective nodes.
The main objective of the module is the study of different types of association (connection / link) between two time series and the networks derived from such associations.
The module is divided in three parts and each part is taught at a 4-hour course (see Course transperancies).
Association networks, correlation networks, cross-correlation, partial cross-correlation, parametric and non-parametric tests of significance of correlation, correlation network from time-series. Examples.
Uni-variate time-series (stationarity, time series decomposition, detrending), autocorrelation and mutual information, test for independence, linear autoregressive models. Bi-variate time-series, cross-correlation and cross-mutual information. Examples.
Linear stochastic and nonlinear deterministic systems. Correlation measures. Construction of correlation networks from time series. Examples.
Nonlinear and nonlinear causality measures. Connectivity networks using causality measures on multivariate time series. Applications to neuroscience and finance.
Networkd from time series in Matlab. Practical application of methods presented in the first four parts using the computational software Matlab.
J. Pearl (1998), "Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference", Morgan Kaufmann.
,"Statistical Analysis of Network Data"
Horvath, S. (2011) Weighted Network Analysis,
Applications in Genomics and Systems Biology. New York:
Fornito, A., Bullmore, E. T. & Zalesky, A. (2016)
Fundamentals of Brain Network Analysis, 1st edn.
Cambridge, Massachusetts, United States: Academic Press, Elsevier
Suggested edited collection of papers:
Reggiani and P. Nijkamp (2006), "Spatial Dynamics, Networks And Modelling
(New Horizons in Regional Science Series)" ,
,Edward Elgar Publishing.
,"Adaptive Networks: Theory, Models and Applications (Understanding Complex Systems)", Springer.
,"Complex Networks: Results of the 1st International Workshop on Complex Networks (CompleNet 2009) (Studies in Computational Intelligence)", Springer.
,"Dynamics On and Of Complex Networks: Applications to Biology, Computer Science, and the Social Sciences (Modeling and Simulation in Science, Engineering and Technology)"
S. K. Dana, P. K. Roy, and J. Kurths, Eds., Complex Dynamics in Physiological Systems: From Heart to Brain, ser. Series: Understanding Complex Systems. Berlin / Heidelberg: Springer, 2009
To view the networks, the software pajek will be used (see http://pajek.imfm.si)
Exercises and computer programs
To view multiple time series in a graphical Matlab environment you may use the toolkit Measures of Time Series Analysis (MATS) that can be downloaded at http://eeganalysis.web.auth.gr (Software).
All Matlab programs for the course in a compressed file: matlab.zip.
Data files in a compressed file: Data.zip
Course examination and marking
The mark for the module "Time series networks" will be determined based on the project the students have to deliver, formed in groups of up to two students, as well as their presence and discussion at the presentation of the projects.
The project will be given at the end of the course.
The teams of one or two students should send the presentation (e.g. in PowerPoint, LaTeX) by e-mail to the teacher (firstname.lastname@example.org) not later than the last day/night before the date of "examination". The examination will take place on 13/2/2019, at 17.00, at the Math computer lab, that is there will be presentations of 8 minutew maximum followed by questions and discussions.