School on Nonlinear Time Series Analysis and Complex Networks in the Big Data Era

February 19 – March 2, 2018

São Paulo, Brazil


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This two-week school will provide participants (mainly PhD students and postdocs) a broad overview of the state-of-the-art in the field of Big Data analysis tools, including the most recent advances in complex networks and methods for the analysis of large time series and datasets, focusing on nonlinear dynamics and network science.

Topics to be covered include:

  • Time delay embedding and phase space reconstruction
  • Tools for chaotic systems (Lyapunov exponents, fractal dimensions)
  • Symbolic encoding techniques
  • Information-theory measures (block entropy, permutation entropy, mutual information, conditional mutual information)
  • Complexity measures
  • Extreme value analysis
  • Structure of Networks
  • Mapping time series to networks (recurrence networks, visibility graphs)
  • From Big data to Networks: Compression sampling, dynamical modal decomposition

Introductory lecturers will be followed by hands-on sessions where the students will have the opportunity to work in small-groups, on real-world datasets. In these sessions the participants will gain practical experience in applying the nonlinear “big-data” tools to the observed output signals of complex systems. This school is part of the topics in Nonlinear Science: Fundamentals and Applications.  There is no registration fee and limited funds are available for travel and local expenses for participants from academic or research institutions.


  • Hilda A. Cerdeira (IFT-UNESP, Brazil)
  • Jesus Gomez-Gardenes (University of Zaragoza, Spain)
  • Cristina Masoller (Universitat Politecnica de Catalunya-Terrassa, Spain) 



  • Alex Arenas (Universitat Rovira i Virgili, Spain)
  • Murilo Baptista (University of Aberdeen, UK)
  • Ernesto Estrada (University of Strathclyde, UK)
  • Marta Gonzalez (MIT, U.S.A.)
  • Osvaldo Rosso (Universidade Federal de Alagoas, Brazil & CONICET, Argentina)

Objectives: This short course will provide participants a broad overview on the new tools based on Information Theory for the time series datasets characterization and identification of its dynamical behavior


1)      Time series and Information Theory. Chaotic dynamics as information sources.

2)      Information Theory quantifiers: Shannon entropy and Fisher Information for continuous and discrete PDFs.

3)      Information Theory quantifiers: Statistical Complexity. Simple and complex. Cristal and ideal gas. Meaning of Complexity. Statistical Complexity, C=HxQ. Disorder H. Disequilibrium Q. Maximum and minimum of Generalized Statistical Complexity. Application to logistic map.

4)      Time series & how to associate a PDF.

5)      PDF – frequency counting. Shakespeare and other English Renaissance authors.

6)      PDF – histogram and amplitudes. The logistic map.

7)      PDF – frequency (Fourier Transform) and frequency bands (Wavelet Transform) representation. EEG tonic-clonic epileptic records.

8)      PDF – ordinal patterns (Bandt-Pompe methodology). Chaos, noise and 1/fk noise. Logistic map and white noise. Chaotic dynamics plus additive noise.

9)      The Amigó paradigm: forbidden/missing patters.

10)  PDF – Horizontal Visibility Graph. Distinguishing chaos from noise. The lambda rule. PDF-HVG and Shannon-Fisher plane.

11)  Causal Fisher Information. Shannon-Fisher plane.

Applications: Stochastic resonance. Econophysics. Neuronal activity. Pseudo Random Generators. Electric load and vehicle behavior. Classical-quantum transition. El Niño/Southern Oscillation. Lasers dynamics.Handwritten signatures.





Click here for online application

Application deadline: December 1, 2017

School Program


Additional Information