European Nonlinear Analysis Workshop
June 26-30, 2017

Nick Stergiou

This workshop is an introduction to nonlinear analysis methods

The purpose is to introduce scientists, clinicians, educators, and students to a variety of nonlinear methods for the analysis of biological time series data.


Nicholas Stergiou, PhD

University of Nebraska Omaha, USA

Ana Diniz, PhD

Faculdade de Motricidade Humana – Universidade de Lisboa, Portugal

João Rocha Vaz, PhD

Universidade Europeia, Lisboa, Portugal

Luís Silva, PhD

Escola Superior de Hotelaria e Turismo do Estoril, Portugal / Instituto Piaget, Almada, Portugal

Orlando Fernandes, PhD

Universidade de Évora, Portugal


Pedro Pezarat-Correia, PhD

Faculdade de Motricidade Humana – Universidade de Lisboa, Portugal

Participants will learn how to use nonlinear methods to analyze real biological data by first learning about the underlying mathematics of each nonlinear method in a simple and friendly way. Participants with varied backgrounds are welcome.

The workshop includes a strong practical component. Instructors will use class discussions and hands-on practice to facilitate understanding of the material covered in the lectures. Additionally, the participants will have the unique opportunity to discuss their own works/projects in individual sessions with Professor Nick Stergiou.


At the beginning of the course, participants are required to show evidence of having:

Knowledge of college algebra, basic trigonometry, basic statistics and basic computer skills (needed to be successful in this workshop). This course is designed to be a comprehensive introduction to nonlinear analysis tools. Researchers, clinicians, and graduate students of all levels are encouraged to attend.

Click Here to Apply


At the end of the course, participants should be able to:

  1. Understand the basic concepts in nonlinear dynamics and chaos.

  2. Describe what each nonlinear method measures.

  3. Understand the basic mathematical algorithm behind each nonlinear method.

  4. Understand parameter selection for each nonlinear analysis method.

  5. Understand how to apply different nonlinear methods to biological time series data.

  6. Know which nonlinear methods are used to analyze biological time series data.

  7. Understand the uses and applications of nonlinear analysis.

  8. Understand limitations of nonlinear methods.

  9. Apply nonlinear analysis in professional settings.


26 June


day 1

Introduction to Dynamical Systems

This day is dedicated to a basic introduction to many important concepts that will be referred to during the rest of the week.

27 June


day 2

Fractal Analysis

This day is dedicated to a discussion of the basis of fractals, what they are, and how they may be analyzed. Several techniques are introduced, including the advantages or shortcomings of the different algorithms.

28 June


day 3

State Space Reconstruction and Lyapunov Exponent

You will be introduced to the concept of state space reconstruction based on Taken's theorem. In addition, the mathematical basis of Lyapunov exponent will be introduced, as well as two algorithms for its calculation for biological time series, Wolf's and Rosenstein's.

29 June


day 4

Entropy and Surrogation

On Day 4, there is a full discussion about entropy, the mathematical basis of entropy, and why it has been "approximated" for use in biology. Different algorithms are discussed including: approximate, sample, and symbolic. In addition, this day includes a discussion of several algorithms of surrogation analysis.

30 June


day 5


The last day of the week will be dedicated to applications of nonlinear analysis.


Hours 26-06-2017
Speakers Nick Stergiou
09:00 - 10:30 Introduction to Variability in Human Movement Fractal Analysis I Reconstruction of state space, correletion dimension Entropy Applications
10:30 - 11:00 Coffee Break
11:00 - 12:30 Introduction to dynamical systems, time series, power spectrum, sampling, filtering, and smoothing Fractal Analysis II Lyapunov exponent Surrogation Applications
12:30 - 13:00 Lunch Time
Speakers Nick Stergiou, Orlando Fernandes, Ana Diniz, João Vaz, Luís Silva
13:30 -15:30 Hands-on Session
15:30 - 16:00
16:00 - 17:30 testing
19:00 - 21:30 Worshop Dinner Farewell Dinner

Topics Covered

  • Introduction to time series
  • Reconstruction of the state space
  • Different Nonlinear Methods
  • Lyapunov Exponent Correlation Dimension
  • Capacity Dimension
  • Fractal Analysis Topics
  • Hurst Exponent
  • Detrended Fluctuation Analysis (DFA)
  • Entropy
  • Shannon’s Entropy
  • Approximate Entropy
  • Sample Entropy
  • Symbolic Entropy
  • Surrogate methods
  • Theiler's Algorithms
  • Pseudoperiodic Surrogate Method
Speaker Nicholas Stergiou

Nicholas Stergiou, PhD

University of Nebraska Omaha, USA

Dr. Nick Stergiou is the Distinguished Community Research Chair in Biomechanics, Chair and Professor of the Department of Biomechanics and Director for the Center for Research in Human Movement Variability at the University of Nebraska at Omaha. His research focuses on understanding variability inherent in human movement. He is an international authority in the study of Nonlinear Dynamics and has published more than 200 peer reviewed articles. Dr. Stergiou’s research spans from infant development to older adult fallers, and has impacted training techniques of surgeons and treatment and rehabilitation techniques of pathologies, such as peripheral arterial disease. He has received more 30 million dollars in personal funding from NIH, NASA, NSF, the NIDRR/US Department of Education, and many other agencies and foundations. He has also several inventions and has procured a private donation of $6 million to build the 23,000 square feet Biomechanics Research Building that has opened in August of 2013. This is the first building dedicated to biomechanics research in the world. His last book is Nonlinear Analysis for Human Movement Variability.

Speaker Orlando Fernandes

Orlando Fernandes, PhD

Universidade de Évora, Portugal

Orlando J. Fernandes, born in 1962 is graduated, Master and PhD, in Sports Science. Currently is Assistant Professor in Évora University, teaching Analyses of Human Movement and Biomechanics in Sports Science and Physical Therapy. His research focus on Biomechanical Analysis of Human Movement specifically related to injury prevention and nonlinear methods applied to human movement. Research topics: Sports and physical therapy Biomechanics, Motor Control, Neuromuscular function, Movement Variability and Data processing.

Speaker Luís Silve

Luís Silva, PhD

Escola Superior de Hotelaria e Turismo do Estoril, Portugal / Instituto Piaget, Almada, Portugal

Luís Silva received his Ph.D. degree in Human Kinetics – Motor Behavior from the Universidade de Lisboa. He is graduated in Sport Science – Physical Condition, and in Management. He is also M.Sc. in Statistics and Mathematics, and in Artistic Performance. Currently, he is professor at the Estoril Institute for Tourism and Hotel Studies, Portugal, and researcher at the Laboratory of Motor Behavior of the Faculty of Human Kinetics, Universidade de Lisboa. His research topics are: physical exercise, kinesiology, and statistics.

Speaker - João Vaz

João Rocha Vaz, PhD

Universidade Europeia, Lisboa, Portugal

João is graduated in Physiotherapy, and completed his PhD in Human Kinetics – Motor Behaviour. Currently, he holds the positions of Adjunct Professor at Atlântica – University Higher Institution, and Assistant Professor at Universidade Europeia – Laureate International Universities. He is also working as a physiotherapist in sports and musculoskeletal disorders. His research interests are related to sports science and medicine, particularly in terms of how variability can improve the injury risk clinical assessment, as well as monitoring the rehabilitation process which ultimately may help in the return to play decision. Keywords: Biomechanics, Sports Medicine, Sports Sciences, Human Movement Variability, Injury Prevention.

Speaker - Ana Diniz

Ana Diniz, PhD

Faculty of Human Kinetics – Universidade de Lisboa, Portugal

Ana Diniz, PhD in Human Kinetics/Mathematical Methods, is Assistant Professor and researcher at the Autonomous Section of Mathematical Methods of the Faculty of Human Kinetics of the University of Lisbon, Portugal. She is also a Full Member of the Interdisciplinary Centre for the Study of Human Performance (CIPER) of this Faculty. Her investigation includes mathematical/statistical methods and formal models mainly related to time series of motor control and interpersonal coordination processes (e.g., fractal analysis, dynamical systems, etc.). She published several book chapters, peer-reviewed papers in scientific journals, and participated in numerous international seminars.


  • Early Registration

    April 5th - May 12th 2017

  • Late Registration

    May 13th - June 16th 2017

Click Here to Apply



250€ (Late registration: 300€).

* A letter from your advisor/mentor stating that you are a student in an academic program must be submitted to Dr. Ricardo Dinis

Professors or researchers affiliated to a university*

350€ (Late registration: 400€).

* Affiliation evidence must be provided by a university or research laboratory and submitted to Dr. Ricardo Dinis


500€ (Late registration: 550€).

Payment must be made online via our website (see APPLICATION).
Participants will receive an invoice after registration is accepted.
*The course fee is NOT refundable.

What's Included

Lecture handouts will be distributed during the course.

Participants are encouraged to use data from their own laboratory during the hands-on sessions, however sample data from the Biomechanics Research Building (University of Nebraska Omaha) and the Laboratory of Motor Behavior (Universidade de Lisboa) will also be provided to practice using the nonlinear tools.

  • Laptops with necessary software (Matlab) are provided during the workshop.

  • Class slides, research articles, and Matlab routines will be provided to the participants.

  • Daily Lunch and snacks.

  • Workshop Dinner (Wednesday) and Farewell Dinner (Friday)

Pratical Information

Universidade de Lisboa
Faculty of Human Kinetics
Estrada da Costa
1499-002 Cruz Quebrada - Dafundo, Portugal
+351 21 4149100

Phone Numbers

Emergency: 112
Taxi Cascais: +351 214 660 101
Lisboa Portela Airport: +351 218 413 500



Accommodation at the Sports Training Center of National Stadium is available upon request. This Training Center is just 100 meters from the Faculty of Human Kinetics. Accommodation in triple rooms, with shared bathroom. Sheets, pillow, blanket and towels included. Price per night with breakfast: 12,5€. Lunch and dinner are available (8€).


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