Annual Nonlinear Analysis Workshop
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 fashion. Instructors will use class discussions and hands-on practice to facilitate understanding of the material covered in the lectures. Participants with varied backgrounds are welcome.
- At the completion 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.
PREREQUISITES FOR THE COURSE
Knowledge of college algebra, basic trigonometry, basic statistics and basic computer skills are 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.
- Nick Stergiou, PhD
- Sara Myers, PhD
- Vivien Marmelat, PhD
Jenna Yentes, PhD
- Troy Rand, PhDc
- Vivien Marmelat, PhD
PREVIOUS COURSE SCHEDULE
CONTENT AND ORGANIZATION
Day 1: Introduction to Dynamical Systems
This day is a basic introduction to many important concepts that will be referenced during the remainder of the week.
Day 2: Fractal Analysis
This day is 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.
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.
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.
Day 5: Examples and Applications
The last day of the week will cover recurrence quantification analysis as well as cross-recurrence quantification analysis.
Topics covered throughout the week:
|Introduction to time series||Reconstruction of the state
|Different Nonlinear Methods|
|Lyapunov Exponent Correlation
|Capacity Dimension||Fractal Analysis Topics|
|Hurst Exponent||Detrended Fluctuation Analysis
|Shannon’s Entropy||Approximate Entropy||Sample Entropy|
|Symbolic Entropy||Surrogate methods||Theiler’s Algorithms|
|Small Shuffle Surrogate
- Lecture notes: lecture notes 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 will also be provided to practice using the nonlinear tools.
- Laptops with necessary software are provided during the course of the workshop.
- Breakfast and snacks each day.
- $10/day for lunch to use on UNO's campus.
- Participants will be given a copy of all software and slides.
TEXTBOOK AND READINGS
Readings will not be assigned during the course. Prior to arrival in Omaha, workshop participants may be sent research articles of interest which may help facilitate discussion of course topics. To supplement the lecture notes, workshop participants may benefit from reading:
- Stergiou N. (2016). Nonlinear Analysis for Human Movement Variability. CRC PRESS.
- Stergiou N, Decker LM. (2011) Human movement variability, nonlinear dynamics, and pathology: Is there a connection? Hum Mov Sci. 30:(5): 869-888.
- Harrison SJ, Stergiou N. (2015). Complex Adaptive Behavior and Dexterous Action. Nonlinear Dynamics Psychol Life Sci. 2015 Oct;19(4):345-94.
- Stergiou N, Harbourne R, Cavanaugh J. (2006). Optimal movement variability: a new theoretical perspective for neurologic physical therapy. J Neurol Phys Ther. 30(3):120-9.
- Harbourne RT, Stergiou N. (2009). Movement variability and the use of nonlinear tools: principles to guide physical therapist practice. Phys Ther. 89(3):267-82.
Scott Hall (MAP) is available upon request. Under Nebraska state laws the use or possession of alcohol is prohibited on University property. Housing includes sheets, pillow, blanket and towels. Each suite has 4 private bedrooms and one bathroom. The dining hall is on the first floor and arrangements can be made for you to pay cash for meals if desired. Please contact email@example.com for pricing details and to reserve a room. Reservations must be made by May 15, 2017.
For any hotel: Each individual guest must make their own reservations by calling the hotel and requesting the UNO Rate. All reservations must be guaranteed and accompanied by a first night room deposit or guaranteed with a major credit card.
Courtyard Marriott – Aksarben Village
1625 S 67th Street
Omaha, NE 68106 USA
1 - (402) 951-4300
This hotel is within walking distance from UNO or a shuttle can be taken from the Aksarben area to UNO's Dodge Street Campus. Bistro café is available for breakfast, prices range from $4-10 per item.
Standard room has either a king size bed with a sofa bed pull out or two queen size beds.
2. Residence Inn Omaha, Aksarben Village
1717 S 67th St.,
Omaha, NE 68106 USA
This hotel is within walking distance from UNO or a shuttle can be taken from the Aksarben area to UNO's Dodge Street Campus. Modern extended-stay hotel with an indoor pool and a putting green, plus free WiFi & hot breakfast. Suites will sleep 4 – 5 people comfortably.
3. More lodging near UNO (star denote workshop location):
1) Daily complimentary lunches on UNO Campus
2) Biomechanics Research Building Lab visit social (Monday)
3) Downtown Omaha with provided transportation (Wednesday)
4) Social event at KANEKO (Thursday)
5) Pizza Party at Biomechanics Research Building (Friday)
For course information:
Dr. Nick Stergiou
Phone: 1- (402) - 554-3247
Fax: 1- (402) - 554-3693
The course is open to all UNO graduate students. Please use MavLINK and register for BMCH 8100 NONLINEAR ANALYSIS FOR MOVEMENT SCIENCES.
Graduate students outside UNO, the course fee* is $450. A letter from your advisor/mentor verifying that you are a student in an academic program must be submitted to Ms. Laura Campbell at firstname.lastname@example.org.
Professionals, course fee* is $950.
Registration cost includes breakfast and lunch on the UNO campus each day of the workshop, all PowerPoint slides presented, and software. Additionally, laptops with necessary software are provided during the course of the workshop.
*The course fee is NOT refundable.
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