by Damian Kelty-Stephen, PhD, Grinnell College, USA

This workshop will review general concerns in investigating data suspected to arise from self-organizing cascade processes. Cascades constitute a generic class of random variables whose development depends upon the interactions of interdependent factors across very many scales. They include all those models entailing the successive splittings, spreadings, or clusterings of events. Cascade processes generate temporal and/or spatial patterns with deeply knit texture, and whereas non-cascade processes lend themselves to simple linear description, the subtle texture of cascade processes present a daunting challenge to classic conceptions of dimensionality and diffusion implicit in linear statistical methods. Two features highlight this challenge: 1) scale invariance and 2) nonlinear dependence. This workshop will review these two concepts and present a rudimentary introduction to the fractal and multifractal methods designed to diagnose and describe these features in empirical data.

The workshop will take place at the Interacting Minds Centre.

Tuesday, June 3rd (9:00-11:00 & 13:00-16:00)

- Preliminary remarks on self-organization and cascades
- Statistical issues of dimensionality and diffusion: Linear approaches
- Problems of scale
- Scale invariance in probability distributions and time series
- Basic fractal analysis: Exploring the distance matrix and the variance

Wednesday, June 4th (10:00-12:00 & 13:00-16:00)

- Origins of scaling: Linear approximations and cascades
- Multifractality: generalized scale invariance
- Proportion-based multifractality
- Variance-based methods for multifractality

Thursday, June 5th (10:00-12:00 & 13:00-16:00)

- Recap
- Implications of multifractal or cascade-related results for theory
- Examples from timing, reading behavior, and postural sway
- Analysis of attendees’ data

The workshop is hosted by MINDLab, and there is no registration fee. Lunch and coffee will be provided.
You will need to bring your own laptop to participate in the data analyses training.

REGISTRATION

If you want to participate, send an email to Sebastian Wallot (sewa@hum.au.dk)  We have room for 20 participants, first come - first serve.

RESOURCES

- An introduction to fractals can be found here.
- A basic tutorial for simple fractal analysis in time-series data can be found here.
- A basic tutorial for multifractal analysis in time-series data can be found here.