Neuman, Y, et. al., "Change in the Embedding Dimension as an Indicator of an Approaching Transition" (2014)

Interesting article about a novel method for predicting the onset of a change.  Summarized in Conclusions below.

https://drive.google.com/open?id=0B9oPg7GYw1qnSHladDN1NFRvVE0


Conclusions 

In this paper, we introduce a new method for identifying an approaching transition in behavioral data. The idea is that the complexity of behavioral signals usually resides in what social scientists describe as ‘‘context’’, or what [22] in his classical work describes as the totality of signals that directed the behavior of the organism. A transition in the behavior of the signal is expected if the context in which this signal is embedded undergoes changes in itself. Using changes in the embedding dimension as an indication of an approaching transition is therefore a shift from focusing on the dynamics of the signal to the dynamics of the meta-system in which it is subordinated. This idea is here tested for the first time and currently under further developments. We also see a wide applicability of the suggested optimal embedding transition detection (OPERAND) approach. Changes in embedding as well as transitivity dimension might also be able to detect important transition points, e.g, in the climate system or in financial markets [5].

Thoughts about dynamical systems, chaos and patterns

From reading, viewing online course material, speaking with Pavan, his engineering students, Julian, others and my own experience, here are a few disjointed observations about dynamical systems, chaos, patterns, etc.

  • In the engineering framework, we look at time-series data as, well, time-series data. We run an experiment, make observations, collect data, use mathematical tools to evaluate it, communicate the results, and draw conclusions. This is generally a sequential process over time.
  • In the AME framework, we are working real-time. We are processing video, audio, movement, etc. signals as they occur (or closely to it) and creating output that is interesting. I've come to view the human as a multi-dimensional sensory system.
  • Both the engineering and the AME frameworks iterate information to create meaning but the timeline is vastly different between the two approaches.
  • Dynamical systems use time-series data. There needs to be enough data for evaluation.
  • It is absolutely possible to create patterns, quasi-chaotic data streams, and chaotic data streams real-time using (a) closed form analytical models, (b) evolving signals with feedback (i.e., interaction), or (c) a combination of both.
  • Creating predictive tools to permit AME researchers to design transitions in/out/around chaos (i.e., bifurcations) would be highly interesting in situations where the signals are multidimensional, complex and not necessarily intentional.
  • This is where the Lyapunov exponents may be of value. How to evaluate them over sufficiently large data streams without bogging down the action? What is good enough? What does this look like?
  • My guess is that the outcome will contend with tradeoffs between time and accuracy.
  • I'm beginning to see patterns as the lower energy condition of complex systems. I believe that entrainment and synchronicity are easier than chaos. The most interesting region may be quasi-chaotic systems that dip in and out of patterns on one hand, and chaos on the other. I think humans like to dip in and out, traveling between pattern and quasi-chaotic modes. Consciousness lives in quasi-chaos.


My goal this week is to continue to look at this and come up with a simple sand box for experimenting with these methods and ideas. Running a bit open-loop so I appreciate your thoughts, reactions and feedback.

NSF GFRP notes and deadlines, etc.

Notes

The NSF web site is down right now due to a power outage, so I'll check back on the current solicitations on Monday. 

I think I'm eligible because it has been >2 years since I completed my last degree or certificate, and I have been a full-time student in my current grad program for < 12 months.


Questions

1.  I'm not sure what area of study to list.  Would this be Computer and Information Science and Engineering?  Can we make this argument since my degree will be a joint degree between Herberger and Fulton?

From looking at the GRFP guidelines, it seems that yes CISE would be a good primary target with video as a key part.  The second target could be Mathematics (topology).



2017 GRFP Deadlines

All applications are due at 5:00 p.m. local time, as determined by the applicant’s mailing address.

October 24, 2016 (Monday)

  • Geosciences
  • Life Sciences

October 25, 2016 (Tuesday)

  • Computer and Information Science and Engineering
  • Engineering
  • Materials Research

October 27, 2016 (Thursday)

  • Psychology
  • Social Sciences
  • STEM Education and Learning

October 28, 2016 (Friday)

  • Chemistry
  • Mathematical Sciences
  • Physics and Astronomy

November 3, 2016 (Friday)

  • All reference letters must be received by 5:00 p.m., Eastern Time Zone

  

Important Dates

→ Late July/Early August - Program Solicitation Released

→ Early August - FastLane Application Opened

→ Late October/Early November - Application Deadlines (determined by discipline)

→ Early April - Awards Announced

→ Early May - Fellows Acceptance Deadline