Predicting Critical Transitions

This report delves into the concept of critical transitions and explores its implications in diverse fields, showcasing case studies and successful examples. From ecological shifts to neurological conditions, learn how predicting critical transitions can offer valuable insights. Discover the use of toy models and population-based data parameters in analyzing complex systems, and explore the intersection of critical transitions with baseball analytics. Gain a dynamic systems perspective on understanding critical transitions as a crucial element in different scenarios.

• Critical transitions
• Case studies
• Ecological shifts
• Neurological conditions
• Baseball analytics

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1. Predicting Critical Transitions Final Report Keith Heyde

2. Diks et al. 2012

3. What Are Critical Transitions?

4. Predicting Critical Transitions: Case Study Lake Eutrophication Wang et al. 2012

5. Previous Successful (Published) Examples Stock Market (mixed results) Climate Flickering and critical slowing at Younger Dryas Cold Period Ecosystems- Vegetation and Desertification Agri/Aquaculture- Fishing stocks Neurological- Epilepsy/ Depression Leemput et al. 2013

6. Toy Models- Population Based

7. Population Data Parameters: public good production (B2) Multiple equilibria (including zero) Sample data processing within MATLAB (autocorrelation and variance analysis) MASSIVE FAILURE Tanouchi et al. 2012

8. When the going gets tough The tough take on a new project! And hit it out of the park?

9. Baseball Crash Course (for our purposes) Players come up to the plate during the game Players try and hit the ball Players either get a hit or get out Players are commonly evaluated offensively by their batting average Is this a good metric?

10. Baseball Streak Analysis Classical

11. Turn Batting into a Signal!

12. A Dynamical Systems Motivation Batting Batting Games Played Games Played

13. Real Player Data

14. Zoom in!

15. Underlying Structure? Motivation: Cool Videos Pay Attention http://www.sciencemag.org/content/suppl/201 2/09/19/science.1227079.DC1/1227079s1.mov http://www.sciencemag.org/content/suppl/201 2/09/19/science.1227079.DC1/1227079s2.mov http://www.sciencemag.org/content/suppl/201 2/09/19/science.1227079.DC1/1227079s3.mov (Sugihara, 2012)

16. Underlying Structure? Time Delay Lag 4 Change in BA vs BA 0.7 0.4 0.6 0.3 0.5 0.2 0.4 0.1 0.3 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.2 -0.1 0.1 -0.2 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 -0.3

17. Analyzing Chaotic Signals Cont

18. Conclusions and Next Steps Conclusions Next Steps Preform a more comprehensive analysis on chaotic signals in baseball Early warning signs for bistable critical transitions do not seem to fit for baseball hitting signal Multi-dimensionality of signal Not enough granularity of data Compare trends for dimensionality of streaky players vs non-streaky See if there are any other metrics available to further refine phase space Larger dimension structures do appear to exist -> Even 2D structures seem to exist in time delay for many players Examine network dynamics of team to construct team dynamical system

19. Potential Phase Space Reconstruction

20. Thanks! Thanks to Prof. Ross and all of my reviewers