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Predicting Critical Transitions

This report explores predicting critical transitions across various systems, including lake eutrophication, stock markets, and neurological conditions such as epilepsy and depression. It highlights successful case studies and offers a unique analysis of baseball dynamics as a model for understanding critical transitions. The findings suggest that early warning signs often don't align with traditional metrics, calling for innovative approaches to data analysis and the identification of underlying structures. The report emphasizes future research directions, including assessment of chaotic signals in baseball performance.

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Predicting Critical Transitions

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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 AnalysisClassical

  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/2012/09/19/science.1227079.DC1/1227079s1.mov http://www.sciencemag.org/content/suppl/2012/09/19/science.1227079.DC1/1227079s2.mov http://www.sciencemag.org/content/suppl/2012/09/19/science.1227079.DC1/1227079s3.mov (Sugihara, 2012)

  16. Underlying Structure?

  17. Analyzing Chaotic Signals Cont…

  18. Conclusions and Next Steps • Conclusions • 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 • Larger dimension structures do appear to exist • -> Even 2D structures seem to exist in time delay for many players Next Steps • Preform a more comprehensive analysis on chaotic signals in baseball • Compare trends for dimensionality of streaky players vs non-streaky • See if there are any other metrics available to further refine phase space • 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

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