Complex Systems Measurements

1) Bred Vector: tool underlying chaotic systems analysis and ensemble forecasting (NASA profile). "Perturbation" is defined using a Monte Carlo simulation of stochastic environmental noise.

2) Model for converging operations in human-machine interface design (diagrams are from my unfinished work notebook).

3) Model for data assimilation using empirical data and models (data generation box) common to mammalian sleep dynamics. Method taken from: Sedigh-Sarvestani, Schiff, S.J., and Gluckman, B.J. (2012). Reconstructing Mammalian Sleep Dynamics with Data Assimilation. PLoS Computational Biology, 8(11), e1002788.

4) My notes on Empirical Orthogonal Eigenfunctions (EOFs), used extensively in statistical learning, signal processing, and predictive modeling. COURTESY: Lorenz (1956).

5) My notes on belief functions (original formulation), used in theoretical AI. COURTESY: "A Theory of Evidence".

6) Outline of the Hub-Authority score algorithm used in social network analysis. COURTESY: Kleinberg, Journal of the ACM, 46(5), 604-632 (1999).

7) Granger causality: Seth, Artificial Life, 16(2), 179-196 (2010).

a) G-causality: Signal B is dependent upon Signal A.

* if the historical trace of signal A predicting the future of signal B is more statistically significant than the historical trace of signal B predicting the future of signal B.

b) Statistical significance: Bivariate regression model.

where p is the maximum number of lagged observations, A are coefficients, ξ1 and ξ2 are the residuals for each series.

If the variance of ξ1 is reduced by the inclusion of X2, then X2 G-causes X1.

* X1 and  X2 must satisfy covariance stationarity (e.g. unchanging x̄ and δ2).

* magnitude of interaction measured by log ratio of prediction error variances.

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