We applied coupled heterogeneous association rule mining (CHARM), Lasso multivariate regression, and dynamic Bayesian networks to find relationships within a complex system, and explored means with which to obtain a consensus result from the application of such varied methodologies. Using this fusion of approaches, we identified relationships among climate factors that fall into two categories: well-known associations from prior knowledge, and putative links that invite further research.

In order to refine our understanding of how fluid inclusions were trapped in the host minerals, we observed mercury inclusions in quartz samples using X-ray computed tomography technique. We obtained three-dimensional spatial distributions, and analyzed them using fractal and multifractal methods. Given the fractal dimension and its implied mechanism, the mercury-bearing fluids were not primary fluid inclusions, but migrated into the pre-existing cracks of quartz crystals by diffusion processes.

Non-Gaussian joint PDFs and Shannon negentropies allow for nonlinear correlations and synergetic interaction information among random variables. Third-order cross-cumulants (triadic correlations -- TCs) under pair-wise (total or partial) independence are maximized on projections and orthogonal rotations of the full PDF. Fourier analysis allows decomposing TCs as wave resonant triads working as non-Gaussian sources of dynamical predictability. An illustration is given in a minimal fluid model.