Causal Patterns: Extraction of multiple causal relationships by Mixture of Probabilistic Partial Canonical Correlation Analysis

In this paper, we propose a mixture of probabilistic partial canonical correlation analysis (MPPCCA) that extracts the Causal Patterns from two multivariate time series. Causal patterns refer to the signal patterns within interactions of two elements having multiple types of mutually causal relationships, rather than a mixture of simultaneous correlations or the absence of presence of a causal relationship between the elements. In multivariate statistics, partial canonical correlation analysis (PCCA) evaluates the correlation between two multivariates after subtracting the effect of the third multivariate. PCCA can calculate the Granger Causal- ity Index (which tests whether a time-series can be predicted from an- other time-series), but is not applicable to data containing multiple partial canonical correlations. After introducing the MPPCCA, we propose an expectation-maxmization (EM) algorithm that estimates the parameters and latent variables of the MPPCCA. The MPPCCA is expected to ex- tract multiple partial canonical correlations from data series without any supervised signals to split the data as clusters. The method was then eval- uated in synthetic data experiments. In the synthetic dataset, our method estimated the multiple partial canonical correlations more accurately than the existing method. To determine the types of patterns detectable by the method, experiments were also conducted on real datasets. The method estimated the communication patterns In motion-capture data. The MP- PCCA is applicable to various type of signals such as brain signals, human communication and nonlinear complex multibody systems.Comment: DSAA2017 - The 4th IEEE International Conference on Data Science and Advanced Analytic

Dynamics of postcritically bounded polynomial semigroups II: fiberwise dynamics and the Julia sets

We investigate the dynamics of semigroups generated by polynomial maps on the Riemann sphere such that the postcritical set in the complex plane is bounded. Moreover, we investigate the associated random dynamics of polynomials. Furthermore, we investigate the fiberwise dynamics of skew products related to polynomial semigroups with bounded planar postcritical set. Using uniform fiberwise quasiconformal surgery on a fiber bundle, we show that if the Julia set of such a semigroup is disconnected, then there exist families of uncountably many mutually disjoint quasicircles with uniform dilatation which are parameterized by the Cantor set, densely inside the Julia set of the semigroup. Moreover, we give a sufficient condition for a fiberwise Julia set $J_{\gamma}$ to satisfy that $J_{\gamma}$ is a Jordan curve but not a quasicircle, the unbounded component of the complement of $J_{\gamma}$ is a John domain and the bounded component of the complement of $J_{\gamma}$ is not a John domain. We show that under certain conditions, a random Julia set is almost surely a Jordan curve, but not a quasicircle. Many new phenomena of polynomial semigroups and random dynamics of polynomials that do not occur in the usual dynamics of polynomials are found and systematically investigated.Comment: 24 pages, 1 figure. Published in J. London Math. Soc. (2) 88 (2013) 294--318. See also http://www.math.sci.osaka-u.ac.jp/~sumi/welcomeou-e.htm

Lane formation in a lattice model for oppositely driven binary particles

Oppositely driven binary particles with repulsive interactions on the square lattice are investigated at the zero-temperature limit. Two classes of steady states related to stuck configurations and lane formations have been constructed in systematic ways under certain conditions. A mean-field type analysis carried out using a percolation problem based on the constructed steady states provides an estimation of the phase diagram, which is qualitatively consistent with numerical simulations. Further, finite size effects in terms of lane formations are discussed.Comment: 6 pages, 8 figures,v2; some corrections in the text have been mad

Z-actions on AH algebras and Z^2-actions on AF algebras

We consider Z-actions (single automorphisms) on a unital simple AH algebra with real rank zero and slow dimension growth and show that the uniform outerness implies the Rohlin property under some technical assumptions. Moreover, two Z-actions with the Rohlin property on such a C^*-algebra are shown to be cocycle conjugate if they are asymptotically unitarily equivalent. We also prove that locally approximately inner and uniformly outer Z^2-actions on a unital simple AF algebra with a unique trace have the Rohlin property and classify them up to cocycle conjugacy employing the OrderExt group as classification invariants.Comment: 24 page