Luiza Ochnio

Persistent Correlations in Major Indices of the World Stock Markets

Time-dependent cross-correlation functions have been calculated between returns of the major indices of the world stock markets. One-, two-, and three-day shifts have been considered. Surprisingly high and persistent-in-time correlations have been found among some of the indices. Part of those correlations can attributed to the geographical factors, for instance, strong correlations between two major Japanese indices have been observed. The reason for other, somewhat exotic correlations, appear to be as much accidental as it is apparent. It seems that the observed correlations may be of practical value in the stock market speculations.

Application of Automated Theorem-Proving to Philosophical Thought: Spinoza’s Ethics

We have applied the automatic theorem-prover Prover9 to prove first eleven theorems of Part 1 of Benedict de Spinoza’s Ethics. We have used a previous formalization of that segment developed by Blum and Malinovich. We have found Prover9 to be very efficient, providing proofs in tens of miliseconds. It appears that the only, but fundamental, limitation for testing philosophical reasoning is related to the difficulty of unique formalization.

Shapes of leaves with parallel venation. Modelling of the Epipactis sp. (Orchidaceae) leaves with the help of a system of coupled elastic beams

Static properties of leaves with parallel venation, with particular emphasis on the genus EpipactisZinn, 1757 (Orchidaceae, Neottieae) have been modelled with coupled quasi-parallel elastic “beams.” The non-linear theory of strongly bended beams have been employed. The resulting boundary-value problem has been solved numerically with the help of the finite-difference method. Possible dislocations resulting in additional Dirac-delta like forces have been take into account. Morphological similarity of the model and real leaves has been obtained. In particular, the concentrated forces have been shown to cause undulation in the leaves.

Clusterization of Indices and Assets in the Stock Market

K-means clustering algorithm has been used to classify major world stock market indices as well as most important assets in the Warsaw stock exchange (GPW). In addition, to obtain information about mutual connections between indices and stocks, the Granger-causality test has been applied and the Pearson R correlation coefficients have been calculated. It has been found that the three procedures applied provide qualitatively different kind of information about the groups of financial data. Not surprisingly, the major world stock market indices appear to be very strictly interconnects from the point of view of both Granger-causality and correlation. Such connections are less transparent in the case of individual stocks. However, the “cluster leaders” can be identified which leads to the possibility of more efficient trading.