Markov random fields provide a compact representation of joint probability distributions by representing its independence properties in an undirected graph. The well-known Hammersley-Clifford theorem uses these conditional independences to factorize a Gibbs distribution into a set of factors. However, an important issue of using a graph to represent independences is that it cannot encode some t...

The purpose of this research is to establish the variety of expanded narratives generated by children aged 6 based on a series of pictures, which is determined by his or her individual neuropsychological characteristics, as well as by the maturity of perception and of processing visual-spatial information. The material of the research is a number of stories produced by Russian children based on...

Using the recently discovered Clifford statistics we propose a simple model for the grand canonical ensemble of the carriers in the theory of fractional quantum Hall effect. The model leads to a temperature limit associated with the permutational degrees of freedom of such an ensemble. We also relate Schur’s theory of projective representations of the permutation groups to physics, and remark o...

The String Uncertainty Relations have been known for some time as the stringy corrections to the original Heisenberg's Uncertainty principle. In this letter the Stringy Uncertainty relations, and corrections thereof, are explicitly derived from the New Relativity Principle that treats all dimensions and signatures on the same footing and which is based on the postulate that the Planck scale is ...

The swing-twist decomposition is a standard routine in motion planning for humanoid limbs. In this paper the decomposition formulas are derived and discussed in terms of Clifford algebra. With the decomposition one can express an arbitrary spinor as a product of a twist-free spinor and a swingfree spinor (or vice-versa) in 3-dimensional Euclidean space. It is shown that in the derived decomposi...