In this article we describe a new Hermite series based sequential estimator for the Spearman rank correlation coefficient and provide algorithms applicable in both stationary non-stationary settings. To treat setting, introduce novel, exponentially weighted correlation, which allows local nonparametric of bivariate data stream to be tracked. best our knowledge is first algorithm proposed estima...

The Mallows model (MM) occupies a central role in parametric modelling of ranking data to learn preferences population judges. Despite the wide range metrics for rankings that can be considered specification, choice is typically limited Kendall, Cayley or Hamming distances, due closed-form expression related normalizing constant. This work instead focuses on with Spearman distance (MMS). A nove...

Identification of programs for computable functions from their graphs by algorithmic devices is a well studied problem in learning theory. Freivalds and Chen consider identification of ‘minimal’ and ‘nearly minimal’ programs for functions from their graphs. Freivalds showed that there exists a Gödel numbering in which only finite classes of functions can be identified using minimal programs. To...

Kolmogorov complexity is a measure of the information contained in a binary string. We investigate here the notion of quantum Kolmogorov complexity, a measure of the information required to describe a quantum state. We show that for any definition of quantum Kolmogorov complexity measuring the number of classical bits required to describe a pure quantum state, there exists a pure n-qubit state ...

A novel topological and computational method for ‘motion’ is described. Motion is constrained by inequalities in terms of Kolmogorov Complexity. Causality is obtained as the output of a high-pass filter, passing through only high values of Kolmogorov Complexity. Motion under the electromagnetic field described with immediate relationship with G2 Holonomy group and its corresponding dense free 2...

Identification of programs for computable functions from their graphs by algorithmic devices is a well studied problem in learning theory. Freivalds and Chen consider identification of ‘minimal’ and ‘nearly minimal’ programs for functions from their graphs. To address certain problems in minimal identification for Gödel numberings, Freivalds later considered minimal identification in Kolmogorov...

The Chapman-Kolmogorov equation with fractional integrals is derived. An integral of fractional order is considered as an approximation of the integral on fractal. Fractional integrals can be used to describe the fractal media. Using fractional integrals, the fractional generalization of the Chapman-Kolmogorov equation is obtained. From the fractional Chapman-Kolmogorov equation, the Fokker-Pla...

The Chapman–Kolmogorov equation with fractional integrals is derived. An integral of fractional order is considered as an approximation of the integral on fractal. Fractional integrals can be used to describe the fractal media. Using fractional integrals, the fractional generalization of the Chapman–Kolmogorov equation is obtained. From the fractional Chapman–Kolmogorov equation, the Fokker–Pla...