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The statistical modeling was used in the analysis of structures containing heterogeneous masses. The statistical probability of a system of coupled oscillators was found taking into account the mass dependence of energy levels. It is essentially a new approach. Both the low as well as high temperature expressions for diffusion coefficient were found. Comparison with experimental data gave satisfactory agreement.

In a recent paper several species of octagonal patterns have been introduced with the help of a construction which allows us to derive them by means of inflation rules. Non-deterministic patterns can be generated by composition of the inflation rules. In this paper we show how a similar construction produces patterns with hexagonal symmetry. The non-deterministic rhombus–triangle tilings are obtained by local rearrangements of tiles which are included in the inflation rules. This property allows to compute the configurational entropy.

The ubiquitous presence of complexity in nature makes it necessary to seek new mathematical tools which can probe physical systems beyond linear or perturbative approximations. The random matrix theory is one such tool in which the statistical behavior of a system is modeled by an ensemble of its replicas. This paper is an attempt to review the basic aspects of the theory in a simplified language, aimed at students from diverse areas of physics.

An interpretation of Icosahedral Danzer tilings in terms of algebraic substitutions is used in order to study the Fourier transform of suitable mass distributions. Numerical results are obtained for a mass distribution placed on vertex positions.

The ability to calculate precise likelihood ratios is fundamental to science, from Quantum Information Theory through to Quantum State Estimation. However, there is no assumption-free statistical methodology to achieve this. For instance, in the absence of data relating to covariate overlap, the widely used Bayes’ theorem either defaults to the marginal probability driven “naive Bayes’ classifier”, or requires the use of compensatory expectation-maximization techniques. This paper takes an information-theoretic approach in developing a new statistical formula for the calculation of likelihood ratios based on the principles of quantum entanglement, and demonstrates that Bayes’ theorem is a special case of a more general quantum mechanical expression.