Characteristic features of the Shannon information entropy of dipolar Bose-Einstein condensates

Localization in Two-Dimensional Quasicrystalline Lattices

We investigate the emergence of localization in a weakly interacting Bose gas confined in quasicrystalline lattices with three different rotational symmetries: five, eight, and twelve. The analysis, performed at a mean field level and from which localization is detected, relies on the study of two observables: the inverse participation ratio (IPR) and the Shannon entropy in the coordinate space. Those physical quantities were determined from a robust statistical study for the stationary density profiles of the interacting condensate. Localization was identified for each lattice type as a function of the potential depth. Our analysis revealed a range of the potential depths for which the condensate density becomes localized, from partially at random lattice sites to fully in a single site. We found that localization in the case of five-fold rotational symmetry appears for (6ER,9ER), while it occurs in the interval (12ER,15ER) for octagonal and dodecagonal symmetries.

Intelligent terminal security technology of power grid sensing layer based upon information entropy data mining

The power grid is an important connection between power sources and users, responsible for supplying and distributing electric energy to users. Modern power grids are widely distributed and large in scale, and their security faces new problems and challenges. Information entropy theory is an objective weighting method that compares the information order of each evaluation index to judge the weight value. With the wide application of entropy theory in various disciplines, the subject of introducing entropy into the power system has been gradually concerned. This article aims to study the smart terminal security technology of the power grid perception layer based on information entropy data mining. This article analyzes its related methods and designs a smart terminal for the power grid. On this basis, a data analysis platform is built and a safety plan is designed. The result is that the average absolute error, root mean square error, average absolute percentage error, and mean square error of the platform's power load forecast are 1.58, 1.96, 8.2%, and 3.93, respectively. These error values are within the ideal range, and the data processing ability is strong. The packet loss rate of the adversary's eavesdropping was tested, and the average packet loss rates at locations a, b, c, and d were 1.05, 1.2, 1.81, and 2.2%, respectively. Data packets will be definitely lost, so the platform is highly secure.

A Generalized Relative (α, β)-Entropy: Geometric Properties and Applications to Robust Statistical Inference

Entropy and relative entropy measures play a crucial role in mathematical information theory. The relative entropies are also widely used in statistics under the name of divergence measures which link these two fields of science through the minimum divergence principle. Divergence measures are popular among statisticians as many of the corresponding minimum divergence methods lead to robust inference in the presence of outliers in the observed data; examples include the ϕ -divergence, the density power divergence, the logarithmic density power divergence and the recently developed family of logarithmic super divergence (LSD). In this paper, we will present an alternative information theoretic formulation of the LSD measures as a two-parameter generalization of the relative α -entropy, which we refer to as the general ( α , β ) -entropy. We explore its relation with various other entropies and divergences, which also generates a two-parameter extension of Renyi entropy measure as a by-product. This paper is primarily focused on the geometric properties of the relative ( α , β ) -entropy or the LSD measures; we prove their continuity and convexity in both the arguments along with an extended Pythagorean relation under a power-transformation of the domain space. We also derive a set of sufficient conditions under which the forward and the reverse projections of the relative ( α , β ) -entropy exist and are unique. Finally, we briefly discuss the potential applications of the relative ( α , β ) -entropy or the LSD measures in statistical inference, in particular, for robust parameter estimation and hypothesis testing. Our results on the reverse projection of the relative ( α , β ) -entropy establish, for the first time, the existence and uniqueness of the minimum LSD estimators. Numerical illustrations are also provided for the problem of estimating the binomial parameter.