Order and information in the patterns of spinning magnetic micro-disks at the air-water interface

A local measure based on the Shannon entropy establishes connections among information, structures, and interactions.

A Black Hole-Aided Deep-Helix Channel Model for DNA

In this article, we present a black-hole-aided deep-helix (bh-dh) channel model to enhance information bound and mitigate a multiple-helix directional issue in Deoxyribonucleic acid (DNA) communications. The recent observations of DNA do not match with Shannon bound due to their multiple-helix directional issue. Hence, we propose a bh-dh channel model in this paper. The proposed bh-dh channel model follows a similar fashion of DNA and enriches the earlier DNA observations as well as achieving a composite like information bound. To do successfully the proposed bh-dh channel model, we first define a black-hole-aided Bernoulli-process and then consider a symmetric bh-dh channel model. After that, the geometric and graphical insight shows the resemblance of the proposed bh-dh channel model in DNA and Galaxy layout. In our exploration, the proposed bh-dh symmetric channel geometrically sketches a deep-pair-ellipse when a deep-pair information bit or digit is distributed in the proposed channel. Furthermore, the proposed channel graphically shapes as a beautiful circulant ring. The ring contains a central-hole, which looks like a central-black-hole of a Galaxy. The coordinates of the inner-ellipses denote a deep-double helix, and the coordinates of the outer-ellipses sketch a deep-parallel strand. Finally, the proposed bh-dh symmetric channel significantly outperforms the traditional binary-symmetric channel and is verified by computer simulations in terms of Shannon entropy and capacity bound.

Using the Hurst Exponent and Entropy Measures to Predict Effective Transmissibility in Empirical Series of Malaria Incidence

We analyze the empirical series of malaria incidence, using the concepts of autocorrelation, Hurst exponent and Shannon entropy with the aim of uncovering hidden variables in those series. From the simulations of an agent model for malaria spreading, we first derive models of the malaria incidence, the Hurst exponent and the entropy as functions of gametocytemia, measuring the infectious power of a mosquito to a human host. Second, upon estimating the values of three observables—incidence, Hurst exponent and entropy—from the data set of different malaria empirical series we predict a value of the gametocytemia for each observable. Finally, we show that the independent predictions show considerable consistency with only a few exceptions which are discussed in further detail.

𝑯𝑵- Entropy: A New Measureof Information And Its Properties

Entropy measures the amount of uncertainty and dispersion of an unknown or random quantity, this concept introduced at first by Shannon (1948), it is important for studies in many areas. Like, information theory: entropy measures the amount of information in each message received, physics: entropy is the basic concept that measures the disorder of the thermodynamical system, and others. Then, in this paper, we introduce an alternative measure of entropy, called 𝐻𝑁- entropy, unlike Shannon entropy, this proposed measure of order α and β is more flexible than Shannon. Then, the cumulative residual 𝐻𝑁- entropy, cumulative 𝐻𝑁- entropy, and weighted version have been introduced. Finally, comparison between Shannon entropy and 𝐻𝑁- entropy and numerical results have been introduced.

Refinements of Jensen's inequality and applications

<abstract><p>The principal aim of this research work is to establish refinements of the integral Jensen's inequality. For the intended refinements, we mainly use the notion of convexity and the concept of majorization. We derive some inequalities for power and quasi–arithmetic means while utilizing the main results. Moreover, we acquire several refinements of Hölder inequality and also an improvement of Hermite–Hadamard inequality as consequences of obtained results. Furthermore, we secure several applications of the acquired results in information theory, which consist bounds for Shannon entropy, different divergences, Bhattacharyya coefficient, triangular discrimination and various distances.</p></abstract>

Characteristics of merging behavior in large crowds

Merging pedestrian flow can be observed often at public intersections and locations where two or more channels merge. Because of restrictions on the flow, pedestrian congestion, or even crowd disasters (e.g. Hajj crush 2015) happen easily at these junctions. However, studies on merging behaviors in large crowds remain rare. This paper investigates the merging characteristics of the pedestrian flow with controlled experiments under laboratory conditions. The formation of lanes is observed, and the lane separation width can vary for different density levels. Shannon entropy is used to analyze the utilization of the passage. The space usage in the merging area is most efficient when the width of the two branches is half that of the main corridor. Furthermore, the branch and main channel can mutually bottleneck each other in the large crowds and the flowrates for the upstream, downstream and branches are investigated. This study uses spatiotemporal diagrams to explore the clogging propagation of the merging flow as well as the relationship of the velocity and position. The results can be used as references for the design of public infrastructure and human safety management.