Kendall Transformation: A Robust Representation of Continuous Data for Information Theory

Kendall transformation is a conversion of an ordered feature into a vector of pairwise order relations between individual values. This way, it preserves ranking of observations and represents it in a categorical form. Such transformation allows for generalisation of methods requiring strictly categorical input, especially in the limit of small number of observations, when discretisation becomes problematic.In particular, many approaches of information theory can be directly applied to Kendall-transformed continuous data without relying on differential entropy or any additional parameters. Moreover, by filtering information to this contained in ranking, Kendall transformation leads to a better robustness at a reasonable cost of dropping sophisticated interactions which are anyhow unlikely to be correctly estimated. In bivariate analysis, Kendall transformation can be related to popular non-parametric methods, showing the soundness of the approach.The paper also demonstrates its efficiency in multivariate problems, as well as provides an example analysis of a real-world data.

Hygroscopic Properties of Sweet Cherry Powder: Thermodynamic Properties and Microstructural Changes

Understanding sorption isotherms is crucial in food science for optimizing the drying processes, enhancing the shelf-life of food, and maintaining food quality during storage. This study investigated the isotherms of sweet cherry powder (SCP) using the static gravimetric method. The experimental water sorption curves of lyophilized sweet cherry powder were determined at 30°C, 40°C, and 50°C. The curves were then fitted to six isotherm models: Modified GAB, Halsey, Smith, Oswin, Caurie, and Kühn models. To define the energy associated with the sorption process, the isosteric sorption heat, differential entropy, and spreading pressure were derived from the isotherms. Among the six models, the Smith model is the most reliable in predicting the sorption of the cherry powder with a determination coefficient (R2) of 0.9978 and a mean relative error (MRE) ≤1.61. The values of the net isosteric heat and differential entropy for the cherry increased exponentially as the moisture content decreased. The net isosteric heat values varied from 10.63 to 90.97 kJ mol−1, while the differential entropy values varied from 27.94 to 273.39 J. mol−1K−1. Overall, the enthalpy-entropy compensation theory showed that enthalpy-controlled mechanisms could be used to regulate water adsorption in cherry powders.

Entropic model of network dynamics of clocking network synchronization

The main task of the clocking network synchronization (CNS) network subsystem is the formation, transmission, distribution and delivery of synchronization signals to the telecommunication system (TCS) digital equipment for the purpose of its coordinated interaction. Indicators of the telecommunication services quality are inextricably linked with the indicators of the CNS network functioning quality, in this regard, the process of monitoring and managing the CNS network comes to the fore for the purpose of prompt detection of failures and their subsequent elimination. The article provides an overview of the main classes of CNS network equipment and their diagnostic parameters, and also indicates the significant influence of the CNS network functioning process on the entire TCS functioning. To assess the technical condition of the CNS network an approach using the entropy analysis of the diagnostic parameters of the CNS network elements is proposed. The entropy model of the network dynamics is obtained in CNS work, which can later be used to develop a methodology for monitoring the technical condition of the CNS network. Using this model, it is possible to estimate not only the differential entropy of each CNS network element, but also to estimate the differential entropy of the entire CNS network or a separate fragment of the CNS network. Differential entropy parameters reflect the technical state of the CNS network.

Differential Entropy: An Appropriate Analysis to Interpret the Shape Complexity of Self-Similar Organic Islands

Differential entropy, along with fractal dimension, is herein employed to describe and interpret the shape complexity of self-similar organic islands. The islands are imaged with in situ Atomic Force Microscopy, following, step-by-step, the evolution of their shape while deposition proceeds. The fractal dimension shows a linear correlation with the film thickness, whereas the differential entropy presents an exponential plateau. Plotting differential entropy versus fractal dimension, a linear correlation can be found. This analysis enables one to discern the 6T growth on different surfaces, i.e., native SiOx or 6T layer, and suggests a more comprehensive interpretation of the shape evolution. Changes in fractal dimension reflect rougher variations of the island contour, whereas changes in differential entropy correlates with finer contour details. The computation of differential entropy therefore helps to obtain more physical information on the island shape dependence on the substrate, beyond the standard description obtained with the fractal dimension.