The heart-rate dynamics are one of the most analyzed physiological interactions. Many mathematical methods were proposed to evaluate heart-rate variability. These methods have been successfully applied in research to expand knowledge concerning the cardiovascular dynamics in healthy as well as in pathological conditions. Notwithstanding, they are still far from clinical practice. In this paper, we aim to review the nonlinear methods most used to assess heart-rate dynamics. We focused on methods based on concepts of chaos, fractality, and complexity: Poincaré plot, recurrence plot analysis, fractal dimension (and the correlation dimension), detrended fluctuation analysis, Hurst exponent, Lyapunov exponent entropies (Shannon, conditional, approximate, sample entropy, and multiscale entropy), and symbolic dynamics. We present the description of the methods along with their most notable applications.

About 160 years ago, the concept of entropy was introduced in thermodynamics by Rudolf Clausius. Since then, it has been continually extended, interpreted, and applied by researchers in many scientific fields, such as general physics, information theory, chaos theory, data mining, and mathematical linguistics. This paper presents The Entropy Universe, which aims to review the many variants of entropies applied to time-series. The purpose is to answer research questions such as: How did each entropy emerge? What is the mathematical definition of each variant of entropy? How are entropies related to each other? What are the most applied scientific fields for each entropy? We describe in-depth the relationship between the most applied entropies in time-series for different scientific fields, establishing bases for researchers to properly choose the variant of entropy most suitable for their data. The number of citations over the past sixteen years of each paper proposing a new entropy was also accessed. The Shannon/differential, the Tsallis, the sample, the permutation, and the approximate entropies were the most cited ones. Based on the ten research areas with the most significant number of records obtained in the Web of Science and Scopus, the areas in which the entropies are more applied are computer science, physics, mathematics, and engineering. The universe of entropies is growing each day, either due to the introducing new variants either due to novel applications. Knowing each entropy’s strengths and of limitations is essential to ensure the proper improvement of this research field.

There is no generally accepted definition of conditional Rényi entropy. The (unconditional) Rényi entropy depends on a parameter α, which for the case of min-entropy takes the value ∞. Even for this particular case, there are several proposals for the definition of conditional entropy. This paper describes three general definitions of conditional Rényi entropy that were found or suggested in the literature. Their properties are studied and their values, as a function of α, are compared. The particular case of min-entropy is widely used in cryptography as a security parameter; this case is studied in some detail.

Access control models describe frameworks that dictate how subjects (e.g. users) access resources. In the role-based access control (RBAC) model access to resources is based on the role the user holds within the organization. RBAC is a rigid model where access control decisions have only two output options: grant or deny. break the glass (BTG) policies on the other hand are flexible and allow users to break or override the access controls in a controlled and justifiable manner. The main objective of this paper is to integrate BTG within the NIST/ANSI RBAC model in a transparent and secure way so that it can be adopted generically in any domain where unanticipated or emergency situations may occur. The new proposed model, called BTG-RBAC, provides a third decision option BTG, which grants authorized users permission to break the glass rather than be denied access. This can easily be implemented in any application without major changes to either the application code or the RBAC authorization infrastructure, apart from the decision engine. Finally, in order to validate the model, we discuss how the BTG-RBAC model is being introduced within a Portuguese healthcare institution where the legislation requires that genetic information must be accessed by a restricted group of healthcare professionals. These professionals, advised by the ethical committee, have required and asked for the implementation of the BTG concept in order to comply with the said legislation.

Kolmogorov complexity and Shannon entropy are conceptually different measures. However, for any recursive probability distribution, the expected value of Kolmogorov complexity equals its Shannon entropy, up to a constant. We study if a similar relationship holds for R´enyi and Tsallis entropies of order α, showing that it only holds for α = 1. Regarding a time-bounded analogue relationship, we show that, for some distributions we have a similar result. We prove that, for universal time-bounded distribution m^t(x), Tsallis and Rényi entropies converge if and only if α is greater than 1. We also establish the uniform continuity of these entropies.