Entropy analysis of human death uncertainty.

Uncertainty about the time of death is part of one's life, and plays an important role in demographic and actuarial sciences. Entropy is a measure useful for characterizing complex systems. This paper analyses death uncertainty through the concept of entropy. For that purpose, the Shannon and the cumulative residual entropies are adopted. The first may be interpreted as an average information. The second was proposed more recently and is related to reliability measures such as the mean residual lifetime. Data collected from the Human Mortality Database and describing the evolution of 40 countries during several decades are studied using entropy measures. The emerging country and inter-country entropy patterns are used to characterize the dynamics of mortality. The locus of the two entropies gives a deeper insight into the dynamical evolution of the human mortality data series.

Advances in the computational analysis of SARS-COV2 genome.

Given a data-set of Ribonucleic acid (RNA) sequences we can infer the phylogenetics of the samples and tackle the information for scientific purposes. Based on current data and knowledge, the SARS-CoV-2 seemingly mutates much more slowly than the influenza virus that causes seasonal flu. However, very recent evolution poses some doubts about such conjecture and shadows the out-coming light of people vaccination. This paper adopts mathematical and computational tools for handling the challenge of analyzing the data-set of different clades of the severe acute respiratory syndrome virus-2 (SARS-CoV-2). On one hand, based on the mathematical paraphernalia of tools, the concept of distance associated with the Kolmogorov complexity and Shannon information theories, as well as with the Hamming scheme, are considered. On the other, advanced data processing computational techniques, such as, data compression, clustering and visualization, are borrowed for tackling the problem. The results of the synergistic approach reveal the complex time dynamics of the evolutionary process and may help to clarify future directions of the SARS-CoV-2 evolution.

Fractional-order modelling of epoxy resin.

This paper describes epoxy resins by means of electrical impedance spectroscopy (EIS) and the mathematical tool of fractional calculus (FC). Two stages are considered: first, the EIS is used for testing the samples and, second, the measured data are approximated using integer and fractional order models. The FC-based modelling describes the epoxy resins using a small number of parameters that reflect their main characteristics. The EIS data gathered for the epoxies samples are compared with those of different adhesives and sealants by means of a hierarchical clustering algorithm that unravels the relationships between the distinct materials. This article is part of the theme issue 'Advanced materials modelling via fractional calculus: challenges and perspectives'.

Rare and extreme events: the case of COVID-19 pandemic.

Complex systems have characteristics that give rise to the emergence of rare and extreme events. This paper addresses an example of such type of crisis, namely the spread of the new Coronavirus disease 2019 (COVID-19). The study deals with the statistical comparison and visualization of country-based real-data for the period December 31, 2019, up to April 12, 2020, and does not intend to address the medical treatment of the disease. Two distinct approaches are considered, the description of the number of infected people across time by means of heuristic models fitting the real-world data, and the comparison of countries based on hierarchical clustering and multidimensional scaling. The computational and mathematical modeling lead to the emergence of patterns, highlighting similarities and differences between the countries, pointing toward the main characteristics of the complex dynamics.

Computational analysis of the SARS-CoV-2 and other viruses based on the Kolmogorov's complexity and Shannon's information theories.

This paper tackles the information of 133 RNA viruses available in public databases under the light of several mathematical and computational tools. First, the formal concepts of distance metrics, Kolmogorov complexity and Shannon information are recalled. Second, the computational tools available presently for tackling and visualizing patterns embedded in datasets, such as the hierarchical clustering and the multidimensional scaling, are discussed. The synergies of the common application of the mathematical and computational resources are then used for exploring the RNA data, cross-evaluating the normalized compression distance, entropy and Jensen-Shannon divergence, versus representations in two and three dimensions. The results of these different perspectives give extra light in what concerns the relations between the distinct RNA viruses.

Commensurate and Non-Commensurate Fractional-Order Discrete Models of an Electric Individual-Wheel Drive on an Autonomous Platform.

This paper presents integer and linear time-invariant fractional order (FO) models of a closed-loop electric individual-wheel drive implemented on an autonomous platform. Two discrete-time FO models are tested: non-commensurate and commensurate. A classical model described by the second-order linear difference equation is used as the reference. According to the sum of the squared error criterion (SSE), we compare a two-parameter integer order model with four-parameter non-commensurate and three-parameter commensurate FO descriptions. The computer simulation results are compared with the measured velocity of a real autonomous platform powered by a closed-loop electric individual-wheel drive.

Entropy Analysis of Soccer Dynamics.

This paper adopts the information and fractional calculus tools for studying the dynamics of a national soccer league. A soccer league season is treated as a complex system (CS) with a state observable at discrete time instants, that is, at the time of rounds. The CS state, consisting of the goals scored by the teams, is processed by means of different tools, namely entropy, mutual information and Jensen-Shannon divergence. The CS behavior is visualized in 3-D maps generated by multidimensional scaling. The points on the maps represent rounds and their relative positioning allows for a direct interpretation of the results.

Complexity Analysis of Escher's Art.

Art is the output of a complex system based on the human spirit and driven by several inputs that embed social, cultural, economic and technological aspects of a given epoch. A solid quantitative analysis of art poses considerable difficulties and reaching assertive conclusions is a formidable challenge. In this paper, we adopt complexity indices, dimensionality-reduction and visualization techniques for studying the evolution of Escher's art. Grayscale versions of 457 artworks are analyzed by means of complexity indices and represented using the multidimensional scaling technique. The results are correlated with the distinct periods of Escher's artistic production. The time evolution of the complexity and the emergent patterns demonstrate the effectiveness of the approach for a quantitative characterization of art.

On the Complexity Analysis and Visualization of Musical Information.

This paper considers several distinct mathematical and computational tools, namely complexity, dimensionality-reduction, clustering, and visualization techniques, for characterizing music. Digital representations of musical works of four artists are analyzed by means of distinct indices and visualized using the multidimensional scaling technique. The results are then correlated with the artists' musical production. The patterns found in the data demonstrate the effectiveness of the approach for assessing the complexity of musical information.

A soluble inorganic pyrophosphatase from the cattle tick Rhipicephalus microplus capable of hydrolysing polyphosphates.

Polyphosphates have been found in all cell types examined to date and play diverse roles depending on the cell type. In eukaryotic organisms, polyphosphates have been investigated mainly in mammalian cells, and only a few studies have addressed arthropods. Pyrophosphatases have been shown to regulate polyphosphate metabolism. However, these studies were restricted to trypanosomatids. Here we focus on the tick Rhipicephalus microplus, a haematophagous ectoparasite that is highly harmful to cattle. We produced a recombinant R. microplus pyrophosphatase (rRmPPase) with the aim of investigating its kinetic parameters using polyphosphates as substrate. Molecular docking assays of RmPPase with polyphosphates were also carried out. The kinetic and Hill coefficient parameters indicated that rRmPPase has a greater affinity, higher catalytic efficiency and increased cooperativity for sodium phosphate glass type 15 (polyP15 ) than for sodium tripolyphosphate (polyP3 ). Through molecular docking, we found that polyP3 binds close to the Mg2+ atoms in the catalytic region of the protein, participating in their coordination network, whereas polyP15 interactions involve negatively charged phosphate groups and basic amino acid residues, such as Lys56, Arg58 and Lys193; polyP15 has a more favourable theoretical binding affinity than polyP3 , thus supporting the kinetic data. This study shows, for the first time in arthropods, a pyrophosphatase with polyphosphatase activity, suggesting its participation in polyphosphate metabolism.

Complexity Analysis of Global Temperature Time Series.

Climate has complex dynamics due to the plethora of phenomena underlying its evolution. These characteristics pose challenges to conducting solid quantitative analysis and reaching assertive conclusions. In this paper, the global temperature time series (TTS) is viewed as a manifestation of the climate evolution, and its complexity is calculated by means of four different indices, namely the Lempel-Ziv complexity, sample entropy, signal harmonics power ratio, and fractal dimension. In the first phase, the monthly mean TTS is pre-processed by means of empirical mode decomposition, and the TTS trend is calculated. In the second phase, the complexity of the detrended signals is estimated. The four indices capture distinct features of the TTS dynamics in a 4-dim space. Hierarchical clustering is adopted for dimensional reduction and visualization in the 2-dim space. The results show that TTS complexity exhibits space-time variability, suggesting the presence of distinct climate forcing processes in both dimensions. Numerical examples with real-world data demonstrate the effectiveness of the approach.

Complex Systems and Fractional Dynamics.

Complex systems (CS) are pervasive in many areas of science and technology, namely in financialmarkets, transportation, telecommunication and social networks, world and country economies,immunological systems, living organisms, computational systems, and electrical and mechanicalstructures [...].

New insights into the infection of the American cockroach Periplaneta americana nymphs with Metarhizium anisopliae s.l. (Ascomycota: Hypocreales).

AIMS: To study the marked resistance of Periplaneta americana to entomopathogenic Metarhizium anisopliae. METHODS AND RESULTS: The low susceptibility of 4th instar nymphs applied topically with conidia seemed to be related to an active removal of conidia by the cockroach and to a disabled or retarded germination and subsequent development of conidia on the cuticle (up to 80% germination in the next 7 days after application). Inhibitions or delays of germination were related to the composition of the epicuticular fatty acids (30·1% w/w oleic, 28·3% w/w linoleic, 24·5% w/w palmitic and 11·7% w/w stearic acid) reported here. Propagules invading the nymphs through the cuticle took at least 3 days to reach the haemocoel, and no propagules were found after day 8 post-treatment. Strain IP 46 infected >50% of nymphs treated with doses ≥2 × 104  hyphal bodies (HB) nymph-1 and reduced the survival of nymphs ≤50%. Most nymphs (>70%) survived after injection of 6 × 103 and 2 × 103  HB nymph-1 . CONCLUSIONS: Findings emphasize a distinct resistance of nymphs of the American cockroach to infections by M. anisopliae. SIGNIFICANCE AND IMPACT OF THE STUDY: Our findings provide support for the development of biological control of this synanthropic cockroach pest.

Design and implementation of grid multi-scroll fractional-order chaotic attractors.

This paper proposes a novel approach for generating multi-scroll chaotic attractors in multi-directions for fractional-order (FO) systems. The stair nonlinear function series and the saturated nonlinear function are combined to extend equilibrium points with index 2 in a new FO linear system. With the help of stability theory of FO systems, stability of its equilibrium points is analyzed, and the chaotic behaviors are validated through phase portraits, Lyapunov exponents, and Poincaré section. Choosing the order 0.96 as an example, a circuit for generating 2-D grid multiscroll chaotic attractors is designed, and 2-D 9 × 9 grid FO attractors are observed at most. Numerical simulations and circuit experimental results show that the method is feasible and the designed circuit is correct.

On exact traveling-wave solutions for local fractional Korteweg-de Vries equation.

This paper investigates the Korteweg-de Vries equation within the scope of the local fractional derivative formulation. The exact traveling wave solutions of non-differentiable type with the generalized functions defined on Cantor sets are analyzed. The results for the non-differentiable solutions when fractal dimension is 1 are also discussed. It is shown that the exact solutions for the local fractional Korteweg-de Vries equation characterize the fractal wave on shallow water surfaces.

Multidimensional scaling analysis of the dynamics of a country economy.

This paper analyzes the Portuguese short-run business cycles over the last 150 years and presents the multidimensional scaling (MDS) for visualizing the results. The analytical and numerical assessment of this long-run perspective reveals periods with close connections between the macroeconomic variables related to government accounts equilibrium, balance of payments equilibrium, and economic growth. The MDS method is adopted for a quantitative statistical analysis. In this way, similarity clusters of several historical periods emerge in the MDS maps, namely, in identifying similarities and dissimilarities that identify periods of prosperity and crises, growth, and stagnation. Such features are major aspects of collective national achievement, to which can be associated the impact of international problems such as the World Wars, the Great Depression, or the current global financial crisis, as well as national events in the context of broad political blueprints for the Portuguese society in the rising globalization process.

Rosiglitazone, a PPAR-γ agonist, inhibits VEGF secretion by peripheral blood mononuclear cells and ROS production by human leukocytes.

OBJECTIVE: To investigate the effects of rosiglitazone, a peroxisome proliferator-activated receptor-γ agonist, on the secretion of vascular endothelial growth factor (VEGF) by peripheral blood mononuclear cells (PBMCs) and on the generation of reactive oxygen species (ROS) by leukocytes. METHODS: PBMCs and leukocytes were obtained from venous blood samples collected from 20 healthy individuals. VEGF secretion was evaluated using a commercial ELISA kit, while ROS production was determined using a luminol-dependent chemiluminescence assay. RESULTS: Rosiglitazone and calphostin C (a protein kinase C inhibitor) inhibited VEGF secretion by PBMCs by 63.7 and 62.3%, respectively. Both agents reduced ROS production in non-stimulated human leukocytes and down-regulated the enhanced generation of ROS in leukocytes that had been stimulated with the PKC activator phorbol 12,13-dibutyrate. CONCLUSION: The results support the involvement of PKC as a direct, and/or NADPH-oxidase as an indirect, target for the action of rosiglitazone on VEGF secretion by PBMCs and ROS production in human leukocytes.

Multidimensional scaling applied to histogram-based DNA analysis.

This paper aims to study the relationships between chromosomal DNA sequences of twenty species. We propose a methodology combining DNA-based word frequency histograms, correlation methods, and an MDS technique to visualize structural information underlying chromosomes (CRs) and species. Four statistical measures are tested (Minkowski, Cosine, Pearson product-moment, and Kendall τ rank correlations) to analyze the information content of 421 nuclear CRs from twenty species. The proposed methodology is built on mathematical tools and allows the analysis and visualization of very large amounts of stream data, like DNA sequences, with almost no assumptions other than the predefined DNA "word length." This methodology is able to produce comprehensible three-dimensional visualizations of CR clustering and related spatial and structural patterns. The results of the four test correlation scenarios show that the high-level information clusterings produced by the MDS tool are qualitatively similar, with small variations due to each correlation method characteristics, and that the clusterings are a consequence of the input data and not method's artifacts.