Toplological Entropy in the Syncronization of Piecewise Linear and Monotone Maps. Coupled Duffing Oscillators

In this paper is presented a relationship between the synchronization and the topological entropy. We obtain the values for the coupling parameter, in terms of the topological entropy, to achieve synchronization of two unidirectional and bidirectional coupled piecewise linear maps. In addition, we prove a result that relates the synchronizability of two m-modal maps with the synchronizability of two conjugated piecewise linear maps. An application to the unidirectional and bidirectional coupled identical chaotic Duffing equations is given. We discuss the complete synchronization of two identical double-well Duffing oscillators, from the point of view of symbolic dynamics. Working with Poincare cross-sections and the return maps associated, the synchronization of the two oscillators, in terms of the coupling strength, is characterized.

Entropy analysis of DNA code dynamics in human chromosomes

Deoxyribonucleic acid, or DNA, is the most fundamental aspect of life but present day scientific knowledge has merely scratched the surface of the problem posed by its decoding. While experimental methods provide insightful clues, the adoption of analysis tools supported by the formalism of mathematics will lead to a systematic and solid build-up of knowledge. This paper studies human DNA from the perspective of system dynamics. By associating entropy and the Fourier transform, several global properties of the code are revealed. The fractional order characteristics emerge as a natural consequence of the information content. These properties constitute a small piece of scientific knowledge that will support further efforts towards the final aim of establishing a comprehensive theory of the phenomena involved in life.

Shannon, rényie and tsallis entropy analysis of DNA using phase plane

This paper analyzes DNA information using entropy and phase plane concepts. First, the DNA code is converted into a numerical format by means of histograms that capture DNA sequence length ranging from one up to ten bases. This strategy measures dynamical evolutions from 4 up to 410 signal states. The resulting histograms are analyzed using three distinct entropy formulations namely the Shannon, Rényie and Tsallis definitions. Charts of entropy versus sequence length are applied to a set of twenty four species, characterizing 486 chromosomes. The information is synthesized and visualized by adapting phase plane concepts leading to a categorical representation of chromosomes and species.

Analysing organochlorine pesticides in strawberry jams using GC-ECD, GC-MS/MS and QuEChERS sample preparation

This paper describes a comparison of adaptations of the QuEChERS (quick, easy, cheap, effective, rugged and safe) approach for the determination of 14 organochlorine pesticide (OCP) residues in strawberry jam by concurrent use of gas chromatography (GC) coupled to electron capture detector (ECD) and GC tandem mass spectrometry (GC-MS/MS). Three versions were tested based on the original QuEChERS method. The results were good (overall average of 89% recoveries with 15% RSD) using the ultrasonic bath at five spiked levels. Performance characteristics, such as accuracy, precision, linear range, limits of detection (LOD) and quantification (LOQ), were determined for each pesticide. LOD ranged from 0.8 to 8.9 microg kg-1 ; LOQ was in the range of 2.5–29.8 microg kg- 1; and calibration curves were linear (r2>0.9970) in the whole range of the explored concentrations (5–100 microg kg- 1). The LODs of these pesticides were much lower than the maximum residue levels (MRLs) allowed in Europe for strawberries. The method was successfully applied to the quantification of OCP in commercially available jams. The OCPs were detected lower than the LOD.

QuEChERS: a new sample preparation approach for the determination of ibuprofen and its metabolites in soils

Ibuprofen is one of the most used active pharmaceutical ingredients worldwide. A new method for the analysis of ibuprofen and its metabolites, hydroxyibuprofen and carboxyibuprofen, in soils is presented. The extraction of these compounds from the soil matrices was performed by using a modified quick, easy, cheap, effective, rugged, and safe (QuEChERS) method. The method involves a single extraction of the investigated compounds with purified water (acidified at pH 2.5 with hydrochloric acid), and a slow and continuous addition of the QuEChERS content, followed by the addition of acidified acetonitrile (1% acetic acid), prior to the determination by liquid chromatography coupled with fluorescence detection (LC–FLD). Validation studies were carried out using soil samples with a range of organic carbon contents. Recoveries of the fortified samples ranged from 79.5% to 101%. Relative standard deviations for all matrix–compound combinations did not exceed 3%. The method quantification limits were ≤22.4 μg kg−1 in all cases. The developed method was applied to the analysis of sixteen real samples.

Management of agricultural waste on a sample of farms on the island of São Miguel (Açores)

Dissertação de Mestrado em Ambiente, Saúde e Segurança.

Entropy diversity in multi-objective particle swarm optimization

Multi-objective particle swarm optimization (MOPSO) is a search algorithm based on social behavior. Most of the existing multi-objective particle swarm optimization schemes are based on Pareto optimality and aim to obtain a representative non-dominated Pareto front for a given problem. Several approaches have been proposed to study the convergence and performance of the algorithm, particularly by accessing the final results. In the present paper, a different approach is proposed, by using Shannon entropy to analyzethe MOPSO dynamics along the algorithm execution. The results indicate that Shannon entropy can be used as an indicator of diversity and convergence for MOPSO problems.

Power law and entropy analysis of catastrophic phenomena

Catastrophic events, such as wars and terrorist attacks, tornadoes and hurricanes, earthquakes, tsunamis, floods and landslides, are always accompanied by a large number of casualties. The size distribution of these casualties has separately been shown to follow approximate power law (PL) distributions. In this paper, we analyze the statistical distributions of the number of victims of catastrophic phenomena, in particular, terrorism, and find double PL behavior. This means that the data sets are better approximated by two PLs instead of a single one. We plot the PL parameters, corresponding to several events, and observe an interesting pattern in the charts, where the lines that connect each pair of points defining the double PLs are almost parallel to each other. A complementary data analysis is performed by means of the computation of the entropy. The results reveal relationships hidden in the data that may trigger a future comprehensive explanation of this type of phenomena.

Shannon entropy analysis of the genome code

This paper studies the chromosome information of twenty five species, namely, mammals, fishes, birds, insects, nematodes, fungus, and one plant. A quantifying scheme inspired in the state space representation of dynamical systems is formulated. Based on this algorithm, the information of each chromosome is converted into a bidimensional distribution. The plots are then analyzed and characterized by means of Shannon entropy. The large volume of information is integrated by averaging the lengths and entropy quantities of each species. The results can be easily visualized revealing quantitative global genomic information.

Assessing usual dietary intake in complex sample design surveys: the National Dietary Survey

The National Cancer Institute (NCI) method allows the distributions of usual intake of nutrients and foods to be estimated. This method can be used in complex surveys. However, the user must perform additional calculations, such as balanced repeated replication (BRR), in order to obtain standard errors and confidence intervals for the percentiles and mean from the distribution of usual intake. The objective is to highlight adaptations of the NCI method using data from the National Dietary Survey. The application of the NCI method was exemplified analyzing the total energy (kcal) and fruit (g) intake, comparing estimations of mean and standard deviation that were based on the complex design of the Brazilian survey with those assuming simple random sample. Although means point estimates were similar, estimates of standard error using the complex design increased by up to 60% compared to simple random sample. Thus, for valid estimates of food and energy intake for the population, all of the sampling characteristics of the surveys should be taken into account because when these characteristics are neglected, statistical analysis may produce underestimated standard errors that would compromise the results and the conclusions of the survey.

Entropy analysis of integer and fractional dynamical systems

This paper investigates the adoption of entropy for analyzing the dynamics of a multiple independent particles system. Several entropy definitions and types of particle dynamics with integer and fractional behavior are studied. The results reveal the adequacy of the entropy concept in the analysis of complex dynamical systems.

Jamming detection in GNSS signals using the sample covariance matrix.

We propose a blind method to detect interference in GNSS signals whereby the algorithms do not require knowledge of the interference or channel noise features. A sample covariance matrix is constructed from the received signal and its eigenvalues are computed. The generalized likelihood ratio test (GLRT) and the condition number test (CNT) are developed and compared in the detection of sinusoidal and chirp jamming signals. A computationally-efficient decision threshold was proposed for the CNT.

Topological entropy of catalytic sets: Hypercycles revisited

The dynamics of catalytic networks have been widely studied over the last decades because of their implications in several fields like prebiotic evolution, virology, neural networks, immunology or ecology. One of the most studied mathematical bodies for catalytic networks was initially formulated in the context of prebiotic evolution, by means of the hypercycle theory. The hypercycle is a set of self-replicating species able to catalyze other replicator species within a cyclic architecture. Hypercyclic organization might arise from a quasispecies as a way to increase the informational containt surpassing the so-called error threshold. The catalytic coupling between replicators makes all the species to behave like a single and coherent evolutionary multimolecular unit. The inherent nonlinearities of catalytic interactions are responsible for the emergence of several types of dynamics, among them, chaos. In this article we begin with a brief review of the hypercycle theory focusing on its evolutionary implications as well as on different dynamics associated to different types of small catalytic networks. Then we study the properties of chaotic hypercycles with error-prone replication with symbolic dynamics theory, characterizing, by means of the theory of topological Markov chains, the topological entropy and the periods of the orbits of unimodal-like iterated maps obtained from the strange attractor. We will focus our study on some key parameters responsible for the structure of the catalytic network: mutation rates, autocatalytic and cross-catalytic interactions.

Behavioural development in a matching-to-sample task and token use by an infant chimpanzee reared by his mother

Animal Cognition, V.6, pp. 259–267