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.

Food consumption, physical activity and socio-economic status related to BMI, waist circumference and waist-to-height ratio in adolescents

Objective: To examine the association between obesity and food group intakes, physical activity and socio-economic status in adolescents. Design: A cross-sectional study was carried out in 2008. Cole’s cut-off points were used to categorize BMI. Abdominal obesity was defined by a waist circumference at or above the 90th percentile, as well as a waist-to-height ratio at or above 0?500. Diet was evaluated using an FFQ, and the food group consumption was categorized using sex-specific tertiles of each food group amount. Physical activity was assessed via a self-report questionnaire. Socio-economic status was assessed referring to parental education and employment status. Data were analysed separately for girls and boys and the associations among food consumption, physical activity, socio-economic status and BMI, waist circumference and waist-to-height ratio were evaluated using logistic regression analysis, adjusting the results for potential confounders. Setting: Public schools in the Azorean Archipelago, Portugal. Subjects: Adolescents (n 1209) aged 15–18 years. Results: After adjustment, in boys, higher intake of ready-to-eat cereals was a negative predictor while vegetables were a positive predictor of overweight/ obesity and abdominal obesity. Active boys had lower odds of abdominal obesity compared with inactive boys. Boys whose mother showed a low education level had higher odds of abdominal obesity compared with boys whose mother presented a high education level. Concerning girls, higher intake of sweets and pastries was a negative predictor of overweight/obesity and abdominal obesity. Girls in tertile 2 of milk intake had lower odds of abdominal obesity than those in tertile 1. Girls whose father had no relationship with employment displayed higher odds of abdominal obesity compared with girls whose father had high employment status. Conclusions: We have found that different measures of obesity have distinct associations with food group intakes, physical activity and socio-economic status.

Local fractional variational iteration and decomposition methods for wave equation on cantor sets within local fractional operators

We perform a comparison between the fractional iteration and decomposition methods applied to the wave equation on Cantor set. The operators are taken in the local sense. The results illustrate the significant features of the two methods which are both very effective and straightforward for solving the differential equations with local fractional derivative.

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.

Systems of Navier-Stokes equations on cantor sets

We present systems of Navier-Stokes equations on Cantor sets, which are described by the local fractional vector calculus. It is shown that the results for Navier-Stokes equations in a fractal bounded domain are efficient and accurate for describing fluid flow in fractal media.

Fractional dynamics of genetic algorithms using hexagonal space tessellation

The paper formulates a genetic algorithm that evolves two types of objects in a plane. The fitness function promotes a relationship between the objects that is optimal when some kind of interface between them occurs. Furthermore, the algorithm adopts an hexagonal tessellation of the two-dimensional space for promoting an efficient method of the neighbour modelling. The genetic algorithm produces special patterns with resemblances to those revealed in percolation phenomena or in the symbiosis found in lichens. Besides the analysis of the spacial layout, a modelling of the time evolution is performed by adopting a distance measure and the modelling in the Fourier domain in the perspective of fractional calculus. The results reveal a consistent, and easy to interpret, set of model parameters for distinct operating conditions.

Observability of nonlinear fractional dynamical systems

We study the observability of linear and nonlinear fractional differential systems of order 0 < α < 1 by using the Mittag-Leffler matrix function and the application of Banach’s contraction mapping theorem. Several examples illustrate the concepts.

Root-locus practical sketching rules for fractional-order system

For integer-order systems, there are well-known practical rules for RL sketching. Nevertheless, these rules cannot be directly applied to fractional-order (FO) systems. Besides, the existing literature on this topic is scarce and exclusively focused on commensurate systems, usually expressed as the ratio of two noninteger polynomials. The practical rules derived for those do not apply to other symbolic expressions, namely, to transfer functions expressed as the ratio of FO zeros and poles. However, this is an important case as it is an extension of the classical integer-order problem usually addressed by control engineers. Extending the RL practical sketching rules to such FO systems will contribute to decrease the lack of intuition about the corresponding system dynamics. This paper generalises several RL practical sketching rules to transfer functions specified as the ratio of FO zeros and poles. The subject is presented in a didactic perspective, being the rules applied to several examples.

Multidimensional scaling for orthodontic root resorption

The paper investigates the risk factors for the severity of orthodontic root resorption. The multidimensional scaling (MDS) visualization method is used to investigate the experimental data from patients who received orthodontic treatment at the Department of Orthodontics and Dentofacial Orthopedics, Faculty of Dentistry, “Carol Davila” University of Medicine and Pharmacy, during a period of 4 years. The clusters emerging in the MDS plots reveal features and properties not easily captured by classical statistical tools. The results support the adoption of MDS for tackling the dentistry information and overcoming noise embedded into the data. The method introduced in this paper is rapid, efficient, and very useful for treating the risk factors for the severity of orthodontic root resorption.

Fractional coins and fractional derivatives

This paper discusses the fundamentals of negative probabilities and fractional calculus. The historical evolution and the main mathematical concepts are discussed, and several analogies between the two apparently unrelated topics are established. Based on the new conceptual perspective, some experiments are performed shading new light into possible future progress.

Stability of fractional order systems

The theory and applications of fractional calculus (FC) had a considerable progress during the last years. Dynamical systems and control are one of the most active areas, and several authors focused on the stability of fractional order systems. Nevertheless, due to the multitude of efforts in a short period of time, contributions are scattered along the literature, and it becomes difficult for researchers to have a complete and systematic picture of the present day knowledge. This paper is an attempt to overcome this situation by reviewing the state of the art and putting this topic in a systematic form. While the problem is formulated with rigour, from the mathematical point of view, the exposition intends to be easy to read by the applied researchers. Different types of systems are considered, namely, linear/nonlinear, positive, with delay, distributed, and continuous/discrete. Several possible routes of future progress that emerge are also tackled.

Geostatistical Prediction of Ocean Outfall Plume Characteristics Based on an Autonomous Underwater Vehicle

Geostatistics has been successfully used to analyze and characterize the spatial variability of environmental properties. Besides giving estimated values at unsampled locations, it provides a measure of the accuracy of the estimate, which is a significant advantage over traditional methods used to assess pollution. In this work universal block kriging is novelty used to model and map the spatial distribution of salinity measurements gathered by an Autonomous Underwater Vehicle in a sea outfall monitoring campaign, with the aim of distinguishing the effluent plume from the receiving waters, characterizing its spatial variability in the vicinity of the discharge and estimating dilution. The results demonstrate that geostatistical methodology can provide good estimates of the dispersion of effluents that are very valuable in assessing the environmental impact and managing sea outfalls. Moreover, since accurate measurements of the plume’s dilution are rare, these studies might be very helpful in the future to validate dispersion models.

Hydroxycinnamic acid antioxidants: an electrochemical overview

Hydroxycinnamic acids (such as ferulic, caffeic, sinapic, and p-coumaric acids) are a group of compounds highly abundant in food that may account for about one-third of the phenolic compounds in our diet. Hydroxycinnamic acids have gained an increasing interest in health because they are known to be potent antioxidants. These compounds have been described as chain-breaking antioxidants acting through radical scavenging activity, that is related to their hydrogen or electron donating capacity and to the ability to delocalize/stabilize the resulting phenoxyl radical within their structure.The free radical scavenger ability of antioxidants can be predicted from standard one-electron potentials. Thus, voltammetric methods have often been applied to characterize a diversity of natural and synthetic antioxidants essentially to get an insight into their mechanism and also as an important tool for the rational design of new and potent antioxidants.The structure-property-activity relationships (SPARs) correlations already established for this type of compounds suggest that redox potentials could be considered a good measure of antioxidant activity and an accurate guideline on the drug discovery and development process. Due to its magnitude in the antioxidant field, the electrochemistry of hydroxycinnamic acid-based antioxidants is reviewed highlighting the structure-property-activity relationships (SPARs) obtained so far.

Photostabilization of phenoxyacetic acid herbicides MCPA and mecoprop by hydroxypropyl-β-cyclodextrin

New strategies to reduce the environmental and economic costs of pesticides use are currently under study. Microencapsulation has been used as a versatile tool for the production of controlled release agricultural formulations. In this study, the photochemical degradation of the herbicides MCPA and mecoprop has been investigated in different aqueous media such as ultrapure and river water under simulated solar irradiation. To explore the possibility of introducing cyclodextrins in the herbicide formulations, the photodegradation study of the inclusion complexes of MCPA and mecoprop with (2-hydroxypropyl)-β-cyclodextrin (HP-β-CD) was also performed. The half-lives of MCPA and mecoprop inclusion complexes were increased approximately by a factor of three related to the free molecules. Additionally, it has been shown that the photodegradation of MCPA and mecoprop is influenced by their structural features. The additional methyl group existing in mecoprop molecular structure has a positive influence on the stabilization of the radical intermediate formed in the first stage of photodegradation of both herbicides. The results found indicated that MCPA and mecoprop form inclusion complexes with HP-β-CD showing higher photostability compared to free herbicides indicating that HP-β-CD may serve as ingredient in these herbicide formulations.

Host-Guest interaction between herbicide oxadiargyl and hydroxypropyl-β-cyclodextrin

In the face of a growing human population and increased urbanization, the demand for pesticides will simply rise. Farmers must escalate yields on increasingly fewer farm acres. However, the risks of pesticides, whether real or perceived, may force changes in the way these chemicals are used. Scientists are working toward pest control plans that are environmentally sound, effective, and profitable. In this context the development of new pesticide formulations which may improve application effectiveness, safety, handling, and storage can be pointed out as a solution. As a contribution to the area, the microencapsulation of the herbicide oxadiargyl (OXA) in (2-hydroxypropyl)-β-cyclodextrin (HP-β-CD) was performed. The study was conducted in different aqueous media (ultrapure water and in different pH buffer solutions). In all cases an increment of the oxadiargyl solubility as a function of the HP-β-CD concentration that has been related to the formation of an inclusion complex was verified. UV-Vis and NMR experiments allowed concluding that the stoichiometry of the OXA/HP-β-CD complex formed is 1 : 1. The gathered results can be regarded as an important step for its removal from industrial effluents and/or to increase the stabilizing action, encapsulation, and adsorption in water treatment plants.