Fractional dynamics and MDS visualization of earthquake phenomena

This paper analyses earthquake data in the perspective of dynamical systems and fractional calculus (FC). This new standpoint uses Multidimensional Scaling (MDS) as a powerful clustering and visualization tool. FC extends the concepts of integrals and derivatives to non-integer and complex orders. MDS is a technique that produces spatial or geometric representations of complex objects, such that those objects that are perceived to be similar in some sense are placed on the MDS maps forming clusters. In this study, over three million seismic occurrences, covering the period from January 1, 1904 up to March 14, 2012 are analysed. The events are characterized by their magnitude and spatiotemporal distributions and are divided into fifty groups, according to the Flinn–Engdahl (F–E) seismic regions of Earth. Several correlation indices are proposed to quantify the similarities among regions. MDS maps are proven as an intuitive and useful visual representation of the complex relationships that are present among seismic events, which may not be perceived on traditional geographic maps. Therefore, MDS constitutes a valid alternative to classic visualization tools for understanding the global behaviour of earthquakes.

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.

Effects of home environment and center-based child care quality on children’s

This study examined the joint effects of home environment and center-based child care quality on children’s language, communication, and early literacy development, while also considering prior developmental level. Participants were 95 children (46 boys), assessed as toddlers (mean age = 26.33 months;Time 1) and preschoolers (mean age = 68.71 months; Time 2) and their families. At both times, children attended center-based child care classrooms in the metropolitan area of Porto, Portugal. Results from hierarchical linear models indicated that home environment and preschool quality, but not center-based toddler child care quality, were associated with children’s language and literacy outcomes at Time 2. Moreover, the quality of preschool classrooms moderated the association between home environment quality and children’s language and early literacy skills – but not communication skills – at Time 2, suggesting the positive cumulative effects of home environment and preschool quality. Findings further support the existence of a detrimental effect of low preschool quality on children’s language and early literacy outcomes: positive associations among home environment quality and children’s developmental outcomes were found to reduce substantially when children attended low-quality preschool classrooms.

Nutritional value and influence of the thermal processing on a traditional Portuguese fermented sausage (alheira)

Alheiras are a traditional, smoked, fermented meat sausage, produced in Portugal, with an undeniable cultural and gastronomic legacy. In this study, we assessed the nutritional value of this product, as well as the influence of different types of thermal processing. Alheiras from Mirandela were submitted to six different procedures: microwave, skillet, oven, charcoal grill, electric fryer and electric grill. Protein, fat, carbohydrate, minerals, NaCl, and cholesterol contents, as well as fatty acid profile were evaluated. The results show that alheiras are not hypercaloric but an unbalanced foodstuff (high levels of proteins and lipids) and the type of processing has a major impact on their nutritional value. Charcoal grill is the healthiest option: less fat (12.5 g/100 g) and cholesterol (29.3 mg/100 g), corresponding to a lower caloric intake (231.8 kcal, less 13% than the raw ones). Inversely, fried alheiras presented the worst nutritional profile, with the highest levels of fat (18.1 g/100 g) and cholesterol (76.0 g/100 g).

Angolan cymbopogon citratus used for therapeutic benefits: nutritional composition and influence of solvents in phytochemicals content and antioxidant activity of leaf extracts

Folk medicine is a relevant and effective part of indigenous healthcare systems which are, in practice, totally dependent on traditional healers. An outstanding coincidence between indigenous medicinal plant uses and scientifically proved pharmacological properties of several phytochemicals has been observed along the years. This work focused on the leaves of a medicinal plant traditionally used for therapeutic benefits (Angolan Cymbopogon citratus), in order to evaluate their nutritional value. The bioactive phytochemical composition and antioxidant activity of leaf extracts prepared with different solvents (water, methanol and ethanol) were also evaluated. The plant leaves contained ~60% of carbohydrates, protein (~20%), fat (~5%), ash (~4%) and moisture (~9%). The phytochemicals screening revealed the presence of tannins, flavonoids, and terpenoids in all extracts. Methanolic extracts also contained alkaloids and steroids. Several methods were used to evaluate total antioxidant capacity of the different extracts (DPPH; NO; and H2O2 scavenging assays, reducing power, and FRAP). Ethanolic extracts presented a significantly higher antioxidant activity (p < 0.05) except for FRAP, in which the best results were achieved by the aqueous extracts. Methanolic extracts showed the lowest radical scavenging activities for both DPPH; and NO; radicals.

Dynamic analysis of earthquake phenomena by means of pseudo phase plane

This paper analyses earthquake data in the perspective of dynamical systems and its Pseudo Phase Plane representation. The seismic data is collected from the Bulletin of the International Seismological Centre. The geological events are characterised by their magnitude and geographical location and described by means of time series of sequences of Dirac impulses. Fifty groups of data series are considered, according to the Flinn-Engdahl seismic regions of Earth. For each region, Pearson’s correlation coefficient is used to find the optimal time delay for reconstructing the Pseudo Phase Plane. The Pseudo Phase Plane plots are then analysed and characterised.

A review of power laws in real life phenomena

Power law distributions, also known as heavy tail distributions, model distinct real life phenomena in the areas of biology, demography, computer science, economics, information theory, language, and astronomy, amongst others. In this paper, it is presented a review of the literature having in mind applications and possible explanations for the use of power laws in real phenomena. We also unravel some controversies around power laws.

Fractional order inductive phenomena based on the skin effect

The Maxwell equations play a fundamental role in the electromagnetic theory and lead to models useful in physics and engineering. This formalism involves integer-order differential calculus, but the electromagnetic diffusion points towards the adoption of a fractional calculus approach. This study addresses the skin effect and develops a new method for implementing fractional-order inductive elements. Two genetic algorithms are adopted, one for the system numerical evaluation and another for the parameter identification, both with good results.

Electrical skin phenomena: a fractional calculus analysis

The internal impedance of a wire is the function of the frequency. In a conductor, where the conductivity is sufficiently high, the displacement current density can be neglected. In this case, the conduction current density is given by the product of the electric field and the conductance. One of the aspects of the high-frequency effects is the skin effect (SE). The fundamental problem with SE is it attenuates the higher frequency components of a signal.

Filtering method in backlash phenomena analysis

The behavior of robotic manipulators with backlash is analyzed. Based on the pseudo-phase plane two indices are proposed to evaluate the backlash effect upon the robotic system: the root mean square error and the fractal dimension. For the dynamical analysis the noisy signals captured from the system are filtered through wavelets. Several tests are developed that demonstrate the coherence of the results.

Performance of fractional PID algorithms controlling nonlinear systems with saturation and backlash phenomena

The development of fractional-order controllers is currently one of the most promising fields of research. However, most of the work in this area addresses the case of linear systems. This paper reports on the analysis of fractional-order control of nonlinear systems. The performance of discrete fractional-order PID controllers in the presence of several nonlinearities is discussed. Some results are provided that indicate the superior robustness of such algorithms.

Effect of peel and seed removal on the nutritional value and antioxidant activity of tomato (Lycopersicon esculentum L.) fruits

The effect of peel and seed removal, two commonly practiced procedures either at home or by the processing industry, on the physicochemical properties, bioactive compounds contents and antioxidant capacity of tomato fruits of four typical Portuguese cultivars (cereja, chucha, rama and redondo) were appraised. Both procedures caused significant nutritional and antioxidant activity losses in fruits of every cultivar. In general, peeling was more detrimental, since it caused a higher decrease in lycopene, bcarotene, ascorbic acid and phenolics contents (averages of 71%, 50%, 14%, and 32%, respectively) and significantly lowered the antioxidant capacity of the fruits (8% and 10%, using DPPH. and b-carotene linoleate model assays, correspondingly). Although seeds removal favored the increase of both color and sweetness, some bioactive compounds (11% of carotenoids and 24% of phenolics) as well as antioxidant capacity (5%) were loss. The studied cultivars were differently influenced by these procedures. The fruits most affected by peeling were those from redondo cultivar (-66% lycopene, -44% b-carotene, -26% ascorbic acid and -38% phenolics). Seeds removal, in turn, was more injurious for cereja tomatoes (-10% lycopene, -38% b-carotene, -25% ascorbic acid and -63% phenolics). Comparatively with the remaining ones, the rama fruits were less affected by the trimming procedures.

Assessment of nutritional and metabolic profiles of pea shoots: The new ready-to-eat baby-leaf vegetable

Pea-shoots are a new option as ready-to-eat baby-leaf vegetable. However, data about the nutritional composition and the shelf-life stability of these leaves, especially their phytonutrient composition is scarce. In this work, the macronutrient, micronutrient and phytonutrients profile of minimally processed pea shoots were evaluated at the beginning and at the end of a 10-day storage period. Several physicochemical characteristics (color, pH, total soluble solids, and total titratable acidity) were also monitored. Standard AOAC methods were applied in the nutritional value evaluation, while chromatographic methods with UV–vis and mass detection were used to analyze free forms of vitamins (HPLC-DAD-ESI-MS/MS), carotenoids (HPLC-DAD-APCI-MSn) and flavonoid compounds (HPLC-DAD-ESI-MSn). Atomic absorption spectrometry (HR-CS-AAS) was employed to characterize the mineral content of the leaves. As expected, pea leaves had a high water (91.5%) and low fat (0.3%) and carbohydrate (1.9%) contents, being a good source of dietary fiber (2.1%). Pea shoots showed a high content of vitamins C, E and A, potassium and phosphorous compared to other ready-to-eat green leafy vegetables. The carotenoid profile revealed a high content of β-carotene and lutein, typical from green leafy vegetables. The leaves had a mean flavonoid content of 329 mg/100 g of fresh product, mainly composed by glycosylated quercetin and kaempferol derivatives. Pea shoots kept their fresh appearance during the storage being color maintained throughout the shelf-life. The nutritional composition was in general stable during storage, showing some significant (p < 0.05) variation in certain water-soluble vitamins.

Nutritional composition of low protein and phenylalanine-restricted dishes prepared for phenylketonuric patients

Nutritional management is essential for Phenylketonuria (PKU) treatment, consisting in a semi-synthetic and low phenylalanine (Phe) diet, which includes strictly controlled amounts of low protein natural foods (essentially fruits and vegetables) supplemented with Phe-free protein substitutes and dietetic low-protein products. PKU diet has to be carefully planned, providing the best ingredient combinations, so that patients can achieve good metabolic control and an adequate nutritional status. Hereupon, it is mandatory to know the detailed composition of natural and/or cooked foodstuffs prepared specifically for these patients. We intended to evaluate sixteen dishes specifically prepared for PKU patients, regarding the nutritional composition, Phe and tyrosine (Tyr) contents, fatty acids profile, and vitamins E and B12 amounts. The nutritional composition of the cooked samples was 15.5–92.0 g/100 g, for moisture; 0.7–3.2 g/100 g, for protein; 0.1–25.0 g/100 g, for total fat; and 5.0–62.0 g/100 g, for total carbohydrates. Fatty acids profile and vitamin E amount reflected the type of fat used. All samples were poor in vitamin B12 (0.3–0.8 μg/100 g). Boiled rice presented the highest Phe content: 50.3 mg/g of protein. These data allow a more accurate calculation of the diet portions to be ingested by the patients according to their individual tolerance.

Octopus Lipid and Vitamin E Composition: Interspecies, Interorigin, and Nutritional Variability

Octopus vulgaris, Octopus maya, and Eledone cirrhosa from distinct marine environments [Northeast Atlantic (NEA), Northwest Atlantic (NWA), Eastern Central Atlantic, Western Central Atlantic (WCA), Pacific Ocean, and Mediterranean Sea] were characterized regarding their lipid and vitamin E composition. These species are those commercially more relevant worldwide. Significant interspecies and interorigin differences were observed. Unsaturated fatty acids account for more than 65% of total fatty acids, mostly ω-3 PUFA due to docosahexaenoic (18.4−29.3%) and eicosapentanoic acid (11.4− 23.9%) contributions. The highest ω-3 PUFA amounts and ω-3/ω-6 ratios were quantified in the heaviest specimens, O. vulgaris from NWA, with high market price, and simultaneously in the lowest graded samples, E. cirrhosa from NEA, of reduced dimensions. Although having the highest cholesterol contents, E. cirrhosa from NEA and O. maya from WCA have also higher protective fatty acid indexes. Chemometric discrimination allowed clustering the selected species and several origins based on lipid and vitamin E profiles.