Explosion of smoothness from a point to everywhere for conjugacies between diffeomorphisms on surfaces

For diffeomorphisms on surfaces with basic sets, we show the following type of rigidity result: if a topological conjugacy between them is differentiable at a point in the basic set then the conjugacy has a smooth extension to the surface. These results generalize the similar ones of D. Sullivan, E. de Faria and ours for one-dimensional expanding dynamics.

Distributed Forest Fire Monitoring Using Wireless Sensor Networks

Disaster management is one of the most relevant application fields of wireless sensor networks. In this application, the role of the sensor network usually consists of obtaining a representation or a model of a physical phenomenon spreading through the affected area. In this work we focus on forest firefighting operations, proposing three fully distributed ways for approximating the actual shape of the fire. In the simplest approach, a circular burnt area is assumed around each node that has detected the fire and the union of these circles gives the overall fire’s shape. However, as this approach makes an intensive use of the wireless sensor network resources, we have proposed to incorporate two in-network aggregation techniques, which do not require considering the complete set of fire detections. The first technique models the fire by means of a complex shape composed of multiple convex hulls representing different burning areas, while the second technique uses a set of arbitrary polygons. Performance evaluation of realistic fire models on computer simulations reveals that the method based on arbitrary polygons obtains an improvement of 20% in terms of accuracy of the fire shape approximation, reducing the overhead in-network resources to 10% in the best case.

Host-Tailored Sensors for Leucomalachite Green Potentiometric Measurements

A new biomimetic sensor for leucomalachite green host-guest interactions and potentiometric transduction is presented. The artificial host was imprinted in methacrylic acid or acrylamido-2-methyl-1-propanesulfonic acid-based polymers. Molecularly imprinted particles were dispersed in 2-nitrophenyloctyl ether and trapped in poly(vinyl chloride). The potentiometric sensors exhibited a near-Nernstian response in steady state evaluations, with slopes and detection limits ranging from 45.8 to 81.2 mV and 0.28 to 1.01 , respectively. They were independent from the pH of test solutions within 3 to 5. Good selectivity was observed towards drugs that may contaminate water near fish cultures, such as oxycycline, doxycycline, enrofloxacin, trimethoprim, creatinine, chloramphenicol, and dopamine. The sensors were successfully applied to field monitoring of leucomalachite green in river samples. The method offered the advantages of simplicity, accuracy, applicability to colored and turbid samples, and automation feasibility.

Local Fractional Variational Iteration Method for Local Fractional Poisson Equations in Two Independent Variables

The local fractional Poisson equations in two independent variables that appear in mathematical physics involving the local fractional derivatives are investigated in this paper. The approximate solutions with the nondifferentiable functions are obtained by using the local fractional variational iteration method.

Fractional Dynamics of Computer Virus Propagation

We propose a fractional model for computer virus propagation. The model includes the interaction between computers and removable devices. We simulate numerically the model for distinct values of the order of the fractional derivative and for two sets of initial conditions adopted in the literature. We conclude that fractional order systems reveal richer dynamics than the classical integer order counterpart. Therefore, fractional dynamics leads to time responses with super-fast transients and super-slow evolutions towards the steady-state, effects not easily captured by the integer order models.

Dynamic Analysis and Pattern Visualization of Forest Fires

This paper analyses forest fires in the perspective of dynamical systems. Forest fires exhibit complex correlations in size, space and time, revealing features often present in complex systems, such as the absence of a characteristic length-scale, or the emergence of long range correlations and persistent memory. This study addresses a public domain forest fires catalogue, containing information of events for Portugal, during the period from 1980 up to 2012. The data is analysed in an annual basis, modelling the occurrences as sequences of Dirac impulses with amplitude proportional to the burnt area. First, we consider mutual information to correlate annual patterns. We use visualization trees, generated by hierarchical clustering algorithms, in order to compare and to extract relationships among the data. Second, we adopt the Multidimensional Scaling (MDS) visualization tool. MDS generates maps where each object corresponds to a point. Objects that are perceived to be similar to each other are placed on the map forming clusters. The results are analysed in order to extract relationships among the data and to identify forest fire patterns.

Dynamical Analysis and Visualization of Tornadoes Time Series

In this paper we analyze the behavior of tornado time-series in the U.S. from the perspective of dynamical systems. A tornado is a violently rotating column of air extending from a cumulonimbus cloud down to the ground. Such phenomena reveal features that are well described by power law functions and unveil characteristics found in systems with long range memory effects. Tornado time series are viewed as the output of a complex system and are interpreted as a manifestation of its dynamics. Tornadoes are modeled as sequences of Dirac impulses with amplitude proportional to the events size. First, a collection of time series involving 64 years is analyzed in the frequency domain by means of the Fourier transform. The amplitude spectra are approximated by power law functions and their parameters are read as an underlying signature of the system dynamics. Second, it is adopted the concept of circular time and the collective behavior of tornadoes analyzed. Clustering techniques are then adopted to identify and visualize the emerging patterns.

Analysis of World Economic Variables Using Multidimensional Scaling

Waves of globalization reflect the historical technical progress and modern economic growth. The dynamics of this process are here approached using the multidimensional scaling (MDS) methodology to analyze the evolution of GDP per capita, international trade openness, life expectancy, and education tertiary enrollment in 14 countries. MDS provides the appropriate theoretical concepts and the exact mathematical tools to describe the joint evolution of these indicators of economic growth, globalization, welfare and human development of the world economy from 1977 up to 2012. The polarization dance of countries enlightens the convergence paths, potential warfare and present-day rivalries in the global geopolitical scene.

Efficient Legendre spectral tau algorithm for solving two-sided space-time Caputo fractional advection-dispersion equation

In this paper we present the operational matrices of the left Caputo fractional derivative, right Caputo fractional derivative and Riemann–Liouville fractional integral for shifted Legendre polynomials. We develop an accurate numerical algorithm to solve the two-sided space–time fractional advection–dispersion equation (FADE) based on a spectral shifted Legendre tau (SLT) method in combination with the derived shifted Legendre operational matrices. The fractional derivatives are described in the Caputo sense. We propose a spectral SLT method, both in temporal and spatial discretizations for the two-sided space–time FADE. This technique reduces the two-sided space–time FADE to a system of algebraic equations that simplifies the problem. Numerical results carried out to confirm the spectral accuracy and efficiency of the proposed algorithm. By selecting relatively few Legendre polynomial degrees, we are able to get very accurate approximations, demonstrating the utility of the new approach over other numerical methods.

State Space Analysis of Forest Fires

This paper studies forest fires from the perspective of dynamical systems. Burnt area, precipitation and atmospheric temperatures are interpreted as state variables of a complex system and the correlations between them are investigated by means of different mathematical tools. First, we use mutual information to reveal potential relationships in the data. Second, we adopt the state space portrait to characterize the system’s behavior. Third, we compare the annual state space curves and we apply clustering and visualization tools to unveil long-range patterns. We use forest fire data for Portugal, covering the years 1980–2003. The territory is divided into two regions (North and South), characterized by different climates and vegetation. The adopted methodology represents a new viewpoint in the context of forest fires, shedding light on a complex phenomenon that needs to be better understood in order to mitigate its devastating consequences, at both economical and environmental levels.

Limit Cycle Prediction of Systems with Fractional Controllers and Backlash

This article investigates the limit cycle (LC) prediction of systems with backlash by means of the describing function (DF) when using discrete fractional-order (FO) algorithms. The DF is an approximate method that gives good estimates of LCs. The implementation of FO controllers requires the use of rational approximations, but such realizations produce distinct dynamic types of behavior. This study analyzes the accuracy in the prediction of LCs, namely their amplitude and frequency, when using several different algorithms. To illustrate this problem we use FO-PID algorithms in the control of systems with backlash.

Modeling Vegetable Fractals by means of Fractional-order Equations

This paper characterizes four ‘fractal vegetables’: (i) cauliflower (brassica oleracea var. Botrytis); (ii) broccoli (brassica oleracea var. italica); (iii) round cabbage (brassica oleracea var. capitata) and (iv) Brussels sprout (brassica oleracea var. gemmifera), by means of electrical impedance spectroscopy and fractional calculus tools. Experimental data is approximated using fractional-order models and the corresponding parameters are determined with a genetic algorithm. The Havriliak-Negami five-parameter model fits well into the data, demonstrating that classical formulae can constitute simple and reliable models to characterize biological structures.

Role of the DHH1 Gene in the Regulation of Monocarboxylic Acids Transporters Expression in Saccharomyces cerevisiae

Previous experiments revealed that DHH1, a RNA helicase involved in the regulation of mRNA stability and translation, complemented the phenotype of a Saccharomyces cerevisiae mutant affected in the expression of genes coding for monocarboxylic-acids transporters, JEN1 and ADY2 (Paiva S, Althoff S, Casal M, Leao C. FEMS Microbiol Lett, 1999, 170∶301–306). In wild type cells, JEN1 expression had been shown to be undetectable in the presence of glucose or formic acid, and induced in the presence of lactate. In this work, we show that JEN1 mRNA accumulates in a dhh1 mutant, when formic acid was used as sole carbon source. Dhh1 interacts with the decapping activator Dcp1 and with the deadenylase complex. This led to the hypothesis that JEN1 expression is post-transcriptionally regulated by Dhh1 in formic acid. Analyses of JEN1 mRNAs decay in wild-type and dhh1 mutant strains confirmed this hypothesis. In these conditions, the stabilized JEN1 mRNA was associated to polysomes but no Jen1 protein could be detected, either by measurable lactate carrier activity, Jen1-GFP fluorescence detection or western blots. These results revealed the complexity of the expression regulation of JEN1 in S. cerevisiae and evidenced the importance of DHH1 in this process. Additionally, microarray analyses of dhh1 mutant indicated that Dhh1 plays a large role in metabolic adaptation, suggesting that carbon source changes triggers a complex interplay between transcriptional and post-transcriptional effects.

Effects of Soil Compaction and Organic Carbon Content on Preferential Flow in Loamy Field Soils

Abstract: Preferential flow and transport through macropores affect plant water use efficiency and enhance leaching of agrochemicals and the transport of colloids, thereby increasing the risk for contamination of groundwater resources. The effects of soil compaction, expressed in terms of bulk density (BD), and organic carbon (OC) content on preferential flow and transport were investigated using 150 undisturbed soil cores sampled from 15 × 15–m grids on two field sites. Both fields had loamy textures, but one site had significantly higher OC content. Leaching experiments were conducted in each core by applying a constant irrigation rate of 10 mm h−1 with a pulse application of tritium tracer. Five percent tritium mass arrival times and apparent dispersivities were derived from each of the tracer breakthrough curves and correlated with texture, OC content, and BD to assess the spatial distribution of preferential flow and transport across the investigated fields. Soils from both fields showed strong positive correlations between BD and preferential flow. Interestingly, the relationships between BD and tracer transport characteristics were markedly different for the two fields, although the relationship between BD and macroporosity was nearly identical. The difference was likely caused by the higher contents of fines and OC at one of the fields leading to stronger aggregation, smaller matrix permeability, and a more pronounced pipe-like pore system with well-aligned macropores.

Physical therapy with drug treatment in bell palsy: a focused review

ABSTRACT: The physical therapy (PT) associated with standard drug treatment (SDT) in Bell palsy has never been investigated. Randomized controlled trials or quasirandomized controlled trials have compared facial PT (except treatments such as acupuncture and osteopathic) combined with SDT against a control group with SDT alone. Participants included those older than 15 yrs with a clinical diagnosis of Bell palsy, and the primary outcome measure was motor function recovery by the House-Brackmann scale. The methodologic quality of each study was also independently assessed by two reviewers using the PEDro scale. Four studies met the inclusion criteria. Three trials indicate that PT in association with SDT supports higher motor function recovery than SDT alone between 15 days and 1 yr of follow-up. On the other hand, one trial showed that electrical stimulation added to conventional PT with SDT did not influence treatment outcomes. The present review suggests that the current practice of Bell palsy treatment by PT associated with SDT seems to have a positive effect on grade and time recovery compared with SDT alone. However, there is very little quality evidence from randomized controlled trials, and such evidence is insufficient to decide whether combined treatment is beneficial in the management of Bell palsy.