A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: explorations and mechanisms for the breakdown of hyperbolicity

In two previous papers [J. Differential Equations, 228 (2006), pp. 530 579; Discrete Contin. Dyn. Syst. Ser. B, 6 (2006), pp. 1261 1300] we have developed fast algorithms for the computations of invariant tori in quasi‐periodic systems and developed theorems that assess their accuracy. In this paper, we study the results of implementing these algorithms and study their performance in actual implementations. More importantly, we note that, due to the speed of the algorithms and the theoretical developments about their reliability, we can compute with confidence invariant objects close to the breakdown of their hyperbolicity properties. This allows us to identify a mechanism of loss of hyperbolicity and measure some of its quantitative regularities. We find that some systems lose hyperbolicity because the stable and unstable bundles approach each other but the Lyapunov multipliers remain away from 1. We find empirically that, close to the breakdown, the distances between the invariant bundles and the Lyapunov multipliers which are natural measures of hyperbolicity depend on the parameters, with power laws with universal exponents. We also observe that, even if the rigorous justifications in [J. Differential Equations, 228 (2006), pp. 530-579] are developed only for hyperbolic tori, the algorithms work also for elliptic tori in Hamiltonian systems. We can continue these tori and also compute some bifurcations at resonance which may lead to the existence of hyperbolic tori with nonorientable bundles. We compute manifolds tangent to nonorientable bundles.

A simple halide-to-anion exchange method for heteroaromatic salts and ionic liquids

A broad and simple method permitted halide ions in quaternary heteroaromatic and ammonium salts to be exchanged for a variety of anions using an anion exchange resin (A− form) in non-aqueous media. The anion loading of the AER (OH− form) was examined using two different anion sources, acids or ammonium salts, and changing the polarity of the solvents. The AER (A− form) method in organic solvents was then applied to several quaternary heteroaromatic salts and ILs, and the anion exchange proceeded in excellent to quantitative yields, concomitantly removing halide impurities. Relying on the hydrophobicity of the targeted ion pair for the counteranion swap, organic solvents with variable polarity were used, such as CH3OH, CH3CN and the dipolar nonhydroxylic solvent mixture CH3CN:CH2Cl2 (3:7) and the anion exchange was equally successful with both lipophilic cations and anions.

RNA interference is ineffective as a routine method for gene silencing in chick embryos as monitored by fgf8 silencing.

The in vivo accessibility of the chick embryo makes it a favoured model system for experimental developmental biology. Although the range of available techniques now extends to miss-expression of genes through in ovo electroporation, it remains difficult to knock out individual gene expression. Recently, the possibility of silencing gene expression by RNAi in chick embryos has been reported. However, published studies show only discrete quantitative differences in the expression of the endogenous targeted genes and unclear morphological alterations. To elucidate whether the tools currently available are adequate to silence gene expression sufficiently to produce a clear and specific null-like mutant phenotype, we have performed several experiments with different molecules that trigger RNAi: dsRNA, siRNA, and shRNA produced from a plasmid coexpressing green fluorescent protein as an internal marker. Focussing on fgf8 expression in the developing isthmus, we show that no morphological defects are observed, and that fgf8 expression is neither silenced in embryos microinjected with dsRNA nor in embryos microinjected and electroporated with a pool of siRNAs. Moreover, fgf8 expression was not significantly silenced in most isthmic cells transformed with a plasmid producing engineered shRNAs to fgf8. We also show that siRNA molecules do not spread significantly from cell to cell as reported for invertebrates, suggesting the existence of molecular differences between different model systems that may explain the different responses to RNAi. Although our results are basically in agreement with previously reported studies, we suggest, in contrast to them, that with currently available tools and techniques the number of cells in which fgf8 gene expression is decreased, if any, is not sufficient to generate a detectable mutant phenotype, thus making RNAi useless as a routine method for functional gene analysis in chick embryos.

Microscopic-macroscopic approach for binding energies with the Wigner-Kirkwood method. II. Deformed nuclei

The binding energies of deformed even-even nuclei have been analyzed within the framework of a recently proposed microscopic-macroscopic model. We have used the semiclassical Wigner-Kirkwood ̄h expansion up to fourth order, instead of the usual Strutinsky averaging scheme, to compute the shell corrections in a deformed Woods-Saxon potential including the spin-orbit contribution. For a large set of 561 even-even nuclei with Z 8 and N 8, we find an rms deviation from the experiment of 610 keV in binding energies, comparable to the one found for the same set of nuclei using the finite range droplet model of Moller and Nix (656 keV). As applications of our model, we explore its predictive power near the proton and neutron drip lines as well as in the superheavy mass region. Next, we systematically explore the fourth-order Wigner-Kirkwood corrections to the smooth part of the energy. It is found that the ratio of the fourth-order to the second-order corrections behaves in a very regular manner as a function of the asymmetry parameter I=(N−Z)/A. This allows us to absorb the fourth-order corrections into the second-order contributions to the binding energy, which enables us us to simplify and speed up the calculation of deformed nuclei.

A radiochemical method for carbamoyl-phosphate synthetase I: application to rats fed a hyperproteic diet

A method for the measurement of carbamoyl-phosphate synthetase I activity in animal tissues has been developed using the livers of rats under normal and hyperproteic diets. The method is based on the incorporation of 14C-ammonium bicarbonate to carbamoyl-phosphate in the presence of ATP-Mg and N-acetyl-glutamate. The reaction is stopped by chilling, lowering the pH and adding ethanol. Excess bicarbonate is flushed out under a gentle stream of cold CO2. The only label remaining in the medium was that incorporated into carbamoyl-phosphate, since all 14C-CO2 from bicarbonate was eliminated. The method is rapid and requires only a low pressure supply of CO2 to remove the excess substrate. The reaction is linear up to 10 min using homogenate dilutions of 1:20 to 1:200 (w/v). Rat liver activity was in the range of 89±8 nkat/g. Hyperproteic diet resulted in a significant 1.4-fold increase. The design of the method allows for the processing of multiple samples at the same time, and incubation medium manipulation is unnecessary, since the plastic incubation vial and its contents are finally counted together.

EMS mutagenesis in mature seed-derived rice calli as a new method for rapidly obtaining tilling mutant populations.

Background: TILLING (Targeting Induced Local Lesions IN Genomes) is a reverse genetic method that combines chemical mutagenesis with high-throughput genome-wide screening for point mutation detection in genes of interest. However, this mutation discovery approach faces a particular problem which is how to obtain a mutant population with a sufficiently high mutation density. Furthermore, plant mutagenesis protocols require two successive generations (M1, M2) for mutation fixation to occur before the analysis of the genotype can begin. Results: Here, we describe a new TILLING approach for rice based on ethyl methanesulfonate (EMS) mutagenesis of mature seed-derived calli and direct screening of in vitro regenerated plants. A high mutagenesis rate was obtained (i.e. one mutation in every 451 Kb) when plants were screened for two senescence-related genes. Screening was carried out in 2400 individuals from a mutant population of 6912. Seven sense change mutations out of 15 point mutations were identified. Conclusions: This new strategy represents a significant advantage in terms of time-savings (i.e. more than eight months), greenhouse space and work during the generation of mutant plant populations. Furthermore, this effective chemical mutagenesis protocol ensures high mutagenesis rates thereby saving in waste removal costs and the total amount of mutagen needed thanks to the mutagenesis volume reduction.

A method for decision making with the OWA operator

A new method for decision making that uses the ordered weighted averaging (OWA) operator in the aggregation of the information is presented. It is used a concept that it is known in the literature as the index of maximum and minimum level (IMAM). This index is based on distance measures and other techniques that are useful for decision making. By using the OWA operator in the IMAM, we form a new aggregation operator that we call the ordered weighted averaging index of maximum and minimum level (OWAIMAM) operator. The main advantage is that it provides a parameterized family of aggregation operators between the minimum and the maximum and a wide range of special cases. Then, the decision maker may take decisions according to his degree of optimism and considering ideals in the decision process. A further extension of this approach is presented by using hybrid averages and Choquet integrals. We also develop an application of the new approach in a multi-person decision-making problem regarding the selection of strategies.

A copula-based method for synthetic microarray data generation

In this work, we propose a copula-based method to generate synthetic gene expression data that account for marginal and joint probability distributions features captured from real data. Our method allows us to implant significant genes in the synthetic dataset in a controlled manner, giving the possibility of testing new detection algorithms under more realistic environments.

Microscopic-macroscopic approach for binding energies with the Wigner-Kirkwood method

The semiclassical Wigner-Kirkwood ̄h expansion method is used to calculate shell corrections for spherical and deformed nuclei. The expansion is carried out up to fourth order in ̄h. A systematic study of Wigner-Kirkwood averaged energies is presented as a function of the deformation degrees of freedom. The shell corrections, along with the pairing energies obtained by using the Lipkin-Nogami scheme, are used in the microscopic-macroscopic approach to calculate binding energies. The macroscopic part is obtained from a liquid drop formula with six adjustable parameters. Considering a set of 367 spherical nuclei, the liquid drop parameters are adjusted to reproduce the experimental binding energies, which yields a root mean square (rms) deviation of 630 keV. It is shown that the proposed approach is indeed promising for the prediction of nuclear masses.

New method for measuring longitudinal fuctuations and directed flow in ultrarelativistic heavy ion reactions

It has been shown in recent ALICE@LHC measurements that the odd flow harmonics, in particular, a directed flow v1, occurred to be weak and dominated by random fluctuations. In this work we propose a new method, which makes the measurements more sensitive to the flow patterns showing global collective symmetries. We demonstrate how the longitudinal center of mass rapidity fluctuations can be identified, and then the collective flow analysis can be performed in the event-by-event center of mass frame. Such a method can be very effective in separating the flow patterns originating from random fluctuations, and the flow patterns originating from the global symmetry of the initial state.

On the computation of reducible invariant tori on a parallel computer

We present an algorithm for the computation of reducible invariant tori of discrete dynamical systems that is suitable for tori of dimensions larger than 1. It is based on a quadratically convergent scheme that approximates, at the same time, the Fourier series of the torus, its Floquet transformation, and its Floquet matrix. The Floquet matrix describes the linearization of the dynamics around the torus and, hence, its linear stability. The algorithm presents a high degree of parallelism, and the computational effort grows linearly with the number of Fourier modes needed to represent the solution. For these reasons it is a very good option to compute quasi-periodic solutions with several basic frequencies. The paper includes some examples (flows) to show the efficiency of the method in a parallel computer. In these flows we compute invariant tori of dimensions up to 5, by taking suitable sections.

Method development for the simultaneous determination of methylmercury and inorganic mercury in seafood

This paper reports the method development for the simultaneous determination of methylmercury MeHgþ) and inorganic mercury (iHg) species in seafood samples. The study focused on the extraction and quantification of MeHgþ (the most toxic species) by liquid chromatography coupled to on-line UV irradiation and cold vapour atomic fluorescence spectroscopy (LC-UV-CV-AFS), using HCl 4 mol/L as the extractant agent. Accuracy of the method has been verified by analysing three certified reference materials and different spiked samples. The values found for total Hg and MeHgþ for the CRMs did not differ significantly from certified values at a 95% confidence level, and recoveries between 85% and 97% for MeHgþ, based on spikes, were achieved. The detection limits (LODs) obtained were 0.001 mg Hg/kg for total mercury, 0.0003 mg Hg/kg for MeHgþ and 0.0004 mg Hg/kg for iHg. The quantification limits (LOQs) established were 0.003 mg Hg/kg for total mercury, 0.0010 mg Hg/kg for MeHgþ and 0.0012 mg Hg/kg for iHg. Precision for each mercury species was established, being 12% in terms of RSD in all cases. Finally, the developed method was applied to 24 seafood samples from different origins and total mercury contents. The concentrations for Total Hg, MeHg and iHg ranged from 0.07 to 2.33, 0.003-2.23 and 0.006-0.085 mg Hg/kg, respectively. The established analytical method allows to obtain results for mercury speciation in less than 1 one hour including both, sample pretreatment and measuring step.

Therapeutic benefits of body percussion using the BAPNE method

Body percussion using to the BAPNE method is a means of cognitive stimulation with multiple applications. The aim of this research is to assess their full potential as a source of therapy. The methodology used is theoretical in nature and makes use of a wide bibliography to find evidence for its therapeutic effect. In essence, body percussion can be seen to lead to improvements in three areas. the Physical, as it stimulates awareness of the body, control of movement and muscular strength, coordination and balance; the Mental, as it improves concentration, memory and perception; and finally Socio-affective, as it helps to build egalitarian relationships and leads to a decrease in anxiety in social interactions. This means of therapy has several different uses and it is targeted at different groups. In the present investigation we categorise them into five main groups: individuals with neurodegenerative diseases like Alzheimer's or Parkinson's disease; individuals with learning disorders such as dyslexia or ADHD; patients affected by diseases of the spinal cord, cranial neuropathies and trauma (Neurorehabilitation); and for the treatment of addictive behavior (addiction); and depressive disorders or anxiety disorders.After thorough analysis, we have found scientific evidence that the therapeutic body percussion using the BAPNE method improves the quality of life of patients and it is an important factor in stabilizing the development of different diseases.In addition, evidence involving certain biological indicators (in control and experimental groups, and through a pre-test and post-test) show its effect on levels of stress and anxiety (reduction of cortisol), as well as improvement of social relations as a result of working as a group (increased levels of oxytocin), and improvements seen in self-esteem and in a variety of personal aspects through the Aspects of Identity questionnaire.

A nonparametric method for the measurement of size diversity with emphasis on data standardization

The most suitable method for estimation of size diversity is investigated. Size diversity is computed on the basis of the Shannon diversity expression adapted for continuous variables, such as size. It takes the form of an integral involving the probability density function (pdf) of the size of the individuals. Different approaches for the estimation of pdf are compared: parametric methods, assuming that data come from a determinate family of pdfs, and nonparametric methods, where pdf is estimated using some kind of local evaluation. Exponential, generalized Pareto, normal, and log-normal distributions have been used to generate simulated samples using estimated parameters from real samples. Nonparametric methods include discrete computation of data histograms based on size intervals and continuous kernel estimation of pdf. Kernel approach gives accurate estimation of size diversity, whilst parametric methods are only useful when the reference distribution have similar shape to the real one. Special attention is given for data standardization. The division of data by the sample geometric mean is proposedas the most suitable standardization method, which shows additional advantages: the same size diversity value is obtained when using original size or log-transformed data, and size measurements with different dimensionality (longitudes, areas, volumes or biomasses) may be immediately compared with the simple addition of ln k where kis the dimensionality (1, 2, or 3, respectively). Thus, the kernel estimation, after data standardization by division of sample geometric mean, arises as the most reliable and generalizable method of size diversity evaluation

A Computer program for estimating population size by the removal method

A BASIC computer program (REMOVAL) was developed to compute in a VAXNMS environment all the calculations of the removal method for population size estimation (catch-effort method for closed populations with constant sampling effort). The program follows the maximum likelihood methodology,checks the failure conditions, applies the appropriate formula, and displays the estimates of population size and catchability, with their standard deviations and coefficients of variation, and two goodness-of-fit statistics with their significance levels. Data of removal experiments for the cyprinodontid fish Aphanius iberus in the Alt Emporda wetlands are used to exemplify the use of the program