On the Hilbert transform in the framework of generalized functions

In this paper, a definition of the Hilbert transform operating on Colombeau's temperated generalized functions is given. Similar results to some theorems that hold in the classical theory, or in certain subspaces of Schwartz distributions, have been obtained in this framework.

Levels of Selenomonas species in generalized aggressive periodontitis

Goncalves LFH, Fermiano D, Feres M, Figueiredo LC, Teles FRP, Mayer MPA, Faveri M. Levels of Selenomonas species in generalized aggressive periodontitis. J Periodont Res 2012; 47: 711718. (c) 2012 John Wiley & Sons A/S Background and Objective: To compare the levels of Selenomonas sputigena and uncultivated/unrecognized Selenomonas species in subgingival biofilms from periodontally healthy subjects and from subjects with generalized aggressive periodontitis. Material and Methods: Fifteen periodontally healthy subjects and 15 subjects with generalized aggressive periodontitis were recruited and their clinical periodontal parameters were evaluated. Nine subgingival plaque samples were collected from each subject and all were individually analyzed for the levels of 10 bacterial taxa, including cultured and uncultivated/unrecognized microorganisms, using the RNA-oligonucleotide quantification technique. Between-group differences in the levels of the test taxa were determined using the MannWhitney U-test. Results: Subjects with generalized aggressive periodontitis showed significantly higher mean counts of Porphyromonas gingivalis, S. sputigena and the Mitsuokella sp. Human Oral Taxon (HOT) 131 (previously described as Selenomonas sp. oral clone CS002), while higher mean counts of Actinomyces gerencseriae and Streptococcus sanguinis were found in periodontally healthy subjects (p < 0.01). Selenomonas sp. HOT 146 was only detected in the generalized aggressive periodontitis group. In the generalized aggressive periodontitis group, the levels of P.gingivalis and S.sputigena were higher in deep sites (probing depth = 5 mm) than in shallow sites (probing depth = 3 mm) (p < 0.01). Furthermore, in subjects with generalized aggressive periodontitis, sites with probing depth of = 3 mm harbored higher levels of these two species than sites with the same probing depth in periodontally healthy subjects. There were positive correlations between probing depth and the levels of P.gingivalis (r = 0.77; p < 0.01), S.sputigena (r = 0.60; p < 0.01) and Selenomonas dianae (previously described as Selenomonas sp. oral clone EW076) (r = 0.42, p < 0.05). Conclusion: S. sputigena and Mitsuokella sp. HOT 131 may be associated with the pathogenesis of generalized aggressive periodontitis, and their role in the onset and progression of this infection should be investigated further.

Evaluation of physiologic complexity in time series using generalized sample entropy and surrogate data analysis

Complexity in time series is an intriguing feature of living dynamical systems, with potential use for identification of system state. Although various methods have been proposed for measuring physiologic complexity, uncorrelated time series are often assigned high values of complexity, errouneously classifying them as a complex physiological signals. Here, we propose and discuss a method for complex system analysis based on generalized statistical formalism and surrogate time series. Sample entropy (SampEn) was rewritten inspired in Tsallis generalized entropy, as function of q parameter (qSampEn). qSDiff curves were calculated, which consist of differences between original and surrogate series qSampEn. We evaluated qSDiff for 125 real heart rate variability (HRV) dynamics, divided into groups of 70 healthy, 44 congestive heart failure (CHF), and 11 atrial fibrillation (AF) subjects, and for simulated series of stochastic and chaotic process. The evaluations showed that, for nonperiodic signals, qSDiff curves have a maximum point (qSDiff(max)) for q not equal 1. Values of q where the maximum point occurs and where qSDiff is zero were also evaluated. Only qSDiff(max) values were capable of distinguish HRV groups (p-values 5.10 x 10(-3); 1.11 x 10(-7), and 5.50 x 10(-7) for healthy vs. CHF, healthy vs. AF, and CHF vs. AF, respectively), consistently with the concept of physiologic complexity, and suggests a potential use for chaotic system analysis. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4758815]

Thermodynamics of Ising model with infinite-range interactions by generalized canonical ensemble

In this work we present the idea of how generalized ensembles can be used to simplify the operational study of non-additive physical systems. As alternative of the usual methods of direct integration or mean-field theory, we show how the solution of the Ising model with infinite-range interactions is obtained by using a generalized canonical ensemble. We describe how the thermodynamical properties of this model in the presence of an external magnetic field are founded by simple parametric equations. Without impairing the usual interpretation, we obtain an identical critical behaviour as observed in traditional approaches.

Generalized beta-generated distributions

This article introduces generalized beta-generated (GBG) distributions. Sub-models include all classical beta-generated, Kumaraswamy-generated and exponentiated distributions. They are maximum entropy distributions under three intuitive conditions, which show that the classical beta generator skewness parameters only control tail entropy and an additional shape parameter is needed to add entropy to the centre of the parent distribution. This parameter controls skewness without necessarily differentiating tail weights. The GBG class also has tractable properties: we present various expansions for moments, generating function and quantiles. The model parameters are estimated by maximum likelihood and the usefulness of the new class is illustrated by means of some real data sets. (c) 2011 Elsevier B.V. All rights reserved.

Toward the Optimization of an e-Tongue System Using Information Visualization: A Case Study with Perylene Tetracarboxylic Derivative Films in the Sensing Units

The wide variety of molecular architectures used in sensors and biosensors and the large amount of data generated with some principles of detection have motivated the use of computational methods, such as information visualization techniques, not only to handle the data but also to optimize sensing performance. In this study, we combine projection techniques with micro-Raman scattering and atomic force microscopy (AFM) to address critical issues related to practical applications of electronic tongues (e-tongues) based on impedance spectroscopy. Experimentally, we used sensing units made with thin films of a perylene derivative (AzoPTCD acronym), coating Pt interdigitated electrodes, to detect CuCl(2) (Cu(2+)), methylene blue (MB), and saccharose in aqueous solutions, which were selected due to their distinct molecular sizes and ionic character in solution. The AzoPTCD films were deposited from monolayers to 120 nm via Langmuir-Blodgett (LB) and physical vapor deposition (PVD) techniques. Because the main aspects investigated were how the interdigitated electrodes are coated by thin films (architecture on e-tongue) and the film thickness, we decided to employ the same material for all sensing units. The capacitance data were projected into a 2D plot using the force scheme method, from which we could infer that at low analyte concentrations the electrical response of the units was determined by the film thickness. Concentrations at 10 mu M or higher could be distinguished with thinner films tens of nanometers at most-which could withstand the impedance measurements, and without causing significant changes in the Raman signal for the AzoPTCD film-forming molecules. The sensitivity to the analytes appears to be related to adsorption on the film surface, as inferred from Raman spectroscopy data using MB as analyte and from the multidimensional projections. The analysis of the results presented may serve as a new route to select materials and molecular architectures for novel sensors and biosensors, in addition to suggesting ways to unravel the mechanisms behind the high sensitivity obtained in various sensors.

Synthesis and characterization of the atropisomeric relationships of a substituted N-phenyl-bipyrazole derivative with anti-inflammatory properties

This work describes the atropisomeric relationships of 3-methyl-5-(3-methyl-5-phenyl-1H-pyrazol-1-yl)-1-phenyl-1H-pyrazol-4-amine (2d), which belongs to series 4-aminobipyrazole derivatives designed as anti-inflammatory agents. The 1H nuclear magnetic resonance spectra obtained in the presence of a chiral lanthanide shift salt associated to chiral high-performance liquid chromatography analysis, X-ray diffraction, and molecular modeling tools confirmed that ortho bis-functionalized bipyrazole 2d exists as a mixture of aR,aS-atropisomers. These results provide useful information to understand the pharmacological profile of this derivative and of other 4-aminobipyrazole analogs. Chirality 24:463470, 2012. (c) 2012 Wiley Periodicals, Inc.

The log-exponentiated generalized gamma regression model for censored data

For the first time, we introduce a generalized form of the exponentiated generalized gamma distribution [Cordeiro et al. The exponentiated generalized gamma distribution with application to lifetime data, J. Statist. Comput. Simul. 81 (2011), pp. 827-842.] that is the baseline for the log-exponentiated generalized gamma regression model. The new distribution can accommodate increasing, decreasing, bathtub- and unimodal-shaped hazard functions. A second advantage is that it includes classical distributions reported in the lifetime literature as special cases. We obtain explicit expressions for the moments of the baseline distribution of the new regression model. The proposed model can be applied to censored data since it includes as sub-models several widely known regression models. It therefore can be used more effectively in the analysis of survival data. We obtain maximum likelihood estimates for the model parameters by considering censored data. We show that our extended regression model is very useful by means of two applications to real data.

A generalized finite element method with global-local enrichment functions for confined plasticity problems

The main feature of partition of unity methods such as the generalized or extended finite element method is their ability of utilizing a priori knowledge about the solution of a problem in the form of enrichment functions. However, analytical derivation of enrichment functions with good approximation properties is mostly limited to two-dimensional linear problems. This paper presents a procedure to numerically generate proper enrichment functions for three-dimensional problems with confined plasticity where plastic evolution is gradual. This procedure involves the solution of boundary value problems around local regions exhibiting nonlinear behavior and the enrichment of the global solution space with the local solutions through the partition of unity method framework. This approach can produce accurate nonlinear solutions with a reduced computational cost compared to standard finite element methods since computationally intensive nonlinear iterations can be performed on coarse global meshes after the creation of enrichment functions properly describing localized nonlinear behavior. Several three-dimensional nonlinear problems based on the rate-independent J (2) plasticity theory with isotropic hardening are solved using the proposed procedure to demonstrate its robustness, accuracy and computational efficiency.

Higher spatial derivative field theories

In this work, we employ renormalization group methods to study the general behavior of field theories possessing anisotropic scaling in the spacetime variables. The Lorentz symmetry breaking that accompanies these models are either soft, if no higher spatial derivative is present, or it may have a more complex structure if higher spatial derivatives are also included. Both situations are discussed in models with only scalar fields and also in models with fermions as a Yukawa-like model.

Generalized Metropolis dynamics with a generalized master equation: An approach for time-independent and time-dependent Monte Carlo simulations of generalized spin systems

The extension of Boltzmann-Gibbs thermostatistics, proposed by Tsallis, introduces an additional parameter q to the inverse temperature beta. Here, we show that a previously introduced generalized Metropolis dynamics to evolve spin models is not local and does not obey the detailed energy balance. In this dynamics, locality is only retrieved for q = 1, which corresponds to the standard Metropolis algorithm. Nonlocality implies very time-consuming computer calculations, since the energy of the whole system must be reevaluated when a single spin is flipped. To circumvent this costly calculation, we propose a generalized master equation, which gives rise to a local generalized Metropolis dynamics that obeys the detailed energy balance. To compare the different critical values obtained with other generalized dynamics, we perform Monte Carlo simulations in equilibrium for the Ising model. By using short-time nonequilibrium numerical simulations, we also calculate for this model the critical temperature and the static and dynamical critical exponents as functions of q. Even for q not equal 1, we show that suitable time-evolving power laws can be found for each initial condition. Our numerical experiments corroborate the literature results when we use nonlocal dynamics, showing that short-time parameter determination works also in this case. However, the dynamics governed by the new master equation leads to different results for critical temperatures and also the critical exponents affecting universality classes. We further propose a simple algorithm to optimize modeling the time evolution with a power law, considering in a log-log plot two successive refinements.

delta-Lactam derivative from thermophilic soil fungus exhibits in vitro anti-allergic activity

From cultures of thermophilic soil fungus Humicola grisea var thermoidea, a delta-lactam derivative (3-(2-(4-hydroxyphenyl)-2-oxoethyl)-5,6-dihydropyridin-2( 1H)-one) that displayed anti-allergic activity was isolated, which was predicted by in silico computational chemistry approaches. The in vitro anti-allergic activity was investigated by beta-hexosaminidase release assay in rat basophilic leukaemia RBL-2H3 cells. The delta-lactam derivative exhibited similar anti-allergic activity (IC50 = 18.7 +/- 6.7 mu M) in comparison with ketotifen fumarate (IC50 = 15.0 +/- 1.3 mu M) and stronger anti-allergic activity than azelastine (IC50 = 32.0 mu M). Also, the MTT cytotoxicity assay with RBL-2H3 cells showed that delta-lactam does not display cytotoxicity at concentrations lower than 50 mu M. This study suggests that the delta-lactam derivative has the potential to be used as a lead compound in the development of anti-allergic drugs for clinical use in humans.

Generalized non-commutative inflation

Non-commutative geometry indicates a deformation of the energy-momentum dispersion relation f (E) = E/pc (not equal 1) for massless particles. This distorted energy-momentum relation can affect the radiation-dominated phase of the universe at sufficiently high temperature. This prompted the idea of non-commutative inflation by Alexander et al (2003 Phys. Rev. D 67 081301) and Koh and Brandenberger (2007 JCAP06(2007) 021 and JCAP11(2007) 013). These authors studied a one-parameter family of a non-relativistic dispersion relation that leads to inflation: the a family of curves f (E) = 1 + (lambda E)(alpha). We show here how the conceptually different structure of symmetries of non-commutative spaces can lead, in a mathematically consistent way, to the fundamental equations of non-commutative inflation driven by radiation. We describe how this structure can be considered independently of (but including) the idea of non-commutative spaces as a starting point of the general inflationary deformation of SL(2, C). We analyze the conditions on the dispersion relation that leads to inflation as a set of inequalities which plays the same role as the slow-roll conditions on the potential of a scalar field. We study conditions for a possible numerical approach to obtain a general one-parameter family of dispersion relations that lead to successful inflation.

On Wald Residuals in Generalized Linear Models

A rigorous asymptotic theory for Wald residuals in generalized linear models is not yet available. The authors provide matrix formulae of order O(n(-1)), where n is the sample size, for the first two moments of these residuals. The formulae can be applied to many regression models widely used in practice. The authors suggest adjusted Wald residuals to these models with approximately zero mean and unit variance. The expressions were used to analyze a real dataset. Some simulation results indicate that the adjusted Wald residuals are better approximated by the standard normal distribution than the Wald residuals.

ON THE CONSISTENCY OF TWISTED GENERALIZED WEYL ALGEBRAS

A twisted generalized Weyl algebra A of degree n depends on a. base algebra R, n commuting automorphisms sigma(i) of R, n central elements t(i) of R and on some additional scalar parameters. In a paper by Mazorchuk and Turowska, it is claimed that certain consistency conditions for sigma(i) and t(i) are sufficient for the algebra to be nontrivial. However, in this paper we give all example which shows that this is false. We also correct the statement by finding a new set of consistency conditions and prove that the old and new conditions together are necessary and sufficient for the base algebra R to map injectively into A. In particular they are sufficient for the algebra A to be nontrivial. We speculate that these consistency relations may play a role in other areas of mathematics, analogous to the role played by the Yang-Baxter equation in the theory of integrable systems.