Levy stable distributions via associated integral transform

We present a method of generation of exact and explicit forms of one-sided, heavy-tailed Levy stable probability distributions g(alpha)(x), 0 <= x < infinity, 0 < alpha < 1. We demonstrate that the knowledge of one such a distribution g a ( x) suffices to obtain exactly g(alpha)p ( x), p = 2, 3, .... Similarly, from known g(alpha)(x) and g(beta)(x), 0 < alpha, beta < 1, we obtain g(alpha beta)( x). The method is based on the construction of the integral operator, called Levy transform, which implements the above operations. For a rational, alpha = l/k with l < k, we reproduce in this manner many of the recently obtained exact results for g(l/k)(x). This approach can be also recast as an application of the Efros theorem for generalized Laplace convolutions. It relies solely on efficient definite integration. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4709443]

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.

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.

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.

GENERALIZED FINITE ELEMENT METHOD ON NONCONVENTIONAL HYBRID-MIXED FORMULATION

The generalized finite element method (GFEM) is applied to a nonconventional hybrid-mixed stress formulation (HMSF) for plane analysis. In the HMSF, three approximation fields are involved: stresses and displacements in the domain and displacement fields on the static boundary. The GFEM-HMSF shape functions are then generated by the product of a partition of unity associated to each field and the polynomials enrichment functions. In principle, the enrichment can be conducted independently over each of the HMSF approximation fields. However, stability and convergence features of the resulting numerical method can be affected mainly by spurious modes generated when enrichment is arbitrarily applied to the displacement fields. With the aim to efficiently explore the enrichment possibilities, an extension to GFEM-HMSF of the conventional Zienkiewicz-Patch-Test is proposed as a necessary condition to ensure numerical stability. Finally, once the extended Patch-Test is satisfied, some numerical analyses focusing on the selective enrichment over distorted meshes formed by bilinear quadrilateral finite elements are presented, thus showing the performance of the GFEM-HMSF combination.

Bilateral subthalamic nucleus stimulation for generalized dystonia after bilateral pallidotomy

Background: Thalamotomies and pallidotomies were commonly performed before the deep brain stimulation (DBS) era. Although ablative procedures can lead to significant dystonia improvement, longer periods of analysis reveal disease progression and functional deterioration. Today, the same patients seek additional treatment possibilities. Methods: Four patients with generalized dystonia who previously had undergone bilateral pallidotomy came to our service seeking additional treatment because of dystonic symptom progression. Bilateral subthalamic nucleus DBS (B-STN-DBS) was the treatment of choice. The patients were evaluated with the BurkeFahnMarsden Dystonia Rating Scale (BFMDRS) and the Unified Dystonia Rating Scale (UDRS) before and 2 years after surgery. Results: All patients showed significant functional improvement, averaging 65.3% in BFMDRS (P = .014) and 69.2% in UDRS (P = .025). Conclusions: These results suggest that B-STN-DBS may be an interesting treatment option for generalized dystonia, even for patients who have already undergone bilateral pallidotomy. (c) 2012 Movement Disorder Society

Study of La2-xCaxCuO4 perovskites for the low temperature water gas shift reaction

The effects of small fractions of calcium (x = 0, 0.05, 0.1, 0.15, and 0.20) on the structure and the catalytic properties of La2-xCaxCuO4 peroviskites have been investigated. The samples have been synthesized using the co-precipitation method. Perovskite-type oxides were characterized by XRD, TPR, XPS, XANES, SEM, and TEM. Catalytic tests for the water gas shift reaction (WGSR) were carried out in a tubular reactor at 290 degrees C. All samples showed a well-defined perovskite structure with surface areas between 6 and 18 m(2) g(-1). The partial substitution of La by Ca enhanced the stability of the perovskites and increased their reduction temperature. All catalysts were actives for WGSR, and the best catalytic performance was obtained for the La1.85Ca0.15CuO4 catalyst, but the samples with 5 and 10% of Ca had the best TOF values for reaction. These results can be associated to promoter effect of calcium, the high surface area, and the reducible species Cu-0 and Cu1+. (C) 2011 Elsevier B.V. All rights reserved.

A note on the use of the generalized odds ratio in meta-analysis of association studies involving bi- and tri-allelic polymorphisms

Abstract Background The generalized odds ratio (GOR) was recently suggested as a genetic model-free measure for association studies. However, its properties were not extensively investigated. We used Monte Carlo simulations to investigate type-I error rates, power and bias in both effect size and between-study variance estimates of meta-analyses using the GOR as a summary effect, and compared these results to those obtained by usual approaches of model specification. We further applied the GOR in a real meta-analysis of three genome-wide association studies in Alzheimer's disease. Findings For bi-allelic polymorphisms, the GOR performs virtually identical to a standard multiplicative model of analysis (e.g. per-allele odds ratio) for variants acting multiplicatively, but augments slightly the power to detect variants with a dominant mode of action, while reducing the probability to detect recessive variants. Although there were differences among the GOR and usual approaches in terms of bias and type-I error rates, both simulation- and real data-based results provided little indication that these differences will be substantial in practice for meta-analyses involving bi-allelic polymorphisms. However, the use of the GOR may be slightly more powerful for the synthesis of data from tri-allelic variants, particularly when susceptibility alleles are less common in the populations (≤10%). This gain in power may depend on knowledge of the direction of the effects. Conclusions For the synthesis of data from bi-allelic variants, the GOR may be regarded as a multiplicative-like model of analysis. The use of the GOR may be slightly more powerful in the tri-allelic case, particularly when susceptibility alleles are less common in the populations.

Natural blood feeding and temperature shift modulate the global transcriptional profile of Rickettsia rickettsii infecting its tick vector

Rickettsia rickettsii is an obligate intracellular tick-borne bacterium that causes Rocky Mountain Spotted Fever (RMSF), the most lethal spotted fever rickettsiosis. When an infected starving tick begins blood feeding from a vertebrate host, R. rickettsii is exposed to a temperature elevation and to components in the blood meal. These two environmental stimuli have been previously associated with the reactivation of rickettsial virulence in ticks, but the factors responsible for this phenotype conversion have not been completely elucidated. Using customized oligonucleotide microarrays and high-throughput microfluidic qRT-PCR, we analyzed the effects of a 10 degrees C temperature elevation and of a blood meal on the transcriptional profile of R. rickettsii infecting the tick Amblyomma aureolatum. This is the first study of the transcriptome of a bacterium in the genus Rickettsia infecting a natural tick vector. Although both stimuli significantly increased bacterial load, blood feeding had a greater effect, modulating five-fold more genes than the temperature upshift. Certain components of the Type IV Secretion System (T4SS) were up-regulated by blood feeding. This suggests that this important bacterial transport system may be utilized to secrete effectors during the tick vector's blood meal. Blood feeding also up-regulated the expression of antioxidant enzymes, which might correspond to an attempt by R. rickettsii to protect itself against the deleterious effects of free radicals produced by fed ticks. The modulated genes identified in this study, including those encoding hypothetical proteins, require further functional analysis and may have potential as future targets for vaccine development.

The Wiener criterion for the Laplacian and the heat operator

La tesi presenta il criterio di regolarità di Wiener dell’ambito classico dell’operatore di Laplace ed in seguito alcune nozioni di teoria del potenziale e la dimostrazione del criterio nel caso dell’operatore del calore; in questa seconda sezione viene dedicata particolare attenzione alle formule di media e ad una diseguaglianza forte di Harnack, che risultano fondamentali nella trattazione dell’argomento centrale.

Sviluppo di nuovi catalizzatori per la reazione di water gas shift a media temperatura

L’idrogeno è un elemento di elevato interesse economico, con una produzione industriale che supera i 55 x 1010 m3/anno e notevoli prospettive di sviluppo delle sue applicazioni. Attualmente l’idrogeno è prodotto principalmente in impianti di larga scala (circa 1000 m3/h) da combustibili fossili attraverso processi di steam reforming ed ossidazione parziale catalitica. Per aumentare la produzione di idrogeno un ruolo fondamentale è svolto dalla reazione di water gas shift (WGS) che abbatte il contenuto di CO, massimizzando la produzione di idrogeno. La reazione è condotta industrialmente in due stadi, operanti ad alta temperatura (HTS, circa 350 °C) e bassa temperatura (LTS, circa 250 °C), utilizzando rispettivamente catalizzatori a base di ferro o rame. Tuttavia, è evidente l’interesse per nuove formulazioni in grado di operare in un unico stadio a temperatura intermedia (MTS), mantenendo le caratteristiche ottimali di attività e stabilità. In questo lavoro di tesi, condotto in collaborazione con AIR LIQUIDE (F), è stato affrontato uno studio della reazione di WGS finalizzato allo sviluppo di nuove formulazioni attive e stabili nell’MTS. In particolare, sono stati sintetizzati precursori idrotalcitici Cu/Zn/Al (contenenti carbonati o silicati), con bassi contenuti di rame (diversamente da quanto riportato in letteratura), modulandone le proprietà chimico-fisiche, l’attività catalitica e la stabilità con il tempo di reazione. Si è osservato come i catalizzatori con minori contenuti di rame ed ottenuti da precursori contenenti carbonati mostrassero un’elevata attività e selettività nell’MTS, raggiungendo valori di conversione del CO analoghi a quelli all’equilibrio termodinamico già a 300 °C, indipendentemente dai valori del rapporto S/DG e del tempo di contatto. Tutti i catalizzatori mostrano un’elevata stabilità con il tempo di reazione, con incrementi del quantitativo del CO in uscita dopo 100h di circa lo 0,7 % v/v. I catalizzatori scaricati dopo le prove catalitiche evidenziano gli effetti dei processi di sinterizzazione (diminuzione dell’area superficiale ed incremento delle dimensioni dei cristalliti), la cui entità diminuisce al diminuire del contenuto di rame. Infine, confrontando l’attività dei migliori catalizzatori preparati in questo lavoro di tesi con quella di uno dei più utilizzati catalizzatori commerciali per la reazione di WGS a bassa temperatura, si sono osservati valori di attività analoghi, raggiungendo quelli di equilibrio per temperature  300°C, ma con una attività significativamente superiore nelle condizioni LTS, soprattutto considerando il valore del tempo di contatto inferiore a quelli comunemente utilizzati negli impianti industriali.