Bivariate gamma-geometric law and its induced Levy process

In this article we introduce a three-parameter extension of the bivariate exponential-geometric (BEG) law (Kozubowski and Panorska, 2005) [4]. We refer to this new distribution as the bivariate gamma-geometric (BGG) law. A bivariate random vector (X, N) follows the BGG law if N has geometric distribution and X may be represented (in law) as a sum of N independent and identically distributed gamma variables, where these variables are independent of N. Statistical properties such as moment generation and characteristic functions, moments and a variance-covariance matrix are provided. The marginal and conditional laws are also studied. We show that BBG distribution is infinitely divisible, just as the BEG model is. Further, we provide alternative representations for the BGG distribution and show that it enjoys a geometric stability property. Maximum likelihood estimation and inference are discussed and a reparametrization is proposed in order to obtain orthogonality of the parameters. We present an application to a real data set where our model provides a better fit than the BEG model. Our bivariate distribution induces a bivariate Levy process with correlated gamma and negative binomial processes, which extends the bivariate Levy motion proposed by Kozubowski et al. (2008) [6]. The marginals of our Levy motion are a mixture of gamma and negative binomial processes and we named it BMixGNB motion. Basic properties such as stochastic self-similarity and the covariance matrix of the process are presented. The bivariate distribution at fixed time of our BMixGNB process is also studied and some results are derived, including a discussion about maximum likelihood estimation and inference. (C) 2012 Elsevier Inc. All rights reserved.

The exponential COM-Poisson distribution

The Conway-Maxwell Poisson (COMP) distribution as an extension of the Poisson distribution is a popular model for analyzing counting data. For the first time, we introduce a new three parameter distribution, so-called the exponential-Conway-Maxwell Poisson (ECOMP) distribution, that contains as sub-models the exponential-geometric and exponential-Poisson distributions proposed by Adamidis and Loukas (Stat Probab Lett 39:35-42, 1998) and KuAY (Comput Stat Data Anal 51:4497-4509, 2007), respectively. The new density function can be expressed as a mixture of exponential density functions. Expansions for moments, moment generating function and some statistical measures are provided. The density function of the order statistics can also be expressed as a mixture of exponential densities. We derive two formulae for the moments of order statistics. The elements of the observed information matrix are provided. Two applications illustrate the usefulness of the new distribution to analyze positive data.

The geometric Birnbaum-Saunders regression model with cure rate

In this paper, we propose a cure rate survival model by assuming the number of competing causes of the event of interest follows the Geometric distribution and the time to event follow a Birnbaum Saunders distribution. We consider a frequentist analysis for parameter estimation of a Geometric Birnbaum Saunders model with cure rate. Finally, to analyze a data set from the medical area. (C) 2011 Elsevier B.V. All rights reserved.

On scale-mixture Birnbaum-Saunders distributions

We present for the first time a justification on the basis of central limit theorems for the family of life distributions generated from scale-mixture of normals. This family was proposed by Balakrishnan et al. (2009) and can be used to accommodate unexpected observations for the usual Birnbaum-Saunders distribution generated from the normal one. The class of scale-mixture of normals includes normal, slash, Student-t, logistic, double-exponential, exponential power and many other distributions. We present a model for the crack extensions where the limiting distribution of total crack extensions is in the class of scale-mixture of normals. (C) 2012 Elsevier B.V. All rights reserved.

A new long-term lifetime distribution induced by a latent complementary risk framework

In this paper, we proposed a new three-parameter long-term lifetime distribution induced by a latent complementary risk framework with decreasing, increasing and unimodal hazard function, the long-term complementary exponential geometric distribution. The new distribution arises from latent competing risk scenarios, where the lifetime associated scenario, with a particular risk, is not observable, rather we observe only the maximum lifetime value among all risks, and the presence of long-term survival. The properties of the proposed distribution are discussed, including its probability density function and explicit algebraic formulas for its reliability, hazard and quantile functions and order statistics. The parameter estimation is based on the usual maximum-likelihood approach. A simulation study assesses the performance of the estimation procedure. We compare the new distribution with its particular cases, as well as with the long-term Weibull distribution on three real data sets, observing its potential and competitiveness in comparison with some usual long-term lifetime distributions.

GEOMETRIC RELATIONS BETWEEN SPACES OF NUCLEAR OPERATORS AND SPACES OF COMPACT OPERATORS

We extend and provide a vector-valued version of some results of C. Samuel about the geometric relations between the spaces of nuclear operators N(E, F) and spaces of compact operators K(E, F), where E and F are Banach spaces C(K) of all continuous functions defined on the countable compact metric spaces K equipped with the supremum norm. First we continue Samuel's work by proving that N(C(K-1), C(K-2)) contains no subspace isomorphic to K(C(K-3), C(K-4)) whenever K-1, K-2, K-3 and K-4 are arbitrary infinite countable compact metric spaces. Then we show that it is relatively consistent with ZFC that the above result and the main results of Samuel can be extended to C(K-1, X), C(K-2,Y), C(K-3, X) and C(K-4, Y) spaces, where K-1, K-2, K-3 and K-4 are arbitrary infinite totally ordered compact spaces; X comprises certain Banach spaces such that X* are isomorphic to subspaces of l(1); and Y comprises arbitrary subspaces of l(p), with 1 < p < infinity. Our results cover the cases of some non-classical Banach spaces X constructed by Alspach, by Alspach and Benyamini, by Benyamini and Lindenstrauss, by Bourgain and Delbaen and also by Argyros and Haydon.

Lyotropic mixture made of potassium laurate/1-undecanol/K2SO4/water presenting high birefringences and large biaxial nematic phase domain: a laser conoscopy study

The lyotropic liquid crystalline quaternary mixture made of potassium laurate (KL), potassium sulphate, 1-undecanol and water was investigated by experimental optical methods (optical microscopy and laser conoscopy). In a particular temperature and relative concentrations range, the three nematic phases (two uniaxial and one biaxial) were identified. The biaxial domain in the temperature/KL concentration surface is larger when compared to other lyotropic mixtures. Moreover, this new mixture gives nematic phases with higher birefringence than similar systems. The behavior of the symmetric tensor order parameter invariants sigma(3) and sigma(2) calculated from the measured optical birefringences supports that the uniaxial-to-biaxial transitions are of second order, described by a mean-field theory.

Further monoterpene chromane esters from Peperomia obtusifolia: VCD determination of the absolute configuration of a new diastereomeric mixture

A reinvestigation of the monoterpene chromane ester enriched fraction from Peperomia obtusifolia using chiral chromatography led to the identification of a minor peak, which was elucidated by NMR and HRMS as fenchyl-3,4-dihydro-5-hydroxy-2,7-dimethyl-8-(3 ''-methyl-2 ''-butenyl)-2-(4'-methyl-1',3'-pentadienyl)-2H-1-benzopyran-6-carboxylate, the same structure assigned to two other fenchyl esters described previously, pointing out a stereoisomeric relationship among them. Further NMR analysis revealed that it was actually a mixture of two compounds, whose absolute configurations were determined by VCD measurements. Although, almost no vibrational transitions could be assigned to the chiral chromane, the experimental VCD spectrum was largely opposite to that obtained for the average experimental VCD [(2S,1'''R,2'''R,4'''S + 2R,1'''R,2'''R,4'''S)/2] for fenchol derivatives. These results allowed us to assign the putative compounds as a racemic mixture of the chiral chromane esterified with the monoterpene (1S,2S,4R)fenchol, which had not been identified in our early work. (C) 2012 Elsevier Ltd. All rights reserved.

Biaxial nematic phase in the Maier-Saupe model for a mixture of discs and cylinders

We analyze the global phase diagram of a Maier-Saupe lattice model with the inclusion of shape-disordered degrees of freedom to mimic a mixture of oblate and prolate molecules (discs and cylinders). In the neighborhood of a Landau multicritical point, solutions of the statistical problem can be written as a Landau-de Gennes expansion for the free energy. If the shape-disordered degrees of freedom are quenched, we confirm the existence of a biaxial nematic structure. If orientational and disorder degrees of freedom are allowed to thermalize, this biaxial solution becomes thermodynamically unstable. Also, we use a two-temperature formalism to mimic the presence of two distinct relaxation times, and show that a slight departure from complete thermalization is enough to stabilize a biaxial nematic phase.

Effect of alkyl chain length of alcohols on nematic uniaxial-to-biaxial phase transitions in a potassium laurate/alcohol/K2SO4/water lyotropic mixture

Lyotropic liquid crystalline quaternary mixtures of potassium laurate (KL), potassium sulphate (K2SO4)/alcohol (n-OH)/water, with the alcohols having different numbers of carbon atoms in the alkyl chain (n), from 1-octanol to 1-hexadecanol, were investigated by optical techniques (optical microscopy and laser conoscopy). The biaxial nematic phase domain is present in a window of values of n = n(KL) +/- 2, where n(KL) = 11 is the number of carbon atoms in the alkyl chain of KL. The biaxial phase domain became smaller and the uniaxial-to-biaxial phase transition temperatures shifted to relatively higher temperatures upon going from 1-nonanol to 1-tridecanol. Moreover, compared with other lyotropic mixtures these new mixtures present high birefringence values, which we expect to be related to the micellar shape anisotropy. Our results are interpreted assuming that alcohol molecules tend to segregate in the micelles in a way that depends on the relative value of n with respect to nKL. The larger the value of n, the more alcohol molecules tend to be located in the curved parts of the micelle, favoring the uniaxial nematic calamitic phase with respect to the biaxial and uniaxial discotic nematic phases.

Infiltration of a mixture of immune cells may be related to good prognosis in patients with differentiated thyroid carcinoma

Objective Immune responses against differentiated thyroid carcinomas (DTC) have long been recognized. We aimed to investigate the role of immune cell infiltration in the progression of DTC. Design We studied 398 patients 253 with papillary and 13 with follicular thyroid cancers, as well as 132 with nonmalignant tissues. Patients and measurements Immune cell infiltration was identified using CD3, CD4, CD8, CD20, CD68 and FoxP3 immunohistochemical markers. In addition, we assessed colocalization of CD4 and IL-17 to identify Th17 lymphocytic infiltration and colocalization of CD33 and CD11b to identify infiltration of myeloid-derived suppressor cells (MDSC). Results Immune cells infiltrated malignant tissues more often than benign lesions. The presence of chronic lymphocytic thyroiditis (CLT) concurrent to DTC, CD68+, CD4+, CD8+, CD20+, FoxP3+ and Th17 lymphocytes but not MDSCs was associated with clinical and pathological features of lower tumour aggressiveness and a more favourable patient outcome. A log-rank test confirmed an association between concurrent CLT, tumour-associated macrophage infiltration, and CD8+ lymphocytes and an increased in disease-free survival, suggesting that evidence of these immune reactions is associated with a favourable prognosis. Conclusion Our data suggest that the tumour or peri-tumoural microenvironment may act to modify the observed pattern of immune response. Immune cell infiltration and the presence of concurrent CLT helped characterize specific tumour histotypes associated with favourable prognostic features.

Exploring the coordination chemistry of isomerizable terpyridine derivatives for successful analyses of cis and trans isomers by travelling wave ion mobility mass spectrometry

The photochemical cis-trans isomerization of the 4-{4-[2-(pyridin-4-yl)ethenyl]phenyl}-2,2': 6',2''-terpyridine ligand (vpytpy) was investigated by UV-vis, NMR and TWIM-MS. Ion mobility mass spectrometry was performed pursuing the quantification of the isomeric composition during photolysis, however an in-source trans-to-cis isomerization process was observed. In order to overcome this inherent phenomenon, the isomerization of the vpytpy species was suppressed by complexation, reacting with iron(II) ions, and forming the [Fe(vpytpy)(2)](2+) complex. The strategy of "freezing" the cis-trans isomerizable ligand at a given geometric conformation was effective, preventing further isomerization, thus allowing the distinction of each one of the isomers in the photolysed mixture. In addition, the experimental drift times were related to the calculated surface areas of the three possible cis-cis, cis-trans and trans-trans iron(II) complex isomers. The stabilization of the ligand in a given conformation also allows us to obtain the cis-cis and cis-trans complexes exhibiting the ligand in the metastable cis-conformation, as well as in the thermodynamically stable trans-conformation.