The Dirichlet distribution with respect to the Aitchison measure on the simplex - a first approach

The algebraic-geometric structure of the simplex, known as Aitchison geometry, is used to look at the Dirichlet family of distributions from a new perspective. A classical Dirichlet density function is expressed with respect to the Lebesgue measure on real space. We propose here to change this measure by the Aitchison measure on the simplex, and study some properties and characteristic measures of the resulting density

A new distribution on the simplex containing the Dirichlet family

The Dirichlet family owes its privileged status within simplex distributions to easyness of interpretation and good mathematical properties. In particular, we recall fundamental properties for the analysis of compositional data such as closure under amalgamation and subcomposition. From a probabilistic point of view, it is characterised (uniquely) by a variety of independence relationships which makes it indisputably the reference model for expressing the non trivial idea of substantial independence for compositions. Indeed, its well known inadequacy as a general model for compositional data stems from such an independence structure together with the poorness of its parametrisation. In this paper a new class of distributions (called Flexible Dirichlet) capable of handling various dependence structures and containing the Dirichlet as a special case is presented. The new model exhibits a considerably richer parametrisation which, for example, allows to model the means and (part of) the variance-covariance matrix separately. Moreover, such a model preserves some good mathematical properties of the Dirichlet, i.e. closure under amalgamation and subcomposition with new parameters simply related to the parent composition parameters. Furthermore, the joint and conditional distributions of subcompositions and relative totals can be expressed as simple mixtures of two Flexible Dirichlet distributions. The basis generating the Flexible Dirichlet, though keeping compositional invariance, shows a dependence structure which allows various forms of partitional dependence to be contemplated by the model (e.g. non-neutrality, subcompositional dependence and subcompositional non-invariance), independence cases being identified by suitable parameter configurations. In particular, within this model substantial independence among subsets of components of the composition naturally occurs when the subsets have a Dirichlet distribution

Vertebrates Limb Geometry in the Simplex space

A novel metric comparison of the appendicular skeleton (fore and hind limb) of different vertebrates using the Compositional Data Analysis (CDA) methodological approach it’s presented. 355 specimens belonging in various taxa of Dinosauria (Sauropodomorpha, Theropoda, Ornithischia and Aves) and Mammalia (Prothotheria, Metatheria and Eutheria) were analyzed with CDA. A special focus has been put on Sauropodomorpha dinosaurs and the Aitchinson distance has been used as a measure of disparity in limb elements proportions to infer some aspects of functional morphology

Experimental design on the simplex

Optimum experimental designs depend on the design criterion, the model and the design region. The talk will consider the design of experiments for regression models in which there is a single response with the explanatory variables lying in a simplex. One example is experiments on various compositions of glass such as those considered by Martin, Bursnall, and Stillman (2001). Because of the highly symmetric nature of the simplex, the class of models that are of interest, typically Scheff´e polynomials (Scheff´e 1958) are rather different from those of standard regression analysis. The optimum designs are also rather different, inheriting a high degree of symmetry from the models. In the talk I will hope to discuss a variety of modes for such experiments. Then I will discuss constrained mixture experiments, when not all the simplex is available for experimentation. Other important aspects include mixture experiments with extra non-mixture factors and the blocking of mixture experiments. Much of the material is in Chapter 16 of Atkinson, Donev, and Tobias (2007). If time and my research allows, I would hope to finish with a few comments on design when the responses, rather than the explanatory variables, lie in a simplex. References Atkinson, A. C., A. N. Donev, and R. D. Tobias (2007). Optimum Experimental Designs, with SAS. Oxford: Oxford University Press. Martin, R. J., M. C. Bursnall, and E. C. Stillman (2001). Further results on optimal and efficient designs for constrained mixture experiments. In A. C. Atkinson, B. Bogacka, and A. Zhigljavsky (Eds.), Optimal Design 2000, pp. 225–239. Dordrecht: Kluwer. Scheff´e, H. (1958). Experiments with mixtures. Journal of the Royal Statistical Society, Ser. B 20, 344–360. 1

Effect of viral load on the outcome of herpes zoster

Varicella-zoster virus (VZV) is a member of the Herpesviridae family, primary infection with which causes varicella, more commonly known as chicken pox. Characteristic of members of the alphaherpesvirus subfamily, VZV is neurotropic and establishes latency in sensory neurons. Reactivation of VZV causes herpes zoster, also known as shingles. The most frequent complication following zoster is chronic and often debilitating pain called postherpetic neuralgia (PHN), which can last for months after the disappearance of a rash. During episodes of acute zoster, VZV viremia occurs in some, but not all, patients; however, the effect of the viral load on the disease outcome is not known. Here we describe the development of a highly specific, sensitive, and reproducible real-time PCR assay to investigate the factors that may contribute to the presence and levels of baseline viremia in patients with zoster and to determine the relationship between viremia and the development and persistence of PHN. VZV DNA was detected in the peripheral blood mononuclear cells (PBMCs) of 78% of patients with acute zoster and in 9% of healthy asymptomatic blood donors. The presence of VZV in the PBMCs of patients with acute zoster was independently associated with age and being on antivirals but not with gender, immune status, extent of rash, the age of the rash at the time of blood sampling, having a history of prodromal pain, or the extent of acute pain. Prodromal pain was significantly associated with higher baseline viral loads. Viral load levels were not associated with the development or persistence of PHN at 6, 12, or 26 weeks.

Persistence of varicella-zoster virus viraemia in patients with herpes zoster.

BACKGROUND: Herpes zoster is caused by the reactivation of varicella-zoster virus from sensory neurons. The commonest complication following zoster is chronic pain termed post herpetic neuralgia. OBJECTIVES: To investigate the dynamics of VZV viraemia and viral load following the resolution of zoster and its relationship to PHN development. STUDY DESIGN: Blood samples were collected at baseline, 1 month, 3 months and 6 month from a prospective study of 63 patients with active zoster. Quantification of VZV DNA in whole blood was performed using a real-time PCR assay. RESULTS: During acute zoster, all patients had detectable VZV DNA in their blood. VZV DNA remained detectable in the blood of 91% of patients at 6 months although levels declined significantly (p<0.0001). A history of prodromal symptoms (p=0.005) and severity of pain at baseline (p=0.038) as well as taking antivirals (p=0.046) and being immunocompromised (p=0.043) were associated, with longer time to recovery from PHN. Viral DNA loads were consistently higher in patients with risk factors for PHN and higher viral DNA loads over time were associated with longer time to recovery (p=0.058 overall and 0.038 in immunocompetent). CONCLUSIONS: Based on these observations we hypothesise that VZV replication persists following acute shingles and that higher viral DNA loads contribute to the risk factors for PHN.

Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex

In this paper we study convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d >= 2. Optimal error estimates are established in the case of Sobolev regularity and illustrated on several numerical examples. The proof is based on the collapsed coordinate transform and the expansion into various polynomial bases involving Jacobi polynomials and their antiderivatives. The results of the present paper generalize corresponding estimates for cubes in Rd from [P. Houston, C. Schwab, E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002), no. 6, 2133-2163].

Implementação paralela escalável e eficiente do algoritmo simplex padrão em arquitetura multicore

This work presents a scalable and efficient parallel implementation of the Standard Simplex algorithm in the multicore architecture to solve large scale linear programming problems. We present a general scheme explaining how each step of the standard Simplex algorithm was parallelized, indicating some important points of the parallel implementation. Performance analysis were conducted by comparing the sequential time using the Simplex tableau and the Simplex of the CPLEXR IBM. The experiments were executed on a shared memory machine with 24 cores. The scalability analysis was performed with problems of different dimensions, finding evidence that our parallel standard Simplex algorithm has a better parallel efficiency for problems with more variables than constraints. In comparison with CPLEXR , the proposed parallel algorithm achieved a efficiency of up to 16 times better

Cellular immune responses in mice immunized with Anisakis simplex larval antigens

Cellular immune responses to Anisakis simplex L3 antigens were investigated in BALB/c mice injected subcutaneously with a homologous crude extract (CE). Popliteal lymph nodes (PLN) were found to be increased in size and weight after A. simplex CE footpad injection. The effects of A. simplex CE in vitro proliferation were assayed with non-fractionated PLN cells or nylon-wool purified T cells derived from pooled lymph node cells of mice subcutaneously injected with CE. Spleen cells from immunized animals (antigen alone, or larva alone, or antigen plus larva) were studied by flow cytometry. The immunization induced a high proportion of CD4 + and TCR alpha beta + T cells. The number of B cells (CD45 + and TCR alpha beta-) in pre-immunized and infected mice was lower than that observed in animals subjected to infection only. The number of CD4 + T cells increased in the infected and in the pre-immunized and infected mice. In the latter, a decrease of CD8a + T cells was noted. The greatest increase in CD8a+ and TCR alpha beta- T cells was found in mice that had been subjected to infection only. Histological analysis showed that the most prominent lesions were gastric and intestinal in animals infected orally with one larva.

Reformulation of variational inequalities on a simplex and compactification of complementarity problems

Many variational inequality problems (VIPs) can be reduced, by a compactification procedure, to a VIP on the canonical simplex. Reformulations of this problem are studied, including smooth reformulations with simple constraints and unconstrained reformulations based on the penalized Fischer-Burmeister function. It is proved that bounded level set results hold for these reformulations under quite general assumptions on the operator. Therefore, it can be guaranteed that minimization algorithms generate bounded sequences and, under monotonicity conditions, these algorithms necessarily nd solutions of the original problem. Some numerical experiments are presented.

Herpes Virus Bovino tipo 1 (BoHV-1) como posible causa de encefalitis en bovinos de la región del Magdalena Medio Colombiano. Estudio serológico y análisis epidemiológico

The bovine Herpesvirus type 1 and type 5 (BoHV-1 and BoHV-5), causing diseases and significant economic losses in farms of worldwide. Both affect the nervous system of cattle, although BoHV-5 has been the most associated with this type of pathogenesis. Given the death of animals with nervous symptoms and negative diagnoses for rabies virus in the area of study, this research focused on the detection of positive reactors to bovine herpes virus serum neutralization. We collected 518 blood samples from animals without Herpesvirus vaccine, in the municipalities of Caparrapi, Cimitarra, Honda and Victoria, in the Middle Magdalena River Region. In addition, epidemiological information useful to discuss neurological disease was collected through primary and secondary sources. For the analysis of data was used chi-square test by identification of relationship between evidence of viral infection and the variables recorded. The results revealed that 286 cases were positive for Herpesvirus infection, corresponding to a prevalence of 55.5%, however, there was no statistical relationship (p < 0.05) between the presence of antibodies and the variables analyzed. In conclusion, some cases of neurological disease in cattle in this region could be due to infection with herpes viruses. We discussed about the presence of BoHV-1 and BoHV-5 in the ambient, diagnosis and monitoring plans, as well as economic losses, which may cause in herds in this area.

Planejamento da expansão de sistemas de transmissão usando algoritmos tipo dual simplex especializados em uma estrutura branch and bound

Pós-graduação em Engenharia Elétrica - FEIS

OPUS: interactive software for solving linear programming models using the simplex algorithm

Includes bibliography

Regressão Simplex aplicada a delineamentos de mistura e utilização do Algoritmo Boosting

In the composition of this work are present two parts. The first part contains the theory used. The second part contains the two articles. The first article examines two models of the class of generalized linear models for analyzing a mixture experiment, which studied the effect of different diets consist of fat, carbohydrate, and fiber on tumor expression in mammary glands of female rats, given by the ratio mice that had tumor expression in a particular diet. Mixture experiments are characterized by having the effect of collinearity and smaller sample size. In this sense, assuming normality for the answer to be maximized or minimized may be inadequate. Given this fact, the main characteristics of logistic regression and simplex models are addressed. The models were compared by the criteria of selection of models AIC, BIC and ICOMP, simulated envelope charts for residuals of adjusted models, odds ratios graphics and their respective confidence intervals for each mixture component. It was concluded that first article that the simplex regression model showed better quality of fit and narrowest confidence intervals for odds ratio. The second article presents the model Boosted Simplex Regression, the boosting version of the simplex regression model, as an alternative to increase the precision of confidence intervals for the odds ratio for each mixture component. For this, we used the Monte Carlo method for the construction of confidence intervals. Moreover, it is presented in an innovative way the envelope simulated chart for residuals of the adjusted model via boosting algorithm. It was concluded that the Boosted Simplex Regression model was adjusted successfully and confidence intervals for the odds ratio were accurate and lightly more precise than the its maximum likelihood version.