Hypotheses Testing on a Multivariate Null Intercept Errors-in-Variables Model

Considering the Wald, score, and likelihood ratio asymptotic test statistics, we analyze a multivariate null intercept errors-in-variables regression model, where the explanatory and the response variables are subject to measurement errors, and a possible structure of dependency between the measurements taken within the same individual are incorporated, representing a longitudinal structure. This model was proposed by Aoki et al. (2003b) and analyzed under the bayesian approach. In this article, considering the classical approach, we analyze asymptotic test statistics and present a simulation study to compare the behavior of the three test statistics for different sample sizes, parameter values and nominal levels of the test. Also, closed form expressions for the score function and the Fisher information matrix are presented. We consider two real numerical illustrations, the odontological data set from Hadgu and Koch (1999), and a quality control data set.

Three-dimensional description and mathematical characterization of the parasellar internal carotid artery in human infants

Inside the `cavernous sinus` or `parasellar region` the human internal carotid artery takes the shape of a siphon that is twisted and torqued in three dimensions and surrounded by a network of veins. The parasellar section of the internal carotid artery is of broad biological and medical interest, as its peculiar shape is associated with temperature regulation in the brain and correlated with the occurrence of vascular pathologies. The present study aims to provide anatomical descriptions and objective mathematical characterizations of the shape of the parasellar section of the internal carotid artery in human infants and its modifications during ontogeny. Three-dimensional (3D) computer models of the parasellar section of the internal carotid artery of infants were generated with a state-of-the-art 3D reconstruction method and analysed using both traditional morphometric methods and novel mathematical algorithms. We show that four constant, demarcated bends can be described along the infant parasellar section of the internal carotid artery, and we provide measurements of their angles. We further provide calculations of the curvature and torsion energy, and the total complexity of the 3D skeleton of the parasellar section of the internal carotid artery, and compare the complexity of this in infants and adults. Finally, we examine the relationship between shape parameters of the parasellar section of the internal carotid artery in infants, and the occurrence of intima cushions, and evaluate the reliability of subjective angle measurements for characterizing the complexity of the parasellar section of the internal carotid artery in infants. The results can serve as objective reference data for comparative studies and for medical imaging diagnostics. They also form the basis for a new hypothesis that explains the mechanisms responsible for the ontogenetic transformation in the shape of the parasellar section of the internal carotid artery.

Efficient solutions to factored MDPs with imprecise transition probabilities

When modeling real-world decision-theoretic planning problems in the Markov Decision Process (MDP) framework, it is often impossible to obtain a completely accurate estimate of transition probabilities. For example, natural uncertainty arises in the transition specification due to elicitation of MOP transition models from an expert or estimation from data, or non-stationary transition distributions arising from insufficient state knowledge. In the interest of obtaining the most robust policy under transition uncertainty, the Markov Decision Process with Imprecise Transition Probabilities (MDP-IPs) has been introduced to model such scenarios. Unfortunately, while various solution algorithms exist for MDP-IPs, they often require external calls to optimization routines and thus can be extremely time-consuming in practice. To address this deficiency, we introduce the factored MDP-IP and propose efficient dynamic programming methods to exploit its structure. Noting that the key computational bottleneck in the solution of factored MDP-IPs is the need to repeatedly solve nonlinear constrained optimization problems, we show how to target approximation techniques to drastically reduce the computational overhead of the nonlinear solver while producing bounded, approximately optimal solutions. Our results show up to two orders of magnitude speedup in comparison to traditional ""flat"" dynamic programming approaches and up to an order of magnitude speedup over the extension of factored MDP approximate value iteration techniques to MDP-IPs while producing the lowest error of any approximation algorithm evaluated. (C) 2011 Elsevier B.V. All rights reserved.

Symmetry breaking in the genetic code: Finite groups

We investigate the possibility of interpreting the degeneracy of the genetic code, i.e., the feature that different codons (base triplets) of DNA are transcribed into the same amino acid, as the result of a symmetry breaking process, in the context of finite groups. In the first part of this paper, we give the complete list of all codon representations (64-dimensional irreducible representations) of simple finite groups and their satellites (central extensions and extensions by outer automorphisms). In the second part, we analyze the branching rules for the codon representations found in the first part by computational methods, using a software package for computational group theory. The final result is a complete classification of the possible schemes, based on finite simple groups, that reproduce the multiplet structure of the genetic code. (C) 2010 Elsevier Ltd. All rights reserved.

The gas-phase alcoholysis of protonated homoleptic alkoxysilanes

Tetra-alkoxysilanes are common and useful reagents in sol-gel processes and understanding their reactivity is important in the design of new materials. The mechanism of gas-phase reactions that mimic alcoholyis of Si(OMe)(4) (usually known as TMOS) under acidic conditions have been studied by Fourier transform ion cyclotron resonance techniques and density functional calculations at the B3LYP/6-311+G(d,p) level. The proton affinity of TMOS has been estimated at 836.4 kJ mol(-1) and protonation of TMOS gives rise to an ionic species that is best represented as trimethoxysilyl cations associated with a methanol molecule. Protonated TMOS undergoes rapid and sequential substitution of the methoxy groups in the gas-phase upon reaction with alcohols. The calculated energy profile of the reaction indicates that the substitution reaction through an S(N)2 type mechanism may be more favorable than frontal attack at silicon. Furthermore, the sequential substitution reactions are promoted by a mechanism that involves proton shuttle from the most favorable protonation site to the oxygen of the departing group mediated by the neutral reagent molecule.

Structure of chemically prepared poly-(para-phenylenediamine) investigated by spectroscopic techniques

The structure of chemically prepared poly-p-phenylenediamine (PpPD) was investigated by Resonance Raman (RR), FTIR, UV-VIS-NIR, X-ray photoelectron (XPS), X-ray Absorption at Nitrogen K edge (N K XANES), and Electron paramagnetic Resonance (EPR) spectroscopies. XPS, EPR and N K XANES data reveal that polymeric structure is formed mainly by radical cations and dication nitrogens. It excludes the possibility that PpPD chains have azo or phenazinic nitrogens, as commonly is supposed in the literature. The RR spectrum of PpPD shows two characteristic bands at 1527 cm(-1) and 1590 cm(-1) that were assigned to nu C=N and nu C=C of dication units, respectively, similar to polyaniline in pernigraniline base form. The presence of radical cations was confirmed by Raman data owing to the presence of bands at 1325/1370 cm(-1), characteristic of nu C-N of polaronic segments. Thus, all results indicate that PpPD has a doped PANT-like structure, with semi-quinoid and quinoid rings, and has no phenazinic rings, as observed for poly-o-phenylenediamine. (C) 2009 Elsevier Ltd. All rights reserved.