Absolute determination of soluble potassium in tea infusion by gamma-ray spectroscopy

Potassium content in tea brew was determined by gamma-ray spectroscopy, Using the 1461 keV gamma-ray fro M (40)K, the naturally occurring radioactive isotope of potassium. We measured radiation with a shielded HPGe detector from individual test samples of tea leaves, before and after infusion preparation, and from commercial instant tea powder. The correction factor for the gamma-ray self-absorption in the extended source was determined with the help of Monte-Carlo simulations. This gamma-ray spectroscopy technique enabled the absolute determination of potassium content with a relative uncertainty smaller than 4%, at the one standard deviation confidence level, showing the feasibility of this method. An experiment to evaluate a possible systematic Uncertainty due to K distribution heterogeneity in the sample was performed, with file result that the corresponding relative standard deviation is smaller than 2% at 95% confidence level. (C) 2009 Elsevier Ltd. All rights reserved.

Shared information in stationary states at criticality

We consider bipartitions of one-dimensional extended systems whose probability distribution functions describe stationary states of stochastic models. We define estimators of the information shared between the two subsystems. If the correlation length is finite, the estimators stay finite for large system sizes. If the correlation length diverges, so do the estimators. The definition of the estimators is inspired by information theory. We look at several models and compare the behaviors of the estimators in the finite-size scaling limit. Analytical and numerical methods as well as Monte Carlo simulations are used. We show how the finite-size scaling functions change for various phase transitions, including the case where one has conformal invariance.

Density profiles in the raise and peel model with and without a wall; physics and combinatorics

We consider the raise and peel model of a one-dimensional fluctuating interface in the presence of an attractive wall. The model can also describe a pair annihilation process in disordered unquenched media with a source at one end of the system. For the stationary states, several density profiles are studied using Monte Carlo simulations. We point out a deep connection between some profiles seen in the presence of the wall and in its absence. Our results are discussed in the context of conformal invariance ( c = 0 theory). We discover some unexpected values for the critical exponents, which are obtained using combinatorial methods. We have solved known ( Pascal`s hexagon) and new (split-hexagon) bilinear recurrence relations. The solutions of these equations are interesting in their own right since they give information on certain classes of alternating sign matrices.

Culture-area relation in Axelrod`s model for culture dissemination

Axelrod`s model for culture dissemination offers a nontrivial answer to the question of why there is cultural diversity given that people`s beliefs have a tendency to become more similar to each other`s as they interact repeatedly. The answer depends on the two control parameters of the model, namely, the number F of cultural features that characterize each agent, and the number q of traits that each feature can take on, as well as on the size A of the territory or, equivalently, on the number of interacting agents. Here, we investigate the dependence of the number C of distinct coexisting cultures on the area A in Axelrod`s model, the culture-area relationship, through extensive Monte Carlo simulations. We find a non-monotonous culture-area relation, for which the number of cultures decreases when the area grows beyond a certain size, provided that q is smaller than a threshold value q (c) = q (c) (F) and F a parts per thousand yen 3. In the limit of infinite area, this threshold value signals the onset of a discontinuous transition between a globalized regime marked by a uniform culture (C = 1), and a completely polarized regime where all C = q (F) possible cultures coexist. Otherwise, the culture-area relation exhibits the typical behavior of the species-area relation, i.e., a monotonically increasing curve the slope of which is steep at first and steadily levels off at some maximum diversity value.

The n-site approximation for the triplet-creation model

The nonequilibrium phase transition of the one-dimensional triplet-creation model is investigated using the n-site approximation scheme. We find that the phase diagram in the space of parameters (gamma, D), where gamma is the particle decay probability and D is the diffusion probability, exhibits a tricritical point for n >= 4. However, the fitting of the tricritical coordinates (gamma(t), D(t)) using data for 4 <= n <= 13 predicts that gamma(t) becomes negative for n >= 26, indicating thus that the phase transition is always continuous in the limit n -> infinity. However, the large discrepancies between the critical parameters obtained in this limit and those obtained by Monte Carlo simulations, as well as a puzzling non-monotonic dependence of these parameters on the order of the approximation n, argue for the inadequacy of the n-site approximation to study the triplet-creation model for computationally feasible values of n.

Random number generators for the generalized Birnbaum-Saunders distribution

The generalized Birnbaum-Saunders distribution pertains to a class of lifetime models including both lighter and heavier tailed distributions. This model adapts well to lifetime data, even when outliers exist, and has other good theoretical properties and application perspectives. However, statistical inference tools may not exist in closed form for this model. Hence, simulation and numerical studies are needed, which require a random number generator. Three different ways to generate observations from this model are considered here. These generators are compared by utilizing a goodness-of-fit procedure as well as their effectiveness in predicting the true parameter values by using Monte Carlo simulations. This goodness-of-fit procedure may also be used as an estimation method. The quality of this estimation method is studied here. Finally, through a real data set, the generalized and classical Birnbaum-Saunders models are compared by using this estimation method.

Improved maximum likelihood estimators in a heteroskedastic errors-in-variables model

This paper develops a bias correction scheme for a multivariate heteroskedastic errors-in-variables model. The applicability of this model is justified in areas such as astrophysics, epidemiology and analytical chemistry, where the variables are subject to measurement errors and the variances vary with the observations. We conduct Monte Carlo simulations to investigate the performance of the corrected estimators. The numerical results show that the bias correction scheme yields nearly unbiased estimates. We also give an application to a real data set.

Signed likelihood ratio tests in the Birnbaum-Saunders regression model

The Birnbaum-Saunders regression model is becoming increasingly popular in lifetime analyses and reliability studies. In this model, the signed likelihood ratio statistic provides the basis for testing inference and construction of confidence limits for a single parameter of interest. We focus on the small sample case, where the standard normal distribution gives a poor approximation to the true distribution of the statistic. We derive three adjusted signed likelihood ratio statistics that lead to very accurate inference even for very small samples. Two empirical applications are presented. (C) 2010 Elsevier B.V. All rights reserved.

Improved likelihood inference in beta regression

We consider the issue of performing accurate small-sample likelihood-based inference in beta regression models, which are useful for modelling continuous proportions that are affected by independent variables. We derive small-sample adjustments to the likelihood ratio statistic in this class of models. The adjusted statistics can be easily implemented from standard statistical software. We present Monte Carlo simulations showing that inference based on the adjusted statistics we propose is much more reliable than that based on the usual likelihood ratio statistic. A real data example is presented.

Regression analysis of mean quality-adjusted survival time based on pseudo-observations

Regression models for the mean quality-adjusted survival time are specified from hazard functions of transitions between two states and the mean quality-adjusted survival time may be a complex function of covariates. We discuss a regression model for the mean quality-adjusted survival (QAS) time based on pseudo-observations, which has the advantage of directly modeling the effect of covariates in the QAS time. Both Monte Carlo Simulations and a real data set are studied. Copyright (C) 2009 John Wiley & Sons, Ltd.

Testing hypotheses in the Birnbaum-Saunders distribution under type-II censored samples

The two-parameter Birnbaum-Saunders distribution has been used successfully to model fatigue failure times. Although censoring is typical in reliability and survival studies, little work has been published on the analysis of censored data for this distribution. In this paper, we address the issue of performing testing inference on the two parameters of the Birnbaum-Saunders distribution under type-II right censored samples. The likelihood ratio statistic and a recently proposed statistic, the gradient statistic, provide a convenient framework for statistical inference in such a case, since they do not require to obtain, estimate or invert an information matrix, which is an advantage in problems involving censored data. An extensive Monte Carlo simulation study is carried out in order to investigate and compare the finite sample performance of the likelihood ratio and the gradient tests. Our numerical results show evidence that the gradient test should be preferred. Further, we also consider the generalized Birnbaum-Saunders distribution under type-II right censored samples and present some Monte Carlo simulations for testing the parameters in this class of models using the likelihood ratio and gradient tests. Three empirical applications are presented. (C) 2011 Elsevier B.V. All rights reserved.

The influence of ARIMA-GARCH parameters in feed forward neural networks prediction

The objective of this article is to find out the influence of the parameters of the ARIMA-GARCH models in the prediction of artificial neural networks (ANN) of the feed forward type, trained with the Levenberg-Marquardt algorithm, through Monte Carlo simulations. The paper presents a study of the relationship between ANN performance and ARIMA-GARCH model parameters, i.e. the fact that depending on the stationarity and other parameters of the time series, the ANN structure should be selected differently. Neural networks have been widely used to predict time series and their capacity for dealing with non-linearities is a normally outstanding advantage. However, the values of the parameters of the models of generalized autoregressive conditional heteroscedasticity have an influence on ANN prediction performance. The combination of the values of the GARCH parameters with the ARIMA autoregressive terms also implies in ANN performance variation. Combining the parameters of the ARIMA-GARCH models and changing the ANN`s topologies, we used the Theil inequality coefficient to measure the prediction of the feed forward ANN.

Local power of some tests in exponential family nonlinear models

In this paper we obtain asymptotic expansions up to order n(-1/2) for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in exponential family nonlinear models (Cordeiro and Paula, 1989), under a sequence of Pitman alternatives. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters and for testing the dispersion parameter, thus generalising the results given in Cordeiro et al. (1994) and Ferrari et al. (1997). We also present Monte Carlo simulations in order to compare the finite-sample performance of these tests. (C) 2010 Elsevier B.V. All rights reserved.

Solvatochromic Shift of the pi -> pi* Transition in All-Trans, Cis-13, Cis-11, Cis-9, and Cis-7 Retinal Isomers Induced by Water and Methanol

The solvatochromic shift of the lowest singlet it pi -> pi* electronic transition in the all-trans, cis-13, cis-11, cis-9, and cis-7 retinal isomers were computed under the influence of water, methanol, and benzene solvents. Excitation energies were calculated in gas phase and in solution. The calculations in solution were performed considering the sequential Monte Carlo (MC) /Quantum Mechanical approach. The MC simulations were performed considering the full retinal isomer molecules and 900 water molecules, 900 methanol, or 400 benzene ones. The OPLS/AA parametrization was chosen for retinal, methanol, and benzene molecules and the SPC model was used for water one. From the MC calculations 100 independent configurations were selected, with 100 solvent molecules in thermodynamical equilibrium at T = 298.15 K. Average point-charges were obtained from those independent configurations for water, methanol, and benzene solvent. TDDFT and CASSCF//CASPT2 methodologies were used to compute the vertical excitation energy of the retinal isomers in different environment. (C) 2010 Wiley Periodicals, Inc. Int J Quantum Chem 110: 2076-2087, 2010

Photophysics and photostability of adenine in aqueous solution: A theoretical study

The sequential Monte Carlo/CASPT2 approach was employed to investigate deactivation and emission processes from the lowest-lying pi pi * and n pi * excited states of 9H-adenine in aqueous solution. It is found that conical intersections connecting the pi pi* and n pi* states with the ground state are also present in solution, whereas the barriers for the deactivation paths are significantly smaller on solvated conditions. The large destabilization of the n pi* state found in solution possibly prevents its involvement in the deactivation photophysics and explains the change from a bi- to a mono-exponential decay for the molecule in the gas phase and solution, respectively. (C) 2010 Elsevier B.V. All rights reserved.