Random sums of exchangeable variables and actuarial applications

In this paper we study the accumulated claim in some fixed time period, skipping the classical assumption of mutual independence between the variables involved. Two basic models are considered: Model I assumes that any pair of claims are equally correlated which means that the corresponding square-integrable sequence is exchangeable one. Model 2 states that the correlations between the adjacent claims are the same. Recurrence and explicit expressions for the joint probability generating function are derived and the impact of the dependence parameter (correlation coefficient) in both models is examined. The Markov binomial distribution is obtained as a particular case under assumptions of Model 2. (C) 2007 Elsevier B.V. All rights reserved.

LOCAL HEAD LOSS OF NON-COAXIAL EMITTERS INSERTED IN POLYETHYLENE PIPE

The design of a lateral line for drip irrigation requires accurate evaluation of head losses in not only the pipe but in the emitters as well. A procedure was developed to determine localized head losses within the emitters by the formulation of a mathematical model that accounts for the obstruction caused by the insertion point. These localized losses can be significant when compared with tire total head losses within the system due to the large number of emitters typically installed along the lateral line. Air experiment was carried out by altering flow characteristics to create Reynolds numbers (R) from 7,480 to 32,597 to provide turbulent flow and a maximum velocity of 2.0 m s(-1). The geometry of the emitter was determined by an optical projector and sensor An equation was formulated to facilitate the localized head loss calculation using the geometric characteristics of the emitter (emitter length, obstruction ratio, and contraction coefficient). The mathematical model was tested using laboratory measurements on four emitters. The local head loss was accurately estimated for the Uniram (difference of +13.6%) and Drip Net (difference of +7.7%) emitters, while appreciable deviations were found for the Twin Plus (-21.8%) and Tiran (+50%) emitters. The head loss estimated by the model was sensitive to the variations in the obstruction area of the emitter However, the variations in the local head loss did not result in significant variations in the maximum length of the lateral lines. In general, for all the analyzed emitters, a 50% increase in the local head loss for the emitters resulted in less than an 8% reduction in the maximum lateral length.

Surface plasmon resonance of gold nanoparticles formed by cathodic arc plasma ion implantation into polymer

Shallow subsurface layers of gold nanoclusters were formed in polymethylmethacrylate (PMMA) polymer by very low energy (49 eV) gold ion implantation. The ion implantation process was modeled by computer simulation and accurately predicted the layer depth and width. Transmission electron microscopy (TEM) was used to image the buried layer and individual nanoclusters; the layer width was similar to 6-8 nm and the cluster diameter was similar to 5-6 nm. Surface plasmon resonance (SPR) absorption effects were observed by UV-visible spectroscopy. The TEM and SPR results were related to prior measurements of electrical conductivity of Au-doped PMMA, and excellent consistency was found with a model of electrical conductivity in which either at low implantation dose the individual nanoclusters are separated and do not physically touch each other, or at higher implantation dose the nanoclusters touch each other to form a random resistor network (percolation model). (C) 2009 American Vacuum Society. [DOI: 10.1116/1.3231449]

The rating of perceived exertion predicts intermittent vertical jump demand and performance

The aims of this study were (a) to assess the ability of the rating of perceived exertion (RPE) to predict performance (i.e. number of vertical jumps performed to a fixed jump height) of an intermittent vertical jump exercise, and (b) to determine the ability of RPE to describe the physiological demand of such exercise. Eight healthy men performed intermittent vertical jumps with rest periods of 4, 5, and 6s until fatigue. Heart rate and RPE were recorded every five jumps throughout the sessions. The number of vertical jumps performed was also recorded. Random coefficient growth curve analysis identified relationships between the number of vertical jumps and both RPE and heart rate for which there were similar slopes. In addition, there were no differences between individual slopes and the mean slope for either RPE or heart rate. Moreover, RPE and number of jumps were highly correlated throughout all sessions (r=0.97-0.99; P0.001), as were RPE and heart rate (r=0.93-0.97; P0.001). The findings suggest that RPE can both predict the performance of intermittent vertical jump exercise and describe the physiological demands of such exercise.

Effective Electromechanical Coupling Coefficients of Piezoelectric Adaptive Structures: Critical Evaluation and Optimization

This work presents a critical analysis of methodologies to evaluate the effective (or generalized) electromechanical coupling coefficient (EMCC) for structures with piezoelectric elements. First, a review of several existing methodologies to evaluate material and effective EMCC is presented. To illustrate the methodologies, a comparison is made between numerical, analytical and experimental results for two simple structures: a cantilever beam with bonded extension piezoelectric patches and a simply-supported sandwich beam with an embedded shear piezoceramic. An analysis of the electric charge cancelation effect on the effective EMCC observed in long piezoelectric patches is performed. It confirms the importance of reinforcing the electrodes equipotentiality condition in the finite element model. Its results indicate also that smaller (segmented) and independent piezoelectric patches could be more interesting for energy conversion efficiency. Then, parametric analyses and optimization are performed for a cantilever sandwich beam with several embedded shear piezoceramic patches. Results indicate that to fully benefit from the higher material coupling of shear piezoceramic patches, attention must be paid to the configuration design so that the shear strains in the patches are maximized. In particular, effective square EMCC values higher than 1% were obtained embedding nine well-spaced short piezoceramic patches in an aluminum/foam/aluminum sandwich beam.

Who should wear mask against airborne infections? Altering the contact network for controlling the spread of contagious diseases

There are several ways of controlling the propagation of a contagious disease. For instance, to reduce the spreading of an airborne infection, individuals can be encouraged to remain in their homes and/or to wear face masks outside their domiciles. However, when a limited amount of masks is available, who should use them: the susceptible subjects, the infective persons or both populations? Here we employ susceptible-infective-recovered (SIR) models described in terms of ordinary differential equations and probabilistic cellular automata in order to investigate how the deletion of links in the random complex network representing the social contacts among individuals affects the dynamics of a contagious disease. The inspiration for this study comes from recent discussions about the impact of measures usually recommended by health public organizations for preventing the propagation of the swine influenza A (H1N1) virus. Our answer to this question can be valid for other eco-epidemiological systems. (C) 2010 Elsevier BM. All rights reserved.

The Relationship between Intraocular Pressure Reduction and Rates of Progressive Visual Field Loss in Eyes with Optic Disc Hemorrhage

Purpose: To evaluate rates of visual field progression in eyes with optic disc hemorrhages and the effect of intraocular pressure (IOP) reduction on these rates. Design: Observational cohort study. Participants: The study included 510 eyes of 348 patients with glaucoma who were recruited from the Diagnostic Innovations in Glaucoma Study (DIGS) and followed for an average of 8.2 years. Methods: Eyes were followed annually with clinical examination, standard automated perimetry visual fields, and optic disc stereophotographs. The presence of optic disc hemorrhages was determined on the basis of masked evaluation of optic disc stereophotographs. Evaluation of rates of visual field change during follow-up was performed using the visual field index (VFI). Main Outcome Measures: The evaluation of the effect of optic disc hemorrhages on rates of visual field progression was performed using random coefficient models. Estimates of rates of change for individual eyes were obtained by best linear unbiased prediction (BLUP). Results: During follow-up, 97 (19%) of the eyes had at least 1 episode of disc hemorrhage. The overall rate of VFI change in eyes with hemorrhages was significantly faster than in eyes without hemorrhages (-0.88%/year vs. -0.38%/year, respectively, P < 0.001). The difference in rates of visual field loss pre- and post-hemorrhage was significantly related to the reduction of IOP in the post-hemorrhage period compared with the pre-hemorrhage period (r = -0.61; P < 0.001). Each 1 mmHg of IOP reduction was associated with a difference of 0.31%/year in the rate of VFI change. Conclusions: There was a beneficial effect of treatment in slowing rates of progressive visual field loss in eyes with optic disc hemorrhage. Further research should elucidate the reasons why some patients with hemorrhages respond well to IOP reduction and others seem to continue to progress despite a significant reduction in IOP levels. Financial Disclosure(s): Proprietary or commercial disclosure may be found after the references. Ophthalmology 2010; 117: 2061-2066 (C) 2010 by the American Academy of Ophthalmology.

Liquid-liquid equilibria for systems composed of refined soybean oil, free fatty acids, ethanol, and water at different temperatures

Soybean oil can be deacidified by liquid-liquid extraction with ethanol. In the present paper, the liquid-liquid equilibria of systems composed of refined soybean oil, commercial linoleic acid, ethanol and water were investigated at 298.2 K. The experimental data set obtained from the present study (at 298.2 K) and the results of Mohsen-Nia et al. [1] (at 303.2 K) and Rodrigues et al. [2] (at 323.2 K) were correlated by applying the non-random two liquid (NRTL) model. The results of the present study indicated that the mutual solubility of the compounds decreased with an increase in the water content of the solvent and a decrease in the temperature of the solution. Among variables, the water content of the solvent had the strongest effect on the solubility of the components. The maximum deviation and average variance between the experimental and calculated compositions were 1.60% and 0.89%, indicating that the model could accurately predict the behavior of the compounds at different temperatures and degrees of hydration. (C) 2010 Elsevier B.V. All rights reserved.

Predator-prey models: an application for the plankton dynamics of lake Geneva

In this paper we present a hierarchical Bayesian analysis for a predator-prey model applied to ecology considering the use of Markov Chain Monte Carlo methods. We consider the introduction of a random effect in the model and the presence of a covariate vector. An application to ecology is considered using a data set related to the plankton dynamics of lake Geneva for the year 1990. We also discuss some aspects of discrimination of the proposed models.

Very low optical absorptions and analyte concentrations in water measured by Optimized Thermal Lens Spectrometry

Thermal Lens Spectrometry has traditionally been carried out in the single-beam and the mode-mismatched dual-beam configurations. Recently, a much more sensitive dual-beam TL setup was developed, where the probe beam is expanded and collimated. This feature optimizes Thermal Lens (TL) signal and allows the use of thicker samples, further improving the sensitivity. In this paper, we have made comparisons between the conventional and optimized TL configurations, and presented applications such as measurements of very low absorptions and concentrations in water and Cr(III) aqueous solution in the UV-vis range. For pure water we found linear absorption coefficients as low as the Raman scattering one due to the stretching vibrational modes of OH group. The detection limit was estimated 1 x 10(-6) cm(-1) with a 180-mW excitation power using a 100-mm cell length. This sensitivity is very high, considering that water has a photothermal enhancement factor similar to 33 times smaller than CCl(4), for example. For Cr(III) species in aqueous solution, the limit of detection (LOD) was estimated in similar to 40 ng mL(-1) at 514 nm, or similar to 10ng mL(-1) at 405 nm, which is similar to 30 times smaller than the LOD achieved with conventional transmission techniques. The more recent TL configuration is very attractive to obtain absorption spectra, since the result does not depend critically on the beam parameters, unlike the other configurations. The main drawbacks of this optimized TL configuration are the longer acquisition time and the need for larger samples. (C) 2011 Published by Elsevier B.V.

Multifractality in the random parameter model for multivariate time series

The Random Parameter model was proposed to explain the structure of the covariance matrix in problems where most, but not all, of the eigenvalues of the covariance matrix can be explained by Random Matrix Theory. In this article, we explore the scaling properties of the model, as observed in the multifractal structure of the simulated time series. We use the Wavelet Transform Modulus Maxima technique to obtain the multifractal spectrum dependence with the parameters of the model. The model shows a scaling structure compatible with the stylized facts for a reasonable choice of the parameter values. (C) 2009 Elsevier B.V. All rights reserved.

Simulation of the Barkhausen Noise using random field Ising model with long-range interaction

We present a method to simulate the Magnetic Barkhausen Noise using the Random Field Ising Model with magnetic long-range interaction. The method allows calculating the magnetic flux density behavior in particular sections of the lattice reticule. The results show an internal demagnetizing effect that proceeds from the magnetic long-range interactions. This demagnetizing effect induces the appearing of a magnetic pattern in the region of magnetic avalanches. When compared with the traditional method, the proposed numerical procedure neatly reduces computational costs of simulation. (c) 2008 Published by Elsevier B.V.

Parametric correlation functions to model the structure of permanent environmental (co)variances in milk yield random regression models

The objective of the present study was to estimate milk yield genetic parameters applying random regression models and parametric correlation functions combined with a variance function to model animal permanent environmental effects. A total of 152,145 test-day milk yields from 7,317 first lactations of Holstein cows belonging to herds located in the southeastern region of Brazil were analyzed. Test-day milk yields were divided into 44 weekly classes of days in milk. Contemporary groups were defined by herd-test-day comprising a total of 2,539 classes. The model included direct additive genetic, permanent environmental, and residual random effects. The following fixed effects were considered: contemporary group, age of cow at calving (linear and quadratic regressions), and the population average lactation curve modeled by fourth-order orthogonal Legendre polynomial. Additive genetic effects were modeled by random regression on orthogonal Legendre polynomials of days in milk, whereas permanent environmental effects were estimated using a stationary or nonstationary parametric correlation function combined with a variance function of different orders. The structure of residual variances was modeled using a step function containing 6 variance classes. The genetic parameter estimates obtained with the model using a stationary correlation function associated with a variance function to model permanent environmental effects were similar to those obtained with models employing orthogonal Legendre polynomials for the same effect. A model using a sixth-order polynomial for additive effects and a stationary parametric correlation function associated with a seventh-order variance function to model permanent environmental effects would be sufficient for data fitting.

Predicting random effects with an expanded finite population mixed model

Prediction of random effects is an important problem with expanding applications. In the simplest context, the problem corresponds to prediction of the latent value (the mean) of a realized cluster selected via two-stage sampling. Recently, Stanek and Singer [Predicting random effects from finite population clustered samples with response error. J. Amer. Statist. Assoc. 99, 119-130] developed best linear unbiased predictors (BLUP) under a finite population mixed model that outperform BLUPs from mixed models and superpopulation models. Their setup, however, does not allow for unequally sized clusters. To overcome this drawback, we consider an expanded finite population mixed model based on a larger set of random variables that span a higher dimensional space than those typically applied to such problems. We show that BLUPs for linear combinations of the realized cluster means derived under such a model have considerably smaller mean squared error (MSE) than those obtained from mixed models, superpopulation models, and finite population mixed models. We motivate our general approach by an example developed for two-stage cluster sampling and show that it faithfully captures the stochastic aspects of sampling in the problem. We also consider simulation studies to illustrate the increased accuracy of the BLUP obtained under the expanded finite population mixed model. (C) 2007 Elsevier B.V. All rights reserved.

The UV/H2O2 - photodegradation of poly(ethyleneglycol) and model compounds

The general mechanism for the photodegradation of polyethyleneglycol (PEG) by H2O2/UV was determined studying the photooxidation of small model molecules, like low molecular weight ethyleneglycols (tetra-, tri-, di-, and ethyleneglycol). After 30 min of irradiation the average molar mass (Mw) of the degradated PEG, analysed by GPC, fall to half of its initial value, with a concomitant increase in polydispersitivity and number of average chain scission (S), characterizing a random chain scission process yielding oligomers and smaller size ethyleneglycols. HPLC analysis of the photodegradation of the model ethyleneglycols proved that the oxidation mechanism involved consecutive reactions, where the larger ethyleneglycols gave rise, successively, to smaller ones. The photodegradation of ethyleneglycol lead to the formation of low molecular weight carboxylic acids, like glycolic, oxalic and formic acids.