Comparison of the polynomial model against explicit measurements of noise components for different mammography systems.

Given the adverse impact of image noise on the perception of important clinical details in digital mammography, routine quality control measurements should include an evaluation of noise. The European Guidelines, for example, employ a second-order polynomial fit of pixel variance as a function of detector air kerma (DAK) to decompose noise into quantum, electronic and fixed pattern (FP) components and assess the DAK range where quantum noise dominates. This work examines the robustness of the polynomial method against an explicit noise decomposition method. The two methods were applied to variance and noise power spectrum (NPS) data from six digital mammography units. Twenty homogeneously exposed images were acquired with PMMA blocks for target DAKs ranging from 6.25 to 1600 µGy. Both methods were explored for the effects of data weighting and squared fit coefficients during the curve fitting, the influence of the additional filter material (2 mm Al versus 40 mm PMMA) and noise de-trending. Finally, spatial stationarity of noise was assessed.Data weighting improved noise model fitting over large DAK ranges, especially at low detector exposures. The polynomial and explicit decompositions generally agreed for quantum and electronic noise but FP noise fraction was consistently underestimated by the polynomial method. Noise decomposition as a function of position in the image showed limited noise stationarity, especially for FP noise; thus the position of the region of interest (ROI) used for noise decomposition may influence fractional noise composition. The ROI area and position used in the Guidelines offer an acceptable estimation of noise components. While there are limitations to the polynomial model, when used with care and with appropriate data weighting, the method offers a simple and robust means of examining the detector noise components as a function of detector exposure.

Survival of Lactobacillus plantarum in model solutions and fruit juices

The aim of the work was to study the survival of Lactobacillus plantarum NCIMB 8826 in model solutions and develop a mathematical model describing its dependence on pH, citric acid and ascorbic acid. A Central Composite Design (CCD) was developed studying each of the three factors at five levels within the following ranges, i.e., pH (3.0-4.2), citric acid (6-40 g/L), and ascorbic acid (100-1000 mg/L). In total, 17 experimental runs were carried out. The initial cell concentration in the model solutions was approximately 1 × 10(8)CFU/mL; the solutions were stored at 4°C for 6 weeks. Analysis of variance (ANOVA) of the stepwise regression demonstrated that a second order polynomial model fits well the data. The results demonstrated that high pH and citric acid concentration enhanced cell survival; one the other hand, ascorbic acid did not have an effect. Cell survival during storage was also investigated in various types of juices, including orange, grapefruit, blackcurrant, pineapple, pomegranate, cranberry and lemon juice. The model predicted well the cell survival in orange, blackcurrant and pineapple, however it failed to predict cell survival in grapefruit and pomegranate, indicating the influence of additional factors, besides pH and citric acid, on cell survival. Very good cell survival (less than 0.4 log decrease) was observed after 6 weeks of storage in orange, blackcurrant and pineapple juice, all of which had a pH of about 3.8. Cell survival in cranberry and pomegranate decreased very quickly, whereas in the case of lemon juice, the cell concentration decreased approximately 1.1 logs after 6 weeks of storage, albeit the fact that lemon juice had the lowest pH (pH~2.5) among all the juices tested. Taking into account the results from the compositional analysis of the juices and the model, it was deduced that in certain juices, other compounds seemed to protect the cells during storage; these were likely to be proteins and dietary fibre In contrast, in certain juices, such as pomegranate, cell survival was much lower than expected; this could be due to the presence of antimicrobial compounds, such as phenolic compounds.

The role of no-arbitrage on forecasting: lessons from a parametric term structure model

Parametric term structure models have been successfully applied to innumerous problems in fixed income markets, including pricing, hedging, managing risk, as well as studying monetary policy implications. On their turn, dynamic term structure models, equipped with stronger economic structure, have been mainly adopted to price derivatives and explain empirical stylized facts. In this paper, we combine flavors of those two classes of models to test if no-arbitrage affects forecasting. We construct cross section (allowing arbitrages) and arbitrage-free versions of a parametric polynomial model to analyze how well they predict out-of-sample interest rates. Based on U.S. Treasury yield data, we find that no-arbitrage restrictions significantly improve forecasts. Arbitrage-free versions achieve overall smaller biases and Root Mean Square Errors for most maturities and forecasting horizons. Furthermore, a decomposition of forecasts into forward-rates and holding return premia indicates that the superior performance of no-arbitrage versions is due to a better identification of bond risk premium.

Fractional polynomial response surface models

Second-order polynomial models have been used extensively to approximate the relationship between a response variable and several continuous factors. However, sometimes polynomial models do not adequately describe the important features of the response surface. This article describes the use of fractional polynomial models. It is shown how the models can be fitted, an appropriate model selected, and inference conducted. Polynomial and fractional polynomial models are fitted to two published datasets, illustrating that sometimes the fractional polynomial can give as good a fit to the data and much more plausible behavior between the design points than the polynomial model. © 2005 American Statistical Association and the International Biometric Society.

Assessment of the effect on statistical power of regression model misspecification by using techniques of mathematical statistics and simulation study

Objectives. This paper seeks to assess the effect on statistical power of regression model misspecification in a variety of situations. ^ Methods and results. The effect of misspecification in regression can be approximated by evaluating the correlation between the correct specification and the misspecification of the outcome variable (Harris 2010).In this paper, three misspecified models (linear, categorical and fractional polynomial) were considered. In the first section, the mathematical method of calculating the correlation between correct and misspecified models with simple mathematical forms was derived and demonstrated. In the second section, data from the National Health and Nutrition Examination Survey (NHANES 2007-2008) were used to examine such correlations. Our study shows that comparing to linear or categorical models, the fractional polynomial models, with the higher correlations, provided a better approximation of the true relationship, which was illustrated by LOESS regression. In the third section, we present the results of simulation studies that demonstrate overall misspecification in regression can produce marked decreases in power with small sample sizes. However, the categorical model had greatest power, ranging from 0.877 to 0.936 depending on sample size and outcome variable used. The power of fractional polynomial model was close to that of linear model, which ranged from 0.69 to 0.83, and appeared to be affected by the increased degrees of freedom of this model.^ Conclusion. Correlations between alternative model specifications can be used to provide a good approximation of the effect on statistical power of misspecification when the sample size is large. When model specifications have known simple mathematical forms, such correlations can be calculated mathematically. Actual public health data from NHANES 2007-2008 were used as examples to demonstrate the situations with unknown or complex correct model specification. Simulation of power for misspecified models confirmed the results based on correlation methods but also illustrated the effect of model degrees of freedom on power.^

On the multicomponent polynomial solution models

The present study addresses the problem of predicting the properties of multicomponent systems from those of corresponding binary systems. Two types of multicomponent polynomial models have been analysed. A probabilistic interpretation of the parameters of the Polynomial model, which explicitly relates them with the Gibbs free energies of the generalised quasichemical reactions, is proposed. The presented treatment provides a theoretical justification for such parameters. A methodology of estimating the ternary interaction parameter from the binary ones is presented. The methodology provides a way in which the power series multicomponent models, where no projection is required, could be incorporated into the Calphad approach.

Temperature regulation of a pilot-scale batch reaction system via explicit model predictive control

In this paper, the temperature of a pilot-scale batch reaction system is modeled towards the design of a controller based on the explicit model predictive control (EMPC) strategy -- Some mathematical models are developed from experimental data to describe the system behavior -- The simplest, yet reliable, model obtained is a (1,1,1)-order ARX polynomial model for which the mentioned EMPC controller has been designed -- The resultant controller has a reduced mathematical complexity and, according to the successful results obtained in simulations, will be used directly on the real control system in a next stage of the entire experimental framework

Xylooligosaccharides Production from Alkali-Pretreated Sugarcane Bagasse Using Xylanases from Thermoascus aurantiacus

Sugarcane bagasse hemicellulose was isolated in a one-step chemical extraction using hydrogen peroxide in alkaline media. The polysaccharide containing 80.9% xylose and small amounts of L-arabinose, 4-O-methyl-D-glucuronic acid and glucose, was hydrolyzed by crude enzymatic extracts from Thermoascus aurantiacus at 50 degrees C. Conditions of enzymatic hydrolysis leading to the best yields of xylose and xylooligosaccharides (DP 2-5) were investigated using substrate concentration in the range 0.5-3.5% (w/v), enzyme load 40-80 U/g of the substrate, and reaction time from 3 to 96 h, applying a 22 factorial design. The maximum conversion to xylooligosaccharides (37.1%) was obtained with 2.6% of substrate and xylanase load of 60 U/g. The predicted maximum yield of xylobiose by a polynomial model was 41.6%. Crude enzymatic extract of T. aurantiacus generate from sugarcane bagasse hemicellulose 39% of xylose, 59% of xylobiose, and 2% of other xylooligosaccharides.

Pectinase production by solid fermentation from Aspergillus niger by a new prescription experiment

The Ordos Plateau in China is covered with up to 300,000 ha of peashrub (Caragana) which is the dominant natural vegetation and ideal for fodder production. To exploit peashrub fodder, it is crucially important to optimize the culture conditions, especially culture substrate to produce pectinase complex. In this study, a new prescription process was developed. The process, based on a uniform experimental design, first optimizes the solid substrate and second, after incubation, applies two different temperature treatments (30 degrees C for the first 30 h and 23 degrees C for the second 42 h) in the fermentation process. A multivariate regression analysis is applied to a number of independent variables (water, wheat bran, rice dextrose, ammonium sulfate, and Tween 80) to develop a predictive model of pectinase activity. A second-degree polynomial model is developed which accounts for an excellent proportion of the explained variation (R-2 = 97.7%). Using unconstrained mathematical programming, an optimized substrate prescription for pectinase production is subsequently developed. The mathematical analysis revealed that the optimal formula for pectinase production from Aspergillus niger by solid fermentation under the conditions of natural aeration, natural substrate pH (about 6.5), and environmental humidity of 60% is rice dextrose 8%, wheat bran 24%, ammonium sulfate ((NH4)(2)SO4) 6%, and water 61%. Tween 80 was found to have a negative effect on the production of pectinase in solid substrate. With this substrate prescription, pectinase produced by solid fermentation of A. niger reached 36.3IU/(gDM). Goats fed on the pectinase complex obtain an incremental increase of 0.47 kg day(-1) during the initial 25 days of feeding, which is a very promising new feeding prospect for the local peashrub. It is concluded that the new formula may be very useful for the sustainable development of and and semiarid pastures such as those of the Ordos Plateau. (c) 2005 Elsevier Inc. All rights reserved.

Likelihood-based approaches to modeling demand for medical care

We review recent likelihood-based approaches to modeling demand for medical care. A semi-nonparametric model along the lines of Cameron and Johansson's Poisson polynomial model, but using a negative binomial baseline model, is introduced. We apply these models, as well a semiparametric Poisson, hurdle semiparametric Poisson, and finite mixtures of negative binomial models to six measures of health care usage taken from the Medical Expenditure Panel survey. We conclude that most of the models lead to statistically similar results, both in terms of information criteria and conditional and unconditional prediction. This suggests that applied researchers may not need to be overly concerned with the choice of which of these models they use to analyze data on health care demand.

Parametric Approach to Blind Deconvolution of Nonlinear Channels

A parametric procedure for the blind inversion of nonlinear channels is proposed, based on a recent method of blind source separation in nonlinear mixtures. Experiments show that the proposed algorithms perform efficiently, even in the presence of hard distortion. The method, based on the minimization of the output mutual information, needs the knowledge of log-derivative of input distribution (the so-called score function). Each algorithm consists of three adaptive blocks: one devoted to adaptive estimation of the score function, and two other blocks estimating the inverses of the linear and nonlinear parts of the channel, (quasi-)optimally adapted using the estimated score functions. This paper is mainly concerned by the nonlinear part, for which we propose two parametric models, the first based on a polynomial model and the second on a neural network, while [14, 15] proposed non-parametric approaches.

Método extendido de Hildebrand en la predicción de la solubilidad del ketoprofeno en mezclas cosolventes etanol + agua

Extended Hildebrand Solubility Approach (EHSA) developed by Martin et al. was applied to evaluate the solubility of ketoprofen (KTP) in ethanol + water cosolvent mixtures at 298.15 K. Calculated values of molar volume and solubility parameter for KTP were used. A good predictive capacity of EHSA was found by using a regular polynomial model in order five to correlate the W interaction parameter and the solubility parameters of cosolvent mixtures (δmix). Nevertheless, the deviations obtained in the estimated solubilities with respect to the experimental solubilities were on the same order like those obtained directly by means of an empiric regression of the logarithmic experimental solubilities as a function of δmix values.

Indomethacin solubility estimation in 1,4-dioxane + water mixtures by the extended hildebrand solubility approach

Extended Hildebrand Solubility Approach (EHSA) was successfully applied to evaluate the solubility of Indomethacin in 1,4-dioxane + water mixtures at 298.15 K. An acceptable correlation-performance of EHSA was found by using a regular polynomial model in order four of the W interaction parameter vs. solubility parameter of the mixtures (overall deviation was 8.9%). Although the mean deviation obtained was similar to that obtained directly by means of an empiric regression of the experimental solubility vs. mixtures solubility parameters, the advantages of EHSA are evident because it requires physicochemical properties easily available for drugs.

Development of capacitive sensor for measuring soil water content

The irrigation management based on the monitoring of the soil water content allows for the minimization of the amount of water applied, making its use more efficient. Taking into account these aspects, in this work, a sensor for measuring the soil water content was developed to allow real time automation of irrigation systems. This way, problems affecting crop yielding such as irregularities in the time to turn on or turn off the pump, and excess or deficit of water can be solved. To develop the sensors were used stainless steel rods, resin, and insulating varnish. The sensors measuring circuit was based on a microcontroller, which gives its output signal in the digital format. The sensors were calibrated using soil of the type “Quartzarenic Neosoil”. A third order polynomial model was fitted to the experimental data between the values of water content corresponding to the field capacity and the wilting point to correlate the soil water content obtained by the oven standard method with those measured by the electronic circuit, with a coefficient of determination of 93.17%, and an accuracy in the measures of ±0.010 kg kg-1. Based on the results, it was concluded that the sensor and its implemented measuring circuit can be used in the automation process of irrigation systems.

Optimization of the extraction of carrageenan from Kappaphycus alvarezii using response surface methodology

This study aims to optimize an alternative method of extraction of carrageenan without previous alkaline treatment and ethanol precipitation using Response Surface Methodology (RSM). In order to introduce an innovation in the isolation step, atomization drying was used reducing the time for obtaining dry carrageenan powder. The effects of extraction time and temperature on yield, gel strength, and viscosity were evaluated. Furthermore, the extracted material was submitted to structural analysis, by infrared spectroscopy and nuclear magnetic resonance spectroscopy (¹H-NMR), and chemical composition analysis. Results showed that the generated regression models adequately explained the data variation. Carrageenan yield and gel viscosity were influenced only by the extraction temperature. However, gel strength was influenced by both, extraction time and extraction temperature. Optimal extraction conditions were 74 ºC and 4 hours. In these conditions, the carrageenan extract properties determined by the polynomial model were 31.17%, 158.27 g.cm-2, and 29.5 cP for yield, gel strength, and viscosity, respectively, while under the experimental conditions they were 35.8 ± 4.68%, 112.50 ± 4.96 g.cm-2, and 16.01 ± 1.03 cP, respectively. The chemical composition, nuclear magnetic resonance spectroscopy, and infrared spectroscopy analyses showed that the crude carrageenan extracted is composed mainly of κ-carrageenan.