Nonlinear Estimates in Anisotropic Gevrey Spaces

2002 Mathematics Subject Classification: 35G20, 47H30

Percentiles de grasa corporal por bioimpedancia eléctrica en niños y adolescentes de Bogotá, Colombia: Estudio FUPRECOL

Objetivo: Recientemente, se han propuesto varios dispositivos de impedancia bioeléctrica (BIA) para la estimación rápida de la grasa corporal. Sin embargo, no han sido publicadas referencias de grasa corporal para niños y adolescentes en población Colombiana. El objetivo de este estudio fue establecer percentiles de grasa corporal por BIA en niños y adolescentes de Bogotá, Colombia de entre 9 y 17.9 años, pertenecientes al estudio FUPRECOL. Métodos: Estudio descriptivo y transversal, realizado en 2.526 niños y 3.324 adolescentes de entre 9 y 17.9 años de edad, pertenecientes a instituciones educativas oficiales de Bogotá, Colombia. El porcentaje de grasa corporal fue medido con Tanita® Analizador de Composición Corporal (Modelo BF-689), según edad y sexo. Se tomaron medidas de peso, talla, circunferencia de cintura, circunferencia de cadera y estado de maduración sexual por auto-reporte. Se calcularon los percentiles (P3, P10, P25, P50, P75, P90 y P97) y curvas centiles por el método LMS según sexo y edad y se realizó una comparación entre los valores de la CC observados con estándares internacionales. Resultados: Se presentan valores de porcentaje de grasa corporal y las curvas de percentiles. En la mayoría de los grupos etáreos la grasa corporal de las chicas fue mayor a la de los chicos. Sujetos cuyo porcentaje de grasa corporal estaba por encima del percentil 90 de la distribución estándar normal se consideró que tenían un elevado riesgo cardiovascular (chicos desde 23,4-28,3 y chicas desde 31,0-34,1). En general, nuestros porcentajes de grasa corporal fueron inferiores a los valores de Turquía, Alemania, Grecia, España y Reino Unido. Conclusiones: Se presentan percentiles del porcentaje de grasa por BIA según edad y sexo que podrán ser usados de referencia en la evaluación del estado nutricional y en la predicción del riesgo cardiovascular desde edades tempranas.

Multi-frequency segmental bio-impedance device:design, development and applications

Bio-impedance analysis (BIA) provides a rapid, non-invasive technique for body composition estimation. BIA offers a convenient alternative to standard techniques such as MRI, CT scan or DEXA scan for selected types of body composition analysis. The accuracy of BIA is limited because it is an indirect method of composition analysis. It relies on linear relationships between measured impedance and morphological parameters such as height and weight to derive estimates. To overcome these underlying limitations of BIA, a multi-frequency segmental bio-impedance device was constructed through a series of iterative enhancements and improvements of existing BIA instrumentation. Key features of the design included an easy to construct current-source and compact PCB design. The final device was trialled with 22 human volunteers and measured impedance was compared against body composition estimates obtained by DEXA scan. This enabled the development of newer techniques to make BIA predictions. To add a ‘visual aspect’ to BIA, volunteers were scanned in 3D using an inexpensive scattered light gadget (Xbox Kinect controller) and 3D volumes of their limbs were compared with BIA measurements to further improve BIA predictions. A three-stage digital filtering scheme was also implemented to enable extraction of heart-rate data from recorded bio-electrical signals. Additionally modifications have been introduced to measure change in bio-impedance with motion, this could be adapted to further improve accuracy and veracity for limb composition analysis. The findings in this thesis aim to give new direction to the prediction of body composition using BIA. The design development and refinement applied to BIA in this research programme suggest new opportunities to enhance the accuracy and clinical utility of BIA for the prediction of body composition analysis. In particular, the use of bio-impedance to predict limb volumes which would provide an additional metric for body composition measurement and help distinguish between fat and muscle content.

Error estimates for a fully discrete spectral scheme for a class of nonlinear, nonlocal dispersive wave equations

We analyze a fully discrete spectral method for the numerical solution of the initial- and periodic boundary-value problem for two nonlinear, nonlocal, dispersive wave equations, the Benjamin–Ono and the Intermediate Long Wave equations. The equations are discretized in space by the standard Fourier–Galerkin spectral method and in time by the explicit leap-frog scheme. For the resulting fully discrete, conditionally stable scheme we prove an L2-error bound of spectral accuracy in space and of second-order accuracy in time.

Capacity estimates for optical transmission based on the nonlinear Fourier transform

What is the maximum rate at which information can be transmitted error-free in fibre-optic communication systems? For linear channels, this was established in classic works of Nyquist and Shannon. However, despite the immense practical importance of fibre-optic communications providing for >99% of global data traffic, the channel capacity of optical links remains unknown due to the complexity introduced by fibre nonlinearity. Recently, there has been a flurry of studies examining an expected cap that nonlinearity puts on the information-carrying capacity of fibre-optic systems. Mastering the nonlinear channels requires paradigm shift from current modulation, coding and transmission techniques originally developed for linear communication systems. Here we demonstrate that using the integrability of the master model and the nonlinear Fourier transform, the lower bound on the capacity per symbol can be estimated as 10.7 bits per symbol with 500 GHz bandwidth over 2,000 km.

Per capita versus adult-equivalent estimates of calorie availability in household budget surveys

This study aims to estimate an adult-equivalent scale for calorie requirements and to determine the differences between adult-equivalent and per capita measurements of calorie availability in the Brazilian population. The study used data from the 2002-2003 Brazilian Household Budget Survey. The calorie requirement for a reference adult individual was based on the mean requirements for adult males and females (2,550kcal/day). The conversion factors were defined as the ratios between the calorie requirements for each age group and gender and that of the reference adult. The adult-equivalent calorie availability levels were higher than the per capita levels, with the largest differences in rural and low-income households. Differences in household calorie availability varied from 22kcal/day (households with adults and an adolescent) to 428kcal/day (households with elderly individuals), thus showing that per capital measurements can underestimate the real calorie availability, since they overlook differences in household composition.

Trajectory Sensitivity Method and Master-Slave Synchronization to Estimate Parameters of Nonlinear Systems

A combination of trajectory sensitivity method and master-slave synchronization was proposed to parameter estimation of nonlinear systems. It was shown that master-slave coupling increases the robustness of the trajectory sensitivity algorithm with respect to the initial guess of parameters. Since synchronization is not a guarantee that the estimation process converges to the correct parameters, a conditional test that guarantees that the new combined methodology estimates the true values of parameters was proposed. This conditional test was successfully applied to Lorenz's and Chua's systems, and the proposed parameter estimation algorithm has shown to be very robust with respect to parameter initial guesses and measurement noise for these examples. Copyright (C) 2009 Elmer P. T. Cari et al.

Effects of Variations in Nonlinear Damping Coefficients on the Parametric Vibration of a Cantilever Beam with a Lumped Mass

Uncertainties in damping estimates can significantly affect the dynamic response of a given flexible structure. A common practice in linear structural dynamics is to consider a linear viscous damping model as the major energy dissipation mechanism. However, it is well known that different forms of energy dissipation can affect the structure's dynamic response. The major goal of this paper is to address the effects of the turbulent frictional damping force, also known as drag force on the dynamic behavior of a typical flexible structure composed of a slender cantilever beam carrying a lumped-mass on the tip. First, the system's analytical equation is obtained and solved by employing a perturbation technique. The solution process considers variations of the drag force coefficient and its effects on the system's response. Then, experimental results are presented to demonstrate the effects of the nonlinear quadratic damping due to the turbulent frictional force on the system's dynamic response. In particular, the effects of the quadratic damping on the frequency-response and amplitude-response curves are investigated. Numerically simulated as well as experimental results indicate that variations on the drag force coefficient significantly alter the dynamics of the structure under investigation. Copyright (c) 2008 D. G. Silva and P. S. Varoto.

PARTIAL STABILITY FOR A CLASS OF NONLINEAR SYSTEMS

This paper studies a nonlinear, discrete-time matrix system arising in the stability analysis of Kalman filters. These systems present an internal coupling between the state components that gives rise to complex dynamic behavior. The problem of partial stability, which requires that a specific component of the state of the system converge exponentially, is studied and solved. The convergent state component is strongly linked with the behavior of Kalman filters, since it can be used to provide bounds for the error covariance matrix under uncertainties in the noise measurements. We exploit the special features of the system-mainly the connections with linear systems-to obtain an algebraic test for partial stability. Finally, motivated by applications in which polynomial divergence of the estimates is acceptable, we study and solve a partial semistability problem.

SYNCHRONIZATION OF A CLASS OF SECOND-ORDER NONLINEAR SYSTEMS

The asymptotic behavior of a class of coupled second-order nonlinear dynamical systems is studied in this paper. Using very mild assumptions on the vector-field, conditions on the coupling parameters that guarantee synchronization are provided. The proposed result does not require solutions to be ultimately bounded in order to prove synchronization, therefore it can be used to study coupled systems that do not globally synchronize, including synchronization of unbounded solutions. In this case, estimates of the synchronization region are obtained. Synchronization of two-coupled nonlinear pendulums and two-coupled Duffing systems are studied to illustrate the application of the proposed theory.

Valve friction and nonlinear process model closed-loop identification

Among several process variability sources, valve friction and inadequate controller tuning are supposed to be two of the most prevalent. Friction quantification methods can be applied to the development of model-based compensators or to diagnose valves that need repair, whereas accurate process models can be used in controller retuning. This paper extends existing methods that jointly estimate the friction and process parameters, so that a nonlinear structure is adopted to represent the process model. The developed estimation algorithm is tested with three different data sources: a simulated first order plus dead time process, a hybrid setup (composed of a real valve and a simulated pH neutralization process) and from three industrial datasets corresponding to real control loops. The results demonstrate that the friction is accurately quantified, as well as ""good"" process models are estimated in several situations. Furthermore, when a nonlinear process model is considered, the proposed extension presents significant advantages: (i) greater accuracy for friction quantification and (ii) reasonable estimates of the nonlinear steady-state characteristics of the process. (C) 2010 Elsevier Ltd. All rights reserved.

Prediction of the chemical composition of lamb carcasses from multi-frequency impedance data

Multi-frequency bioimpedance analysis (MFBIA) was used to determine the impedance, reactance and resistance of 103 lamb carcasses (17.1-34.2 kg) immediately after slaughter and evisceration. Carcasses were halved, frozen and one half subsequently homogenized and analysed for water, crude protein and fat content. Three measures of carcass length were obtained. Diagonal length between the electrodes (right side biceps femoris to left side of neck) explained a greater proportion of the variance in water mass than did estimates of spinal length and was selected for use in the index L-2/Z to predict the mass of chemical components in the carcass. Use of impedance (Z) measured at the characteristic frequency (Z(c)) instead of 50 kHz (Z(50)) did not improve the power of the model to predict the mass of water, protein or fat in the carcass. While L-2/Z(50) explained a significant proportion of variation in the masses of body water (r(2) 0.64), protein (r(2) 0.34) and fat (r(2) 0.35), its inclusion in multi-variate indices offered small or no increases in predictive capacity when hot carcass weight (HCW) and a measure of rib fat-depth (GR) were present in the model. Optimized equations were able to account for 65-90 % of the variance observed in the weight of chemical components in the carcass. It is concluded that single frequency impedance data do not provide better prediction of carcass composition than can be obtained from measures of HCW and GR. Indices of intracellular water mass derived from impedance at zero frequency and the characteristic frequency explained a similar proportion of the variance in carcass protein mass as did the index L-2/Z(50).

Predicting composition of leg sections with anthropometry and bioelectrical impedance analysis using magnetic resonance imaging as reference

Magnetic resonance imaging (MRI) was used to evaluate and compare with anthropometry a fundamental bioelectrical impedance analysis (BIA) method for predicting muscle and adipose tissue composition in the lower limb. Healthy volunteers (eight men and eight women), aged 41 to 62 years, with mean (S.D.) body mass indices of 28.6 (5.4) kg/m(2) and 25.1 (5.4) kg/m(2) respectively, were subjected to MRI leg scans, from which 20-cm sections of thigh and IO-cm sections of lower leg (calf) were analysed for muscle and adipose tissue content, using specifically developed software. Muscle and adipose tissue were also predicted from anthropometric measurements of circumferences and skinfold thicknesses, and by use of fundamental BIA equations involving section impedance at 50 kHz and tissue-specific resistivities. Anthropometric assessments of circumferences, cross-sectional areas and volumes for total constituent tissues matched closely MRI estimates. Muscle volume was substantially overestimated (bias: thigh, -40%; calf, -18%) and adipose tissue underestimated (bias: thigh, 43%; calf, 8%) by anthropometry, in contrast to generally better predictions by the fundamental BIA approach for muscle (bias:thigh, -12%; calf, 5%) and adipose tissue (bias:thigh, 17%; calf, -28%). However, both methods demonstrated considerable individual variability (95% limits of agreement 20-77%). In general, there was similar reproducibility for anthropometric and fundamental BIA methods in the thigh (inter-observer residual coefficient of variation for muscle 3.5% versus 3.8%), but the latter was better in the calf (inter-observer residual coefficient of variation for muscle 8.2% versus 4.5%). This study suggests that the fundamental BIA method has advantages over anthropometry for measuring lower limb tissue composition in healthy individuals.

Comparison of different nonlinear functions to describe Nelore cattle growth

This work aims to compare different nonlinear functions for describing the growth curves of Nelore females. The growth curve parameters, their (co) variance components, and environmental and genetic effects were estimated jointly through a Bayesian hierarchical model. In the first stage of the hierarchy, 4 nonlinear functions were compared: Brody, Von Bertalanffy, Gompertz, and logistic. The analyses were carried out using 3 different data sets to check goodness of fit while having animals with few records. Three different assumptions about SD of fitting errors were considered: constancy throughout the trajectory, linear increasing until 3 yr of age and constancy thereafter, and variation following the nonlinear function applied in the first stage of the hierarchy. Comparisons of the overall goodness of fit were based on Akaike information criterion, the Bayesian information criterion, and the deviance information criterion. Goodness of fit at different points of the growth curve was compared applying the Gelfand`s check function. The posterior means of adult BW ranged from 531.78 to 586.89 kg. Greater estimates of adult BW were observed when the fitting error variance was considered constant along the trajectory. The models were not suitable to describe the SD of fitting errors at the beginning of the growth curve. All functions provided less accurate predictions at the beginning of growth, and predictions were more accurate after 48 mo of age. The prediction of adult BW using nonlinear functions can be accurate when growth curve parameters and their (co) variance components are estimated jointly. The hierarchical model used in the present study can be applied to the prediction of mature BW in herds in which a portion of the animals are culled before adult age. Gompertz, Von Bertalanffy, and Brody functions were adequate to establish mean growth patterns and to predict the adult BW of Nelore females. The Brody model was more accurate in predicting the birth weight of these animals and presented the best overall goodness of fit.