Mean Quadratic Error Research Articles

Personalization of a compartmental physiological model for an artificial pancreas through integration of patient's state estimation.

Artificial Pancreas (AP) are developed for patients with Type 1 diabetes. This medical device system consists in the association of a subcutaneous continuous glucose monitor (CGM) providing a proxy of the patient's glycaemia and a control algorithm offering the real-time modification of the insulin delivery with an automatic command of the subcutaneous insulin pump. The most complex algorithms are based on a compartmental model of the glucoregulatory system of the patient coupled to an approach of MPC (Model-Predictive-Control) for the command. The automatic and unsupervised control of insulin regulation constitutes a major challenge in AP projects. A given model with its parameterization on the shelf will not directly represent the patient's data behavior and the personalization of the model is a prerequisite before using it in a MPC. The present paper focuses on the personalization of a compartmental showing a method where taking into account the estimation of the patient's state in addition to the parameter estimation improves the results in terms of mean quadratic error.

The Research of the Accuracy of Area Determination on Plans and Maps

Determining land areas on the plans and maps is one of the most common surveying and land management problems in the preparation of cadastral plans of agricultural land, forest inventory, ecology and geology. Although there are various methods of datamining land area, the need to provide acuracy of determining still exists. Thus, the study aims at determining the accuracy of land areas on the basis of geostatistics theory. The authors suggest executing the estimation of accuracy of areas determination on the basis of the theory of geostatistics of J. Materon. One of the basic concepts of the theory is a spatial variable that is considered as the realisation of random function. The mathematical apparatus of the theory of spatial variables was formed arising from the theory of random functions. The authors have obtained the following results. Firstly, a formula for the estimation of accuracy of closed curvilinear contour areas determination by the method of numerical integration on rectangular grid is offered. Secondly, the experimental calculations of precision of areas determination on rectangular grid are executed. The dependence of a relative mean quadratic error on the amount of points, that get in a curvilinear contour, is defined. Finally, it is recommended to use a geostatistical formula for the previous calculation of accuracy, depending on the number of rectangular grid. Thus the conclusions are as follows. The executed researches allow us to recommend the method of integration on a square grid (method of point reticulations) for determination of areas of curvilinear contours on plans and maps. For the previous calculation of accuracy with the aim of determination of density of the square grid, depending on necessary accuracy of areas determination, it is suggested using formula (1) obtained on the basis of the theory of geostatistics.

Mapping of Precipitation, Temperature and Evaporation Distributions in the Porsuk Basin Using Distant Forecasting Methods

Geographical data are of great importance in meteorology and climate science. These data can create the areal distribution models analyzed by spatial interpolation methods. The values of the areas without measurement data are estimated with these distribution models. In this study, distribution of meteorological parameters such as precipitation, temperature and evaporation in Porsuk basin, which is determined as research area, was investigated by Inverse Distance Weighting (IDW) and Ordinary Kriging methods. Actual meteorological data analyzed of the basin do not show a normal distribution statistically. Therefore, the data were firstly subjected to normalization and then analyzed according to the IDW and Ordinary Kriging methods to create distribution maps of precipitation, temperature and evaporation data. Quadratic mean error values were compared to investigate the reliability of analyzes. In this study, the analysis results of precipitation, temperature and evaporation data have been calculated by two different methods. Ordinary Kriging method has been determined as the method making the most accurate estimation.

Layered electric-current approximations of cylindrical sources

Formulations of the equivalence theorem only involving electric currents either imply non-null inner fields, or the inclusion of a bulk perfect magnetic conductor. The possibility of maintaining a homogeneous background medium across the equivalent-current surface and null inner fields without recurring to magnetic currents is here investigated for the case of cylindrical sources. The proposed procedure keeps using the definition of equivalent electric currents as found in A. Love’s theorem, introducing further layers of auxiliary electric currents to mimic the role of the missing magnetic ones. Optimal scalar coefficients applied as weights on each layer current are found, so to minimize the mean quadratic error in the fields radiated outside the auxiliary shell region, while at the same time minimizing internal radiation. The procedure is inherently well-conditioned, thanks to the reduction in the number of degrees of freedom involved, equal to the number of layers, as forced by a regression approach. A thorough numerical analysis is presented, where residual errors are found to be in the range of a few percent points.

A nonlinear system identification approach based on Fuzzy Wavelet Neural Network

This paper concerns the use of an alternative Fuzzy Wavelet Neural Network (FWNN) to model the input-output maps of nonlinear dynamic systems. The analyzed structure uses only wavelet functions in the consequent part of its fuzzy rules. The advantages and disadvantages of using this FWNN in model identification tasks are listed considering a comparative study performed with other FWNN structures found in literature. The evaluations are carried out using a real multisection liquid storage tank with abrupt transitions between its sections. The analysis is based on usual criteria such as: mean quadratic error, number of training epochs, number of adjustable parameters, quadratic error variance, among others. The results indicate that the modified FWNN structure maintains the capability of generalization and other important characteristics presented by traditional networks FWNN, despite the reduction in the complexity of the structure.

Auditory Model Identification Using REVCOR Method

Auditory models are very useful in many applications such as speech coding and compression, cochlea prosthesis, and audio watermarking. In this paper we will develop a new auditory model based on the REVCOR method. This technique is based on the estimation of the impulse response of a suitable filter characterizing the auditory neuron and the cochlea. The first step of our study is focused on the development of a mathematical model based on the gammachirp system. This model is then programmed, implemented and simulated under Matlab. The obtained results are compared with the experimental values (REVCOR experiments) for the validation and a better optimization of the model parameters. Two objective criteria are used in order to optimize the audio model estimation which are the SNR (signal to noise ratio) and the MQE (mean quadratic error). The simulation results demonstrated that for the auditory model, only a reduced number of channels are excited (from 3 to 6). This result is very interesting for auditory implants because only significant channels will be stimulated. Besides, this simplifies the electronic implementation and medical intervention.

Consistency of the recursive nonparametric regression estimation for dependent functional data

We consider the recursive estimation of a regression functional where the explanatory variables take values in some functional space. We prove the almost sure convergence of such estimates for dependent functional data. Also we derive the mean quadratic error of the considered class of estimators. Our results are established with rates and asymptotic appear bounds, under strong mixing condition. Finally, the feasibility of the proposed estimator is illustrated throughout an empirical study.

Pointwise Convergence of the Lloyd I Algorithm in Higher Dimension

We establish the pointwise convergence of the iterative Lloyd I procedure, also known as the $k$-means algorithm, as soon as the starting grid (with size $N\geq2$) induces a lower mean quadratic quantization error than the minimal mean quantization error induced by grids of sizes at most $N-1$ with respect to the same input distribution $\mu$. Such an initialization, known as the splitting method, ensures the convergence even when $\mu$ has an unbounded support. We also show that, if $\mu$ is strongly continuous---but possibly not absolutely continuous---and has a convex support, the running grid cannot degenerate so that the resulting limiting grid always has full size $N$. A variant of the procedure taking advantage of the known asymptotics of the optimal quantizer radius is proposed which forces the boundedness of the iterated grids in an appropriate region where optimal grids lie.

An Evaluation of COSMO-SAC Model and Its Evolutions for the Prediction of Drug-Like Molecule Solubility: Part 1

COSMO-SAC model and its evolutions have been investigated for solubility prediction of six pharmaceutical ingedients (ibuprofen, paracetamol, benzoic acid, salicylic acid, 4-aminobenzoic acid, and anthracene) in 35 solvents. The aim is to check the relevancy of the last improvements of the COSMO-SAC method for solubility prediction. The performance of each COSMO-SAC version has been evaluated following different criteria: the mean quadratic error (mse), the predicted solubility order of magnitude, and the solubility temperature dependence. In addition, solubility predictions in mixed solvents have also been analyzed. The results obtained show that the model refinements are relevants for solid–liquid equilibrium predictions. Compared to the original model, the solubility prediction in polar solvents is more accurate, and the solubility temperature dependences are well-represented. Moreover, the refined models (especially the 2010 version) are also more able to predict the solubility maxima in mixed solvent...

Contraste de la distribución Logística Generalizada en 31 registros históricos de eventos máximos anuales

The Generalized Logistic distribution is the most recent whose application has been established as precept. Thus, comparing it with the other two that preceded it: the Log-Pearson type III in USA and the General Extreme Values in England, is of high importance. In this work, the relevance of probabilistic analysis and the above mentioned distributions in design flood estimation is pointed out. For the most recent, a fitting method of L-moments is described in detail for the estimation of its three parameters, also a fitting by minimizing the quadratic mean error through numerical optimization is proposed. The results of the application of this distribution to 31 records, using both cited methods, are compared with the optimal ones obtained using the General Extreme Values and Log-Pearson type III models. It is concluded that the Generalized Logistic distribution is a good choice for records with high L-kurtosis quotients and its predictions in general are more extreme in high return periods when applied to records with outliers.

Complexo homeopático na prevenção e tratamento de diarréias em leitões lactentes

O trabalho foi realizado com o objetivo de comparar o potencial do antibiótico e de um complexo homeopático sobre a prevenção e tratamento de diarréia em leitões lactentes, bem como comparar e avaliar os resultados de desempenho e mortalidade durante a fase de aleitamento. Foram utilizadas 98 leitegadas, em um total de 988 leitões, de matrizes com ordem média de 5,92 ± 2,65 partos. As leitegadas foram distribuídas em delineamento experimental de blocos ao acaso, composto pelos tratamentos controle, antibiótico e complexo homeopático. Adotou-se a ordem de parto das matrizes como critério de bloqueamento. No segundo dia de vida, as leitegadas foram submetidas à pesagem e aplicação, por via oral, de 2,0mL do antibiótico colistina ou 4,0mL de complexo homeopático por leitão. As leitegadas foram desmamadas com idade média de 22,97 ± 2,43 dias. Não houve efeito dos tratamentos sobre o desempenho e a mortalidade dos leitões. Foi constatada diferença quanto ao percentual de eficiência no tratamento de diarréia, o complexo homeopático apresentou eficiência superior em relação ao antibiótico (95,2% versus 90,0%). Concluiu-se que o complexo homeopático foi eficiente na prevenção e tratamento das diarréias dos leitões lactentes, e pode ser utilizado em substituição aos antibióticos.

Modelagem para o dimensionamento de um sistema de microirrigação utilizando microtubos ramificados

Este trabalho foi realizado com o objetivo de se modelar e avaliar o comportamento hidráulico de microtubos ramificados, com base na relação entre vazão e comprimento dos microtubos para uma pressão de entrada, operando sob regime laminar. Dois modelos matemáticos foram estudados, em que um considerou a perda localizada de carga no dimensionamento dos microtubos ramificados e o outro a desconsiderou. O experimento para validação dos modelos foi conduzido no Laboratrio de Hidráulica da Escola Superior de Agricultura "Luiz de Queiroz" (ESALQ-USP), Piracicaba, SP, medindo-se a vazão dos emissores para as pressões de 14,7; 18,6; 39,2 e 58,9 kPa. A configuração do sistema de irrigação consistiu de uma linha lateral com diâmetro nominal (DN) de 10,0 mm, na qual foram inseridos microtubos conectores com DN de 0,8 mm conectados a um segmento de tubo de derivação e acoplados seis microtubos emissores com DN de 0,7 mm. Verificou-se que, dentre os modelos matemáticos, aquele que considerou a perda localizada de carga apresentou maior exatidão pois teve elevado, um bom índice de Willmott e baixo erro quadrático médio.

Análise de agrupamento na seleção de modelos de regressão não-lineares para curvas de crescimento de ovinos cruzados

Este estudo teve como objetivo utilizar a análise de agrupamento para classificar modelos de regressão não-lineares usados para descrever a curva de crescimento de ovinos cruzados, tendo em vista os resultados de diferentes avaliadores de qualidade de ajuste. Para tanto, utilizaram-se dados de peso-idade dos seguintes cruzamentos entre raças de ovinos de corte: Dorper x Morada Nova, Dorper x Rabo Largo e Dorper x Santa Inês. Após a indicação do melhor modelo, objetivou-se ainda aplicar a técnica de identidade de modelos a fim de identificar o cruzamento mais produtivo. Foram ajustados doze modelos não-lineares, cuja qualidade de ajuste foi medida pelo coeficiente de determinação ajustado, critérios de informação de Akaike e Bayesiano, erro quadrático médio de predição e coeficiente de determinação de predição. A análise de agrupamento indicou o modelo Richards como o mais adequado para descrever as curvas de crescimento dos três grupos genéticos considerados, e os testes de identidade de modelos indicaram o cruzamento Dorper x Santa Inês como sendo o mais indicado para a pecuária local.

Seleção e classificação multivariada de modelos de crescimento não lineares para bovinos Nelore

Utilizou-se análise de agrupamento para classificar e selecionar modelos não lineares de crescimento de bovinos Nelore, tendo em vista os resultados de diferentes avaliadores de qualidade de ajuste. Ajustaram-se 12 modelos não lineares. A qualidade de ajuste dos modelos foi medida pelo coeficiente de determinação (R²), quadrado médio do erro (QME), critério de informação de Akaike (AIC), critério de informação Bayesiano (BIC), erro quadrático médio de predição (MEP) e coeficiente de determinação de predição (R²p). O modelo Brody foi o que apresentou o melhor ajuste para o conjunto de dados.

Complementarity and state estimation

The concept of complementarity (or quasi-orthogonality) is extended to positive operator-valued measurements. It is shown in the setting of unconstrained state estimation that the determinant of the mean quadratic error matrix is minimal if the positive operator-valued measurements are complementary (and informationally complete). Several examples of the scheme are given.

Computer Simulation of Atmospheric Freeze Drying of Carrot Slices in a Fluidized Bed

Nam and Song's model, which describes the first stage of vacuum freeze drying, is adapted to atmospheric pressure conditions in a pulsating fluidized bed, discretizing the differential equations by finite-difference according to the implicit scheme. The generated algebraic systems of equations are solved by the tridiagonal matrix algorithm (TDMA). The effect of the variable time step on computation time is analyzed. The effect of particle size reduction, bed temperature increase, and the incorporation of infrared radiation made it possible to reduce drying times. Comparison with experimental values of the first stage of the freeze drying of carrot slices and the values calculated from the model showed a maximum mean quadratic error of 0.09.

Dynamics of Prediction Errors under the Combined Effect of Initial Condition and Model Errors

Abstract The transient evolution of prediction errors in the short to intermediate time regime is considered under the combined effect of initial condition and model errors. Some generic features are brought out and connected with intrinsic properties. Under the assumption of small uncorrelated initial errors and of small parameter errors, the conditions of existence of a time at which the mean quadratic error reaches a minimum and of a crossover time at which the contribution of initial condition errors matches that of model errors are determined. The results are illustrated and tested on representative low-order models of atmospheric dynamics exhibiting bistability, saddle-point behavior, and chaotic behavior.

Modelling the human pharyngeal airway: validation of numerical simulations using in vitro experiments

In the presented study, a numerical model which predicts the flow-induced collapse within the pharyngeal airway is validated using in vitro measurements. Theoretical simplifications were considered to limit the computation time. Systematic comparisons between simulations and measurements were performed on an in vitro replica, which reflects asymmetries of the geometry and of the tissue properties at the base of the tongue and in pathological conditions (strong initial obstruction). First, partial obstruction is observed and predicted. Moreover, the prediction accuracy of the numerical model is of 4.2% concerning the deformation (mean quadratic error on the constriction area). It shows the ability of the assumptions and method to predict accurately and quickly a fluid-structure interaction.

Análise comparativa de dados meteorológicos obtidos por estação convencional e automática em Londrina - PR

The objective was to compare variables collected with a conventional meteorological station of IAPAR with an automatic station of SIMEPAR, located side by side at the experimental station of IAPAR in Londrina – PR (latitude: 23°22´S; longitude: 51°10´W and altitude: 585m). Daily data of the following meteorological variables were analyzed: rainfall (Prec), maximum (Tmax), minimum (Tmin) and mean (Tmed) temperature, wind speed (V), and mean relative humidity (UR med), during the period from 10/01/ 1999 to 12/31/2006. For data comparisons the following statistical indexes were used: determination coefficient (R2); agreement (d); maximum error (EM); absolute mean error (EAM); efficiency (EF); critical mass coefficient (CRM); square root of the normalized quadratic mean error (RMSE); systematic (Es) and random (Ea) errors. Based on the linear regressions it was concluded that there was a significant agreement for each variable measured in both stations. The largest differences were found in the maximum temperature, mean relative humidity and rainfall, with ME of 4.7ºC, 24.5% e 21.2mm, respectively. The analyses evidenced that data obtained with the automatic meteorological station have high quality and can be used in climatological studies.

Optical Algorithms at Satellite Wavelengths for Total Suspended Matter in Tropical Coastal Waters.

Is it possible to derive accurately Total Suspended Matter concentration or its proxy, turbidity, from remote sensing data in tropical coastal lagoon waters? To investigate this question, hyperspectral remote sensing reflectance, turbidity and chlorophyll pigment concentration were measured in three coral reef lagoons. The three sites enabled us to get data over very diverse environments: oligotrophic and sediment-poor waters in the southwest lagoon of New Caledonia, eutrophic waters in the Cienfuegos Bay (Cuba), and sediment-rich waters in the Laucala Bay (Fiji). In this paper, optical algorithms for turbidity are presented per site based on 113 stations in New Caledonia, 24 stations in Cuba and 56 stations in Fiji. Empirical algorithms are tested at satellite wavebands useful to coastal applications. Global algorithms are also derived for the merged data set (193 stations). The performances of global and local regression algorithms are compared. The best one-band algorithms on all the measurements are obtained at 681 nm using either a polynomial or a power model. The best two-band algorithms are obtained with R412/R620, R443/R670 and R510/R681. Two three-band algorithms based on Rrs620.Rrs681/Rrs412 and Rrs620.Rrs681/Rrs510 also give fair regression statistics. Finally, we propose a global algorithm based on one or three bands: turbidity is first calculated from Rrs681 and then, if < 1 FTU, it is recalculated using an algorithm based on Rrs620.Rrs681/Rrs412. On our data set, this algorithm is suitable for the 0.2-25 FTU turbidity range and for the three sites sampled (mean bias: 3.6 %, rms: 35%, mean quadratic error: 1.4 FTU). This shows that defining global empirical turbidity algorithms in tropical coastal waters is at reach.