Multivariate Linear Regression Approach Research Articles

Prediction of Glass Transition Temperature of Polymer by Support Vector Regression

. Based on two quantum chemical descriptors (the thermal energy Ethermal and the total energy of the whole system EHF) calculated from the structures of the repeat units of polyacrylamides by density functional theory (DFT), the support vector regression (SVR) approach combined with particle swarm optimization (PSO), is proposed to establish a model for prediction of the glass transition temperature (Tg) of polyacrylamides. The prediction performance of SVR was compared with that of multivariate linear regression (MLR). The results show that the mean absolute error (MAE=4.65K), mean absolute percentage error (MAPE=1.28%) and correlation coefficient (R2=0.9818) calculated by leave-one–out cross validation (LOOCV) via SVR models are superior to those achieved by QSPR (MAE=14.25K, MAPE=4.39% and R2=0.9211) and QSPR-LOO (MAE=17.01K, MAPE=5.66% and R2=0.8823) models for the identical samples, respectively. The prediction results strongly demonstrate that the modeling and generalization abilities of SVR model consistently surpass those of QSPR and QSPR-LOO models. It is revealed that the established SVR model is more suitable to be used for prediction of the Tg values for unknown polymers possessing similar structure than the conventional MLR approach. These suggest that SVR is a promising and practical methodology to predict the glass transition temperature of polyacrylamides.

Abstract PL03-01: Discovery of candidate biomarkers of anticancer drug sensitivity by high-throughput cell line screening.

Abstract PL03-01: Discovery of candidate biomarkers of anticancer drug sensitivity by high-throughput cell line screening.

Examining the Relationship between the Lung-to-Head Ratio Measured on Ultrasound and Lung Volumetry by Magnetic Resonance in Fetuses with Isolated Congenital Diaphragmatic Hernia

Purpose: In fetuses with isolated congenital diaphragmatic hernia (CDH), lung development can be measured by the lung-to-head ratio (LHR) using ultrasound as well as by lung volumetry determined by fetal magnetic resonance imaging (MRI). We aimed to investigate their relationship as well as to analyze the factors that may have an impact on it. Material and Methods: In 153 consecutive fetuses with isolated CDH, both the LHR and total fetal lung volume (TFLV) were measured. The observed LHR was calculated by dividing the lung area by the head circumference. On MRI, planimetric measurements of ipsilateral, contralateral and TFLV were performed on T₂-HASTE (half-Fourier acquisition single-shot turbo spin echo) sequences in transverse as well as coronal or sagittal planes. All values were expressed as a ratio of what was observed over what is expected in a gestational age-matched normal fetus. Secondary analyses were performed for right- versus left-sided hernia and for measurements made prior to 25 weeks’ gestation. A multivariate linear regression approach was used to determine the influence of the independent variables such as observed/expected (O/E) LHR, gestational age, liver position and CDH side on the dependent variables O/E TFLV and O/E contralateral FLV, and to determine the optimal formulas for calculation of the O/E TFLV as well as contralateral FLV. Results: In total, 200 pairs of measurements were obtained between 20 and 37 weeks’ gestation (median 26+6). There was a significant association between the O/E contralateral FLV and O/E LHR (R² = 0.44; p < 0.001) as well as between the O/E TFLV and the O/E LHR (R² = 0.37; p < 0.001). After adding the independent variables that were first shown to be significant on univariate analysis, the multiple regression analysis demonstrated that gestational age (p = 0.017) and side of the defect (p < 0.001) were predictive of O/E LHR (p < 0.001) and strongly improved the estimation of O/E TFLV (R² = 0.43 instead of 0.37 when using O/E LHR only). In terms of estimating O/E contralateral FLV, only the O/E LHR was a significant (p < 0.001) independent predictor (R² = 0.44). These correlations also applied when considering only left-sided CDH cases. For measurements done prior to the third trimester, the O/E LHR (p = 0.034), gestational age (p = 0.035) as well as liver herniation (p = 0.029) were significantly correlated to the O/E TFLV (R² = 0.33). In terms of predicting the O/E contralateral FLV (R² = 0.25), only O/E LHR (p = 0.008) and gestational age (p = 0.037) were useful predictors. Conclusion: Measurement of the O/E LHR on ultrasound allows a good estimation of the O/E contralateral FLV as well as TFLV as measured by MRI. Whereas the additional parameters such as gestational age, liver position and side of the defect did not improve the estimation of the contralateral FLV, they did so for estimating the TFLV.

The neural network and multivariate linear regression approach for observing phase transitions of polymers with the differential thermal analysis method

The aim of this study was to correlate the results of experimental data using DTA method and predictions of artificial neural network (ANN) and multivariate linear regression (MLR). Thermal decomposition of polymers was analyzed by simultaneous DTA method, and kinetic parameters (critical points, the change of enthalpy and entropy) of polymers were investigated. A computer model based on multilayer feed forwarding back propagation and multilayer linear regression model were used for the prediction of critical points, phase transitions of low-density polyethylene (LDPE) and mid-density polyethylene. As a result of our study, we concluded that ANN model is more suitable than MLR about prediction of experimental data.

Quantitative micro-computed tomography: A non-invasive method to assess equivalent bone mineral density

One of the many applications of micro computed tomography (µCT) is to accurately visualize and quantify cancellous bone microstructure. However, µCT based assessment of bone mineral density has yet to be thoroughly investigated. Specifically, the effects of varying imaging parameters, such as tube voltage (kVp), current (μA), integration time (ms), object to X-ray source distance (mm), projection number, detector array size and imaging media (surrounding the specimen), on the relationship between equivalent tissue density ( ρ EQ) and its linear attenuation coefficient ( μ) have received little attention. In this study, in house manufactured, hydrogen dipotassium phosphate liquid calibration phantoms (K 2HPO 4) were employed in addition to a resin embedded hydroxyapatite solid calibration phantoms supplied by Scanco Medical AG Company. Variations in current, integration time and projection number had no effect on the conversion relationship between µ and ρ EQ for the K 2HPO 4 and Scanco calibration phantoms [ p > 0.05 for all cases]. However, as expected, variations in scanning tube voltage, object to X-ray source distance, detector array size and imaging media (referring to the solution that surrounds the specimen in the imaging vial) significantly affected the conversion relationship between μ and ρ EQ for K 2HPO 4 and Scanco calibration phantoms [ p < 0.05 for all cases]. A multivariate linear regression approach was used to estimate ρ EQ based on attenuation coefficient, tube voltage, object to X-ray source distance, detector array size and imaging media for K 2HPO 4 liquid calibration phantoms, explaining 90% of the variation in ρ EQ. Furthermore, equivalent density values of bovine cortical bone (converted from attenuation coefficient to equivalent density using the K 2HPO 4 liquid calibration phantoms) samples highly correlated [ R 2 = 0.92] with the ash densities of the samples. In conclusion, Scanco calibration phantoms can be used to assess equivalent bone mineral density; however, they cannot be scanned with a specimen or submerged in a different imaging media. The K 2HPO 4 liquid calibration phantoms provide a cost effective, easy to prepare and convenient means to perform quantitative µCT analysis using any µCT system, with the ability to choose different imaging media according to study needs. However, as with any liquid calibration phantom, they are susceptible to degradation over time.

Geostatistical Mapping of Mountain Precipitation Incorporating Autosearched Effects of Terrain and Climatic Characteristics

Abstract Hydrologic and ecologic studies in mountainous terrain are sensitive to the temporal and spatial distribution of precipitation. In this study a geostatistical model, Auto-Searched Orographic and Atmospheric Effects Detrended Kriging (ASOADeK), is introduced to map mountain precipitation using only precipitation gauge data. The ASOADeK model considers both precipitation spatial covariance and orographic and atmospheric effects in estimating precipitation distribution. The model employs gauge data and a multivariate linear regression approach to autosearch regional and local climatic settings (i.e., infer the spatial gradient in atmospheric moisture distribution and the effective moisture flux direction), and local orographic effects (the effective terrain elevation and aspect). The observed gauge precipitation data are then spatially detrended by the autosearched regression surface. The spatially detrended gauge data are further interpolated by ordinary kriging to generate a residual precipitation surface. The precipitation map is then constructed by adding the regression surface to the kriged residual surface. The ASOADeK model was applied to map monthly precipitation for a mountainous area in semiarid northern New Mexico. The effective moisture flux directions and spatial moisture trends identified by the optimal multiple linear regressions, using only gauge data, agree with the regional climate setting. When compared to a common precipitation mapping product [Precipitation-elevation Regression on Independent Slopes Model (PRISM)], the ASOADeK summer precipitation maps of the study area agree well with the PRISM estimates, and with higher spatial resolution. The ASOADeK winter maps improve upon PRISM estimates. ASOADeK gives better estimates than precipitation kriging and precipitation-elevation cokriging because it considers orographic and atmospheric effects more completely.