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Concept: Mean absolute percentage error


Accurate estimates of chlorophyll-a concentration (Chl-a) from remotely sensed data for inland waters are challenging due to their optical complexity. In this study, a framework of Chl-a estimation is established for optically complex inland waters based on combination of water optical classification and two semi-empirical algorithms. Three spectrally distinct water types (Type I to Type III) are first identified using a clustering method performed on remote sensing reflectance (R(rs)) from datasets containing 231 samples from Lake Taihu, Lake Chaohu, Lake Dianchi, and Three Gorges Reservoir. The classification criteria for each optical water type are subsequently defined for MERIS images based on the spectral characteristics of the three water types. The criteria cluster every R(rs) spectrum into one of the three water types by comparing the values from band 7 (central band: 665nm), band 8 (central band: 681.25nm), and band 9 (central band: 708.75nm) of MERIS images. Based on the water classification, the type-specific three-band algorithms (TBA) and type-specific advanced three-band algorithm (ATBA) are developed for each water type using the same datasets. By pre-classifying, errors are decreased for the two algorithms, with the mean absolute percent error (MAPE) of TBA decreasing from 36.5% to 23% for the calibration datasets, and from 40% to 28% for ATBA. The accuracy of the two algorithms for validation data indicates that optical classification eliminates the need to adjust the optimal locations of the three bands or to re-parameterize to estimate Chl-a for other waters. The classification criteria and the type-specific ATBA are additionally validated by two MERIS images. The framework of first classifying optical water types based on reflectance characteristics and subsequently developing type-specific algorithms for different water types is a valid scheme for reducing errors in Chl-a estimation for optically complex inland waters.

Concepts: Estimator, Optics, Water, Spectrum, Type, Mean absolute percentage error, The Band


We investigated intermodality agreements of strains from two-dimensional echocardiography (2DE) and cardiac magnetic resonance (CMR) feature tracking (FT) in the assessment of right (RV) and left ventricular (LV) mechanics in tetralogy of Fallot (TOF). Patients were prospectively studied with 2DE and CMR performed contiguously. LV and RV strains were computed separately using 2DE and CMR-FT. Segmental and global longitudinal strains (GLS) for the LV and RV were measured from four-chamber views; LV radial (global radial strain [GRS]) and circumferential strains (GCS) measured from short-axis views. Intermodality and interobserver agreements were examined. In 40 patients (20 TOF, mean age 23 years and 20 adult controls), LV, GCS showed narrowest intermodality limits of agreement (mean percentage error 9.5%), followed by GLS (16.4%). RV GLS had mean intermodality difference of 25.7%. GLS and GCS had acceptable interobserver agreement for the LV and RV with both 2DE and CMR-FT, whereas GRS had high interobserver and intermodality variability. In conclusion, myocardial strains for the RV and LV derived using currently available 2DE and CMR-FT software are subject to considerable intermodality variability. For both modalities, LV GCS, LV GLS, and RV GLS are reproducible enough to warrant further investigation of incremental clinical merit.

Concepts: Heart, Tetralogy of Fallot, Mean absolute percentage error


This study tested the validity of revolutions per minute (RPM) measurements from the Pennington Pedal Desk™. Forty-four participants (73 % female; 39 ± 11.4 years-old; BMI 25.8 ± 5.5 kg/m(2) [mean ± SD]) completed a standardized trial consisting of guided computer tasks while using a pedal desk for approximately 20 min. Measures of RPM were concurrently collected by the pedal desk and the Garmin Vector power meter. After establishing the validity of RPM measurements with the Garmin Vector, we performed equivalence tests, quantified mean absolute percent error (MAPE), and constructed Bland-Altman plots to assess agreement between RPM measures from the pedal desk and the Garmin Vector (criterion) at the minute-by-minute and trial level (i.e., over the approximate 20 min trial period).

Concepts: Measurement, Psychometrics, Criterion validity, Frequency, Approximation, Numerical analysis, Mean absolute percentage error, Revolutions per minute


The rapid growth of very elderly populations requires accurate population estimates up to the highest ages. However, it is recognised that estimates derived from census counts are often unreliable. Methods that make use of death data have not previously been evaluated for Australia and New Zealand. The aim was to evaluate a number of nearly-extinct cohort methods for producing very elderly population estimates by age and sex for Australia and New Zealand. The accuracy of official estimates was also assessed. Variants of three nearly-extinct cohort methods, the Survivor Ratio method, the Das Gupta method and a new method explicitly allowing for falling mortality over time, were evaluated by retrospective application over the period 1976-1996. Estimates by sex and single years of age were compared against numbers derived from the extinct cohort method. Errors were measured by the Weighted Mean Absolute Percentage Error. It is confirmed that for Australian females the Survivor Ratio method constrained to official estimates for ages 90+ performed well. However, for Australian males and both sexes in New Zealand, more accurate estimates were obtained by constraining the Survivor Ratio method to official estimates for ages 85+. Official estimates in Australia proved reasonably accurate for ages 90+ but at 100+ they varied significantly in accuracy from year to year. Estimates produced by Statistics New Zealand in aggregate for ages 90+ proved very accurate. We recommend the use of the Survivor Ratio method constrained to official estimates for ages 85+ to create very elderly population estimates for Australia and New Zealand.

Concepts: Male, Female, Demography, Population, Sex, Immigration, New Zealand, Mean absolute percentage error


BACKGROUND: Tuberculosis (TB) is a serious public health issue in developing countries. Early prediction of TB epidemic is very important for its control and intervention. We aimed to develop an appropriate model for predicting TB epidemics and analyze its seasonality in China. METHODS: Data of monthly TB incidence cases from January 2005 to December 2011 were obtained from the Ministry of Health, China. A seasonal autoregressive integrated moving average (SARIMA) model and a hybrid model which combined the SARIMA model and a generalized regression neural network model were used to fit the data from 2005 to 2010. Simulation performance parameters of mean square error (MSE), mean absolute error (MAE) and mean absolute percentage error (MAPE) were used to compare the goodness-of-fit between these two models. Data from 2011 TB incidence data was used to validate the chosen model. RESULTS: Although both two models could reasonably forecast the incidence of TB, the hybrid model demonstrated better goodness-of-fit than the SARIMA model. For the hybrid model, the MSE, MAE and MAPE were 38969150, 3406.593 and 0.030, respectively. For the SARIMA model, the corresponding figures were 161835310, 8781.971 and 0.076, respectively. The seasonal trend of TB incidence is predicted to have lower monthly incidence in January and February and higher incidence from March to June. CONCLUSIONS: The hybrid model showed better TB incidence forecasting than the SARIMA model. There is an obvious seasonal trend of TB incidence in China that differed from other countries.

Concepts: Regression analysis, Epidemiology, Prediction, Futurology, Future, Mean squared error, Forecasting, Mean absolute percentage error


In this paper we assess the predictive power of the self-consistent hybrid functional scPBE0 in calculating the band gap of oxide semiconductors. The computational procedure is based on the self-consistent evaluation of the mixing parameter α by means of an iterative calculation of the static dielectric constant using the perturbation expansion after discretization (PEAD) method and making use of the relation α = 1/ε<sub>∞</sub>. Our materials dataset is formed by 30 compounds covering a wide range of band gaps and dielectric properties, and includes materials with a wide spectrum of application as thermoelectrics, photocatalysis, photovoltaics, transparent conducting oxides, and refractory materials. Our results show that the scPBE0 functional provides better band gaps than the non self-consistent hybrids PBE0 and HSE06, but scPBE0 does not show significant improvement on the description of the static dielectric constants. Overall, the scPBE0 data exhibit a mean absolute percentage error of 14 % (band gaps) and 10 % (α = 1/ε<sub>∞</sub>). For materials with weak dielectric screening and large excitonic biding energies scPBE0, unlike PBE0 and HSE06, overestimates the band gaps, but the value of the gap become very close to the experimental value when excitonic effects are included (e.g. for SiO<sub>2</sub>). However, special caution must be given to the compounds with small band gaps due to the tendency of scPBE0 to overestimate the dielectric constant in proximity of the metallic limit.

Concepts: Electricity, Mathematics, Nitrogen, Band gap, Mean absolute percentage error, Dielectric, Permittivity, Electric and magnetic fields in matter


We present a novel method for estimating the mean scatterer spacing (MSS) of breast tumours using ensemble empirical mode decomposition (EEMD) domain analysis of deconvolved backscattered radio-frequency (RF) data. The autoregressive (AR) spectrum from which the MSS is estimated is obtained from the intrinsic mode functions (IMFs) due to regular scatterers embedded in RF data corrupted by the diffuse scatterers. The IMFs are chosen by giving priority to the presence of an enhanced fundamental harmonic and the presence of a greater number of higher harmonics in the AR spectrum estimated from the IMFs. The AR model order is chosen by minimizing the minimum absolute percentage error (MAPE) criterion. In order to ensure that the backscattered data is indeed from a source of coherent scattering, at first, a non-parametric Kolmogorov-Smirnov (KS) classification test is performed on the backscattered RF data. Deconvolution of the backscattered RF data, which have been classified by the K-S test as sources of significant coherent scattering, is done to reduce the system effect. EEMD domain analysis is then performed on the deconvolved data. The proposed method is able to recover the harmonics associated with the regular scatterers and overcomes many problems encountered while estimating the MSS from the AR spectrum of raw RF data. Using our technique, a mean absolute percentage error (MAPE) of 5:78%is obtained while estimating the MSS from simulated data which is lower than that of the existing techniques. Our proposed method is shown to outperform the state of the art techniques, namely, singular spectrum analysis (SSA), general spectrum (GS), spectral autocorrelation (SAC), and modified SAC for different simulation conditions. The MSS for in vivo normal breast tissue is found to be 0.69 ±0.04mm; for benign and malignant tumors it is found to be 0.73 ±0.03 mm and 0.79 ±0.04 mm, respectively. The separation between the MSS values of normal and benign tissues for our proposed method is similar to the separations obtained for the conventional methods but the separation between the MSS values for benign and malignant tissues for our proposed method is slightly higher than that for the conventional methods. When the MSS is used for classifying between benign and malignant tumors, for a threshold based classifier, the increase in specificity, accuracy, and area under curve are 18%, 19%, and 22%, respectively, and that for statistical classifiers are 9%, 13%, and 19%, respectively, from that of the next best existing technique.

Concepts: Cancer, Breast cancer, Oncology, Statistics, Benign tumor, Signal processing, Mean absolute percentage error, Symmetric mean absolute percentage error


Early childhood caries (ECC) is the most common chronic disease in young children. A reliable predictive model for ECC prevalence is needed in China as a decision supportive tool for planning health resources. In this study, we first established the autoregressive integrated moving average (ARIMA) model and grey predictive model (GM) based on the estimated national prevalence of ECC with meta-analysis from the published articles. The pooled data from 1988 to 2010 were used to establish the model, while the data from 2011 to 2013 were used to validate the models. The fitting and prediction accuracy of the two models were evaluated by mean absolute error (MAE) and mean absolute percentage error (MAPE). Then, we forecasted the annual prevalence from 2014 to 2018, which was 55.8%, 53.5%, 54.0%, 52.9%, 51.2% by ARIMA model and 52.8%, 52.0%, 51.2%, 50.4%, 49.6% by GM. The declining trend in ECC prevalence may be attributed to the socioeconomic developments and improved public health service in China. In conclusion, both ARIMA and GM models can be well applied to forecast and analyze the trend of ECC; the fitting and testing errors generated by the ARIMA model were lower than those obtained from GM.

Concepts: Regression analysis, Public health, Epidemiology, Prediction, Futurology, Forecasting, Mean absolute percentage error, Autoregressive moving average model


The aim of this study is to model the association between weekly time series of dengue case counts and meteorological variables, in a high-incidence city of Colombia, applying Bayesian hierarchical dynamic generalized linear models over the period January 2008 to August 2015. Additionally, we evaluate the model’s short-term performance for predicting dengue cases. The methodology shows dynamic Poisson log link models including constant or time-varying coefficients for the meteorological variables. Calendar effects were modeled using constant or first- or second-order random walk time-varying coefficients. The meteorological variables were modeled using constant coefficients and first-order random walk time-varying coefficients. We applied Markov Chain Monte Carlo simulations for parameter estimation, and deviance information criterion statistic (DIC) for model selection. We assessed the short-term predictive performance of the selected final model, at several time points within the study period using the mean absolute percentage error. The results showed the best model including first-order random walk time-varying coefficients for calendar trend and first-order random walk time-varying coefficients for the meteorological variables. Besides the computational challenges, interpreting the results implies a complete analysis of the time series of dengue with respect to the parameter estimates of the meteorological effects. We found small values of the mean absolute percentage errors at one or two weeks out-of-sample predictions for most prediction points, associated with low volatility periods in the dengue counts. We discuss the advantages and limitations of the dynamic Poisson models for studying the association between time series of dengue disease and meteorological variables. The key conclusion of the study is that dynamic Poisson models account for the dynamic nature of the variables involved in the modeling of time series of dengue disease, producing useful models for decision-making in public health.

Concepts: Regression analysis, Statistics, Prediction, Futurology, Monte Carlo method, Markov chain Monte Carlo, Akaike information criterion, Mean absolute percentage error


Four-component relativistic calculations of (125)Te NMR chemical shifts were performed in the series of 13 organotellurium compounds, potential precursors of the biologically active species, at the density functional theory level under the nonrelativistic and four-component fully relativistic conditions using locally dense basis set scheme derived from relativistic Dyall’s basis sets. The relativistic effects in tellurium chemical shifts were found to be of as much as 20-25% of the total calculated values. The vibrational and solvent corrections to (125)Te NMR chemical shifts are about, accordingly, 6 and 8% of their total values. The PBE0 exchange-correlation functional turned out to give the best agreement of calculated tellurium shifts with their experimental values giving the mean absolute percentage error of 4% in the range of ∼1000 ppm, provided all corrections are taken into account.

Concepts: Chemical shift, Computational chemistry, Kinetic energy, Density functional theory, Quantum chemistry, Basis set, Mean absolute percentage error, Basis set superposition error