Improving reproducibility of proton MRST by optimally averaging temperatures measured from multiple references: theoretical and empirical approaches

Purpose: In 1H MRS-based thermometry of brain, averaging temperatures measured from more than one reference peak offers several advantages including improving the reproducibility, i.e. precision, of the measurement. This paper proposes theoretically and empirically optimal weighting factors to improve the weighted average of temperatures measured from three references. Methods: We first proposed concepts of equivalent noise and equivalent signal-to-noise ratio in terms of frequency measurement and a concept of relative frequency that allows the combination of different peaks in a spectrum for improving the accuracy of frequency measurement. Based on these, we then developed a theoretically optimal weighting factor and suggested an empirical weighting factor for weighted average of temperatures measured from three references in 1H MRS-based thermometry. We assessed the two new weighting factors, together with other two previously proposed weighting factors, by comparing the errors of temperatures measured from individual references and the errors of averaged temperatures using these differing weighting factors. These errors were defined as the standard deviations in repeated measurements and in Monte Carlo studies. We also performed computer simulations to aid error analyses in temperature averaging. Results: Both the proposed theoretical and empirical weighting factors outperformed the other two previously proposed weighting factors as well as the three individual references in all phantom and in vivo experiments. In phantom experiments with 4 Hz or 10 Hz line broadening, the theoretical weighting outperformed the empirical one, but the latter was superior in all other repeated and Monte Carlo tests performed on phantom and in vivo data. Computer simulations offered explanations for the performances of the two new proposed weightings. Conclusion: The proposed two new weighting factors are superior to the two previously proposed weighting factors and can improve the measurement of temperature using 1H MRS-based thermometry.

Single-step genomic evaluation with metafounders for feed conversion ratio and average daily gain in Danish Landrace and Yorkshire pigs

Background The single-step genomic best linear unbiased prediction (SSGBLUP) method is a popular approach for genetic evaluation with high-density genotype data. To solve the problem that pedigree and genomic relationship matrices refer to different base populations, a single-step genomic method with metafounders (MF-SSGBLUP) was put forward. The aim of this study was to compare the predictive ability and bias of genomic evaluations obtained with MF-SSGBLUP and standard SSGBLUP. We examined feed conversion ratio (FCR) and average daily gain (ADG) in DanBred Landrace (LL) and Yorkshire (YY) pigs using both univariate and bivariate models, as well as the optimal weighting factors (ω), which represent the proportions of the genetic variance not captured by markers, for ADG and FCR in SSGBLUP and MF-SSGBLUP. Results In general, SSGBLUP and MF-SSGBLUP showed similar predictive abilities and bias of genomic estimated breeding values (GEBV). In the LL population, the predictive ability for ADG reached 0.36 using uni- or bi-variate SSGBLUP or MF-SSGBLUP, while the predictive ability for FCR was highest (0.20) for the bivariate model using MF-SSGBLUP, but differences between analyses were very small. In the YY population, predictive ability for ADG was similar for the four analyses (up to 0.35), while the predictive ability for FCR was highest (0.36) for the uni- and bi-variate MF-SSGBLUP analyses. SSGBLUP and MF-SSGBLUP exhibited nearly the same bias. In general, the bivariate models had lower bias than the univariate models. In the LL population, the optimal ω for ADG was ~ 0.2 in the univariate or bivariate models using SSGBLUP or MF-SSGBLUP, and the optimal ω for FCR was 0.70 and 0.55 for SSGBLUP and MF-SSGBLUP, respectively. In the YY population, the optimal ω ranged from 0.25 to 0. 35 for ADG across the four analyses and from 0.10 to 0.30 for FCR. Conclusions Our results indicate that MF-SSGBLUP performed slightly better than SSGBLUP for genomic evaluation. There was little difference in the optimal weighting factors (ω) between SSGBLUP and MF-SSGBLUP. Overall, the bivariate model using MF-SSGBLUP is recommended for single-step genomic evaluation of ADG and FCR in DanBred Landrace and Yorkshire pigs.

Linear optimal weighting estimator (LOWE) for efficient parallel hybridization ofload forecasts

Purpose Improving the accuracy and reducing computational costs of predictions, especially the prediction of time series, is one of the most critical parts of the decision-making processes and management in different areas and organizations. One of the best solutions to achieve high accuracy and low computational costs in time series forecasting is to develop and use efficient hybrid methods. Among the combined methods, parallel hybrid approaches are more welcomed by scholars and often have better performance than sequence ones. However, the necessary condition of using parallel combinational approaches is to estimate the appropriate weight of components. This weighting stage of parallel hybrid models is the most effective factor in forecasting accuracy as well as computational costs. In the literature, meta-heuristic algorithms have often been applied to weight components of parallel hybrid models. However, such that algorithms, despite all unique advantages, have two serious disadvantages of local optima and iterative time-consuming optimization processes. The purpose of this paper is to develop a linear optimal weighting estimator (LOWE) algorithm for finding the desired weight of components in the global non-iterative universal manner. Design/methodology/approach In this paper, a LOWE algorithm is developed to find the desired weight of components in the global non-iterative universal manner. Findings Empirical results indicate that the accuracy of the LOWE-based parallel hybrid model is significantly better than meta-heuristic and simple average (SA) based models. The proposed weighting approach can improve 13/96%, 11/64%, 9/35%, 25/05% the performance of the differential evolution (DE), genetic algorithm (GA), particle swarm optimization (PSO) and SA-based parallel hybrid models in electricity load forecasting. While, its computational costs are considerably lower than GA, PSO and DE-based parallel hybrid models. Therefore, it can be considered as an appropriate and effective alternative weighing technique for efficient parallel hybridization for time series forecasting. Originality/value In this paper, a LOWE algorithm is developed to find the desired weight of components in the global non-iterative universal manner. Although it can be generally demonstrated that the performance of the proposed weighting technique will not be worse than the meta-heuristic algorithm, its performance is also practically evaluated in real-world data sets.

Malliavin Calculus and the Optimal Weighting Function in a Pure Jump Lévy Setting

The paper is devoted to the problem of obtaining weighting functions for the Greeks of an option price written on a stock whose dynamics are of pure jump type. The problem is motivated by the work of Fourni\'e et al. [8, 9], who considered the price sensitivities of a frictionless market and proved that Greeks can be computed as the expectation of the product of the discounted payoff $\Phi$ and a suitable weighted function, i.e.Greek = E[Φ(XT)weight]. Since the weighting functions are random variables that need to be explicitly computed on each specific case, we establish necessary and sufficient conditions to be satisfied. The method used relied on the Malliavin calculus for Levy processes.

New Forest Aboveground Biomass Maps of China Integrating Multiple Datasets

Mapping the spatial variation of forest aboveground biomass (AGB) at the national or regional scale is important for estimating carbon emissions and removals and contributing to global stocktake and balancing the carbon budget. Recently, several gridded forest AGB products have been produced for China by integrating remote sensing data and field measurements, yet significant discrepancies remain among these products in their estimated AGB carbon, varying from 5.04 to 9.81 Pg C. To reduce this uncertainty, here, we first compiled independent, high-quality field measurements of AGB using a systematic and consistent protocol across China from 2011 to 2015. We applied two different approaches, an optimal weighting technique (WT) and a random forest regression method (RF), to develop two observationally constrained hybrid forest AGB products in China by integrating five existing AGB products. The WT method uses a linear combination of the five existing AGB products with weightings that minimize biases with respect to the field measurements, and the RF method uses decision trees to predict a hybrid AGB map by minimizing the bias and variance with respect to the field measurements. The forest AGB stock in China was 7.73 Pg C for the WT estimates and 8.13 Pg C for the RF estimates. Evaluation with the field measurements showed that the two hybrid AGB products had a lower RMSE (29.6 and 24.3 Mg/ha) and bias (−4.6 and −3.8 Mg/ha) than all five participating AGB datasets. Our study demonstrated both the WT and RF methods can be used to harmonize existing AGB maps with field measurements to improve the spatial variability and reduce the uncertainty of carbon stocks. The new spatial AGB maps of China can be used to improve estimates of carbon emissions and removals at the national and subnational scales.

Direct Position Determination for Augmented Coprime Arrays via Weighted Subspace Data Fusion Method

Direct position determination (DPD) for augmented coprime arrays is investigated in this paper. Augmented coprime array expands degree of freedom and array aperture and improves positioning accuracy. Because of poor stability and noise sensitivity of the subspace data fusion (SDF) method, we propose two weighted subspace data fusion (W-SDF) algorithms for direct position determination. Simulation results show that two W-SDF algorithms have a prominent promotion in positioning accuracy than SDF, Capon, and propagator method (PM) algorithm for augmented coprime arrays. SDF based on optimal weighting (OW-SDF) is slightly better than SDF based on SNR weighting (SW-SDF) in positioning accuracy. The performance for DPD of the W-SDF method with augmented coprime arrays is better than that of the W-SDF method with uniform arrays.

Blending Noah, SMOS and In-Situ Soil Moisture Using Multiple Weighting and Sampling Schemes

Soil moisture can be obtained from in-situ measurements, satellite observations, and model simulations. This study evaluates the importance of in-situ observations in soil moisture blending, and compares different weighting and sampling methods for combining model, satellite, and in-situ soil moisture data to generate an accurate and spatially-continuous soil moisture product at 4-km resolution. Four different datasets are used: Antecedent Precipitation Index (API), KAPI, which incorporates in-situ soil moisture observations with the API using regression kriging, SMOS L3 soil moisture, and model-simulated soil moisture from the Noah model as part of the North American Land Data Assimilation System (NLDAS). Triple collocation, least square weighting, and equal weighting are used to generate blended soil moisture products. An enumerated weighting scheme is designed to investigate the impact of different weighting schemes. The sensitivity of the blended soil moisture products to sampling schemes, station density and data formats (absolute, anomalies and percentiles) are also investigated. The results reveal KAPI outperforms API. This indicates that incorporating in-situ soil moisture improves the accuracy of the blended soil moisture products. There are no statistically significant (p>0.05) differences between blended soil moisture using triple collocation and equal weighting approaches, and both methods provide sub-optimal weighting. Optimal weighting is achieved by assigning larger weights to KAPI and smaller weights to SMOS. Using multiple sources of soil moisture is helpful for reducing uncertainty and improving accuracy, especially when the sampling density is low, or the sampling stations are less representative. These results are consistent regardless of how soil moisture is represented (absolute, anomalies or percentiles).

A Research on Susceptibility Mapping of Multiple Geological Hazards in Yanzi River Basin, China

Collapses, landslides, and debris flows are the main geological hazards faced by mankind, which bring heavy losses of life and property to people every year. The purpose of this paper is to establish a method for determining the optimal weighting scheme for multiple geological hazard susceptibility mapping. The information gain ratio (IGR) method was used to analyze the predictive ability of the conditioning factors. The support vector machine (SVM) algorithm was used to evaluate the susceptibility to collapse, landslide, and debris flow of the study area. The receiver operating characteristic curves (ROC) and classification statistics of geological hazard samples were applied to evaluate the performance of the models. The analytic hierarchy process (AHP) and frequency ratio (FR) method were combined to determine the optimal weighting scheme for collapse, landslide, and debris flow. All the conditioning factors have shown a certain predictive ability, making the models of collapse, landslide, and debris flow achieve very good performance. The multiple geological hazard susceptibility maps with the weights of 0.297, 0.539, and 0.164 for collapse, landslide, and debris flow was optimal for this study area with high-precision classification of all the geological hazard samples. The conclusions of this paper could provide meaningful references for risk migration and land use in the study area.