A hydrological model skill score and revised R-squared

Despite the advances in methods of statistical and mathematical modeling, there is considerable lack of focus on improving how to judge models’ quality. Coefficient of determination (R2) is arguably the most widely applied ‘goodness-of-fit’ metric in modelling and prediction of environmental systems. However, known issues of R2 are that it: (i) can be low and high for an accurate and imperfect model, respectively; (ii) yields the same value when we regress observed on modelled series and vice versa; and (iii) does not quantify a model's bias (B). A new model skill score E and revised R-squared (RRS) are presented to combine correlation, term B and capacity to capture variability. Differences between E and RRS lie in the forms of correlation and the term B used for each metric. Acceptability of E and RRS was demonstrated through comparison of results from a large number of hydrological simulations. By applying E and RRS, the modeller can diagnostically identify and expose systematic issues behind model optimizations based on other ‘goodness-of-fits’ such as Nash–Sutcliffe efficiency (NSE) and mean squared error. Unlike NSE, which varies from −∞ to 1, E and RRS occur over the range 0–1. MATLAB codes for computing E and RRS are provided.

Multi-Label Feature Selection Based on High-Order Label Correlation Assumption

Multi-label data often involve features with high dimensionality and complicated label correlations, resulting in a great challenge for multi-label learning. Feature selection plays an important role in multi-label learning to address multi-label data. Exploring label correlations is crucial for multi-label feature selection. Previous information-theoretical-based methods employ the strategy of cumulative summation approximation to evaluate candidate features, which merely considers low-order label correlations. In fact, there exist high-order label correlations in label set, labels naturally cluster into several groups, similar labels intend to cluster into the same group, different labels belong to different groups. However, the strategy of cumulative summation approximation tends to select the features related to the groups containing more labels while ignoring the classification information of groups containing less labels. Therefore, many features related to similar labels are selected, which leads to poor classification performance. To this end, Max-Correlation term considering high-order label correlations is proposed. Additionally, we combine the Max-Correlation term with feature redundancy term to ensure that selected features are relevant to different label groups. Finally, a new method named Multi-label Feature Selection considering Max-Correlation (MCMFS) is proposed. Experimental results demonstrate the classification superiority of MCMFS in comparison to eight state-of-the-art multi-label feature selection methods.

Effect of the Large-Scale Structure on Turbulent Prandtl Number in a Turbulent Shear Layer

We have run a Direct Numerical Simulation of a spatially developing shear mixing layer. The aim of this study is to clarify the influence of the large-scale structure on the turbulent Prandtl number PrT. As a main conclusion, PrT takes a small value (PrT ∼ 0.5) in the dominant region of the large-scale structure. The budget analyses for the Reynolds stress equation and the scalar flux equation revealed that the differences between the momentum and scalar transfer are caused by terms related to pressure (i.e., pressure-strain correlation term, pressure-scalar gradient correlation term, and pressure diffusion terms). Phenomenally, the momentum in the field where a large-scale vortex coexists tends to be transported toward the counter-gradient direction under the influence of pressure, but the scalar is transported toward the gradient direction. As a result, it is thought that the difference in the driving force between the momentum and scalar transport causes the decrease of the PrT.

The thermopower of NiCr- and PtRh-alloys – a new view

For the interpretation of the Seebeck coefficient S(T) of transition metal alloys where one or both of the alloy partners develop a spin moment, so far spincluster models in connection with the standard Boltzmann-Fermi theory S(T)\sim T have been adopted. However, this interpretation suffers from some obvious inconsistencies, in particular with NiCr-alloys. In this contribution we try to alleviate these inconsistencies by implementing the recently proposed correlated electron thermopower terms which appear in the framework of Fermi-Boltzmann statistics when it is applied to Stoner-Slater intraatomic exchange (J) split electronic states. For both NiCr- and PtRh-alloys we recover the typical electron correlation term of the thermoelectric power, {S_{D}}, while former inconsistencies can be removed. As NiCr and PtRh-alloys are often used in high temperature sensing because of their stability, this new interpretation of the thermoelectric power may help to develop a better calibration and compositional choice of alloy-based thermocouples.

Checking Default Correlation and Score Correlation in a Breakpoint Model for Rating Classification

In credit risk, debtors with different creditworthiness are divided into rating classes. One problem is to define the borders of the rating classes. A natural way to estimate these breakpoints from default observations comes out of the field of change point analysis. In order to account for dependency between the debtors, the literature proposes a combination of a breakpoint model with a one-factor model. One finds strongly consistent estimators for the threshold of the rating classes and the corresponding default probabilities, also called risk levels. But an investigation of the inherent model properties is as yet missing. For this reason we derive the default correlation and study its relationship to the model parameters, i.e., the breakpoint, the risk levels, and a new correlation term, named score correlation, appearing in a simulation study. Eventually, we check the magnitude of the score correlation used in the simulation study.

Reduced Boundary Sensitivity and Improved Contrast of the Regularized Inverse Problem Solution in Elasticity

We observe that posing the inverse problem as a constrained minimization problem under regularization leads to boundary dependent solutions. In this paper, we propose a modified objective function and show with 2D examples that our method works well to reduce boundary sensitive solutions. The examples consist of two stiff inclusions embedded in a softer unit square. These inclusions could be representative of tumors, which are in general stiffer than their background tissues, thus could potentially be detected based on their stiffness contrast. We modify the objective function for the displacement correlation term by weighting it with a function that depends on the strain field. In a simplified 1D coupled model, we derive an analytical expression and observe the same trends in the reconstructions as for the 2D model. The analysis in this paper is confined to inclusions of similar size and may not overlap when projected on the horizontal axis. They may, however, vary in position along the vertical axis. Furthermore, our analysis holds for an arbitrary number of inclusions having distinct stiffness values. Finally, to increase the overall contrast of the tumors and simultaneously improve the smoothness, we solve the regularized inverse problem in a posterior step, utilizing a spatially varying regularization factor.

The effect of impurities in ultra-thin hydrogenated silicene and germanene: a first principles study

Spin polarized density functional theory within the GGA–PBE and HSE06 approach for the exchange correlation term has been used to investigate the stability and electronic properties of nitrogen and boron impurities in single layers of silicane and germanane.

Mathematical Modeling for Lateral Displacement Induced by Wind Velocity Using Monitoring Data Obtained from Main Girder of Sutong Cable-Stayed Bridge

Based on the health monitoring system installed on the main span of Sutong Cable-Stayed Bridge, GPS displacement and wind field are real-time monitored and analyzed. According to analytical results, apparent nonlinear correlation with certain discreteness exists between lateral static girder displacement and lateral static wind velocity; thus time series of lateral static girder displacement are decomposed into nonlinear correlation term and discreteness term, nonlinear correlation term of which is mathematically modeled by third-order Fourier series with intervention of lateral static wind velocity and discreteness term of which is mathematically modeled by the combined models of ARMA(7,4)and EGARCH(2,1). Additionally, stable power spectrum density exists in time series of lateral dynamic girder displacement, which can be well described by the fourth-order Gaussian series; thus time series of lateral dynamic girder displacement are mathematically modeled by harmonic superposition function. By comparison and verification between simulative and monitoring lateral girder displacements from September 1 to September 3, the presented mathematical models are effective to simulate time series of lateral girder displacement from main girder of Sutong Cable-Stayed Bridge.