Inversion Evaluation of Rare Earth Elements in Soil by Visible-Shortwave Infrared Spectroscopy

According to historical information, more than 300 metal smelting enterprises have been in the southwest of Xiongan for 300 years; however, these polluting enterprises have been gradually closed with the increased intensity of environmental protection. In the paper, 264 soil samples were collected and analyzed in the range of 400 nm–2500 nm by the spectra vista corporation (SVC), and the spectral noise was smoothed by the Savitzky–Golay filter. In order to enhance the spectral differences and curve shapes, mathematical transformations, such as the standard normal variate (SNV), first-order differential (FD), second-order differential (SD), multiple scattering correction (MSC), and continuum removal (CR), were performed on the data, and the correlation between spectral transformation and contents of REEs was analyzed. Moreover, three machine learning models—partial least-squares (PLS), random forest (RF), back propagation neural network (BPNN)—were used to predict the contents of REEs. Experimental results prove that REEs are combined with spectral active substances, such as organic compounds, clay minerals, and iron oxide, and it is possible to determine the contents of REEs using the reflection spectrum. The R2 between the predicted values and measured contents reached 0.986 by using BPNN after FD transformation. More importantly, the predicted values basically agree with the actual situation for CASI/SASI airborne hyperspectral images, and this is an effective technique to obtain the contents of REEs in soil at the study area.

Large-deviation asymptotics of condition numbers of random matrices

Let $\mathbf{X}$ be a $p\times n$ random matrix whose entries are independent and identically distributed real random variables with zero mean and unit variance. We study the limiting behaviors of the 2-normal condition number k(p,n) of $\mathbf{X}$ in terms of large deviations for large n, with p being fixed or $p=p(n)\rightarrow\infty$ with $p(n)=o(n)$ . We propose two main ingredients: (i) to relate the large-deviation probabilities of k(p,n) to those involving n independent and identically distributed random variables, which enables us to consider a quite general distribution of the entries (namely the sub-Gaussian distribution), and (ii) to control, for standard normal entries, the upper tail of k(p,n) using the upper tails of ratios of two independent $\chi^2$ random variables, which enables us to establish an application in statistical inference.

Share of Discontinuities in the Ozone Concentration Data from Three Reanalyses

Ozone is a very important trace gas in the stratosphere and, thus, we need to know its time evolution over the globe. However, ground-based measurements are rare, especially in the Southern Hemisphere, and while satellite observations provide broader spatial coverage generally, they are not available everywhere. On the other hand, reanalysis data have regular spatial and temporal structure, which is beneficial for trend analysis, but temporal discontinuities might exist in the data. These discontinuities may influence the results of trend studies. The aim of this paper is to detect discontinuities in ozone data of the following reanalyses: MERRA-2, ERA-5 and JRA-55 with the help of the Pettitt, the Buishand, and the Standard Normal Homogeneity tests above the 500 hPa level. The share of discontinuities varies from 30% to 70% and they are strongly layer dependent. The share of discontinuities is the lowest for JRA-55. Differences between reanalyses were found to be larger than differences between homogeneity tests within one reanalysis. Another aim of this paper is to test the ability of homogeneity tests to detect the discontinuities in 2004 and 2015, when changes in versions of satellite data took place. We showed the discontinuities in 2004 are better detected than those in 2015.

A New Linear Regression Kalman Filter with Symmetric Samples

Nonlinear filtering is of great significance in industries. In this work, we develop a new linear regression Kalman filter for discrete nonlinear filtering problems. Under the framework of linear regression Kalman filter, the key step is minimizing the Kullback–Leibler divergence between standard normal distribution and its Dirac mixture approximation formed by symmetric samples so that we can obtain a set of samples which can capture the information of reference density. The samples representing the conditional densities evolve in a deterministic way, and therefore we need less samples compared with particle filter, as there is less variance in our method. The numerical results show that the new algorithm is more efficient compared with the widely used extended Kalman filter, unscented Kalman filter and particle filter.

Deterministic Sampling from Univariate Normal Distributions with Sierpinski Space-Filling Curves

This work addresses the problem of sampling from Gaussian probability distributions by means of uniform samples obtained deterministically and directly from space-filling curves (SFCs), a purely topological concept. To that end, the well-known inverse cumulative distribution function method is used, with the help of the probit function,which is the inverse of the cumulative distribution function of the standard normal distribution. Mainly due to the central limit theorem, the Gaussian distribution plays a fundamental role in probability theory and related areas, and that is why it has been chosen to be studied in the present paper. Numerical distributions (histograms) obtained with the proposed method, and in several levels of granularity, are compared to the theoretical normal PDF, along with other already established sampling methods, all using the cited probit function. Final results are validated with the Kullback-Leibler and two other divergence measures, and it will be possible to draw conclusions about the adequacy of the presented paradigm. As is amply known, the generation of uniform random numbers is a deterministic simulation of randomness using numerical operations. That said, sequences resulting from this kind of procedure are not truly random. Even so, and to be coherent with the literature, the expression ”random number” will be used along the text to mean ”pseudo-random number”.

Prediction of radiation-induced hypothyroidism using radiomic data analysis does not show superiority over standard normal tissue complication models

State-of-art normal tissue complication probability (NTCP) models do not take into account more complex individual anatomical variations, which can be objectively quantitated and compared in radiomic analysis. The goal of this project was development of radiomic NTCP model for radiation-induced hypothyroidism (RIHT) using imaging biomarkers (radiomics). We gathered CT images and clinical data from 98 patients, who underwent intensity-modulated radiation therapy (IMRT) for head and neck cancers with a planned total dose of 70.0 Gy (33-35 fractions). During the 28-month (median) follow-up 27 patients (28%) developed RIHT. For each patient, we extracted 1316 radiomic features from original and transformed images using manually contoured thyroid masks. Creating models based on clinical, radiomic features or a combination thereof, we considered 3 variants of data preprocessing. Based on their performance metrics (sensitivity, specificity), we picked best models for each variant ((0.8, 0.96), (0.9, 0.93), (0.9, 0.89) variant-wise) and compared them with external NTCP models ((0.82, 0.88), (0.82, 0.88), (0.76, 0.91)). Our models reach accuracy comparable with or better than previously presented non-radiomic NTCP models. The benefit of our approach is obtaining the RIHT predictions before treatment planning to adjust IMRT plan to avoid the thyroid region in most susceptible patients.

Measurement of Human Semicircular Canal Spatial Attitude

Located deep in the temporal bone, the semicircular canal is a subtle structure that requires a spatial coordinate system for measurement and observation. In this study, 55 semicircular canal and eyeball models were obtained by segmentation of MRI data. The spatial coordinate system was established by taking the top of the common crus and the bottom of the eyeball as the horizontal plane. First, the plane equation was established according to the centerline of the semicircular canals. Then, according to the parameters of the plane equation, the plane normal vectors were obtained. Finally, the average unit normal vector of each semicircular canal plane was obtained by calculating the average value of the vectors. The standard normal vectors of the and left posterior semicircular canal, superior semicircular canal and lateral semicircular canal were [−0.651, 0.702, 0.287], [0.749, 0.577, 0.324], [−0.017, −0.299, 0.954], [0.660, 0.702, 0.266], [−0.739, 0.588, 0.329], [0.025, −0.279, 0.960]. The different angles for the different ways of calculating the standard normal vectors of the right and left posterior semicircular canal, superior semicircular canal and lateral semicircular canal were 0.011, 0.028, 0.008, 0.011, 0.024, and 0.006 degrees. The technology for measuring the semicircular canal spatial attitudes in this study are reliable, and the measurement results can guide vestibular function examinations and help with guiding the diagnosis and treatment of BPPV.

Estimating Soil Properties and Nutrients by Visible and Infrared Diffuse Reflectance Spectroscopy to Characterize Vineyards

Visible, near, and shortwave infrared (VIS-NIR-SWIR) reflectance spectroscopy, a cost-effective and rapid means of characterizing soils, was used to predict soil sample properties for four vineyards (central and north-western Spain). Sieved and air-dried samples were measured using a portable spectroradiometer (350–2500 nm) and compared for pistol grip (PG) versus contact probe (CP) setups. Raw data processed using standard normal variate (SVN) and detrending transformation (DT) were grouped into four subsets (VIS: 350–700 nm; NIR: 701–1000 nm; SWIR: 1001–2500 nm; and full range: 350–2500 nm) in order to identify the most suitable range for determining soil characteristics. The performance of partial least squares regression (PLSR) models in predicting soil properties from reflectance spectra was evaluated by cross-validation. The four spectral subsets and transformed reflectances for each setup were used as PLSR predictor variables. The best performing PLSR models were obtained for pH, electrical conductivity, and phosphorous (R2 values above 0.92), while models for sand, nitrogen, and potassium showed moderately good performances (R2 values between 0.69 and 0.77). The SWIR subset and SVN + DT processing yielded the best PLSR models for both the PG and CP setups. VIS-NIR-SWIR reflectance spectroscopy shows promise as a technique for characterizing vineyard soils for precision viticulture purposes. Further studies will be carried out to corroborate our findings.