Quantitative Geochemical Prediction from Spectral Measurements and Its Application to Spatially Dispersed Spectral Data

The efficacy of predicting geochemical parameters with a 2-chain workflow using spectral data as the initial input is evaluated. Spectral measurements spanning the approximate 400–25000 nm spectral range are used to train a workflow consisting of a non-negative matrix function (NMF) step, for data reduction, and a random forest regression (RFR) to predict eight geochemical parameters. Approximately 175,000 spectra with their corresponding chemical analysis were available for training, testing and validation purposes. The samples and their spectral and chemical parameters represent 9399 drillcore. Of those, approximately 20,000 spectra and their accompanying analysis were used for training and 5000 for model validation. The remaining pairwise data (150,000 samples) were used for testing of the method. The data are distributed over two large spatial extents (980 km2 and 3025 km2, respectively) and allowed the proposed method to be tested against samples that are spatially distant from the initial training points. Global R2 scores and wt.% RMSE on the 150,000 validation samples are Fe (0.95/3.01), SiO2 (0.96/3.77), Al2O3 (0.92/1.27), TiO (0.68/0.13), CaO (0.89/0.41), MgO (0.87/0.35), K2O (0.65/0.21) and LOI (0.90/1.14), given as Parameter (R2/RMSE), and demonstrate that the proposed method is capable of predicting the eight parameters and is stable enough, in the environment tested, to extend beyond the training sets initial spatial location.

Quantitative Geochemical Prediction from Spectral Measurements and its Application to Spatially Dispersed Spectral Data

The efficacy of predicting geochemical parameters with a 2-chain workflow using spectral data as the initial input is evaluated. Spectral measurements spanning the approximate 400-25000nm spectral range are used to train a workflow consisting of a non-negative matrix function (NMF) step, for data reduction, and a random forest regression (RFR) to predict 8 geochemical parameters. Approximately 175000 spectra with their corresponding chemical analysis were available for training, testing and validation purposes. The samples and their spectral and chemical parameters represent 9399 drillcore. Of those, approximately 20000 spectra and their accompanying analysis were used for training and 5000 for model validation. The remaining pairwise data (150000 samples) were used for testing of the method. The data are distributed over 2 large spatial extents (980 km2 and 3025 km2 respectively) and allowed the proposed method to be tested against samples that are spatially distant from the initial training points. Global R2 scores and wt.% RMSE on the 150000 validation samples are Fe(0.95/3.01), SiO2(0.96/3.77), Al2O3(0.92/1.27), TiO(0.68/0.13), CaO(0.89/0.41), MgO(0.87/0.35), K2O(0.65/0.21) and LOI(0.90/1.14), given as Parameter(R2/RMSE), and demonstrate that the proposed method is capable of predicting the 8 parameters and is stable enough, in the environment tested, to extend beyond the training sets initial spatial location.

Quantitative Geochemical Prediction from Spectral Measurements and its Application to Spatially Dispersed Spectral Data

The efficacy of predicting geochemical parameters with a 2-chain workflow using spectral data as the initial input is evaluated. Spectral measurements spanning the approximate 400-25000nm spectral range are used to train a workflow consisting of a non-negative matrix function (NMF) step, for data reduction, and a random forest regression (RFR) to predict 8 geochemical parameters. Approximately 175000 spectra with their corresponding chemical analysis were available for training, testing and validation purposes. The samples and their spectral and chemical parameters represent 9399 drillcore. Of those, approximately 20000 spectra and their accompanying analysis were used for training and 5000 for model validation. The remaining pairwise data (150000 samples) were used for testing of the method. The data are distributed over 2 large spatial extents (980 km2 and 3025 km2 respectively) and allowed the proposed method to be tested against samples that are spatially distant from the initial training points. Global R2 scores and wt.% RMSE on the 150000 validation samples are Fe(0.95/3.01), SiO2(0.96/3.77), Al2O3(0.92/1.27), TiO(0.68/0.13), CaO(0.89/0.41), MgO(0.87/0.35), K2O(0.65/0.21) and LOI(0.90/1.14), given as Parameter(R2/RMSE), and demonstrate that the proposed method is capable of predicting the 8 parameters and is stable enough, in the environment tested, to extend beyond the training sets initial spatial location.

On the Matrix Versions of Incomplete Extended Gamma and Beta Functions and Their Applications for the Incomplete Bessel Matrix Functions

In this paper, we first introduce the incomplete extended Gamma and Beta functions with matrix parameters; then, we establish some different properties for these new extensions. Furthermore, we give a specific application for the incomplete Bessel matrix function by using incomplete extended Gamma and Beta functions; at last, we construct the relation between the incomplete confluent hypergeometric matrix functions and incomplete Bessel matrix function.

Orientations and matrix function-based centralities in multiplex network analysis of urban public transport

We study urban public transport systems by means of multiplex networks in which stops are represented as nodes and each line is represented by a layer. We determine and visualize public transport network orientations and compare them with street network orientations of the 36 largest German as well as 18 selected major European cities. We find that German urban public transport networks are mainly oriented in a direction close to the cardinal east-west axis, which usually coincides with one of two orthogonal preferential directions of the corresponding street network. While this behavior is present in only a subset of the considered European cities it remains true that none but one considered public transport network has a distinct north-south-like preferential orientation. Furthermore, we study the applicability of the class of matrix function-based centrality measures, which has recently been generalized from single-layer networks to layer-coupled multiplex networks, to our more general urban multiplex framework. Numerical experiments based on highly efficient and scalable methods from numerical linear algebra show promising results, which are in line with previous studies. The centrality measures allow detailed insights into geometrical properties of urban systems such as the spatial distribution of major transport axes, which can not be inferred from orientation plots. We comment on advantages over existing methodology, elaborate on the comparison of different measures and weight models, and present detailed hyper-parameter studies. All results are illustrated by demonstrative graphical representations.

On the Kampé de Fériet Hypergeometric Matrix Function

In this study, we derive recursion formulas for the Kampé de Fériet hypergeometric matrix function. We also obtain some finite matrix and infinite matrix summation formulas for the Kampé de Fériet hypergeometric matrix function.

Applications Of Matrix Function And Group Action

The article presents some applications of the matrix function and group action to reveal some properties of matrixes and p-groups.