scholarly journals A new statistical approach to the geochemical systematics of Italian alkaline igneous rocks

2020 ◽  
Vol 12 (1) ◽  
pp. 133-147
Author(s):  
Francesco Antonio Ambrosio
Keyword(s):  
Latent Variables ◽  
Principal Component ◽  
Alkaline Rock ◽  
Elemental Content ◽  
Discrete Groups ◽  
Rock Composition ◽  
Rock Types ◽  
Definition Of ◽  
Rock Suite ◽  
Two Parameters

AbstractThe ultra-alkaline rocks have exotic features that frustrated many attempts to group them in a single classification diagram. A consistent classification would be very useful to define a possible consanguinity, an argument that feed a living debate. This paper investigates the petrologic characteristics of the Cenozoic Italian ultra-alkaline rock-suite using -Rank Entropy Anentropy (RHA) and Principal Component Analysis (PCA)-. The RHA formula is the succession of component’s symbols arranged according to the diminishing of their elemental content in the analysis (whole rock composition). Other two parameters considered are an expression of the anentropy and entropy of the system. The PCA allows the definition of new latent variables based on geochemical compositions through linear combinations of the major oxides. Using both statistical methods was possible to create discrete groups of rock-types, associated by genetic relationship. The groups plotted in the Mg-Ca-Al ternary diagram depicts two main evolutionary arrays. We interpret the chemical variance in term of a general magmatic processes based on immiscibility and crystal fractionation. A comparison with similar association worldwide give a more general prospective to the magmato-tectonic assignment of these rocks, which is highly controversial in Italy.

scholarly journals Diesel Spray Macroscopic Parameter Estimation Using a Synthetic Shapes Database

2019 ◽  
Vol 9 (23) ◽  
pp. 5248
Author(s):  
Bottega ◽  
Dongiovanni
Keyword(s):  
Cone Angle ◽  
Principal Component ◽  
Diesel Sprays ◽  
Image Thresholding ◽  
Traditional Procedure ◽  
Analysis Technique ◽  
Thresholding Algorithm ◽  
Definition Of ◽  
Two Parameters

The paper presents a method for the macroscopic characterization of diesel sprays starting from digital images. Macroscopic spray characterization mainly consists in the definition of two parameters, namely penetration and cone angle. The latter can be evaluated according to many possible definitions, all based on the spray contour that is obtained by means of image thresholding. Therefore, the obtained cone angle value depends on the adopted angle definition and on the used thresholding algorithm. In order to avoid this double dependence, an alternative method has hence been proposed. The algorithm does not require the image thresholding and has an intrinsic cone angle definition. The algorithm takes advantage of principal component analysis technique and allows for a direct estimation of spray penetration and cone angle by comparing the original image with a database made of artificial spray images. In the present work, images coming from two different experiments are analyzed with the proposed method and results are compared with those obtained with a traditional procedure based on the Otsu’s image thresholding and four cone angle definitions.

scholarly journals Multi-objective parametrization of interatomic potentials for large deformation pathways and fracture of two-dimensional materials

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Xu Zhang ◽  
Hoang Nguyen ◽  
Jeffrey T. Paci ◽  
Subramanian K. R. S. Sankaranarayanan ◽  
Jose L. Mendoza-Cortes ◽  
...  
Keyword(s):  
Large Deformation ◽  
Functional Form ◽  
Principal Component ◽  
Interatomic Potentials ◽  
Two Dimensional ◽  
Multi Objective ◽  
Multi Objective Genetic Algorithm ◽  
Two Dimensional Materials ◽  
Definition Of

AbstractThis investigation presents a generally applicable framework for parameterizing interatomic potentials to accurately capture large deformation pathways. It incorporates a multi-objective genetic algorithm, training and screening property sets, and correlation and principal component analyses. The framework enables iterative definition of properties in the training and screening sets, guided by correlation relationships between properties, aiming to achieve optimal parametrizations for properties of interest. Specifically, the performance of increasingly complex potentials, Buckingham, Stillinger-Weber, Tersoff, and modified reactive empirical bond-order potentials are compared. Using MoSe2 as a case study, we demonstrate good reproducibility of training/screening properties and superior transferability. For MoSe2, the best performance is achieved using the Tersoff potential, which is ascribed to its apparent higher flexibility embedded in its functional form. These results should facilitate the selection and parametrization of interatomic potentials for exploring mechanical and phononic properties of a large library of two-dimensional and bulk materials.

scholarly journals L2-BETTI NUMBERS OF DISCRETE MEASURED GROUPOIDS

2005 ◽  
Vol 15 (05n06) ◽  
pp. 1169-1188 ◽  
Author(s):  
ROMAN SAUER
Keyword(s):  
Probability Space ◽  
Betti Numbers ◽  
Free Action ◽  
Countable Group ◽  
Equivalence Relations ◽  
Dimension Theory ◽  
Discrete Groups ◽  
Type Ii ◽  
Orbit Equivalent ◽  
Definition Of

There are notions of L2-Betti numbers for discrete groups (Cheeger–Gromov, Lück), for type II1-factors (recent work of Connes-Shlyakhtenko) and for countable standard equivalence relations (Gaboriau). Whereas the first two are algebraically defined using Lück's dimension theory, Gaboriau's definition of the latter is inspired by the work of Cheeger and Gromov. In this work we give a definition of L2-Betti numbers of discrete measured groupoids that is based on Lück's dimension theory, thereby encompassing the cases of groups, equivalence relations and holonomy groupoids with an invariant measure for a complete transversal. We show that with our definition, like with Gaboriau's, the L2-Betti numbers [Formula: see text] of a countable group G coincide with the L2-Betti numbers [Formula: see text] of the orbit equivalence relation [Formula: see text] of a free action of G on a probability space. This yields a new proof of the fact the L2-Betti numbers of groups with orbit equivalent actions coincide.

Effects of Medium and Substituents on Dissociationof 4,4'-Disubstituted Bis(benzenesulfon)imides

1996 ◽  
Vol 61 (8) ◽  
pp. 1205-1214 ◽  
Author(s):  
Miroslav Ludwig ◽  
Pavel Štverka
Keyword(s):  
Latent Variables ◽  
Dissociation Constants ◽  
Substituent Effects ◽  
Principal Component ◽  
H Nmr ◽  
Base Process ◽  
Elemental Analyses ◽  
Substituent Constants ◽  
Model Substances ◽  
Strong Acids

Ten 4,4'-disubstituted bis(arenesulfon)imides of the general formula XC6H4SO2NHSO2C6H4X have been synthesized and their structures confirmed by their 1H NMR spectra. Elemental analyses are presented for the compounds not yet described. The dissociation constants of these model substances have been measured potentiometrically in pyridine, dimethylformamide, methanol, ethanol, propylene carbonate, acetone, acetonitrile, 1,2-dichloroethane and tetramethylene sulfone. The pKHA values obtained have been correlated with three sets of the Hammett substituent constants and the results have been used to discuss the solvent and substituent effects on the dissociation of the compounds studied. Sulfonimides with electron-acceptor substituents behave as rather strong acids in some solvents (pyridine, dimethylformamide, methanol and ethanol), whereas normal substituent dependences are found in other solvents. The experimental data have also been interpreted with the help of the statistical methods based on latent variables. From the calculations it follows that only the first principal component, which correlates well with the substituent constant sets adopted, is statistically significant in describing the substituent effect on the acid-base process studied.

Reaction Monitoring in Explorative Organic Synthesis Using Fiber-Optical NIR Spectroscopy and Principal Component Analysis

1996 ◽  
Vol 50 (12) ◽  
pp. 1541-1544 ◽  
Author(s):  
Hans-René Bjørsvik
Keyword(s):  
Principal Component Analysis ◽  
Data Analysis ◽  
Latent Variables ◽  
Near Infrared ◽  
Nir Spectroscopy ◽  
Principal Component ◽  
Component Analysis ◽  
Quantitative Information ◽  
Chemistry Laboratory ◽  
Reaction Profile

A method of combining spectroscopy and multivariate data analysis for obtaining quantitative information on how a reaction proceeds is presented. The method is an approach for the explorative synthetic organic laboratory rather than the analytical chemistry laboratory. The method implements near-infrared spectroscopy with an optical fiber transreflectance probe as instrumentation. The data analysis consists of decomposition of the spectral data, which are recorded during the course of a reaction by using principal component analysis to obtain latent variables, scores, and loading. From the scores and the corresponding reaction time, it is possible to obtain a reaction profile. This reaction profile can easily be recalculated to obtain the concentration profile over time. This calculation is based on only two quantitative measurements, which can be (1) measurement from the work-up of the reaction or (2) chromatographic analysis from two withdrawn samples during the reaction. The method is applied to the synthesis of 3-amino-propan-1,2-diol.

scholarly journals Adaptabilidade de Objetos de Aprendizagem usando Calibragem e Sequenciamento Adaptativo de Exercícios

2018 ◽  
Vol 26 (1) ◽  
pp. 70
Author(s):  
Rômulo César Silva ◽  
Alexandre Ibrahim Direne ◽  
Diego Marczal ◽  
Ana Carla Borille ◽  
Paulo Ricardo Bittencourt Guimarães ◽  
...  
Keyword(s):  
Problem Solving ◽  
Empirical Study ◽  
Cognitive Skills ◽  
Learning Objects ◽  
Skill Level ◽  
Problem Solution ◽  
Algebraic Expressions ◽  
Student Skill ◽  
Definition Of ◽  
Two Parameters

The work approaches theoretical and implementation issues of a framework for creating and executing Learning Objects (LOs) where problem-solving tasks are ordered according to the matching of two parameters, both calculated automatically: (1) student skill level and (2) problem solution difficulty. They are formally defined as algebraic expressions. The definition of skill level is achieved through a rating-based measure that resembles the ones of game mastery scales, while the solution difficulty is based on mistakes and successes of learners to deal with the problem. An empirical study based on existing students data demonstrated the suitability of the formulas. Besides, the motivational aspects of learning are considered in depth. In this sense, it is important to propose activities according to the student’s level of expertise, which is achieved through presenting students with exercises that are compatible with the difficulty degree of their cognitive skills. Also, the results of an experiment conducted with four highschool classes using the framework for the domain of logarithmic properties are presented.

scholarly journals A spectral theory for Wright’s inbreeding coefficients and related quantities

PLoS Genetics ◽  
2021 ◽  
Vol 17 (7) ◽  
pp. e1009665
Author(s):  
Olivier François ◽  
Clément Gain
Keyword(s):  
Population Structure ◽  
Genetic Variation ◽  
Population Genetic ◽  
Principal Component ◽  
Large Data ◽  
Population Subdivision ◽  
Adaptive Genetic Variation ◽  
Genomic Locus ◽  
Inbreeding Coefficients ◽  
Definition Of

Wright’s inbreeding coefficient, FST, is a fundamental measure in population genetics. Assuming a predefined population subdivision, this statistic is classically used to evaluate population structure at a given genomic locus. With large numbers of loci, unsupervised approaches such as principal component analysis (PCA) have, however, become prominent in recent analyses of population structure. In this study, we describe the relationships between Wright’s inbreeding coefficients and PCA for a model of K discrete populations. Our theory provides an equivalent definition of FST based on the decomposition of the genotype matrix into between and within-population matrices. The average value of Wright’s FST over all loci included in the genotype matrix can be obtained from the PCA of the between-population matrix. Assuming that a separation condition is fulfilled and for reasonably large data sets, this value of FST approximates the proportion of genetic variation explained by the first (K − 1) principal components accurately. The new definition of FST is useful for computing inbreeding coefficients from surrogate genotypes, for example, obtained after correction of experimental artifacts or after removing adaptive genetic variation associated with environmental variables. The relationships between inbreeding coefficients and the spectrum of the genotype matrix not only allow interpretations of PCA results in terms of population genetic concepts but extend those concepts to population genetic analyses accounting for temporal, geographical and environmental contexts.

scholarly journals Igneous Rock Associations 26. Lamproites, Exotic Potassic Alkaline Rocks: A Review of their Nomenclature, Characterization and Origins

2020 ◽  
Vol 47 (3) ◽  
pp. 119-142
Author(s):  
Roger H. Mitchell
Keyword(s):  
Partial Melting ◽  
Lithospheric Mantle ◽  
Tectonic Setting ◽  
Alkaline Rock ◽  
Mantle Metasomatism ◽  
Geochemical Evolution ◽  
Alkaline Rocks ◽  
Isotopic Compositions ◽  
Economic Significance ◽  
Rock Types

Lamproite is a rare ultrapotassic alkaline rock of petrological importance as it is considered to be derived from metasomatized lithospheric mantle, and of economic significance, being the host of major diamond deposits. A review of the nomenclature of lamproite results in the recommendation that members of the lamproite petrological clan be named using mineralogical-genetic classifications to distinguish them from other genetically unrelated potassic alkaline rocks, kimberlite, and diverse lamprophyres. The names “Group 2 kimberlite” and “orangeite” must be abandoned as these rock types are varieties of bona fide lamproite restricted to the Kaapvaal Craton. Lamproites exhibit extreme diversity in their mineralogy which ranges from olivine phlogopite lamproite, through phlogopite leucite lamproite and potassic titanian richterite-diopside lamproite, to leucite sanidine lamproite. Diamondiferous olivine lamproites are hybrid rocks extensively contaminated by mantle-derived xenocrystic olivine. Currently, lamproites are divided into cratonic (e.g. Leucite Hills, USA; Baifen, China) and orogenic (Mediterranean) varieties (e.g. Murcia-Almeria, Spain; Afyon, Turkey; Xungba, Tibet). Each cratonic and orogenic lamproite province differs significantly in tectonic setting and Sr–Nd–Pb–Hf isotopic compositions. Isotopic compositions indicate derivation from enriched mantle sources, having long-term low Sm/Nd and high Rb/Sr ratios, relative to bulk earth and depleted asthenospheric mantle. All lamproites are considered, on the basis of their geochemistry, to be derived from ancient mineralogically complex K–Ti–Ba–REE-rich veins, or metasomes, in the lithospheric mantle with, or without, subsequent contributions from recent asthenospheric or subducted components at the time of genesis. Lamproite primary magmas are considered to be relatively silica-rich (~50–60 wt.% SiO2), MgO-poor (3–12 wt.%), and ultrapotassic (~8–12 wt.% K2O) as exemplified by hyalo-phlogopite lamproites from the Leucite Hills (Wyoming) or Smoky Butte (Montana). Brief descriptions are given of the most important phreatomagmatic diamondiferous lamproite vents. The tectonic processes which lead to partial melting of metasomes, and/or initiation of magmatism, are described for examples of cratonic and orogenic lamproites. As each lamproite province differs with respect to its mineralogy, geochemical evolution, and tectonic setting there is no simple or common petrogenetic model for their genesis. Each province must be considered as the unique expression of the times and vagaries of ancient mantle metasomatism, coupled with diverse and complex partial melting processes, together with mixing of younger asthenospheric and lithospheric material, and, in the case of many orogenic lamproites, with Paleogene to Recent subducted material.

Pattern recognition of enrichment levels of SELEX-based candidate aptamers for human C-reactive protein

2017 ◽  
Vol 62 (3) ◽  
Author(s):  
Xinliang Yu ◽  
Ruqin Yu ◽  
Xiaohai Yang
Keyword(s):  
Pattern Recognition ◽  
Latent Variables ◽  
Molecular Descriptors ◽  
Principal Component ◽  
Support Vector ◽  
C Reactive Protein ◽  
Reactive Protein ◽  
Systematic Evolution ◽  
Model C ◽  
Exponential Enrichment

AbstractSelecting aptamers for human C-reactive protein (CRP) would be of critical importance in predicting the risk for cardiovascular disease. The enrichment level of DNA aptamers is an important parameter for selecting candidate aptamers for further affinity and specificity determination. This paper is the first report on pattern recognition used for CRP aptamer enrichment levels in the systematic evolution of ligands by exponential enrichment (SELEX) process, by applying structure-activity relationship models. After generating 10 rounds of graphene oxide (GO)-SELEX and 1670 molecular descriptors, eight molecular descriptors were selected and five latent variables were then obtained with principal component analysis (PCA), to develop a support vector classification (SVC) model. The SVC model (C=8.1728 and

A Lyapunov Theory-Based Neural Network Approach for Face Recognition

2010 ◽  
pp. 23-48 ◽  
Author(s):  
Li-Minn Ang ◽  
King Hann Lim ◽  
Kah Phooi Seng ◽  
Siew Wen Chin
Keyword(s):  
Neural Network ◽  
Face Recognition ◽  
Principal Component ◽  
Lyapunov Stability Theory ◽  
Recognition System ◽  
Lyapunov Theory ◽  
Neural Network Approach ◽  
Linear Discriminant ◽  
Feature Based ◽  
Definition Of

This chapter presents a new face recognition system comprising of feature extraction and the Lyapunov theory-based neural network. It first gives the definition of face recognition which can be broadly divided into (i) feature-based approaches, and (ii) holistic approaches. A general review of both approaches will be given in the chapter. Face features extraction techniques including Principal Component Analysis (PCA) and Fisher’s Linear Discriminant (FLD) are discussed. Multilayered neural network (MLNN) and Radial Basis Function neural network (RBF NN) will be reviewed. Two Lyapunov theory-based neural classifiers: (i) Lyapunov theory-based RBF NN, and (ii) Lyapunov theory-based MLNN classifiers are designed based on the Lyapunov stability theory. The design details will be discussed in the chapter. Experiments are performed on two benchmark databases, ORL and Yale. Comparisons with some of the existing conventional techniques are given. Simulation results have shown good performance for face recognition using the Lyapunov theory-based neural network systems.

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