Estudio comparativo de la clasificación de rocas plutónicas y volcánicas en los diagramas normativo Q' (F')-ANOR y químico SiO2-100 CaO/(CaO+K2O)

To obtain a classification of igneous rocks, compatible with the QAPF classification, in the absence of modal analyses, a chemical diagram using the same discriminating elements as the Q'(F')-ANOR normative diagram has been proposed. These elements, Si, Ca and K, are essential constituents of quartz, feldspars and feldspathoids. The different proportions between these minerals are the basis of the QAPF modal classification but also those of the normative classification Q'(F')-ANOR. The chemical diagram SiO2 100·CaO/(CaO+K2 O) uses these same elements but with the important difference that they are treated as independent variables. This characteristic allows igneous rocks to be classified with a nomenclature equivalent to that obtained by modal analyses, using only Si, Ca and K analytical data. The plotting of a set of representative plutonic and volcanic rocks reveals a remarkable concordance between both diagrams. However, some discrepancies and overlaps occur in the subsaturated fields due to the inability of the method to determine whether the lower silica content is due to the presence of olivine or feldspathoids. The samples selected belong to igneous series from diverse geotectonic areas , thus helping to evaluate the results in a global contextPara obtener una clasificación de las rocas ígneas, compatible con la clasificación QAPF, cuando no se dispone de análisis modales se ha propuesto un diagrama químico que utiliza los mismos elementos discriminantes que el diagrama normativo Q'(F')-ANOR. Estos elementos, Si, Ca y K, son constituyentes esenciales del cuarzo, los feldespatos y los feldespatoides. Las diferentes proporciones entre estos minerales son la base de la clasificación modal QAPF pero también la de la clasificación normativa Q'(F')-ANOR. El diagrama químico SiO2100·CaO/(CaO+K2O) utiliza estos mismos elementos pero con la importante diferencia de que son tratados como variables independientes. Esta característica permite que puedan clasificarse las rocas ígneas con una nomenclatura equivalente a la obtenida mediante análisis modales disponiendo únicamente de los análisis de Si, Ca y K. La representación gráfica de un conjunto de rocas plutónicas y volcánicas representativas pone de manifiesto una concordancia notable entre ambos diagramas. No obstante, se producen algunas discrepancias y solapamientos en los campos subsaturados debido a la incapacidad del método para distinguir si el menor contenido en sílice se debe a la presencia de olivino o de feldespatoides. Las muestras escogidas pertenecen diversos ámbitos geotectónicos para poder valorar los resultados en un contexto globa

Comparative study of the classification of plutonic and volcanic rocks using the normative Q' (F')-ANOR and chemical SiO2-100·CaO/(CaO+K2O) diagrams

To obtain a classification of igneous rocks, compatible with the QAPF classification, in the absence of modal analyses, a chemical diagram using the same discriminating elements as the Q'(F')-ANOR normative diagram has been proposed. These elements, Si, Ca and K, are essential constituents of quartz, feldspars and feldspathoids. The different proportions between these minerals are the basis of the QAPF modal classification but also those of the normative classification Q'(F')-ANOR. The chemical diagram SiO2100·CaO/(CaO+K2O) uses these same elements but with the important difference that they are treated as independent variables. This characteristic allows igneous rocks to be classified with a nomenclature equivalent to that obtained by modal analyses, using only Si, Ca and K analytical data. The plotting of a set of representative plutonic and volcanic rocks reveals a remarkable concordance between both diagrams. However, some discrepancies and overlaps occur in the subsaturated fields due to the inability of the method to determine whether the lower silica content is due to the presence of olivine or feldspathoids. The samples selected belong to igneous series from diverse geotectonic areas , thus helping to evaluate the results in a global context

Graph Neural Networks Provably Benefit from Structural Information: A Feature Learning Perspective

Graph neural networks (GNNs) have pioneered advancements in graph representation learning, exhibiting superior feature learning and performance over multilayer perceptrons (MLPs) when handling graph inputs. However, understanding the feature learning aspect of GNNs is still in its initial stage. This study aims to bridge this gap by investigating the role of graph convolution within the context of feature learning theory in neural networks using gradient descent training. We provide a distinct characterization of signal learning and noise memorization in two-layer graph convolutional networks (GCNs), contrasting them with two-layer convolutional neural networks (CNNs). Our findings reveal that graph convolution significantly augments the benign overfitting regime over the counterpart CNNs, where signal learning surpasses noise memorization, by approximately factor $\sqrt{D}^{q-2}$, with $D$ denoting a node's expected degree and $q$ being the power of the ReLU activation function where $q > 2$. These findings highlight a substantial discrepancy between GNNs and MLPs in terms of feature learning and generalization capacity after gradient descent training, a conclusion further substantiated by our empirical simulations.Comment: 33 pages, 7 figures. We have provided a clearer roadma