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Knowledge graph embeddings (KGE) have been extensively studied to embed large-scale relational data for many real-world applications. Existing methods have long ignored the fact many KGs contain two fundamentally different views: high-level ontology-view concepts and fine-grained instance-view entities. They usually embed all nodes as vectors in one latent space. However, a single geometric representation fails to capture the structural differences between two views and lacks probabilistic semantics towards concepts’ granularity. We propose Concept2Box, a novel approach that jointly embeds the two views of a KG using dual geometric representations. We model concepts with box embeddings, which learn the hierarchy structure and complex relations such as overlap and disjoint among them. Box volumes can be interpreted as concepts’ granularity. Different from concepts, we model entities as vectors. To bridge the gap between concept box embeddings and entity vector embeddings, we propose a novel vector-to-box distance metric and learn both embeddings jointly. Experiments on both the public DBpedia KG and a newly-created industrial KG showed the effectiveness of Concept2Box. 

Abstract Mixing has been widely used in the interpretation of radiogenic isotope ratios and highly incompatible trace element variations in basalts produced by melting of a heterogeneous mantle. The binary mixing model is constructed by considering mass balance of endmember components, which is independent of physical state and spatial distribution of the endmembers in the mantle source. Variations of radiogenic isotope ratios and highly incompatible trace elements in basalts also depend on the size and spatial distribution of chemical and lithological heterogeneities in the mantle source. Here we present a new mixing model and a mixing scheme that take into account of the size, spatial location, and melting history of enriched mantle (EM) and depleted mantle (DM) parcels in the melting column. We show how Sr, Nd, and Hf concentrations and isotope ratios in the aggregated or pooled melt collected at the top of the melting column vary as a function of location of the EM parcel in the melting column. With changing location of the EM parcel in the upwelling melting column, compositions of the pooled melt do not follow a single mixing curve expected by the binary mixing model. Instead, they define a mixing loop that has an enriched branch and a depleted branch joined by two extreme points in composition space. The origin of the mixing loop can be traced back to four types of EM distribution or configuration in the melting column. The shape of the mixing loop depends on the relative melting rate of the EM to that of the DM and the number and spacing of EM parcels in the melting column. Probabilities of sampling the enriched and depleted branches in the pooled melt are proportional to volume fractions of the enriched and depleted materials in the mantle source. Mixing of pooled melts from a bundle of melting columns results in mixing envelopes in the isotope ratio correlation diagrams. The mixing envelope is a useful tool for studying chemical variations in mantle-derived melts. As an application, we consider scattered correlations in 87Sr/86Sr vs. 143Nd/144Nd and 143Nd/144Nd vs. 176Hf/177Hf in mid-ocean ridge basalts. We show that such correlations arise naturally from melting of a spatially heterogeneous mantle. 

Abstract Pyroxenite veins and dikes are commonly observed in the mantle section of ophiolites. Because of their mantle occurrence, these pyroxenites are free from crustal contamination and offer a unique opportunity for studying mantle compositions and melt–rock interaction processes. We conducted an integrated petrological and geochemical study of a suite of composite orthopyroxenite, websterite, and pyroxene-bearing dunite veins from the Xiugugabu ophiolite located on the western segment of Yarlung–Zangbo Suture Zone. The dunite is separated from the host peridotite by a layer of pyroxenite, forming a composite vein system. Systematic variations in major, minor, and trace element compositions in minerals across the composite veins are observed. Two generations of orthopyroxenes in the pyroxenites are characterized by high Mg#, low TiO2 concentrations, and depleted patterns of incompatible trace elements. Clinopyroxenes in the pyroxenites are characterized by high Mg#, low contents of TiO2 and Na2O, spooned shaped REE patterns, and a negative Zr anomaly. Through major and trace element modeling, we showed that both orthopyroxene and clinopyroxene were in equilibrium with melts with different compositions. This hypothesis is further confirmed by distinct initial Nd and Hf isotope ratios in the two pyroxenes. A model for the formation of composite pyroxenite veins is developed, whereby hydrous and silica-rich melts percolate along the margins of a dunite channel. The orthopyroxenite was formed by the reaction between a hydrous, silica-rich melt and the surrounding peridotite. The websterite is formed by reactive crystallization of a hybrid melt produced by mixing silica-rich melt and the melt formed by remelting of previously depleted peridotite in the deeper part of the mantle column. The extremely enriched Nd–Hf isotope compositions of the pyroxenite veins (εNd = −20.3 to +11.5 and εHf = −13.2 to +25.3, 125 million years ago) can be explained by the addition of ancient, recycled sediments to the mantle source in a supra-subduction setting. Based on the low-Cr# spinel in the Xiugugabu dunites (Cr# = 19–50) and the depleted nature of the parental melt of the Xiugugabu pyroxenites, we deduced that the formation of pyroxenites postdate the formation of the Xiugugabu ophiolite at ~125–130 Ma. Collectively, results from this study have provided support to the hypothesis that the Xiugugabu ophiolite experience a two-stage evolution, i.e., firstly formed in a mid-ocean ridge setting and subsequently modified in a supra subduction zone. 

This article is part of the Top 10 Unanswered Questions in MPMI invited review series. That plants recruit beneficial microbes while simultaneously restricting pathogens is critical to their survival. Plants must exclude pathogens; however, most land plants are able to form mutualistic symbioses with arbuscular mycorrhizal fungi. Plants also associate with the complex microbial communities that form the microbiome. The outcome of each symbiotic interaction—whether a specific microbe is pathogenic, commensal, or mutualistic—relies on the specific interplay of host and microbial genetics and the environment. Here, we discuss how plants use metabolites as a gate to select which microbes can be symbiotic. Once present, we discuss how plants integrate multiple inputs to initiate programs of immunity or mutualistic symbiosis and how this paradigm may be expanded to the microbiome. Finally, we discuss how environmental signals are integrated with immunity to fine-tune a thermostat that determines whether a plant engages in mutualism, resistance to pathogens, and shapes associations with the microbiome. Collectively, we propose that the plant immune thermostat is set to select for and tolerate a largely nonharmful microbiome while receptor-mediated decision making allows plants to detect and dynamically respond to the presence of potential pathogens or mutualists. [Formula: see text] Copyright © 2021 The Author(s). This is an open access article distributed under the CC BY-NC-ND 4.0 International license .