Efficiently Storing Well-Composed Polyhedral Complexes Computed Over 3D Binary Images

A 3D binary image I can be naturally represented by a combinatorial-algebraic structure called cubical complex and denoted by Q(I ), whose basic building blocks are vertices, edges, square faces and cubes. In Gonzalez-Diaz et al. (Discret Appl Math 183:59–77, 2015), we presented a method to “locally repair” Q(I ) to obtain a polyhedral complex P(I ) (whose basic building blocks are vertices, edges, specific polygons and polyhedra), homotopy equivalent to Q(I ), satisfying that its boundary surface is a 2D manifold. P(I ) is called a well-composed polyhedral complex over the picture I . Besides, we developed a new codification system for P(I ), encoding geometric information of the cells of P(I ) under the form of a 3D grayscale image, and the boundary face relations of the cells of P(I ) under the form of a set of structuring elements. In this paper, we build upon (Gonzalez-Diaz et al. 2015) and prove that, to retrieve topological and geometric information of P(I ), it is enough to store just one 3D point per polyhedron and hence neither grayscale image nor set of structuring elements are needed. From this “minimal” codification of P(I ), we finally present a method to compute the 2-cells in the boundary surface of P(I ).Ministerio de Economía y Competitividad MTM2015-67072-

Spatiotemporal Barcodes for Image Sequence Analysis

Taking as input a time-varying sequence of two-dimensional (2D) binary images, we develop an algorithm for computing a spatiotemporal 0–barcode encoding lifetime of connected components on the image sequence over time. This information may not coincide with the one provided by the 0–barcode encoding the 0–persistent homology, since the latter does not respect the principle that it is not possible to move backwards in time. A cell complex K is computed from the given sequence, being the cells of K classified as spatial or temporal depending on whether they connect two consecutive frames or not. A spatiotemporal path is defined as a sequence of edges of K forming a path such that two edges of the path cannot connect the same two consecutive frames. In our algorithm, for each vertex v ∈ K, a spatiotemporal path from v to the “oldest” spatiotemporally-connected vertex is computed and the corresponding spatiotemporal 0–bar is added to the spatiotemporal 0–barcode.Junta de Andalucía FQM-369Ministerio de Economía y Competitividad MTM2012-3270

Encoding Specific 3D Polyhedral Complexes Using 3D Binary Images

We build upon the work developed in [4] in which we presented a method to “locally repair” the cubical complex Q(I) associated to a 3D binary image I, to obtain a “well-composed” polyhedral complex P(I), homotopy equivalent to Q(I). There, we developed a new codification system for P(I), called ExtendedCubeMap (ECM) representation, that encodes: (1) the (geometric) information of the cells of P(I) (i.e., which cells are presented and where), under the form of a 3D grayscale image gP ; (2) the boundary face relations between the cells of P(I), under the form of a set BP of structuring elements. In this paper, we simplify ECM representations, proving that geometric and topological information of cells can be encoded using just a 3D binary image, without the need of using colors or sets of structuring elements. We also outline a possible application in which well-composed polyhedral complexes can be useful.Junta de Andalucía FQM-369Ministerio de Economía y Competitividad MTM2012-32706Ministerio de Economía y Competitividad MTM2015-67072-

Nanomaterial accumulation in boiling brines enhances epithermal bonanzas

This work benefited from Grant NANOMET PID2022-138768OB-I00 funded by MCIN/AEI/10.13039/50110001133 and by “ERDF A way of making Europe” by the “European Union”, Grant IN 218323 funded by PAPIIT-DGAPA-UNAM, and Grant PID 2019-105625RB-C21 funded by MCIN/AEI/10.13039/501100011033. Additional funding was Granted by CONAHCyT (ongoing Ph.D. grant) and the Geological Society of America (Grant Number 13570-22) to the first author. Xavier Llovet, Laura Casado, Isabel Rivas, María del Mar Abad, and Cecilia de la Prada are acknowledged for their assistance during EPMA, FIB-SEM, and HRTEM analyses. We thank UNAM academicians Juan Tomás Vásquez and Edith Fuentes Guzmán for their help during sample preparation. We also thank Baltazar Chávez, Senén Benítez, and the team at Natividad (Oaxaca) for their assistance during the stay at the mine facilities. The manuscript has strongly benefited from insightful reviews by two anonymous reviewers and the handling Editor, Dr. Dan Zhu.Epithermal bonanza-type ores, characterized by weight-percent contents of e.g., gold and silver in a few mm to cm, are generated by mixtures of magmatic-derived hydrothermal brines and external fluids (e.g., meteoric) that transport a variety of metals to the site of deposition. However, the low solubilities of precious metals in hydrothermal fluids cannot justify the high concentrations necessary to produce such type of hyper-enriched metal ore. Here we show that boiling metal-bearing brines can produce, aggregate, and accumulate metal nanomaterials, ultimately leading to focused gold + silver ± copper over-enrichments. We found direct nano-scale evidence of nanoparticulate gold- and/or silver-bearing ores formed via nonclassical growth (i.e., nanomaterial attachment) during boiling in an intermediate-sulfidation epithermal bonanza. The documented processes may explain the generation of bonanzas in metal-rich brines from a range of mineral deposit types.MCIN/AEI/10.13039/50110001133: NANOMET PID2022-138768OB-I00ERDF A way of making Europe, European UnionPAPIIT-DGAPA-UNAM: IN 218323CONAHCyTGeological Society of America 13570-22Dirección General de Asuntos del Personal Académico, Universidad Nacional Autónoma de México MCIN/AEI/10.13039/501100011033, PID 2019-105625RB-C21 DGAPA, UNA

Distribution of critical metals in evolving pyrite from massive sulfide ores of the Iberian Pyrite Belt

Acknowledgements This research is a contribution to the projects CGL2016-79204-R, PID2019-111715GB-I00 which are supported by the Spanish Government, and 18/IF/6347 granted by Science Foundation Ireland (SFI). The authors thank Cambridge Minerals for access to drill core, sampling assistance and the ongoing collaboration. We are also grateful to Teodosio Donaire for his constructive suggestions in petrogenetic aspects of volcanogenic rocks in the IPB as well as Dany Savard and Audrey Lavoie of LabMaTer, UQAC, for their assistance during the laser ablation analyses. Authors would also like to acknowledge the use of Servicio General de Apoyo a la Investigación-SAI, Universidad de Zaragoza.Supplementary data to this article can be found online at https://doi. org/10.1016/j.oregeorev.2022.105275.With >90 known deposits containing original reserves of >2400 Mt of sulfide ore, the Iberian Pyrite Belt (IPB) is the largest volcanogenic massive sulfide (VMS) province on Earth. In these evolving mineral systems, texturally different pyrite exhibits characteristic mineralogy and trace element fingerprints. Pyrite (Py-1), which is well preserved in the polymetallic ores that crystallized at the earliest stage of VMS deposit formation, consists of kernels of pyrite framboids surrounded by concentric colloform bands and ended by faceted outlines. It is rich in some metals like Pb, Zn, Sb and As (mostly hosted as nano-to-micron-sized particles, including galena, tetrahedrite and arsenopyrite) but depleted in Cu, Co and Bi. In contrast, pyrite from the pyritic and Cu-rich ore overprinted by late fluids exhibits spongy-looking (Py-2) or homogenous (Py-3) cores surrounded by external facets with crystallographic continuity across the whole single grains due to re-crystallization. Py-2 is depleted in most trace elements with the exception of Au and Bi, which occur both in solid solutions and as nano-to-micron-sized inclusions. Py-3 has the highest Cu, Ag, Co and Ni (mainly associated to nano-to-micron-sized particles of tennantite, chalcopyrite and gersdorffite) and the lowest Au contents in the form of native gold. The progressive increase in metal contents from inner to outer parts of Py-1 matches with the onset of the economic metal endowment of VMS deposits in the IPB, whereas Py-2 and Py-3 are associated with metal shoot processes that led to both leached and high-grade ores, very likely when mafic rocks were emplaced into the footwall of the deposits.Projects CGL2016-79204-R, PID2019-111715GB-I00 which are supported by the Spanish Government, and 18/IF/6347 granted by Science Foundation Ireland (SFI

Unraveling the Effects of Melt–Mantle Interactions on the Gold Fertility of Magmas

We thank Tony Lanzirotti and Matt Newville for assistance with μ-XANES analyses at the GeoSoilEnviroCars (Sector 13), Advanced Photon Source (APS), Argonne National Laboratory.The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/feart.2020.00029/full#supplementary-materialThe oxidation state of the Earth’s mantle and its partial melting products exert a key control on the behavior and distribution of sulfur and chalcophile and siderophile elements between the mantle and crust, underpinning models of ore deposit formation. Whether the oxidized nature of magmas is inherited from the asthenospheric mantle source or acquired during ascent and differentiation is vigorously debated, limiting our understanding of the mechanisms of extraction of sulfur and metals from the mantle. Here, we focused on the redox-sensitive behavior of sulfur in apatite crystallized from quenched alkaline basaltic melts preserved within a peridotite xenolith from the El Deseado Massif auriferous province in southern Patagonia. We took advantage of this unique setting to elucidate the redox evolution of melts during their ascent through the subcontinental lithospheric mantle (SCLM) and grasp the inner workings of the Earth’s mantle during gold metallogenesis. Our data reveal that an initially reduced silicate melt (ΔFMQ −2.2 to −1.2) was oxidized to ΔFMQ between 0 and 1.2 during percolation and interaction with the surrounding peridotite wall-rock (ΔFMQ 0 to +0.8). This process triggered changes in sulfur speciation and solubility in the silicate melt, boosting the potential of the melt to scavenge ore metals such as gold. We suggest that large redox gradients resulting from the interaction between ascending melts and the surrounding mantle can potentially modify the oxidation state of primitive melts and enhance their metallogenic fertility. Among other factors including an enriched metal source and favorable geodynamic conditions, redox gradients in the mantle may exert a first-order control on the global-scale localization of crustal provinces endowed with gold deposits.This study was funded by the Iniciativa Científica Milenio through Millennium Nucleus for Metal Tracing along Subduction Grant NC130065. Additional funding for analytical work was provided by the FONDAP project 15090013 “Centro de Excelencia en Geotermia de Los Andes, CEGA.” ST acknowledges CONICYT for support through a Ph.D. scholarship #21170857. Grants RTI2018-099157-A-100 and RYC-2015-1796 provided funding for sample preparation and EPMA analyses. This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357. The DID-UACh project #S-201505 financed the fieldwork

¿Esférulas de hierro y vítreas subducidas en el manto superior?

Spherules are documented in ophiolitic mantle rocks such as peridotites and associated chromitites. They consist of: (1) native iron having variable amounts of Ni with/without inclusions of silicate glass or oxides (wüstite), (2) dendritic intergrowth of oxides (magnetite, wüstite and hematite) with/without silicate glass and, (3) silicate glass. Consensually, they are interpreted as indigenous to chromitites and related with high-temperature processes operating in the Earth’s upper mantle. However, their similarity with terrestrial and extraterrestrial spherules found in other settings of the geological record is remarkable. We raise the question on such indigenous origin, relating them to volcanic and cosmic material recycled back to the mantle wedge where chromitites form during subduction.Rocas del manto superior ofiolitico tales como peridotitas y cromititas contienen esferas. Estas consisten de: (1) hierro native con cantidades variables de Ni con y sin inclusiones de vidrio silicatdo y óxidos (wüstite), (2) intercrecimientos dendríticos de óxidos (magnetita, wüstita y hematites) con o sin vidrio silicatado y, (2) vidrio silicatado. Unísonamente, estas esferulas se interpretan como indígenas a las cromititas y relacionadas con procesos de alta temperatura que tienen lugar en el manto superior terrestre. Sin embargo, su parecido con aquellas esferas de origen terrestre y extraterrestre descritas en otros contextos geológicos es reseñable. En este trabajo cuestionamos el origen autóctono de las esferas en las rocas mantélicas, interpretándolas como material de origen volcánico y cósmico que ha sido reciclado atraves de la cuña de manto superior donde ser forman las cromititas durante los procesos de subducción.Junta de Andaluci

Torsion of rational elliptic curves over quadratic fields II

Let E be an elliptic curve defined over Q and let G=E(Q)_tors be the associated torsion group. In a previous paper, the authors studied, for a given G, which possible groups G\leq H could appear such that H=E(K)_tors, for [K:Q]=2. In the present paper, we go further in this study and compute, under this assumption and for every such G, all the possible situations where G\neq H. The result is optimal, as we also display examples for every situation we state as possible. As a consequence, the maximum number of quadratic number fields K such that E(Q)_tors\neq E(K)_tors is easily obtained.Ministerio de Economía y CompetitividadJunta de Andalucí

Comparação de três sistemas de medição diferentes para avaliar a altura do salto vertical

Introduction: The numerous instruments used to measure jump height use different technologies and calculations that can provide variable results. Objective: This study compared the countermovement jump (CMJ) height assessed with a wearable 3D inertial measurement unit (IMU), using flight time and the numerical integration method with a force platform and photocells. Methods: Forty CMJs were analysed, starting from an upright standing position with the hands placed on the waist. Twenty healthy volunteers completed 2 CMJs, which were simultaneously assessed using an IMU placed on the subject’s sacrum, a force platform (considered the gold standard method) and photocells. The maximum height of each CMJ was measured. Results: The results showed a significant overestimation (p<0.001) in jump height for the IMU using the numerical integration method when compared to the force platform (+7 cm). Excellent intraclass correlation coefficients (ICCs) were obtained with the flight time equations for the different types of measurement equipment. Fair to good ICCs were obtained with the IMU using the numerical integration method and force platform. Conclusion: In conclusion, the jump height obtained with the IMU using the numerical integration method showed the poorest agreement compared to the force platform.Introducción: Los numerosos instrumentos usados para medir la altura del salto emplean diferentes tecnologías y cálculos que pueden suministrar resultados variables. Objetivo: Este estudio comparó la altura del salto contramovimiento (SCM) con una un sistema inercial 3D (IMU) portátil, usando el tiempo de vuelo y el método de integración numérica, con plataforma de fuerza y fotocélulas. Métodos: Cuarenta SCMs fueron analizados a partir de la posición ortostática con las manos en la cintura. Veinte voluntarios saludables concluyeron dos SCMs que fueron evaluados simultáneamente con un IMU colocada en el sacro del individuo, una plataforma de fuerza (considerado el método de referencia) y fotocélulas. Fue medida la altura máxima de cada SCM. Resultados: Los resultados mostraron una sobreestimación significativa (p <0,001) de la altura del salto para la IMU con el método de integración numérica, en comparación con la plataforma de fuerza (+7 cm). Fueron obtenidos excelentes coeficientes de correlación intraclase (ICCs) con las ecuaciones de tiempo de vuelo entre los equipamientos de medición. Fueron obtenidos resultados de regulares a buenos de ICC con la IMU por el método de integración numérica y la plataforma de fuerza. Conclusión: La altura de salto obtenida con la IMU con el método de integración numérica mostró la peor concordancia en comparación con la plataforma de fuerza.Introdução: Os numerosos instrumentos usados para medir a altura de salto empregam diferentes tecnologias e cálculos que podem fornecer resultados variáveis. Objetivo: Este estudo comparou a altura de salto contramovimento (SCM) com uma unidade de medida inercial 3D (UMI) portátil, usando o tempo de voo e o método de integração numérica, com plataforma de força e fotocélulas. Métodos: Quarenta SCMs foram analisados a partir da posição ortostática com as mãos na cintura. Vinte voluntários saudáveis concluíram 2 SCMs que foram avaliados simultaneamente com uma UMI colocada no sacro do indivíduo, uma plataforma de força (considerado o método de referência) e fotocélulas. A altura máxima de cada SCM foi medida. Resultados: Os resultados mostraram uma superestimação significativa (p < 0,001) da altura do salto para a UMI com o método de integração numérica, em comparação com a plataforma de força (+7 cm). Foram obtidos excelentes coeficientes de correlação intraclasse (ICCs) com as equações de tempo de voo entre os equipamentos de medição. Foram obtidos resultados de regulares a bons de ICC com a UMI pelo método de integração numérica e a plataforma de força. Conclusão: A altura de salto obtida com a UMI com o método de integração numérica mostrou a pior concordância em comparação com a plataforma de força.This work was funded by the Ministry of Education, Culture and Sports of Spain by grants (ref. FPU13/00162)