Conditional probabilities via line arrangements and point configurations

We study the connection between probability distributions satisfying certain conditional independence (CI) constraints, and point and line arrangements in incidence geometry. To a family of CI statements, we associate a polynomial ideal whose algebraic invariants are encoded in a hypergraph. The primary decompositions of these ideals give a characterisation of the distributions satisfying the original CI statements. Classically, these ideals are generated by 2-minors of a matrix of variables, however, in the presence of hidden variables, they contain higher degree minors. This leads to the study of the structure of determinantal hypergraph ideals whose decompositions can be understood in terms of point and line configurations in the projective space.Comment: 24 pages, 5 figure

Petrology and geochemistry of mafic and ultramafic cumulate rocks from the eastern part of the Sabzevar ophiolite (NE Iran): Implications for their petrogenesis and tectonic setting

The Late Cretaceous Sabzevar ophiolite represents one of the largest and most complete fragments of Tethyan oceanic lithosphere in the NE Iran. It is mainly composed of serpentinized mantle peridotites slices; nonetheless, minor tectonic slices of all crustal sequence constituents are observed in this ophiolite. The crustal sequence contains a well-developed ultramafic and mafic cumulates section, comprising plagioclase-bearing wehrlite, olivine clinopyroxenite, olivine gabbronorite, gabbronorite, amphibole gabbronorite and quartz gabbronorite with adcumulate, mesocumulate, heteradcumulate and orthocumulate textures. The crystallization order for these rocks is olivine chromian spinel → clinopyroxene → plagioclase → orthopyroxene → amphibole. The presence of primary magmatic amphiboles in the cumulate rocks shows that the parent magma evolved under hydrous conditions. Geochemically, the studied rock units are characterized by low TiO2 (0.18–0.57 wt.%), P2O5 (<0.05 wt.%), K2O (0.01–0.51 wt.%) and total alkali contents (0.12–3.04 wt.%). They indicate fractionated trends in the chondrite-normalized rare earth element (REE) plots and multi-element diagrams (spider diagrams). The general trend of the spider diagrams exhibit slight enrichment in large ion lithophile elements (LILEs) relative to high field strength elements (HFSEs) and positive anomalies in Sr, Pb and Eu and negative anomalies in Zr and Nb relative to the adjacent elements. The REE plots of these rocks display increasing trend from La to Sm, positive Eu anomaly (Eu/Eu* ¼ 1.06–1.54) and an almost flat pattern from medium REE (MREE) to heavy REE (HREE) region [(Gd/ Yb)N ¼ 1–1.17]. Moreover, clinopyroxenes from the cumulate rocks have low REE contents and show marked depletion in light REE (LREE) compared to MREE and HREE [(La/Sm)N ¼ 0.10–0.27 and (La/Yb)N ¼ 0.08–0.22]. The composition of calculated melts in equilibrium with the clinopyroxenes from less evolved cumulate samples are closely similar to island arc tholeiitic (IAT) magmas. Modal mineralogy, geochemical features and REE modeling indicate that Sabzevar cumulate rocks were formed by crystal accumulation from a hydrous depleted basaltic melt with IAT affinity. This melt has been produced by moderate to high degree (~15%) of partial melting a depleted mantle source, which partially underwent metasomatic enrichment from subducted slab components in an intra-oceanic arc setting

Optimization of Sustainability and Flood Hazard Resilience for Home Designs

AbstractLife-cycle analysis is a beneficial tool that can be utilized to quantify the performance of buildings within the context of environmental impact metrics (e.g. carbon footprint). While typical life-cycle analysis incorporates regular building maintenance, structural repairs made as a result of natural hazard damages are largely ignored. This study presents an environmental impact design optimization model that can be used to compare multiple coastal, single-family residential (SFR) building designs subjected to coastal flood hazards based on environmental impact factors. For each design, the model measures the environment impact (i.e. embodied energy and carbon footprint) of initial construction plus flood-induced repairs. Repairs are quantified using a probability-based methodology and life-cycle analysis is used to measure environmental impacts. Design options can then be compared and optimal designs that meet performance-based resilience and sustainable design objectives can be selected. A case study is presented for an SFR building located in coastal St. Petersburg, Florida, USA, and demonstrates that up to a 64% reduction in embodied energy and carbon footprint can be achieved over a 50 year building life through more resilient component configurations and materials and by increasing first floor elevations

Shocks in the asymmetric exclusion process with internal degree of freedom

We determine all families of Markovian three-states lattice gases with pair interaction and a single local conservation law. One such family of models is an asymmetric exclusion process where particles exist in two different nonconserved states. We derive conditions on the transition rates between the two states such that the shock has a particularly simple structure with minimal intrinsic shock width and random walk dynamics. We calculate the drift velocity and diffusion coefficient of the shock.Comment: 26 pages, 1 figur