Changing Views on Curves and Surfaces

Visual events in computer vision are studied from the perspective of algebraic geometry. Given a sufficiently general curve or surface in 3-space, we consider the image or contour curve that arises by projecting from a viewpoint. Qualitative changes in that curve occur when the viewpoint crosses the visual event surface. We examine the components of this ruled surface, and observe that these coincide with the iterated singular loci of the coisotropic hypersurfaces associated with the original curve or surface. We derive formulas, due to Salmon and Petitjean, for the degrees of these surfaces, and show how to compute exact representations for all visual event surfaces using algebraic methods.Comment: 31 page

Isotopic Ordering in Eggshells Reflects Body Temperatures and Suggests Differing Thermophysiology in Two Cretaceous Dinosaurs

Our understanding of the evolutionary transitions leading to the modern endothermic state of birds and mammals is incomplete, partly because tools available to study the thermophysiology of extinct vertebrates are limited. Here we show that clumped isotope analysis of eggshells can be used to determine body temperatures of females during periods of ovulation. Late Cretaceous titanosaurid eggshells yield temperatures similar to large modern endotherms. In contrast, oviraptorid eggshells yield temperatures lower than most modern endotherms but ~6˚C higher than co-occurring abiogenic carbonates, implying that this taxon did not have thermoregulation comparable to modern birds, but was able to elevate its body temperature above environmental temperatures. Therefore, we observe no strong evidence for end-member ectothermy or endothermy in the species examined. Body temperatures for these two species indicate that variable thermoregulation likely existed among the non-avian dinosaurs and that not all dinosaurs had body temperatures in the range of that seen in modern birds

Titanium in Muscovite, Biotite, and Hornblende: Modeling, Thermometry, and Rutile Activities of Metapelites and Amphibolites

Reactions involving the VITiIVAl-VIAlIVSi exchange in muscovite, biotite, and hornblende were calibrated thermodynamically using a set of experimental and natural data in rutile-plus quartz/coesite-bearing assemblages. The specific respective reactions are K(Al2)(AlSi3)O10(OH)2 + TiO2 = K(AlTi)(Al2Si2)O10(OH)2 + SiO2 (R1) K(□MgAl)Si4O10(OH)2 + TiO2 = K(□MgTi)AlSi3O10(OH)2 + SiO2 (R2) Ca2Mg3Al2Al2Si6O22(OH)2 + 2TiO2 = Ca2Mg3Ti2Al4Si4O22(OH)2 + 2SiO2. (R3) Ideal mixing on octahedral or octahedral plus tetrahedral sites and a non-ideal van Laar solution model yield the best regression results for thermodynamic fit parameters, with R2 values of 0.98–1.00. Isopleths of the equilibrium constant (Keq) show minimal pressure dependencies of \u3c1 \u3e°C/kbar, implying that the equilibria are poor barometers. Model reproducibility of the ideal portion of the equilibrium constant (Kid) is excellent (ca. ±0.1 to 0.3, 2σ), but the absolute value of the combined term ΔS+Kid is quite small (absolute values from 0 to 4), so calibration residuals propagate to temperature errors \u3e±50–100 °C, 1σ. Whereas the consistency of a mica or hornblende composition with a known T can be evaluated precisely, Ti chemistry in these reactions is sensitive to composition and does not resolve T (or P) well. The activity of TiO2 in rutile [a(rt)] was also evaluated using both the garnet-rutile-ilmenite-plagioclase-quartz (GRIPS) equilibrium and our new calibrations in rutile-absent, ilmenite-bearing rocks whose peak P-T conditions are otherwise known. Metapelites have average a(rt) of 0.9 (GRIPS) and 0.8 (R1), whereas amphibolites have a(rt) of 0.95 (GRIPS and R3). A value for a(rt) of 0.80 ± 0.20 (metapelites) and 0.95 +0.05/−0.25 (amphibolites) is recommended for trace-element thermomobarometers in ilmenite-bearing, rutile-absent rocks. The dependence of Ti contents of minerals on a(rt) and the reequilibration of Ti during metamorphic reactions both deserve further exploration, and may affect application of trace-element thermobarometers

Garnet: Witness to the Evolution of Destructive Plate Boundaries

Thanks to its unique chemical and mechanical properties, garnet records evidence of rocks\u27 paths through the crust at tectonic plate boundaries. The compositions of garnet and coexisting mineral phases permit metamorphic pressure and temperature to be determined, while garnet\u27s compositional zoning allows the evolution of these parameters to be constrained. But careful study of garnet reveals far more, including the dehydration history of subducted oceanic crust, the depths reached during the earliest stages of continental collision, and the mechanisms driving heat and mass flow as orogens develop. Overall, chemical and textural characterization of garnet can be coupled with thermodynamic, thermoelastic, geochronologic, diffusion, and geodynamic models to constrain the evolution of rocks in a wide variety of settings

Petrology and Geochronology of Metamorphic Zircon

Zircon is unusually well suited for investigating metamorphic processes because it is readily analyzed for U‐Pb ages, it harbors diverse mineral inclusions, and its chemistry can be linked to metamorphic parageneses and P‐T paths. Metamorphic zircon chemistry and ages are relevant only at the sub‐grain micron scale, and consequently many analytical methods, such as depth profiling, have been developed to exploit such spatially resolute infor­mation. Here we review how metamorphic zircon grows, and how its chemistry and inclusion assemblages may be used to link the age of a zircon domain to its metamorphic P‐T condition. Domain‐specific ages and inclusion assemblages from ultrahigh‐pressure (UHP) zircons constrain rates of subduction and exhumation. Textures and chemistry of zircon and garnet from high‐ and ultrahigh temperature (UHT) rocks reveal petrogenetic implications of deep crustal heating, melting, and melt crystallization. Trace elements, inclusion assemblages, and oxygen isotopes in zircon show that dehydration reactions may catalyze zircon growth during subduction. Future research should include identifying natural systems that constrain diffusion rates, determining crystal‐chemical controls on trace element uptake in zircon and garnet for understanding how rare earth budgets and patterns change during metamorphism, and identifying underlying principles that govern the dissolution and reprecipitation of zircon during metamorphism

Elastic Thermobarometry

Upon exhumation and cooling, contrasting compressibilities and thermal expansivities induce differential strains (volume mismatches) between a host crystal and its inclusions. These strains can be quantified in situ using Raman spectroscopy or X-ray diffraction. Knowing equations of state and elastic properties of minerals, elastic thermobarometry inverts measured strains to calculate the pressure-temperature conditions under which the stress state was uniform in the host and inclusion. These are commonly interpreted to represent the conditions of inclusion entrapment. Modeling and experiments quantify corrections for inclusion shape, proximity to surfaces, and (most importantly) crystal-axis anisotropy, and they permit accurate application of the more common elastic thermobarometers. New research is exploring the conditions of crystal growth, reaction overstepping, and the magnitudes of differential stresses, as well as inelastic resetting of inclusion and host strain, and potential new thermobarometers for lower-symmetry minerals. A physics-based method is revolutionizing calculations of metamorphic pressures and temperatures. Inclusion shape, crystal anisotropy, and proximity to boundaries affect calculations but can be corrected for. New results are leading petrologists to reconsider pressure-temperature conditions, differential stresses, and thermodynamic equilibrium

Conscience Sensitive Psychiatric Diagnosis of Maltreated Children and Adolescents

The sequelae of maltreatment are conceptualized according to the DSM IV multiaxial system expanded for heuristic purposes. Axis I and Axis IV are expanded to take into account important variables of maltreatment. Differential Axis I diagnoses are identified with special emphasis placed on PTSD, Dissociation, Depression and Disruptive Behavior Disorders. Axes II and III are heuristically expanded to call attention to developmental psychopathology, particularly in the domains of conscience, and associated putative neurobiological sequelae of maltreatment, indicating a pathway to the psychobiology of conscience. Conscience sensitive assessment of maltreated children is illustrated with two case vignettes and selected conscience drawings. A ‘transaxial,’ conscience sensitive approach to DSM nosology is recommended as a corrective. There will likely be additional implications for the psychobiology of conscience as neuroimaging and assessment of conscience functions in health and psychopathology become more refined.Support for this and other work by the I.U. Conscience Project conducted in collaboration with Pleasant Run Inc. has been generously provided by Mr. and Mrs. Jim Irsay and The Indianapolis Colts, The Moore Foundation and other individual anonymous donors

Models of Garnet Differential Geochronology

Rayleigh distillation models are developed to describe theoretical growth zoning of Lu, Hf, Rb, Sr, Sm and Nd in typical garnet crystals from metapelites and metabasites. Effects of diffusion limited transport within the matrix and intracrystalline diffusion are also considered qualitatively. Theoretical zoning profiles show strong depletions of Lu in garnet rims compared to cores, but virtually invariant Hf, Rb, Sr, Sm, and Nd profiles, generally consistent with natural profiles for Lu and Hf and previously published models. Theoretical isochron diagrams for Lu-Hf exhibit distinctive arcuate distributions and high MSWD’s consistent both with Himalayan data, and with expectations that garnet growth durations exceed chronologic resolution by as much as an order of magnitude. Predicted isochron diagrams for Sm-Nd and Rb-Sr exhibit vertical arrays for garnet and high MSWD’s that are generally lower than for Lu-Hf in metapelites. Inherent chronologic resolution for bulk separates is best for Lu-Hf in metapelites and Rb-Sr, but analytical considerations favor Rb-Sr or Sm-Nd for chronologic zoning studies. Diffusion limited transport in the rock matrix strongly influences zoning profiles, but does not change the main trends on isochron diagrams. Intracrystalline diffusion will initially rotate Lu-Hf isochrons to steeper slopes, giving older apparent ages. The natural Himalayan data indicate growth of garnet in one rock from the Greater Himalayan Sequence at ~34 Ma, consistent with previously measured monazite ages from the same rock. Data from another Himalayan rock suggest polymetamorphism that includes a Paleozoic component

Backarc Lithospheric Thickness and Serpentine Stability Control Slab-Mantle Coupling Depths in Subduction Zones

A key feature of subduction zone geodynamics and thermal structure is the point at which the slab and mantle mechanically couple. This point defines the depth at which traction between slab and mantle begins to drive mantle wedge circulation and also corresponds with a rapid increase in temperature along the slab-mantle interface. Here, we consider the effects of the backarc thermal structure and slab thermal parameter on coupling depth using two-dimensional thermomechanical models of oceanic-continental convergent margins. Coupling depth is strongly correlated with backarc lithospheric thickness, and weakly correlated with slab thermal parameter. Slab-mantle coupling becomes significant where weak, hydrous antigorite reacts to form strong, anhydrous olivine and pyroxene along the slab-mantle interface. Highly efficient (predominantly advective) heat transfer in the asthenospheric mantle wedge and inefficient (predominantly conductive) heat transfer in the lithospheric mantle wedge results in competing feedbacks that stabilize the antigorite-out reaction at depths determined primarily by the mechanical thickness of the backarc lithosphere. For subduction zone segments where backarc lithospheric thickness can be inverted from surface heat flow, our results provide a regression model that can be applied with slab thermal parameter to predict coupling depth. Consistently high backarc heat flow in circum-Pacific subduction zones suggests uniformly thin overriding plates likely regulated by lithospheric erosion caused by hydration and melting processes under volcanic arcs. This may also explain a common depth of slab-mantle coupling globally