Uniqueness of the Embedding Continuous Convolution Semigroup of a Gaussian Probability Measure on the Affine Group and an Application in Mathematical Finance

Let {μ(i)t}t≥0 ( i=1,2 ) be continuous convolution semigroups (c.c.s.) of probability measures on Aff(1) (the affine group on the real line). Suppose that μ(1)1=μ(2)1 . Assume furthermore that {μ(1)t}t≥0 is a Gaussian c.c.s. (in the sense that its generating distribution is a sum of a primitive distribution and a second-order differential operator). Then μ(1)t=μ(2)t for all t≥0 . We end up with a possible application in mathematical finance.

Uniqueness of black holes with bubbles in minimal supergravity

We generalize uniqueness theorems for non-extremal black holes with three mutually independent Killing vector fields in five-dimensional minimal supergravity in order to account for the existence of non-trivial two-cycles in the domain of outer communication. The black hole space-times we consider may contain multiple disconnected horizons and be asymptotically flat or asymptotically Kaluza–Klein. We show that in order to uniquely specify the black hole space-time, besides providing its domain structure and a set of asymptotic and local charges, it is necessary to measure the magnetic fluxes that support the two-cycles as well as fluxes in the two semi-infinite rotation planes of the domain diagram.

Uniqueness of minimisers for a Grötzsch-Belinskiĭ type inequality in the Heisenberg group

The modulus method introduced by H. Grötzsch yields bounds for a mean distortion functional of quasiconformal maps between two annuli mapping the respective boundary components onto each other. P. P. Belinskiĭ studied these inequalities in the plane and identified the family of all minimisers. Beyond the Euclidean framework, a Grötzsch-Belinskiĭ-type inequality has been previously considered for quasiconformal maps between annuli in the Heisenberg group whose boundaries are Korányi spheres. In this note we show that--in contrast to the planar situation--the minimiser in this setting is essentially unique.

Dual origins of dairy cattle farming - evidence from a comprehensive survey of European Y-chromosomal variation

BACKGROUND: Diversity patterns of livestock species are informative to the history of agriculture and indicate uniqueness of breeds as relevant for conservation. So far, most studies on cattle have focused on mitochondrial and autosomal DNA variation. Previous studies of Y-chromosomal variation, with limited breed panels, identified two Bos taurus (taurine) haplogroups (Y1 and Y2; both composed of several haplotypes) and one Bos indicus (indicine/zebu) haplogroup (Y3), as well as a strong phylogeographic structuring of paternal lineages. METHODOLOGY AND PRINCIPAL FINDINGS: Haplogroup data were collected for 2087 animals from 138 breeds. For 111 breeds, these were resolved further by genotyping microsatellites INRA189 (10 alleles) and BM861 (2 alleles). European cattle carry exclusively taurine haplotypes, with the zebu Y-chromosomes having appreciable frequencies in Southwest Asian populations. Y1 is predominant in northern and north-western Europe, but is also observed in several Iberian breeds, as well as in Southwest Asia. A single Y1 haplotype is predominant in north-central Europe and a single Y2 haplotype in central Europe. In contrast, we found both Y1 and Y2 haplotypes in Britain, the Nordic region and Russia, with the highest Y-chromosomal diversity seen in the Iberian Peninsula. CONCLUSIONS: We propose that the homogeneous Y1 and Y2 regions reflect founder effects associated with the development and expansion of two groups of dairy cattle, the pied or red breeds from the North Sea and Baltic coasts and the spotted, yellow or brown breeds from Switzerland, respectively. The present Y1-Y2 contrast in central Europe coincides with historic, linguistic, religious and cultural boundaries.

Transport of 234U in the Opalinus Clay on centimetre to decimetre scales

The Opalinus Clay formation in North Switzerland is a potential host rock for a deep underground radioactive waste repository. The distribution of U-238, U-234 and Th-230 was studied in rock samples of the Opalinus Clay from an exploratory borehole at Benken (Canton of Zurich) using MC-ICP-MS. The aim of U-234 was to assess the in situ, long-term migration behaviour in this rock. Very low hydraulic conductivities of the Opalinus Clay, reducing potential of the pore water and its chemical equilibrium with the host rock are expected to render both U-238 and Th-230 immobile. If U is heterogeneously distributed in the Opalinus Clay, gradients in the supply of U-234 from the rock matrix to the pore water by the decay of U-238 will be established. Diffusive redistribution separates U-234 from its immobile parent U-238 resulting in bulk rock U-234/U-238 activity disequilibria. These may provide a means of estimating the mobility of U-234 in the rock if the diffusion rate of U-234 is significant compared to its decay rate. Sampling was carried out on two scales. Drilling of cm-spaced samples from the drill-core was done to study mobility over short distances and elucidate possible small-scale lithological control. Homogenized 25-cm-long portions of a 2-m-long drill-core section were prepared to provide information on transport over a longer distance. Variations in U and/or Th content on the cm-scale between clays and carbonate-sandy layers are revealed by beta-scanning, which shows that the (dominant) clay is richer in both elements. Samples were digested using aqua regia followed by total HF dissolution, yielding two fractions. in all studied samples U was found to be concentrated in the HF digestion fraction. It has a high U/Th ratio and a study by SEM-EDS points to sub-mu m up to several mu m in size zircon grains as the main U-rich phase. This fraction consistently has U-234/U-238 activity ratios below unity. The minute zircon grains constitute the major reservoir of U in the rock and act as constant rate suppliers of U-234 into the rock matrix and the pore water. The aqua regia leach fraction was found to be enriched in Th, and complementary to the HF fraction, having U-234/U-238 activity ratios above unity. It is believed that these U activity ratios reflect the surplus of having U-234 delivered from the zircon grains. Some cm-spaced samples show bulk rock U-234/U-238 activity ratios that are markedly out of equilibrium. In most of them a striking negative correlation between the total U content and the bulk rock U-234/U-238 activity ratios is observed. This is interpreted to indicate net U-234 transfer from regions of higher supply of U-234 towards those of lower supply which is, in most cases, equivalent to transfer from clayey towards carbonate/sandy portions of the rock. In contrast, the 25 cm averaged samples all have uniform bulk rock U-234/U-238 activity ratios in equilibrium, indicating U immobility in the last 1-1.5 Ma on this spatial scale. It is concluded that the small-scale lithological variations which govern U spatial distribution in the Opalinus Clay are the major factor determining U-234 in situ supply rates, regulating its diffusive fluxes and controlling the observed bulk rock U-234/U-238 activity ratios. A simple box-model is presented to simulate the measured bulk rock U-234/U-238 activity ratios and to give an additional insight into the studied system. (C) 2008 Elsevier Ltd. All rights reserved.

The mentalizing network orchestrates the impact of parochial altruism on social norm enforcement.

Parochial altruism - a preference for altruistic behavior towards ingroup members and mistrust or hostility towards outgroup members--is a pervasive feature in human society and strongly shapes the enforcement of social norms. Since the uniqueness of human society critically depends on the enforcement of norms, the understanding of the neural circuitry of the impact of parochial altruism on social norm enforcement is key, but unexplored. To fill this gap, we measured brain activity with functional magnetic resonance imaging (fMRI) while subjects had the opportunity to punish ingroup members and outgroup members for violating social norms. Findings revealed that subjects' strong punishment of defecting outgroup members is associated with increased activity in a functionally connected network involved in sanction-related decisions (right orbitofrontal gyrus, right lateral prefrontal cortex, right dorsal caudatus). Moreover, the stronger the connectivity in this network, the more outgroup members are punished. In contrast, the much weaker punishment of ingroup members who committed the very same norm violation is associated with increased activity and connectivity in the mentalizing-network (dorsomedial prefrontal cortex, bilateral temporo-parietal junction), as if subjects tried to understand or justify ingroup members' behavior. Finally, connectivity analyses between the two networks suggest that the mentalizing-network modulates punishment by affecting the activity in the right orbitofrontal gyrus and right lateral prefrontal cortex, notably in the same areas showing enhanced activity and connectivity whenever third-parties strongly punished defecting outgroup members.

Experimental, theoretical and numerical investigation of the nonlinear micromechanical properties of bone

Aging societies suffer from an increasing incidence of bone fractures. Bone strength depends on the amount of mineral measured by clinical densitometry, but also on the micromechanical properties of the bone hierarchical organization. A good understanding has been reached for elastic properties on several length scales, but up to now there is a lack of reliable postyield data on the lower length scales. In order to be able to describe the behavior of bone at the microscale, an anisotropic elastic-viscoplastic damage model was developed using an eccentric generalized Hill criterion and nonlinear isotropic hardening. The model was implemented as a user subroutine in Abaqus and verified using single element tests. A FE simulation of microindentation in lamellar bone was finally performed show-ing that the new constitutive model can capture the main characteristics of the indentation response of bone. As the generalized Hill criterion is limited to elliptical and cylindrical yield surfaces and the correct shape for bone is not known, a new yield surface was developed that takes any convex quadratic shape. The main advantage is that in the case of material identification the shape of the yield surface does not have to be anticipated but a minimization results in the optimal shape among all convex quadrics. The generality of the formulation was demonstrated by showing its degeneration to classical yield surfaces. Also, existing yield criteria for bone at multiple length scales were converted to the quadric formulation. Then, a computational study to determine the influence of yield surface shape and damage on the in-dentation response of bone using spherical and conical tips was performed. The constitutive model was adapted to the quadric criterion and yield surface shape and critical damage were varied. They were shown to have a major impact on the indentation curves. Their influence on indentation modulus, hardness, their ratio as well as the elastic to total work ratio were found to be very well described by multilinear regressions for both tip shapes. For conical tips, indentation depth was not a significant fac-tor, while for spherical tips damage was insignificant. All inverse methods based on microindentation suffer from a lack of uniqueness of the found material properties in the case of nonlinear material behavior. Therefore, monotonic and cyclic micropillar com-pression tests in a scanning electron microscope allowing a straightforward interpretation comple-mented by microindentation and macroscopic uniaxial compression tests were performed on dry ovine bone to identify modulus, yield stress, plastic deformation, damage accumulation and failure mecha-nisms. While the elastic properties were highly consistent, the postyield deformation and failure mech-anisms differed between the two length scales. A majority of the micropillars showed a ductile behavior with strain hardening until failure by localization in a slip plane, while the macroscopic samples failed in a quasi-brittle fashion with microcracks coalescing into macroscopic failure surfaces. In agreement with a proposed rheological model, these experiments illustrate a transition from a ductile mechanical behavior of bone at the microscale to a quasi-brittle response driven by the growth of preexisting cracks along interfaces or in the vicinity of pores at the macroscale. Subsequently, a study was undertaken to quantify the topological variability of indentations in bone and examine its relationship with mechanical properties. Indentations were performed in dry human and ovine bone in axial and transverse directions and their topography measured by AFM. Statistical shape modeling of the residual imprint allowed to define a mean shape and describe the variability with 21 principal components related to imprint depth, surface curvature and roughness. The indentation profile of bone was highly consistent and free of any pile up. A few of the topological parameters, in particular depth, showed significant correlations to variations in mechanical properties, but the cor-relations were not very strong or consistent. We could thus verify that bone is rather homogeneous in its micromechanical properties and that indentation results are not strongly influenced by small de-viations from the ideal case. As the uniaxial properties measured by micropillar compression are in conflict with the current literature on bone indentation, another dissipative mechanism has to be present. The elastic-viscoplastic damage model was therefore extended to viscoelasticity. The viscoelastic properties were identified from macroscopic experiments, while the quasistatic postelastic properties were extracted from micropillar data. It was found that viscoelasticity governed by macroscale properties has very little influence on the indentation curve and results in a clear underestimation of the creep deformation. Adding viscoplasticity leads to increased creep, but hardness is still highly overestimated. It was possible to obtain a reasonable fit with experimental indentation curves for both Berkovich and spherical indenta-tion when abandoning the assumption of shear strength being governed by an isotropy condition. These results remain to be verified by independent tests probing the micromechanical strength prop-erties in tension and shear. In conclusion, in this thesis several tools were developed to describe the complex behavior of bone on the microscale and experiments were performed to identify its material properties. Micropillar com-pression highlighted a size effect in bone due to the presence of preexisting cracks and pores or inter-faces like cement lines. It was possible to get a reasonable fit between experimental indentation curves using different tips and simulations using the constitutive model and uniaxial properties measured by micropillar compression. Additional experimental work is necessary to identify the exact nature of the size effect and the mechanical role of interfaces in bone. Deciphering the micromechanical behavior of lamellar bone and its evolution with age, disease and treatment and its failure mechanisms on several length scales will help preventing fractures in the elderly in the future.

Influence of the Central American Seaway and Drake Passage on ocean circulation and neodymium isotopes: A model study

The sensitivity of the neodymium isotopic composition (ϵNd) to tectonic rearrangements of seaways is investigated using an Earth System Model of Intermediate Complexity. The shoaling and closure of the Central American Seaway (CAS) is simulated, as well as the opening and deepening of Drake Passage (DP). Multiple series of equilibrium simulations with various intermediate depths are performed for both seaways, providing insight into ϵNd and circulation responses to progressive throughflow evolutions. Furthermore, the sensitivity of these responses to the Atlantic Meridional Overturning Circulation (AMOC) and the neodymium boundary source is examined. Modeled ϵNd changes are compared to sediment core and ferromanganese (Fe-Mn) crust data. The model results indicate that the North Atlantic ϵNd response to the CAS shoaling is highly dependent on the AMOC state, i.e., on the AMOC strength before the shoaling to shallow depths (preclosure). Three scenarios based on different AMOC forcings are discussed, of which the model-data agreement favors a shallow preclosure (Miocene) AMOC (∼6 Sv). The DP opening causes a rather complex circulation response, resulting in an initial South Atlantic ϵNd decrease preceding a larger increase. This feature may be specific to our model setup, which induces a vigorous CAS throughflow that is strongly anticorrelated to the DP throughflow. In freshwater experiments following the DP deepening, ODP Site 1090 is mainly influenced by AMOC and DP throughflow changes, while ODP Site 689 is more strongly influenced by Southern Ocean Meridional Overturning Circulation and CAS throughflow changes. The boundary source uncertainty is largest for shallow seaways and at shallow sites.

Dichotomous Hamiltonians with unbounded entries and solutions of Riccati equations

An operator Riccati equation from systems theory is considered in the case that all entries of the associated Hamiltonian are unbounded. Using a certain dichotomy property of the Hamiltonian and its symmetry with respect to two different indefinite inner products, we prove the existence of nonnegative and nonpositive solutions of the Riccati equation. Moreover, conditions for the boundedness and uniqueness of these solutions are established.

Morphological ripening of fluid inclusions and coupled zone-refining in quartz crystals revealed by cathodoluminescence imaging: Implications for CL-petrography, fluid inclusion analysis and trace-element geothermometry

Cathodoluminescence (CL) studies have previously shown that some secondary fluid inclusions in luminescent quartz are surrounded by dark, non-luminescent patches, resulting from fracture-sealing by late, trace-element-poor quartz. This finding has led to the tacit generalization that all dark CL patches indicate influx of low temperature, late-stage fluids. In this study we have examined natural and synthetic hydrothermal quartz crystals using CL imaging supplemented by in-situ elemental analysis. The results lead us to propose that all natural, liquid-water-bearing inclusions in quartz, whether trapped on former crystal growth surfaces (i.e., of primary origin) or in healed fractures (i.e., of pseudosecondary or secondary origin), are surrounded by three-dimensional, non-luminescent patches. Cross-cutting relations show that the patches form after entrapment of the fluid inclusions and therefore they are not diagnostic of the timing of fluid entrapment. Instead, the dark patches reveal the mechanism by which fluid inclusions spontaneously approach morphological equilibrium and purify their host quartz over geological time. Fluid inclusions that contain solvent water perpetually dissolve and reprecipitate their walls, gradually adopting low-energy euhedral and equant shapes. Defects in the host quartz constitute solubility gradients that drive physical migration of the inclusions over distances of tens of μm (commonly) up to several mm (rarely). Inclusions thus sequester from their walls any trace elements (e.g., Li, Al, Na, Ti) present in excess of equilibrium concentrations, thereby chemically purifying their host crystals in a process analogous to industrial zone refining. Non-luminescent patches of quartz are left in their wake. Fluid inclusions that contain no liquid water as solvent (e.g., inclusions of low-density H2O vapor or other non-aqueous volatiles) do not undergo this process and therefore do not migrate, do not modify their shapes with time, and are not associated with dark-CL zone-refined patches. This new understanding has implications for the interpretation of solids within fluid inclusions (e.g., Ti- and Al-minerals) and for the elemental analysis of hydrothermal and metamorphic quartz and its fluid inclusions by microbeam methods such as LA-ICPMS and SIMS. As Ti is a common trace element in quartz, its sequestration by fluid inclusions and its depletion in zone-refined patches impacts on applications of the Ti-in-quartz geothermometer.

Impact of a Reduced Arctic Sea Ice Cover on Ocean and Atmospheric Properties

The Arctic sea ice cover declined over the last few decades and reached a record minimum in 2007, with a slight recovery thereafter. Inspired by this the authors investigate the response of atmospheric and oceanic properties to a 1-yr period of reduced sea ice cover. Two ensembles of equilibrium and transient simulations are produced with the Community Climate System Model. A sea ice change is induced through an albedo change of 1 yr. The sea ice area and thickness recover in both ensembles after 3 and 5 yr, respectively. The sea ice anomaly leads to changes in ocean temperature and salinity to a depth of about 200 m in the Arctic Basin. Further, the salinity and temperature changes in the surface layer trigger a “Great Salinity Anomaly” in the North Atlantic that takes roughly 8 yr to travel across the North Atlantic back to high latitudes. In the atmosphere the changes induced by the sea ice anomaly do not last as long as in the ocean. The response in the transient and equilibrium simulations, while similar overall, differs in specific regional and temporal details. The surface air temperature increases over the Arctic Basin and the anomaly extends through the whole atmospheric column, changing the geopotential height fields and thus the storm tracks. The patterns of warming and thus the position of the geopotential height changes vary in the two ensembles. While the equilibrium simulation shifts the storm tracks to the south over the eastern North Atlantic and Europe, the transient simulation shifts the storm tracks south over the western North Atlantic and North America. The authors propose that the overall reduction in sea ice cover is important for producing ocean anomalies; however, for atmospheric anomalies the regional location of the sea ice anomalies is more important. While observed trends in Arctic sea ice are large and exceed those simulated by comprehensive climate models, there is little evidence based on this particular model that the seasonal loss of sea ice (e.g., as occurred in 2007) would constitute a threshold after which the Arctic would exhibit nonlinear, irreversible, or strongly accelerated sea ice loss. Caution should be exerted when extrapolating short-term trends to future sea ice behavior.