18,845 research outputs found

    Temporal intervals and temporal order

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    Deformation in Moffat Shale detachment zones in the western part of the Scottish Southern Uplands

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    A study of the décollement zones in the Moffat Shale Group in the Ordovician Northern Belt of the Southern Uplands of Scotland reveals a progressive sequence of deformation and increased channelization of fluid flow. The study concentrates on exposures of imbricated Moffat Shale on the western coast of the Rhins of Galloway. Initial deformation occurred in partially lithified sediments and involved stratal disruption and shearing of the shales. Deformation then became more localized in narrower fault zones characterized by polyphase hydrothermal fluid flow/veining events. Deformation continued after vein formation, resulting in the development of low-temperature crystal plastic microstructures and further veining. Late-stage deformation is recorded as a pressure solution event possibly reflecting the cessation of slip on these faults as the slice became accreted. Most deformation can be ascribed to SE-directed thrusting and incorporation of the individual sheets into the Southern Uplands thrust stack. Later sinistral shear deformation, not observed in overlying turbidites, is also localized in these fault zones. The study reveals the likely structures formed at levels of an accretionary prism deforming under diagenetic to low-grade metamorphic conditions

    QUESTIONING THE ADMISSIBILITY OF NONSCIENTIFIC TESTIMONY AFTER DAUBERT: THE NEED FOR INCREASED JUDICIAL GATEKEEPING TO ENSURE THE RELIABILITY OF ALL EXPERT TESTIMONY

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    This article examines the difficulty of finding a proper standard for evaluating non-scientific expert testimony. It analyzes the legal standard for the admission of expert testimony as set out in the Federal Rule of Evidence and the Daubert case. It reviews a split in courts as to how to apply these standards to non-scientific expert testimony. It ends with some proposals for the application of Daubert to non-scientific expert testimony and suggests an amendment to the Federal Rules of evidence

    Gromov-Monge quasi-metrics and distance distributions

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    Applications in data science, shape analysis and object classification frequently require maps between metric spaces which preserve geometry as faithfully as possible. In this paper, we combine the Monge formulation of optimal transport with the Gromov-Hausdorff distance construction to define a measure of the minimum amount of geometric distortion required to map one metric measure space onto another. We show that the resulting quantity, called Gromov-Monge distance, defines an extended quasi-metric on the space of isomorphism classes of metric measure spaces and that it can be promoted to a true metric on certain subclasses of mm-spaces. We also give precise comparisons between Gromov-Monge distance and several other metrics which have appeared previously, such as the Gromov-Wasserstein metric and the continuous Procrustes metric of Lipman, Al-Aifari and Daubechies. Finally, we derive polynomial-time computable lower bounds for Gromov-Monge distance. These lower bounds are expressed in terms of distance distributions, which are classical invariants of metric measure spaces summarizing the volume growth of metric balls. In the second half of the paper, which may be of independent interest, we study the discriminative power of these lower bounds for simple subclasses of metric measure spaces. We first consider the case of planar curves, where we give a counterexample to the Curve Histogram Conjecture of Brinkman and Olver. Our results on plane curves are then generalized to higher dimensional manifolds, where we prove some sphere characterization theorems for the distance distribution invariant. Finally, we consider several inverse problems on recovering a metric graph from a collection of localized versions of distance distributions. Results are derived by establishing connections with concepts from the fields of computational geometry and topological data analysis.Comment: Version 2: Added many new results and improved expositio
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