Numerical approximation of statistical solutions of scalar conservation laws

We propose efficient numerical algorithms for approximating statistical solutions of scalar conservation laws. The proposed algorithms combine finite volume spatio-temporal approximations with Monte Carlo and multi-level Monte Carlo discretizations of the probability space. Both sets of methods are proved to converge to the entropy statistical solution. We also prove that there is a considerable gain in efficiency resulting from the multi-level Monte Carlo method over the standard Monte Carlo method. Numerical experiments illustrating the ability of both methods to accurately compute multi-point statistical quantities of interest are also presented

The Colorado Plateau Coring Project (CPCP): 100 Million Years of Earth System History

Lasting over 100 million years, the early Mesozoic (252 to 145 Ma) is punctuated by two of the five major mass extinctions of the Phanerozoic (Permo-Triassic and Triassic-Jurassic) plus several smaller extinction events. It witnessed the evolutionary appearance of the modem terrestrial biota including frogs, salamanders, turtles, lizards, crocodilians, dinosaurs, birds, and mammals, and spans a time of dramatic climate changes on the continents. What is arguably the richest record of these events lies in the vast (- 2.5 million km2) complex of epicontinental basins in the western part of Pangea, now largely preserved on the Colorado Plateau (Fig.l). Since the mid-19th century, classic studies of these basins, their strata, and their fossils have made this succession instrumental in framing our context of the early Mesozoic Earth system as reflected in the international literature. Despite this long and distinguished history of study of the Colorado Plateau region, striking ambiguities in temporal resolution, major uncertainties in global correlations, and significant doubts about paleolatitudinal position hamper incorporation of the huge amount of information from the region into-tests of major competing climatic, biotic, and tectonic hypotheses and a fundamental understanding of Earth system processes

The Postcranial Skeleton of an Exceptionally Complete Individual of the Plated Dinosaur Stegosaurus stenops (Dinosauria: Thyreophora) from the Upper Jurassic Morrison Formation of Wyoming, U.S.A.

Copyright: © 2015 Maidment et al. This is an open access article distributed under the terms of the Creative Commons Attribution License [4.0], which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. The attached file is the published version of the article

The Earliest Post-Paleozoic Freshwater Bivalves Preserved in Coprolites from the Karoo Basin, South Africa

Background: Several clades of bivalve molluscs have invaded freshwaters at various times throughout Phanerozoic history. The most successful freshwater clade in the modern world is the Unionoida. Unionoids arose in the Triassic Period, sometime after the major extinction event at the End-Permian boundary and are now widely distributed across all continents except Antarctica. Until now, no freshwater bivalves of any kind were known to exist in the Early Triassic. Principal Findings: Here we report on a faunule of two small freshwater bivalve species preserved in vertebrate coprolites from the Olenekian (Lower Triassic) of the Burgersdorp Formation of the Karoo Basin, South Africa. Positive identification of these bivalves is not possible due to the limited material. Nevertheless they do show similarities with Unionoida although they fall below the size range of extant unionoids. Phylogenetic analysis is not possible with such limited material and consequently the assignment remains somewhat speculative. Conclusions: Bivalve molluscs re-invaded freshwaters soon after the End-Permian extinction event, during the earliest part of the recovery phase during the Olenekian Stage of the Early Triassic. If the specimens do represent unionoids then these Early Triassic examples may be an example of the Lilliput effect. Since the oldest incontrovertible freshwater unionoids are also from sub-Saharan Africa, it is possible that this subcontinent hosted the initial freshwater radiation of the Unionoida. This find also demonstrates the importance of coprolites as microenvironments of exceptional preservation that contai

High Diversity, Low Disparity and Small Body Size in Plesiosaurs (Reptilia, Sauropterygia) from the Triassic–Jurassic Boundary

Invasion of the open ocean by tetrapods represents a major evolutionary transition that occurred independently in cetaceans, mosasauroids, chelonioids (sea turtles), ichthyosaurs and plesiosaurs. Plesiosaurian reptiles invaded pelagic ocean environments immediately following the Late Triassic extinctions. This diversification is recorded by three intensively-sampled European fossil faunas, spanning 20 million years (Ma). These provide an unparalleled opportunity to document changes in key macroevolutionary parameters associated with secondary adaptation to pelagic life in tetrapods. A comprehensive assessment focuses on the oldest fauna, from the Blue Lias Formation of Street, and nearby localities, in Somerset, UK (Earliest Jurassic: 200 Ma), identifying three new species representing two small-bodied rhomaleosaurids (Stratesaurus taylori gen et sp. nov.; Avalonnectes arturi gen. et sp. nov) and the most basal plesiosauroid, Eoplesiosaurus antiquior gen. et sp. nov. The initial radiation of plesiosaurs was characterised by high, but short-lived, diversity of an archaic clade, Rhomaleosauridae. Representatives of this initial radiation were replaced by derived, neoplesiosaurian plesiosaurs at small-medium body sizes during a more gradual accumulation of morphological disparity. This gradualistic modality suggests that adaptive radiations within tetrapod subclades are not always characterised by the initially high levels of disparity observed in the Paleozoic origins of major metazoan body plans, or in the origin of tetrapods. High rhomaleosaurid diversity immediately following the Triassic-Jurassic boundary supports the gradual model of Late Triassic extinctions, mostly predating the boundary itself. Increase in both maximum and minimum body length early in plesiosaurian history suggests a driven evolutionary trend. However, Maximum-likelihood models suggest only passive expansion into higher body size categories

The Osteology of the Basal Archosauromorph Tasmaniosaurus triassicus from the Lower Triassic of Tasmania, Australia

Proterosuchidae are the most taxonomically diverse archosauromorph reptiles sampled in the immediate aftermath of the Permo-Triassic mass extinction and represent the earliest radiation of Archosauriformes (archosaurs and closely related species). Proterosuchids are potentially represented by approximately 15 nominal species collected from South Africa, China, Russia, Australia and India, but the taxonomic content of the group is currently in a state of flux because of the poor anatomic and systematic information available for several of its putative members. Here, the putative proterosuchid Tasmaniosaurus triassicus from the Lower Triassic of Hobart, Tasmania (Australia),is redescribed. The holotype and currently only known specimen includes cranial and postcranial remains and the revision of this material sheds new light on the anatomy of the animal, including new data on the cranial endocast. Several bones are re-identified or reinterpreted, contrasting with the descriptions of previous authors. The new information provided here shows that Tasmaniosaurus closely resembles the South African proterosuchid Proterosuchus, but it differed in the presence of, for example, a slightly downturned premaxilla, a shorter anterior process of maxilla, and a diamond-shaped anterior end of interclavicle. Previous claims for the presence of gut contents in the holotype of Tasmaniosaurus are considered ambiguous. The description of the cranial endocast of Tasmaniosaurus provides for the first time information about the anatomy of this region in proterosuchids. The cranial endocast preserves possibly part of the vomero-nasal (= Jacobson's) system laterally to the olfactory bulbs. Previous claims of the absence of the vomero-nasal organs in archosaurs, which is suggested by the extant phylogenetic bracket, are questioned because its absence in both clades of extant archosaurs seems to be directly related with the independent acquisition of a non-ground living mode of life

Colorado Plateau Coring Project, Phase I (CPCP-I): a continuously cored, globally exportable chronology of Triassic continental environmental change from western North America

Phase 1 of the Colorado Plateau Coring Project (CPCP-I) recovered a total of over 850&thinsp;m of stratigraphically overlapping core from three coreholes at two sites in the Early to Middle and Late Triassic age largely fluvial Moenkopi and Chinle formations in Petrified Forest National Park (PFNP), northeastern Arizona, USA. Coring took place during November and December of 2013 and the project is now in its post-drilling science phase. The CPCP cores have abundant detrital zircon-producing layers (with survey LA-ICP-MS dates selectively resampled for CA-ID-TIMS U-Pb ages ranging in age from at least 210 to 241&thinsp;Ma), which together with their magnetic polarity stratigraphy demonstrate that a globally exportable timescale can be produced from these continental sequences and in the process show that a prominent gap in the calibrated Phanerozoic record can be filled. The portion of core CPCP-PFNP13-1A for which the polarity stratigraphy has been completed thus far spans  ∼ 215 to 209&thinsp;Ma of the Late Triassic age, and strongly validates the longer Newark-Hartford Astrochronostratigraphic-calibrated magnetic Polarity Time-Scale (APTS) based on cores recovered in the 1990s during the Newark Basin Coring Project (NBCP).Core recovery was  ∼ 100&thinsp;% in all holes (Table 1). The coreholes were inclined  ∼ 60–75° approximately to the south to ensure azimuthal orientation in the nearly flat-lying bedding, critical to the interpretation of paleomagentic polarity stratigraphy. The two longest of the cores (CPCP-PFNP13-1A and 2B) were CT-scanned in their entirety at the University of Texas High Resolution X-ray CT Facility in Austin, TX, and subsequently along with 2A, all cores were split and processed at the CSDCO/LacCore Facility, in Minneapolis, MN, where they were scanned for physical property logs and imaging. While remaining the property of the Federal Government, the archive half of each core is curated at the NSF-sponsored LacCore Core Repository and the working half is stored at the Rutgers University Core Repository in Piscataway, NJ, where the initial sampling party was held in 2015 with several additional sampling events following. Additional planned study will recover the rest of the polarity stratigraphy of the cores as additional zircon ages, sedimentary structure and paleosol facies analysis, stable isotope geochemistry, and calibrated XRF core scanning are accomplished. Together with strategic outcrop studies in Petrified Forest National Park and environs, these cores will allow the vast amount of surface paleontological and paleoenvironmental information recorded in the continental Triassic of western North America to be confidently placed in a secure context along with important events such as the giant Manicouagan impact at  ∼ 215.5&thinsp;Ma (Ramezani et al., 2005) and long wavelength astronomical cycles pacing global environmental change and trends in atmospheric gas composition during the dawn of the dinosaurs.</p

The Ontogenetic Osteohistology of Tenontosaurus tilletti

Tenontosaurus tilletti is an ornithopod dinosaur known from the Early Cretaceous (Aptian-Albian) Cloverly and Antlers formations of the Western United States. It is represented by a large number of specimens spanning a number of ontogenetic stages, and these specimens have been collected across a wide geographic range (from central Montana to southern Oklahoma). Here I describe the long bone histology of T. tilletti and discuss histological variation at the individual, ontogenetic and geographic levels. The ontogenetic pattern of bone histology in T. tilletti is similar to that of other dinosaurs, reflecting extremely rapid growth early in life, and sustained rapid growth through sub-adult ontogeny. But unlike other iguanodontians, this dinosaur shows an extended multi-year period of slow growth as skeletal maturity approached. Evidence of termination of growth (e.g., an external fundamental system) is observed in only the largest individuals, although other histological signals in only slightly smaller specimens suggest a substantial slowing of growth later in life. Histological differences in the amount of remodeling and the number of lines of arrested growth varied among elements within individuals, but bone histology was conservative across sampled individuals of the species, despite known paleoenvironmental differences between the Antlers and Cloverly formations. The bone histology of T. tilletti indicates a much slower growth trajectory than observed for other iguanodontians (e.g., hadrosaurids), suggesting that those taxa reached much larger sizes than Tenontosaurus in a shorter time

Revised Lithostratigraphy of the Sonsela Member (Chinle Formation, Upper Triassic) in the Southern Part of Petrified Forest National Park, Arizona

BACKGROUND: Recent revisions to the Sonsela Member of the Chinle Formation in Petrified Forest National Park have presented a three-part lithostratigraphic model based on unconventional correlations of sandstone beds. As a vertebrate faunal transition is recorded within this stratigraphic interval, these correlations, and the purported existence of a depositional hiatus (the Tr-4 unconformity) at about the same level, must be carefully re-examined. METHODOLOGY/PRINCIPAL FINDINGS: Our investigations demonstrate the neglected necessity of walking out contacts and mapping when constructing lithostratigraphic models, and providing UTM coordinates and labeled photographs for all measured sections. We correct correlation errors within the Sonsela Member, demonstrate that there are multiple Flattops One sandstones, all of which are higher than the traditional Sonsela sandstone bed, that the Sonsela sandstone bed and Rainbow Forest Bed are equivalent, that the Rainbow Forest Bed is higher than the sandstones at the base of Blue Mesa and Agate Mesa, that strata formerly assigned to the Jim Camp Wash beds occur at two stratigraphic levels, and that there are multiple persistent silcrete horizons within the Sonsela Member. CONCLUSIONS/SIGNIFICANCE: We present a revised five-part model for the Sonsela Member. The units from lowest to highest are: the Camp Butte beds, Lot's Wife beds, Jasper Forest bed (the Sonsela sandstone)/Rainbow Forest Bed, Jim Camp Wash beds, and Martha's Butte beds (including the Flattops One sandstones). Although there are numerous degradational/aggradational cycles within the Chinle Formation, a single unconformable horizon within or at the base of the Sonsela Member that can be traced across the entire western United States (the "Tr-4 unconformity") probably does not exist. The shift from relatively humid and poorly-drained to arid and well-drained climatic conditions began during deposition of the Sonsela Member (low in the Jim Camp Wash beds), well after the Carnian-Norian transition