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 late Miocene caimanine fauna (Crocodylia: Alligatoroidea) of the Urumaco Formation, Venezuela

The late Miocene Urumaco Formation at Urumaco, Falcón state, Venezuela, is remarkably rich in extinct crocodylians, presenting a diversity hotspot in the Neotropics for the group. Herein, we revise the Caimaninae fauna by including novel fossil material as well as the previously described specimens assignable to this clade. In many instances the taxonomic status of species could be confirmed, which is the case in Caiman brevirostris, Globidentosuchus brevirostris, and Purussaurus mirandai, and novel osteological data is presented to corroborate previous anatomical descriptions. In other cases, specimens needed to be reassigned to different taxa; with material previously identified as Caiman lutescens now considered as belonging to either Caiman latirostris or Caiman wannlangstoni, and material of Melanosuchus fisheri reassigned to Caimaninae aff. Melanosuchus fisheri. Furthermore, Mourasuchus nativus is considered to be a junior synonym of Mourasuchus arendsi herein. This suggests that there are only three species of the duck-billed caimanine Mourasuchus present in the Miocene of South America, having colonised the continent from the northwest (Colombia and Peru) during the middle Miocene and moving to the east and southeast (Venezuela, Brazil and Argentina) in the late Miocene. Other specimens, which were previously identified as belonging to the genus Caiman, lack diagnostic features of the modern genus and are instead considered as Caimaninae indet. Besides improving the knowledge of the late Miocene crocodylians of South America, our results confirm the high taxonomic diversity of the fauna and the outstanding level of sympatry previously reported for the Urumaco Formation

3D model and accompanying dataset related to the publication: A new, exceptionally preserved juvenile specimen of Eusaurosphargis dalsassoi (Diapsida) and implications for Mesozoic marine diapsid phylogeny

The present contribution contains the 3D model and dataset analyzed in the following publication: Scheyer, T. M., J. M. Neenan, T. Bodogan, H. Furrer, C. Obrist, and M. Plamondon. 2017. A new, exceptionally preserved juvenile specimen of Eusaurosphargis dalsassoi (Diapsida) and implications for Mesozoic marine diapsid phylogeny. Scientific Reports, https://doi.org/10.1038/s41598-017-04514-x

Vertebral, rib, and osteoderm morphology and histology of aff. Eusaurosphargis (Diapsida, Middle Triassic) and aff. Saurosphargis voltzi from the western Tethys

Bone histology and microanatomy of neck and dorsal vertebrae, a dorsal rib, and osteoderms from different body regions of Eusaurosphargis aff. dalsassoi from Winterswijk, The Netherlands, are studied by petrographic thin sections and micro-computed tomographic (μCT) data. Osteohistology in the axial elements differs from that of marine reptiles and corroborates a terrestrial or semiaquatic life style for Eusaurosphargis aff. dalsassoi. Not only the outer shape and overall microanatomy of the osteoderms, but also the association and attachment of the osteoderms to the underlying endoskeletal element (i.e., cervical vertebra, rib, appendicular element) vary depending on body region. Furthermore, chondroid bone is identified in the osteoderms of Eusaurosphargis aff. dalsassoi, which is the oldest evidence of this tissue in osteoderms of an extinct tetrapod. For comparison, μCT data of two neural arches tentatively identifiable as pertaining to the enigmatic Middle Triassic Saurosphargis voltzi (the holotype and only specimen of this taxon is considered lost) could be included. They share with Eusaurosphargis aff. dalsassoi the elongated transverse processes and a general similar microstructure, but also present an anteroposteriorly broadened bony sheath of the transverse process in ventral view, which is absent in Eusaurosphargis aff. dalsassoi

New specimen of Psephoderma alpinum (Sauropterygia, Placodontia) from the Late Triassic of Schesaplana Mountain, Graubünden, Switzerland

Psephoderma alpinum is an armoured, durophagous placodont known from the alpine Late Triassic. Here we present a new, well-preserved isolated skull discovered in the Alplihorn Member (Late Norian–Early Rhaetian) of the Kössen Formation, Schesaplana Mountain, which straddles the Swiss/Austrian border. Micro-computed tomographic (µCT) scanning was used to create an accurate osteological reconstruction of the specimen, the first time this has been conducted for Psephoderma. We thus clarify disputed anatomical features from previous descriptions, such as a lack of a lacrimal and a pineal foramen that is enclosed by the parietal. We also present the first description based on µCT data of the lateral braincase wall, sphenoid region and some cranial nerve canals for Psephoderma, with the location of the hypophyseal seat, cerebral carotid foramina, dorsum sellae, prootic foramen, lacrimal foramen, as well as all dental foramina being described. This specimen represents the first skull of Psephoderma recovered in Switzerland, and features such as poorly-sutured braincase elements and its relatively small size compared to other known specimens may indicate that it was a sub-adult

Crushed but not lost: a colubriform snake (Serpentes) from the Miocene Swiss Molasse, identified through the use of micro-CT scanning technology

An incomplete postcranial skeleton of a snake from the middle Miocene of the Swiss Molasse in Käpfnach mine, near Zurich, Switzerland, is described in this paper. The skeleton is rather crushed and resting on a block of coal, with only some articulated vertebrae partially discerned via visual microscopy. We conducted micro-CT scanning in the specimen and we digitally reconstructed the whole preserved vertebral column, allowing a direct and detailed observation of its vertebral morphology. Due to the flattened nature of the fossil specimen, several individual vertebral structures are deformed, not permitting thus a secure precise taxonomic identification. Accordingly, we only refer the specimen to as Colubriformes indet. Nevertheless, this occurrence adds to the exceedingly rare fossil record of snakes from Switzerland, which had so far been formally described solely from three other Eocene and Miocene localities

To glide or to swim? A reinvestigation of the enigmatic Wapitisaurus problematicus (Reptilia) from the Early Triassic of British Columbia, Canada

Wapitisaurus problematicus was initially described as a member of the Weigeltisauridae, a clade of Late Permian gliding reptiles from Eurasia and Madagascar. However, the poor preservation of the holotype and only known specimen, from the lower Sulphur Mountain Formation at Ganoid Ridge (British Columbia, Canada), raised doubts about this assignment. Here, we redescribe W. problematicus and reassess its systematic position among diapsid reptiles. Comparison with all known weigeltisaurids, as well as contemporaneous reptiles from the Sulphur Mountain Formation, indicates that the taxon instead represents a thalattosauroid thalattosauriform, with noted similarities to Thalattosaurus and Paralonectes. This reidentification restricts weigeltisaurids to the Late Permian, with no occurrence in North America. Wapitisaurus problematicus potentially represents one of the oldest thalattosauriforms and increases our understanding of their diversity and disparity during the late Early and Middle Triassic. The close morphological similarities with later (thalattosauroid) thalattosauriforms and their high abundance in (shallow) marine settings may indicate an earlier invasion of this realm than previously assumed. This parallels observations in early ichthyopterygians with widespread opportunistic trophic niche diversification occurring relatively rapidly after the end-Permian mass extinction event

Structure and relaxations in liquid and amorphous Selenium

We report a molecular dynamics simulation of selenium, described by a three-body interaction. The temperatures T_g and T_c and the structural properties are in agreement with experiment. The mean nearest neighbor coordination number is 2.1. A small pre-peak at about 1 AA^-1 can be explained in terms of void correlations. In the intermediate self-scattering function, i.e. the density fluctuation correlation, classical behavior, alpha- and beta-regimes, is found. We also observe the plateau in the beta-regime below T_g. In a second step, we investigated the heterogeneous and/or homogeneous behavior of the relaxations. At both short and long times the relaxations are homogeneous (or weakly heterogeneous). In the intermediate time scale, lowering the temperature increases the heterogeneity. We connect these different domains to the vibrational (ballistic), beta- and alpha-regimes. We have also shown that the increase in heterogeneity can be understood in terms of relaxations