Mechanical Systems with Symmetry, Variational Principles, and Integration Algorithms

This paper studies variational principles for mechanical systems with symmetry and their applications to integration algorithms. We recall some general features of how to reduce variational principles in the presence of a symmetry group along with general features of integration algorithms for mechanical systems. Then we describe some integration algorithms based directly on variational principles using a discretization technique of Veselov. The general idea for these variational integrators is to directly discretize Hamilton’s principle rather than the equations of motion in a way that preserves the original systems invariants, notably the symplectic form and, via a discrete version of Noether’s theorem, the momentum map. The resulting mechanical integrators are second-order accurate, implicit, symplectic-momentum algorithms. We apply these integrators to the rigid body and the double spherical pendulum to show that the techniques are competitive with existing integrators

Equine penile squamous cell carcinoma: expression of biomarker proteins and EcPV2

Equine penile squamous cell carcinoma (EpSCC) is a relatively common cutaneous neoplasm with a poor prognosis. In this study, we aimed to determine the protein expression and colocalisation of FRA1, c-Myc, Cyclin D1, and MMP7 in normal (NT), tumour (T), hyperplastic epidermis and/or squamous papilloma (Hyp/Pap), poorly-differentiated (PDSCC), or well-differentiated (WDSCC) EpSCC using a tissue array approach. Further objectives were to correlate protein expression to (i) levels of inflammation, using a convolutional neural network (ii) equine papillomavirus 2 (EcPV2) infection, detected using PCR amplification. We found an increase in expression of FRA1 in EpSCC compared to NT samples. c-Myc expression was higher in Hyp/Pap and WDSCC but not PDSCC whereas MMP7 was reduced in WDSCC compared with NT. There was a significant increase in the global intersection coefficient (GIC) of FRA1 with MMP7, c-Myc, and Cyclin D1 in EpSCC. Conversely, GIC for MMP7 with c-Myc was reduced in EpSCC tissue. Inflammation was positively associated with EcPV2 infection in both NT and EpSCC but not Hyp/Pap. Changes in protein expression could be correlated with EcPV2 for Cyclin D1 and c-Myc. Our results evaluate novel biomarkers of EpSCC and a putative correlation between the expression of biomarkers, EcPV2 infection and inflammation

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

Syndromic Autism: progressing beyond current levels of description

Genetic syndrome groups at high risk of autism comorbidity, like Down syndrome and fragile X syndrome, have been presented as useful models for understanding risk and protective factors involved in the emergence of autistic traits. Yet despite reaching clinical thresholds, these ‘syndromic’ forms of autism appear to differ in significant ways from the idiopathic or ‘non-syndromic’ autism profile. We explore alternative mechanistic explanations for these differences and propose a developmental interpretation of syndromic autism that takes into account the character of the genetic disorder. This interpretation anticipates syndrome-specific autism phenotypes, since the neurocognitive and behavioural expression of the autism is coloured by syndromically defined atypicalities. To uncover the true nature of comorbidities and of autism per se, we argue that it is key to extend definitions of autism to include the perceptual and neurocognitive characteristics of the disorder and then apply this multilevel conceptualization to the study of syndromic autism profiles