Asymptotics of the Wigner 9j symbol

We present the asymptotic formula for the Wigner 9j-symbol, valid when all quantum numbers are large, in the classically allowed region. As in the Ponzano-Regge formula for the 6j-symbol, the action is expressed in terms of lengths of edges and dihedral angles of a geometrical figure, but the angles require care in definition. Rules are presented for converting spin networks into the associated geometrical figures. The amplitude is expressed as the determinant of a 2x2 matrix of Poisson brackets. The 9j-symbol possesses caustics associated with the fold and elliptic and hyperbolic umbilic catastrophes. The asymptotic formula obeys the exact symmetries of the 9j-symbol.Comment: 17 pages, 7 figure

Visualizing muscle cell migration in situ

AbstractBackground: Cell migration has been studied extensively by manipulating and observing cells bathed in putative chemotactic or chemokinetic agents on planar substrates. This environment differs from that in vivo and, consequently, the cells can behave abnormally. Embryo slices provide an optically accessible system for studying cellular navigation pathways during development. We extended this system to observe the migration of muscle precursors from the somite into the forelimb, their cellular morphology, and the localization of green fluorescent protein (GFP)-tagged adhesion-related molecules under normal and perturbed conditions.Results: Muscle precursors initiated migration synchronously and migrated in broad, rather than highly defined, regions. Bursts of directed migration were followed by periods of meandering or extension and retraction of cell protrusions. Although paxillin did not localize to discernible intracellular structures, we found that α-actinin localized to linear, punctate structures, and the α5 integrin to some focal complexes and/or vesicle-like concentrations. Alterations in the expression of adhesion molecules inhibited migration. The muscle precursors migrating in situ formed unusually large, long-lived protrusions that were polarized in the direction of migration. Unlike wild-type Rac, a constitutively active Rac localized continuously around the cell surface and promoted random protrusive activity and migration.Conclusions: The observation of cellular migration and the dynamics of molecular organization at high temporal and spatial resolution in situ is feasible. Migration from the somite to the wing bud is discontinuous and not highly stereotyped. In situ, local activation of Rac appears to produce large protrusions, which in turn, leads to directed migration. Adhesion can also regulate migration

Big issues for small feet : developmental, biomechanical and clinical narratives on children's footwear

The effects of footwear on the development of children's feet has been debated for many years and recent work from the developmental and biomechanical literature has challenged long-held views about footwear and the impact on foot development. This narrative review draws upon existing studies from developmental, biomechanical and clinical literature to explore the effects of footwear on the development of the foot. The emerging findings from this support the need for progress in [children's] footwear science and advance understanding of the interaction between the foot and shoe. Ensuring clear and credible messages inform practice requires a progressive evidence base but this remains big issue in children's footwear research

The chronostratigraphy of the Haua Fteah cave (Cyrenaica, northeast Libya)

The 1950s excavations by Charles McBurney in the Haua Fteah, a large karstic cave on the coast of northeast Libya, revealed a deep sequence of human occupation. Most subsequent research on North African prehistory refers to his discoveries and interpretations, but the chronology of its archaeological and geological sequences has been based on very early age determinations. This paper reports on the initial results of a comprehensive multi-method dating program undertaken as part of new work at the site, involving radiocarbon dating of charcoal, land snails and marine shell, cryptotephra investigations, optically stimulated luminescence (OSL) dating of sediments, and electron spin resonance (ESR) dating of tooth enamel. The dating samples were collected from the newly exposed and cleaned faces of the upper 7.5 m of the w14.0 m-deep McBurney trench, which contain six of the seven major cultural phases that he identified. Despite problems of sediment transport and reworking, using a Bayesian statistical model the new dating program establishes a robust framework for the five major lithostratigraphic units identified in the stratigraphic succession, and for the major cultural units. The age of two anatomically modern human mandibles found by McBurney in Layer XXXIII near the base of his Levalloiso-Mousterian phase can now be estimated to between 73 and 65 ka (thousands of years ago) at the 95.4% confidence level, within Marine Isotope Stage (MIS) 4. McBurney’s Layer XXV, associated with Upper Palaeolithic Dabban blade industries, has a clear stratigraphic relationship with Campanian Ignimbrite tephra. Microlithic Oranian technologies developed following the climax of the Last Glacial Maximum and the more microlithic Capsian in the Younger Dryas. Neolithic pottery and perhaps domestic livestock were used in the cave from the mid Holocene but there is no certain evidence for plant cultivation until the Graeco-Roman period

The morphology of the enamel-dentine junction in Neanderthal molars: Gross morphology, non-metric traits, and temporal trends

This study explores the morphological differences between the enamel–dentine junction (EDJ) of maxillary and mandibular molars of Neanderthals (n = 150) and recent modern humans (n = 106), and between an earlier Neanderthal sample (consisting of Pre-Eemian and Eemian Neanderthals dating to before 115 ka) and a later Neanderthal sample (consisting of Post-Eemian Neanderthals dating to after 115 ka). The EDJ was visualised by segmenting microtomographic scans of each molar. A geometric morphometric methodology compared the positioning of the dentine horns, the shape of the marginal ridge between the dentine horns, and the shape of the cervix. We also examined the manifestation of non-metric traits at the EDJ including the crista obliqua, cusp 5, and post-paracone tubercle. Furthermore, we report on additional morphological features including centrally placed dentine horn tips and twinned dentine horns. Our results indicate that EDJ morphology can discriminate with a high degree of reliability between Neanderthals and recent modern humans at every molar position, and discriminate between the earlier and the later Neanderthal samples at every molar position, except for the M3 in shape space. The cervix in isolation can also discriminate between Neanderthals and recent modern humans, except at the M3 in form space, and is effective at discriminating between the earlier and the later Neanderthal samples, except at the M2/M2 in form space. In addition to demonstrating the taxonomic valence of the EDJ, our analysis reveals unique manifestations of dental traits in Neanderthals and expanded levels of trait variation that have implications for trait definitions and scoring

knowCube for MCDM – Visual and Interactive Support for Multicriteria Decision Making

In this paper, we present a novel multicriteria decision support system (MCDSS), called knowCube, consisting of components for knowledge organization, generation, and navigation. Knowledge organization rests upon a database for managing qualitative and quantitative criteria, together with add-on information. Knowledge generation serves filling the database via e.g. identification, optimization, classification or simulation. For “finding needles in haycocks”, the knowledge navigation component supports graphical database retrieval and interactive, goal-oriented problem solving. Navigation “helpers” are, for instance, cascading criteria aggregations, modifiable metrics, ergonomic interfaces, and customizable visualizations. Examples from real-life projects, e.g. in industrial engineering and in the life sciences, illustrate the application of our MCDSS