Stanilov-Tsankov-Videv Theory

We survey some recent results concerning Stanilov-Tsankov-Videv theory, conformal Osserman geometry, and Walker geometry which relate algebraic properties of the curvature operator to the underlying geometry of the manifold.Comment: This is a contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Geometric realizations of curvature models by manifolds with constant scalar curvature

We show any Riemannian curvature model can be geometrically realized by a manifold with constant scalar curvature. We also show that any pseudo-Hermitian curvature model, para-Hermitian curvature model, hyper-pseudo-Hermitian curvature model, or hyper-para-Hermitian curvature model can be realized by a manifold with constant scalar and *-scalar curvature

Poly(alkyl methacrylate) tooth coatings for dental care: evaluation of the demineralisation-protection benefit using a time-resolved in vitro method

An in vitro method for the time-resolved quantification of acid-mediated tooth demineralisation has been developed and evaluated against putative non-permanent protective formulations based on a series of poly(alkyl methacrylate)s. Using a thermostatted carousel, dentally relevant substrates consisting of hydroxyapatite discs or sections of bovine teeth have been exposed to aqueous citric acid under controlled conditions, before and after being treated with the polymeric coatings. The dissolution of phosphate was monitored by the determination of 31P by Inductively Coupled Plasma—Mass Spectrometry and by the spectrophotometric phosphovanadomolybdate method. Dose-response plots constructed for both groups of treated substrates have revealed that the coatings significantly reduce erosion rates but are less effective at inhibiting tooth demineralisation than the standard fluoride treatment. The approach has enabled an evaluation of the erosion-protection efficiency of each coating

Stanilov-Tsankov-Videv Theory

We survey some recent results concerning Stanilov-Tsankov-Videv theory, conformal Osserman geometry, and Walker geometry which relate algebraic properties of the curvature operator to the underlying geometry of the manifold

Molecular and cellular mechanisms underlying the evolution of form and function in the amniote jaw.

The amniote jaw complex is a remarkable amalgamation of derivatives from distinct embryonic cell lineages. During development, the cells in these lineages experience concerted movements, migrations, and signaling interactions that take them from their initial origins to their final destinations and imbue their derivatives with aspects of form including their axial orientation, anatomical identity, size, and shape. Perturbations along the way can produce defects and disease, but also generate the variation necessary for jaw evolution and adaptation. We focus on molecular and cellular mechanisms that regulate form in the amniote jaw complex, and that enable structural and functional integration. Special emphasis is placed on the role of cranial neural crest mesenchyme (NCM) during the species-specific patterning of bone, cartilage, tendon, muscle, and other jaw tissues. We also address the effects of biomechanical forces during jaw development and discuss ways in which certain molecular and cellular responses add adaptive and evolutionary plasticity to jaw morphology. Overall, we highlight how variation in molecular and cellular programs can promote the phenomenal diversity and functional morphology achieved during amniote jaw evolution or lead to the range of jaw defects and disease that affect the human condition

Visual Laterality of Calf–Mother Interactions in Wild Whales

Behavioral laterality is known for a variety of vertebrate and invertebrate animals. Laterality in social interactions has been described for a wide range of species including humans. Although evidence and theoretical predictions indicate that in social species the degree of population level laterality is greater than in solitary ones, the origin of these unilateral biases is not fully understood. It is especially poorly studied in the wild animals. Little is known about the role, which laterality in social interactions plays in natural populations. A number of brain characteristics make cetaceans most suitable for investigation of lateralization in social contacts.) in the greatest breeding aggregation in the White Sea. Here we show that young calves (in 29 individually identified and in over a hundred of individually not recognized mother-calf pairs) swim and rest significantly longer on a mother's right side. Further observations along with the data from other cetaceans indicate that found laterality is a result of the calves' preference to observe their mothers with the left eye, i.e., to analyze the information on a socially significant object in the right brain hemisphere.Data from our and previous work on cetacean laterality suggest that basic brain lateralizations are expressed in the same way in cetaceans and other vertebrates. While the information on social partners and novel objects is analyzed in the right brain hemisphere, the control of feeding behavior is performed by the left brain hemisphere. Continuous unilateral visual contacts of calves to mothers with the left eye may influence social development of the young by activation of the contralateral (right) brain hemisphere, indicating a possible mechanism on how behavioral lateralization may influence species life and welfare. This hypothesis is supported by evidence from other vertebrates

Mechanical Influences on Morphogenesis of the Knee Joint Revealed through Morphological, Molecular and Computational Analysis of Immobilised Embryos

Very little is known about the regulation of morphogenesis in synovial joints. Mechanical forces generated from muscle contractions are required for normal development of several aspects of normal skeletogenesis. Here we show that biophysical stimuli generated by muscle contractions impact multiple events during chick knee joint morphogenesis influencing differential growth of the skeletal rudiment epiphyses and patterning of the emerging tissues in the joint interzone. Immobilisation of chick embryos was achieved through treatment with the neuromuscular blocking agent Decamethonium Bromide. The effects on development of the knee joint were examined using a combination of computational modelling to predict alterations in biophysical stimuli, detailed morphometric analysis of 3D digital representations, cell proliferation assays and in situ hybridisation to examine the expression of a selected panel of genes known to regulate joint development. This work revealed the precise changes to shape, particularly in the distal femur, that occur in an altered mechanical environment, corresponding to predicted changes in the spatial and dynamic patterns of mechanical stimuli and region specific changes in cell proliferation rates. In addition, we show altered patterning of the emerging tissues of the joint interzone with the loss of clearly defined and organised cell territories revealed by loss of characteristic interzone gene expression and abnormal expression of cartilage markers. This work shows that local dynamic patterns of biophysical stimuli generated from muscle contractions in the embryo act as a source of positional information guiding patterning and morphogenesis of the developing knee joint