Open Problems on Central Simple Algebras

We provide a survey of past research and a list of open problems regarding central simple algebras and the Brauer group over a field, intended both for experts and for beginners.Comment: v2 has some small revisions to the text. Some items are re-numbered, compared to v

The evolution of rotating stars

First, we review the main physical effects to be considered in the building of evolutionary models of rotating stars on the Upper Main-Sequence (MS). The internal rotation law evolves as a result of contraction and expansion, meridional circulation, diffusion processes and mass loss. In turn, differential rotation and mixing exert a feedback on circulation and diffusion, so that a consistent treatment is necessary. We review recent results on the evolution of internal rotation and the surface rotational velocities for stars on the Upper MS, for red giants, supergiants and W-R stars. A fast rotation is enhancing the mass loss by stellar winds and reciprocally high mass loss is removing a lot of angular momentum. The problem of the ``break-up'' or $\Omega$-limit is critically examined in connection with the origin of Be and LBV stars. The effects of rotation on the tracks in the HR diagram, the lifetimes, the isochrones, the blue to red supergiant ratios, the formation of W-R stars, the chemical abundances in massive stars as well as in red giants and AGB stars, are reviewed in relation to recent observations for stars in the Galaxy and Magellanic Clouds. The effects of rotation on the final stages and on the chemical yields are examined, as well as the constraints placed by the periods of pulsars. On the whole, this review points out that stellar evolution is not only a function of mass M and metallicity Z, but of angular velocity $\Omega$ as well.Comment: 78 pages, 7 figures, review for Annual Review of Astronomy and Astrophysics, vol. 38 (2000

Social interaction, noise and antibiotic-mediated switches in the intestinal microbiota

The intestinal microbiota plays important roles in digestion and resistance against entero-pathogens. As with other ecosystems, its species composition is resilient against small disturbances but strong perturbations such as antibiotics can affect the consortium dramatically. Antibiotic cessation does not necessarily restore pre-treatment conditions and disturbed microbiota are often susceptible to pathogen invasion. Here we propose a mathematical model to explain how antibiotic-mediated switches in the microbiota composition can result from simple social interactions between antibiotic-tolerant and antibiotic-sensitive bacterial groups. We build a two-species (e.g. two functional-groups) model and identify regions of domination by antibiotic-sensitive or antibiotic-tolerant bacteria, as well as a region of multistability where domination by either group is possible. Using a new framework that we derived from statistical physics, we calculate the duration of each microbiota composition state. This is shown to depend on the balance between random fluctuations in the bacterial densities and the strength of microbial interactions. The singular value decomposition of recent metagenomic data confirms our assumption of grouping microbes as antibiotic-tolerant or antibiotic-sensitive in response to a single antibiotic. Our methodology can be extended to multiple bacterial groups and thus it provides an ecological formalism to help interpret the present surge in microbiome data.Comment: 20 pages, 5 figures accepted for publication in Plos Comp Bio. Supplementary video and information availabl

On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators

We consider one-dimensional Schroedinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations in detail. We show that they can be expressed as the sum of the identity and an integral Hilbert-Schmidt operator. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive the similar self-adjoint operator and also find the associated "charge conjugation" operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.Comment: 27 page

Analysis of the potential of cancer cell lines to release tissue factor-containing microvesicles: correlation with tissue factor and PAR2 expression

BackgroundDespite the association of cancer-derived circulating tissue factor (TF)-containing microvesicles and hypercoagulable state, correlations with the incidence of thrombosis remain unclear.MethodsIn this study the upregulation of TF release upon activation of various cancer cell lines, and the correlation with TF and PAR2 expression and/or activity was examined. Microvesicle release was induced by PAR2 activation in seventeen cell lines and released microvesicle density, microvesicle-associated TF activity, and phoshpatidylserine-mediated activity were measured. The time-course for TF release was monitored over 90 min in each cell line. In addition, TF mRNA expression, cellular TF protein and cell-surface TF activities were quantified. Moreover, the relative expression of PAR2 mRNA and cellular protein were analysed. Any correlations between the above parameters were examined by determining the Pearson’s correlation coefficients.ResultsTF release as microvesicles peaked between 30–60 min post-activation in the majority of cell lines tested. The magnitude of the maximal TF release positively correlated with TF mRNA (c = 0.717; p

A model describing diffusion in prostate cancer

PURPOSE: Quantitative diffusion MRI has frequently been studied as a means of grading prostate cancer. Interpretation of results is complicated by the nature of prostate tissue, which consists of four distinct compartments: vascular, ductal lumen, epithelium, and stroma. Current diffusion measurements are an ill-defined weighted average of these compartments. In this study, prostate diffusion is analyzed in terms of a model that takes explicit account of tissue compartmentalization, exchange effects, and the non-Gaussian behavior of tissue diffusion.  METHOD: The model assumes that exchange between the cellular (ie, stromal plus epithelial) and the vascular and ductal compartments is slow. Ductal and cellular diffusion characteristics are estimated by Monte Carlo simulation and a two-compartment exchange model, respectively. Vascular pseudodiffusion is represented by an additional signal at b = 0. Most model parameters are obtained either from published data or by comparing model predictions with the published results from 41 studies. Model prediction error is estimated using 10-fold cross-validation.  RESULTS: Agreement between model predictions and published results is good. The model satisfactorily explains the variability of ADC estimates found in the literature.  CONCLUSION: A reliable model that predicts the diffusion behavior of benign and cancerous prostate tissue of different Gleason scores has been developed. Magn Reson Med, 2016. © 2016 Wiley Periodicals, Inc

Interaction Between Convection and Pulsation

This article reviews our current understanding of modelling convection dynamics in stars. Several semi-analytical time-dependent convection models have been proposed for pulsating one-dimensional stellar structures with different formulations for how the convective turbulent velocity field couples with the global stellar oscillations. In this review we put emphasis on two, widely used, time-dependent convection formulations for estimating pulsation properties in one-dimensional stellar models. Applications to pulsating stars are presented with results for oscillation properties, such as the effects of convection dynamics on the oscillation frequencies, or the stability of pulsation modes, in classical pulsators and in stars supporting solar-type oscillations.Comment: Invited review article for Living Reviews in Solar Physics. 88 pages, 14 figure

Quantitative imaging of concentrated suspensions under flow

We review recent advances in imaging the flow of concentrated suspensions, focussing on the use of confocal microscopy to obtain time-resolved information on the single-particle level in these systems. After motivating the need for quantitative (confocal) imaging in suspension rheology, we briefly describe the particles, sample environments, microscopy tools and analysis algorithms needed to perform this kind of experiments. The second part of the review focusses on microscopic aspects of the flow of concentrated model hard-sphere-like suspensions, and the relation to non-linear rheological phenomena such as yielding, shear localization, wall slip and shear-induced ordering. Both Brownian and non-Brownian systems will be described. We show how quantitative imaging can improve our understanding of the connection between microscopic dynamics and bulk flow.Comment: Review on imaging hard-sphere suspensions, incl summary of methodology. Submitted for special volume 'High Solid Dispersions' ed. M. Cloitre, Vol. xx of 'Advances and Polymer Science' (Springer, Berlin, 2009); 22 pages, 16 fig

The Anatomy of Asilisaurus kongwe, a Dinosauriform from the Lifua Member of the Manda Beds (~Middle Triassic) of Africa

The diagnosis of Dinosauria and interrelationships of the earliest dinosaurs relies on careful documentation of the anatomy of their closest relatives. These close relatives, or dinosaur “precursors,” are typically only documented by a handful of fossils from across Pangea and nearly all specimens are typically missing important regions (e.g., forelimbs, pelves, skulls) that appear to be important to help resolving the relationships of dinosaurs. Here, we fully describe the known skeletal elements of Asilisaurus kongwe, a dinosauriform from the Middle Triassic Manda Beds of the Ruhuhu Basin of Tanzania. The taxon is known from many disarticulated and partially articulated remains and, most importantly, from a spectacularly preserved associated skeleton of an individual containing much of the skull, pectoral and pelvic girdles, forelimb and hindlimb, and parts of the vertebral column including much of the tail. The unprecedented detail of the anatomy indicates that Asilisaurus kongwe had a unique skull that was short and had both a premaxillary and dentary edentulous margin, but retained a number of character states plesiomorphic for Archosauria, including a crocodylian-like ankle configuration and a rather short foot with well-developed metatarsals I and V. Additionally, character states present across the skeleton of Asilisaurus kongwe suggest it is more closely related to Silesaurus opolensis than to dinosaurs; thus suggesting high homoplasy and parallel trends within Silesauridae and within lineages of early dinosaurs. The anatomy of Asilisaurus kongwe and detailed description of early members of clades found outside Dinosauria are clearly needed to untangle the seemingly complex character evolution of the skeleton within avemetatarsalians.Fil: Nesbitt, Sterling J.. Virginia Polytechnic Institute; Estados UnidosFil: Langer, Max C.. Universidade de Sao Paulo; BrasilFil: Ezcurra, Martin Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Museo Argentino de Ciencias Naturales "Bernardino Rivadavia"; Argentin

Influence of single and binary doping of strontium and lithium on in vivo biological properties of bioactive glass scaffolds

Effects of strontium and lithium ion doping on the biological properties of bioactive glass (BAG) porous scaffolds have been checked in vitro and in vivo. BAG scaffolds were prepared by conventional glass melting route and subsequently, scaffolds were produced by evaporation of fugitive pore formers. After thorough physico-chemical and in vitro cell characterization, scaffolds were used for pre-clinical study. Soft and hard tissue formation in a rabbit femoral defect model after 2 and 4 months, were assessed using different tools. Histological observations showed excellent osseous tissue formation in Sr and Li + Sr scaffolds and moderate bone regeneration in Li scaffolds. Fluorochrome labeling studies showed wide regions of new bone formation in Sr and Li + Sr doped samples as compared to Li doped samples. SEM revealed abundant collagenous network and minimal or no interfacial gap between bone and implant in Sr and Li + Sr doped samples compared to Li doped samples. Micro CT of Li + Sr samples showed highest degree of peripheral cancellous tissue formation on periphery and cortical tissues inside implanted samples and vascularity among four compositions. Our findings suggest that addition of Sr and/or Li alters physico-chemical properties of BAG and promotes early stage in vivo osseointegration and bone remodeling that may offer new insight in bone tissue engineering