Branching Asymptotics on Manifolds with Edge

We study pseudo-differential operators on a wedge with continuous and variable discrete branching asymptotics.Comment: 54 pages, 1 figure

ADAM15 modulates outside-in signalling in chondrocyte–matrix interactions

ADAM15 belongs to a family of transmembrane multi-domain proteins implicated in proteolysis, cell–cell and cell–matrix interactions in various disease conditions. In osteoarthritis (OA), ADAM15 is up-regulated in the chondrocytes already at early stages of cartilage degeneration where it seems to exert homeostatic effects likely associated with its ability to enhance integrin-mediated chondrocyte adhesion to the surrounding collagen matrix. The aim of our present study was, therefore, to characterize functional domains of ADAM15 involved in collagen II (CII) interaction and to analyse associated outside-in signalling events. Accordingly, ADAM15 and respective deletion mutants were stably transfected into the chondrocyte cell line T/C28a4. Transfected cells were adhered to CII and phosphoproteins analysed by Western blotting. Co-immunoprecipitation served to identify protein binding to ADAM15. Our results elucidate the prodomain as critical for the capacity of ADAM15 to enhance CII adhesion, thereby identifying for the first time a cell-adhesive role of a metalloproteinase prodomain. Moreover, the cytoplasmic tail of ADAM15 confers a modulatory effect on the autophosphorylation site Y397 of the focal adhesion kinase (FAK) during chondrocyte–collagen interaction. In conclusion, the newly uncovered impact of ADAM15 on signalling events that arise from chondrocyte interactions with its collagen matrix might contribute to the elucidation of the mechanism underlying its proposed chondroprotective role in degenerative cartilage disease

Critical Behavior of the Two-Dimensional Randomly Driven Lattice Gas

We investigate the critical behavior of the two-dimensional randomly driven lattice gas, in which particles are driven along one of the lattice axes by an infinite external field with randomly changing sign. A finite-size scaling (FSS) analysis provides novel evidences that this model is not in the same universality class as the driven lattice gas with a constant drive (DLG), contrarily to what has been recently reported in the literature. Indeed, the FSS functions of transverse observables (i.e., related to order-parameter fluctuations with wave vector perpendicular to the direction of the field) differ from the mean-field behavior predicted and observed within the DLG universality class. At variance with the DLG case, FSS is attained on lattices with fixed aspect ratio and anisotropy exponent equal to 1 and the transverse Binder cumulant does not vanish at the critical point.Comment: 4 pages, 4 figure

Promise and Pitfalls in the Use of 'Secondary' Data-Sets: Income Inequality in OECD Countries

Secondary data-sets have come to play an increasing role in empirical economic research. This paper examines the major new secondary data-set assembled by Klaus Deininger and Lyn Squire (DS) at the World Bank. We concentrate on its coverage of the OECD countries. We have particularly in mind the user of income inequality statistics who does not wish to go back to the original data. In order to motivate the analysis, we first present two examples of the problems which may arise, showing how both cross-country comparisons and time-series analysis may depend sensitively on the choice of data. Section 3 of the paper sets the DS data-set in the historical context of earlier exercises in assembling comparative information on income inequality. In Section 4, we consider the methodological issues which arise in the use of income distribution data and their relation to the different sources of evidence. In Section 5, we discuss their implications for the comparison of income inequality across OECD countries, and the use of dummy variables to allow for definitional and data differences. Section 6 is concerned with changes in income inequality over time, and the establishment of consistent series for individual countries. The lessons to be drawn for use of secondary data-sets in the field of income distribution are summarised at the end of the paper.personal income distribution, secondary data-sets

Characterization of radially symmetric finite time blowup in multidimensional aggregation equations,

This paper studies the transport of a mass $\mu$ in $\real^d, d \geq 2,$ by a flow field $v= -\nabla K*\mu$. We focus on kernels $K=|x|^\alpha/ \alpha$ for $2-d\leq \alpha<2$ for which the smooth densities are known to develop singularities in finite time. For this range This paper studies the transport of a mass $\mu$ in $\real^d, d \geq 2,$ by a flow field $v= -\nabla K*\mu$. We focus on kernels $K=|x|^\alpha/ \alpha$ for $2-d\leq \alpha<2$ for which the smooth densities are known to develop singularities in finite time. For this range we prove the existence for all time of radially symmetric measure solutions that are monotone decreasing as a function of the radius, thus allowing for continuation of the solution past the blowup time. The monotone constraint on the data is consistent with the typical blowup profiles observed in recent numerical studies of these singularities. We prove monotonicity is preserved for all time, even after blowup, in contrast to the case $\alpha >2$ where radially symmetric solutions are known to lose monotonicity. In the case of the Newtonian potential ($\alpha=2-d$), under the assumption of radial symmetry the equation can be transformed into the inviscid Burgers equation on a half line. This enables us to prove preservation of monotonicity using the classical theory of conservation laws. In the case $2 -d < \alpha < 2$ and at the critical exponent $p$ we exhibit initial data in $L^p$ for which the solution immediately develops a Dirac mass singularity. This extends recent work on the local ill-posedness of solutions at the critical exponent.Comment: 30 page

On analysing the world distribution of income

This paper argues that consideration of world inequality should cause us to re-examine the key concepts underlying the welfare approach to the measurement of income inequality and the inter-relation between the measurement of inequality and the measurement of poverty. There are three reasons why we feel that a re-examination is necessary: (i) the extent of global income differences means that we cannot simply carry over the methods used at a national level; we need a more flexible measure; (ii) we have to reconcile measures of world inequality and world poverty; and (iii) we need to explore more fully the different ways in which measures may be relative or absolute. This leads us to propose a new measure, which (a) combines poverty and inequality, including provision for those who are concerned only with poverty, (b) incorporates different approaches to the measurement of inequality; and (c) allows the cost of inequality to be expressed in different ways. Applied to the world distribution for the period 1820-1992, the new measure provides different perspectives on the evolution of global inequality.global income inequality, absolute vs. relative inequality, poverty, world citizens

Spin and magnetism in old neutron stars

The thermal, spin and magnetic evolution of neutron stars in the old low mass binaries is first explored. Recycled to very short periods via accretion torques, the neutron stars lose their magnetism progressively. If accretion proceeds undisturbed for 100 Myrs these stars can rotate close to break up with periods far below the minimum observed of 1.558 ms. We investigate their histories using population synthesis models to show that a tail should exist in the period distribution below 1.558 ms. The search of these ultrafastly spinning neutron stars as pulsars can help discriminating among the various equations of state for nuclear matter, and can shed light into the physics of binary evolution. The evolution of isolated neutron stars in the Galaxy is explored beyond the pulsar phase. Moving through the tenuous interstellar medium, these old solitary neutron stars lose their rotational energy. Whether also their magnetism fades is still a mystery. A population synthesis model has revealed that only a tiny fraction of them is able to accrete from the interstellar medium, shining in the X-rays. There is the hope that these solitary stars will eventually appear as faint sources in the Chandra sky survey. This might give insight on the long term evolution of the magnetic field in isolated objects.Comment: 28 pages, 11 PostScript figures. To be published in "Physics of Neutron Star Interiors" (Lecture Notes in Physics), ed. D. Blaschke, N.K. Glendenning and A. Sedrakian (Springer, 2001