Logical Dreams

We discuss the past and future of set theory, axiom systems and independence results. We deal in particular with cardinal arithmetic

Neuropilins 1 and 2 mediate neointimal hyperplasia and re-endothelialization following arterial injury

AIMS: Neuropilins 1 and 2 (NRP1 and NRP2) play crucial roles in endothelial cell migration contributing to angiogenesis and vascular development. Both NRPs are also expressed by cultured vascular smooth muscle cells (VSMCs) and are implicated in VSMC migration stimulated by PDGF-BB, but it is unknown whether NRPs are relevant for VSMC function in vivo. We investigated the role of NRPs in the rat carotid balloon injury model, in which endothelial denudation and arterial stretch induce neointimal hyperplasia involving VSMC migration and proliferation. METHODS AND RESULTS: NRP1 and NRP2 mRNAs and proteins increased significantly following arterial injury, and immunofluorescent staining revealed neointimal NRP expression. Down-regulation of NRP1 and NRP2 using shRNA significantly reduced neointimal hyperplasia following injury. Furthermore, inhibition of NRP1 by adenovirally overexpressing a loss-of-function NRP1 mutant lacking the cytoplasmic domain (ΔC) reduced neointimal hyperplasia, whereas wild-type (WT) NRP1 had no effect. NRP-targeted shRNAs impaired, while overexpression of NRP1 WT and NRP1 ΔC enhanced, arterial re-endothelialization 14 days after injury. Knockdown of either NRP1 or NRP2 inhibited PDGF-BB-induced rat VSMC migration, whereas knockdown of NRP2, but not NRP1, reduced proliferation of cultured rat VSMC and neointimal VSMC in vivo. NRP knockdown also reduced the phosphorylation of PDGFα and PDGFβ receptors in rat VSMC, which mediate VSMC migration and proliferation. CONCLUSION: NRP1 and NRP2 play important roles in the regulation of neointimal hyperplasia in vivo by modulating VSMC migration (via NRP1 and NRP2) and proliferation (via NRP2), independently of the role of NRPs in re-endothelialization

Analysis of MERCATOR data Part I: variable B stars

We re-classified 31 variable B stars which were observed more than 50 times in the Geneva photometric system with the P7 photometer attached to the MERCATOR telescope (La Palma) during its first 3 years of scientific observations. HD89688 is a possible beta Cephei/slowly pulsating B star hybrid and the main mode of the COROT target HD180642 shows non-linear effects. The Maia candidates are re-classified as either ellipsoidal variables or spotted stars. Although the mode identification is still ongoing, all the well-identified modes so far have a degree l = 0, 1 or 2.Comment: 4 pages, 3 figures. To appear in: Proceedings of JENAM 2005 'Distant worlds', Communications in Asteroseismolog

Critical Exponents of the N-vector model

Recently the series for two RG functions (corresponding to the anomalous dimensions of the fields phi and phi^2) of the 3D phi^4 field theory have been extended to next order (seven loops) by Murray and Nickel. We examine here the influence of these additional terms on the estimates of critical exponents of the N-vector model, using some new ideas in the context of the Borel summation techniques. The estimates have slightly changed, but remain within errors of the previous evaluation. Exponents like eta (related to the field anomalous dimension), which were poorly determined in the previous evaluation of Le Guillou--Zinn-Justin, have seen their apparent errors significantly decrease. More importantly, perhaps, summation errors are better determined. The change in exponents affects the recently determined ratios of amplitudes and we report the corresponding new values. Finally, because an error has been discovered in the last order of the published epsilon=4-d expansions (order epsilon^5), we have also reanalyzed the determination of exponents from the epsilon-expansion. The conclusion is that the general agreement between epsilon-expansion and 3D series has improved with respect to Le Guillou--Zinn-Justin.Comment: TeX Files, 27 pages +2 figures; Some values are changed; references update

A Class of Topological Actions

We review definitions of generalized parallel transports in terms of Cheeger-Simons differential characters. Integration formulae are given in terms of Deligne-Beilinson cohomology classes. These representations of parallel transport can be extended to situations involving distributions as is appropriate in the context of quantized fields.Comment: 41 pages, no figure

Inflation in Realistic D-Brane Models

We find successful models of D-brane/anti-brane inflation within a string context. We work within the GKP-KKLT class of type IIB string vacua for which many moduli are stabilized through fluxes, as recently modified to include `realistic' orbifold sectors containing standard-model type particles. We allow all moduli to roll when searching for inflationary solutions and find that inflation is not generic inasmuch as special choices must be made for the parameters describing the vacuum. But given these choices inflation can occur for a reasonably wide range of initial conditions for the brane and antibrane. We find that D-terms associated with the orbifold blowing-up modes play an important role in the inflationary dynamics. Since the models contain a standard-model-like sector after inflation, they open up the possibility of addressing reheating issues. We calculate predictions for the CMB temperature fluctuations and find that these can be consistent with observations, but are generically not deep within the scale-invariant regime and so can allow appreciable values for $dn_s/d\ln k$ as well as predicting a potentially observable gravity-wave signal. It is also possible to generate some admixture of isocurvature fluctuations.Comment: 39 pages, 21 figures; added references; identified parameters combining successful inflation with strong warping, as needed for consistency of the approximation

Racetrack Inflation

We develop a model of eternal topological inflation using a racetrack potential within the context of type IIB string theory with KKLT volume stabilization. The inflaton field is the imaginary part of the K\"ahler structure modulus, which is an axion-like field in the 4D effective field theory. This model does not require moving branes, and in this sense it is simpler than other models of string theory inflation. Contrary to single-exponential models, the structure of the potential in this example allows for the existence of saddle points between two degenerate local minima for which the slow-roll conditions can be satisfied in a particular range of parameter space. We conjecture that this type of inflation should be present in more general realizations of the modular landscape. We also consider `irrational' models having a dense set of minima, and discuss their possible relevance for the cosmological constant problem.Comment: 23 pages 7 figures. The final version with minor modifications, to appear in JHE

Chiral bosonization for non-commutative fields

A model of chiral bosons on a non-commutative field space is constructed and new generalized bosonization (fermionization) rules for these fields are given. The conformal structure of the theory is characterized by a level of the Kac-Moody algebra equal to $(1+ \theta^2)$ where $\theta$ is the non-commutativity parameter and chiral bosons living in a non-commutative fields space are described by a rational conformal field theory with the central charge of the Virasoro algebra equal to 1. The non-commutative chiral bosons are shown to correspond to a free fermion moving with a speed equal to $c^{\prime} = c \sqrt{1+\theta^2}$ where $c$ is the speed of light. Lorentz invariance remains intact if $c$ is rescaled by $c \to c^{\prime}$. The dispersion relation for bosons and fermions, in this case, is given by $\omega = c^{\prime} | k|$.Comment: 16 pages, JHEP style, version published in JHE

Equilibrium configurations of two charged masses in General Relativity

An asymptotically flat static solution of Einstein-Maxwell equations which describes the field of two non-extreme Reissner - Nordstr\"om sources in equilibrium is presented. It is expressed in terms of physical parameters of the sources (their masses, charges and separating distance). Very simple analytical forms were found for the solution as well as for the equilibrium condition which guarantees the absence of any struts on the symmetry axis. This condition shows that the equilibrium is not possible for two black holes or for two naked singularities. However, in the case when one of the sources is a black hole and another one is a naked singularity, the equilibrium is possible at some distance separating the sources. It is interesting that for appropriately chosen parameters even a Schwarzschild black hole together with a naked singularity can be "suspended" freely in the superposition of their fields.Comment: 4 pages; accepted for publication in Phys. Rev.

Gothic visions of classical architecture in Hablot Knight Browne’s “dark” illustrations for the novels of Charles Dickens

In the early gothic literature of the eighteenth century danger lurked in the darkness beneath the pointed arches of gothic buildings. During the nineteenth century there was a progressive, although never complete, dislocation of gothic literary readings from gothic architecture. This article explores a phase in that development through discussion of a series of ‘dark’ illustrations produced by Hablot Knight Browne to illustrate novels by Charles Dickens. These show the way in which the rounded arches of neo-classical architecture were depicted in the mid-nineteenth century as locales of oppression and obscurity. Such depictions acted, in an age of political and moral reform, to critique the values of the system of power and authority that such architecture represented