Global square and mutual stationarity at the ℵn

AbstractWe give the proof of a theorem of Jensen and Zeman on the existence of a global □ sequence in the Core Model below a measurable cardinal κ of Mitchell order (oM(κ)) equal to κ++, and use it to prove the following theorem on mutual stationarity at ℵn.Let ω1 denote the first uncountable cardinal of V and set Cof(ω1) to be the class of ordinals of cofinality ω1. TheoremIf every sequence (Sn)n<ω of stationary sets Sn⊆Cof(ω1)∩ℵn+2, is mutually stationary, then there is an inner model with infinitely many inaccessibles (κn)n<ω so that for every mthe class of measurables λ with oM(λ)≥κm is, in V, stationary in κn for all n>m. In particular, there is such a model in which for all sufficiently large m<ω, the class of measurables λ with oM(λ)≥ωm is, in V, stationary below ℵm+2

Unitary designs and codes

A unitary design is a collection of unitary matrices that approximate the entire unitary group, much like a spherical design approximates the entire unit sphere. In this paper, we use irreducible representations of the unitary group to find a general lower bound on the size of a unitary t-design in U(d), for any d and t. We also introduce the notion of a unitary code - a subset of U(d) in which the trace inner product of any pair of matrices is restricted to only a small number of distinct values - and give an upper bound for the size of a code of degree s in U(d) for any d and s. These bounds can be strengthened when the particular inner product values that occur in the code or design are known. Finally, we describe some constructions of designs: we give an upper bound on the size of the smallest weighted unitary t-design in U(d), and we catalogue some t-designs that arise from finite groups.Comment: 25 pages, no figure

A molecular dynamics simulation of polymer crystallization from oriented amorphous state

Molecular process of crystallization from an oriented amorphous state was reproduced by molecular dynamics simulation for a realistic polyethylene model. Initial oriented amorphous state was obtained by uniaxial drawing an isotropic glassy state at 100 K. By the temperature jump from 100 K to 330 K, there occurred the crystallization into the fiber structure, during the process of which we observed the developments of various order parameters. The real space image and its Fourier transform revealed that a hexagonally ordered domain was initially formed, and then highly ordered crystalline state with stacked lamellae developed after further adjustment of the relative heights of the chains along their axes.Comment: 4 pages, 3 figure

Shear-banding in a lyotropic lamellar phase, Part 1: Time-averaged velocity profiles

Using velocity profile measurements based on dynamic light scattering and coupled to structural and rheological measurements in a Couette cell, we present evidences for a shear-banding scenario in the shear flow of the onion texture of a lyotropic lamellar phase. Time-averaged measurements clearly show the presence of structural shear-banding in the vicinity of a shear-induced transition, associated to the nucleation and growth of a highly sheared band in the flow. Our experiments also reveal the presence of slip at the walls of the Couette cell. Using a simple mechanical approach, we demonstrate that our data confirms the classical assumption of the shear-banding picture, in which the interface between bands lies at a given stress $\sigma^\star$. We also outline the presence of large temporal fluctuations of the flow field, which are the subject of the second part of this paper [Salmon {\it et al.}, submitted to Phys. Rev. E]

Curved Tails in Polymerization-Based Bacterial Motility

The curved actin ``comet-tail'' of the bacterium Listeria monocytogenes is a visually striking signature of actin polymerization-based motility. Similar actin tails are associated with Shigella flexneri, spotted-fever Rickettsiae, the Vaccinia virus, and vesicles and microspheres in related in vitro systems. We show that the torque required to produce the curvature in the tail can arise from randomly placed actin filaments pushing the bacterium or particle. We find that the curvature magnitude determines the number of actively pushing filaments, independent of viscosity and of the molecular details of force generation. The variation of the curvature with time can be used to infer the dynamics of actin filaments at the bacterial surface.Comment: 8 pages, 2 figures, Latex2

The influence of the spatial frequency content of discrete roughness distributions on the development of the crossflow instability

An experimental investigation on the influence of the spatial frequency content of roughness distributions on the development of crossflow instabilities has been carried out. From previous research it is known that micro roughness elements can have a large influence on the crossflow development. When the spanwise spacing is chosen such that it is the most unstable wavelength (following linear stability analysis), stationary crossflow waves are amplified. While in earlier studies the focus was on the height or spanwise spacing of roughness elements, in the present study it is chosen to vary the shape of the elements. Through the modification of the shape the forcing at the critical wavelength is increased, while the forcing at the harmonics of the critical wavelength is damped. Experiments were carried in the low turbulence wind tunnel at City University London (Tu=0.006%) on a swept flat plate in combination with displacement bodies to create a sufficiently strong favourable pressure gradient. Hot wire measurements across the plate tracked the development of stationary and travelling crossflow waves. Initially, stronger crossflow waves were found for the elements with stronger forcing, while further downstream the effect of forcing diminished. Spatial frequency spectra showed that the stronger forcing at the critical wavelength (via the roughness shape) dominates the response of the flow while low forcing at the harmonics has no notable effect. Additionally, high resolution streamwise hot wire scans showed that the onset of secondary instability is not significantly influenced by the spatial frequency content of the roughness distribution

A proof of the Geroch-Horowitz-Penrose formulation of the strong cosmic censor conjecture motivated by computability theory

In this paper we present a proof of a mathematical version of the strong cosmic censor conjecture attributed to Geroch-Horowitz and Penrose but formulated explicitly by Wald. The proof is based on the existence of future-inextendible causal curves in causal pasts of events on the future Cauchy horizon in a non-globally hyperbolic space-time. By examining explicit non-globally hyperbolic space-times we find that in case of several physically relevant solutions these future-inextendible curves have in fact infinite length. This way we recognize a close relationship between asymptotically flat or anti-de Sitter, physically relevant extendible space-times and the so-called Malament-Hogarth space-times which play a central role in recent investigations in the theory of "gravitational computers". This motivates us to exhibit a more sharp, more geometric formulation of the strong cosmic censor conjecture, namely "all physically relevant, asymptotically flat or anti-de Sitter but non-globally hyperbolic space-times are Malament-Hogarth ones". Our observations may indicate a natural but hidden connection between the strong cosmic censorship scenario and the Church-Turing thesis revealing an unexpected conceptual depth beneath both conjectures.Comment: 16pp, LaTeX, no figures. Final published versio

First genotype-phenotype study in TBX4 syndrome : gain-of-function mutations causative for lung disease

Rationale: Despite the increased recognition of TBX4-associated pulmonary arterial hypertension (PAH), genotype-phenotype associations are lacking and may provide important insights. Methods: We assembled a multi-center cohort of 137 patients harboring monoallelic TBX4 variants and assessed the pathogenicity of missense variation (n = 42) using a novel luciferase reporter assay containing T-BOX binding motifs. We sought genotype-phenotype correlations and undertook a comparative analysis with PAH patients with BMPR2 causal variants (n = 162) or no identified variants in PAH-associated genes (n = 741) genotyped via the NIHR BioResource - Rare Diseases (NBR). Results: Functional assessment of TBX4 missense variants led to the novel finding of gain-of-function effects associated with older age at diagnosis of lung disease compared to loss-of-function (p = 0.038). Variants located in the T-BOX and nuclear localization domains were associated with earlier presentation (p = 0.005) and increased incidence of interstitial lung disease (p = 0.003). Event-free survival (death or transplantation) was shorter in the T-BOX group (p = 0.022) although age had a significant effect in the hazard model (p = 0.0461). Carriers of TBX4 variants were diagnosed at a younger age (p < 0.001) and had worse baseline lung function (FEV1, FVC) (p = 0.009) compared to the BMPR2 and no identified causal variant groups. Conclusions: We demonstrated that TBX4 syndrome is not strictly the result of haploinsufficiency but can also be caused by gain-of-function. The pleiotropic effects of TBX4 in lung disease may be in part explained by the differential effect of pathogenic mutations located in critical protein domains