A general tool for consistency results related to I1

In this paper we provide a general tool to prove the consistency of $I1(\lambda)$ with various combinatorial properties at $\lambda$ typical at settings with $2^\lambda>\lambda^+$, that does not need a profound knowledge of the forcing notions involved. Examples of such properties are the first failure of GCH, a very good scale and the negation of the approachability property, or the tree property at $\lambda^+$ and $\lambda^{++}$

On the Third Critical Speed for Rotating Bose-Einstein Condensates

We study a two-dimensional rotating Bose-Einstein condensate confined by an anharmonic trap in the framework of the Gross-Pitaevksii theory. We consider a rapid rotation regime close to the transition to a giant vortex state. It was proven in [M. Correggi {\it et al}, {\it J. Math. Phys. \textbf{53}(2012)] that such a transition occurs when the angular velocity is of order $\varepsilon ^{-4}$, with $\varepsilon ^{-2}$ denoting the coefficient of the nonlinear term in the Gross-Pitaevskii functional and $\varepsilon \ll 1$ (Thomas-Fermi regime). In this paper we identify a finite value $\Omega_{\mathrm{c}}$ such that, if $\Omega = \Omega_0/\varepsilon ^4$ with $\Omega_0 > \Omega_{\mathrm{c}}$, the condensate is in the giant vortex phase. Under the same condition we prove a refined energy asymptotics and an estimate of the winding number of any Gross-Pitaevskii minimizer.Comment: pdfLaTeX, 39 pages, minor changes, to appear in J. Math. Phy

I0 and rank-into-rank axioms

This is a survey about I0 and rank-into-rank axioms, with some previously unpublished proofs

Totally non-proper ordinals beyond L(V \u3bb+1)

In recent work Woodin has defined new axioms stronger than I0 (the existence of an elementary embedding j from L(V\u3bb+1) to itself), that involve elementary embeddings between slightly larger models. There is a natural correspondence between I0 and determinacy, but to extend this correspondence in this new framework we must insist that these elementary embeddings are proper. While at first this seemed to be a common property, in this paper will be provided a model in which all such elementary embeddings are not proper. This result fills a gap in a theorem by Woodin and justifies the definition of propernes

Origin of the 2009 Mexico influenza virus: a comparative phylogenetic analysis of the principal external antigens and matrix protein

Triple-reassortant swine influenza A (H1) viruses, containing genes from avian, human, and swine influenza viruses, emerged and became an outbreak among humans worldwide. Over a 1,000 cases were identified within the first month, chiefly in Mexico and the United States. Here, the phylogenetic analysis of haemagglutin (HA), neuraminidase (NA), and matrix protein (MP) was carried out. The analysis showed that the H1 of this reassortant originated from American pigs, while NA and MP were more likely from European pigs. All of the 2009 isolates appear homogeneous and cluster together, although they are distinct from classical human A (H1N1) viruses

Rank-into-rank hypotheses and the failure of GCH

In this paper we are concerned about the ways GCH can fail in relation to rank-into-rank hypotheses, i.e., very large cardinals usually denoted by I3, I2, I1 and I0. The main results are a satisfactory analysis of the way the power function can vary on regular cardinals in the presence of rank-into-rank hypotheses and the consistency under I0 of the existence of j:V\u3bb+1 7aV\u3bb+1 with the failure of GCH at \u3bb

Selected amino acid changes in HIV-1 subtype-C gp41 are associated with specific gp120(V3) signatures in the regulation of co-receptor usage

The majority of studies have characterized the tropism of HIV-1 subtype-B isolates, but little is known about the determinants of tropism in other subtypes. So, the goal of the present study was to genetically characterize the envelope of viral proteins in terms of co-receptor usage by analyzing 356 full-length env sequences derived from HIV-1 subtype-C infected individuals. The co-receptor usage of V3 sequences was inferred by using the Geno2Pheno and PSSM algorithms, and also analyzed to the "11/25 rule". All reported env sequences were also analyzed with regard to N-linked glycosylation sites, net charge and hydrophilicity, as well as the binomial correlation phi coefficient to assess covariation among gp120(V3) and gp41 signatures and the average linkage hierarchical agglomerative clustering were also performed. Among env sequences present in Los Alamos Database, 255 and 101 sequences predicted as CCR5 and CXCR4 were selected, respectively. The classical V3 signatures at positions 11 and 25, and other specific V3 and gp41 amino acid changes were found statistically associated with different co-receptor usage. Furthermore, several statistically significant associations between V3 and gp41 signatures were also observed. The dendrogram topology showed a cluster associated with CCR5-usage composed by five gp41 mutated positions, A22V, R133M, E136G, N140L, and N166Q that clustered with T2V(V3) and G24T(V3) (bootstrap=1). Conversely, a heterogeneous cluster with CXCR4-usage, involving S11GR(V3), 13-14insIG/LG(V3), P16RQ(V3), Q18KR(V3), F20ILV(V3), D25KRQ(V3), Q32KR(V3) along with A30T(gp41), S107N(gp41), D148E(gp41), A189S(gp41) was identified (bootstrap=0.86). Our results show that as observed for HIV-1 subtype-B, also in subtype-C specific and different gp41 and gp120V3 amino acid changes are associated individually or together with CXCR4 and/or CCR5 usage. These findings strengthen previous observations that determinants of tropism may also reside in the gp41 protein

The Dynamics of Rayleigh-Taylor Stable and Unstable Contact Discontinuities with Anisotropic Thermal Conduction

We study the effects of anisotropic thermal conduction along magnetic field lines on an accelerated contact discontinuity in a weakly collisional plasma. We first perform a linear stability analysis similar to that used to derive the Rayleigh-Taylor instability (RTI) dispersion relation. We find that anisotropic conduction is only important for compressible modes, as incompressible modes are isothermal. Modes grow faster in the presence of anisotropic conduction, but growth rates do not change by more than a factor of order unity. We next run fully non-linear numerical simulations of a contact discontinuity with anisotropic conduction. The non-linear evolution can be thought of as a superposition of three physical effects: temperature diffusion due to vertical conduction, the RTI, and the heat flux driven buoyancy instability (HBI). In simulations with RTI-stable contact discontinuities, the temperature discontinuity spreads due to vertical heat conduction. This occurs even for initially horizontal magnetic fields due to the initial vertical velocity perturbation and numerical mixing across the interface. The HBI slows this temperature diffusion by reorienting initially vertical magnetic field lines to a more horizontal geometry. In simulations with RTI-unstable contact discontinuities, the dynamics are initially governed by temperature diffusion, but the RTI becomes increasingly important at late times. We discuss the possible application of these results to supernova remnants, solar prominences, and cold fronts in galaxy clusters.Comment: 18 pages, 15 figures, submitted to MNRA