On Time-dependent Collapsing Branes and Fuzzy Odd-dimensional Spheres

We study the time-dependent dynamics of a collection of N collapsing/expanding D0-branes in type IIA String Theory. We show that the fuzzy-S^3 and S^5 provide time-dependent solutions to the Matrix Model of D0-branes and its DBI generalisation. Some intriguing cancellations in the calculation of the non-abelian DBI Matrix actions result in the fuzzy-S^3 and S^5 having the same dynamics at large-N. For the Matrix model, we find analytic solutions describing the time-dependent radius, in terms of Jacobi elliptic functions. Investigation of the physical properties of these configurations shows that there are no bounces for the trajectory of the collapse at large-N. We also write down a set of useful identities for fuzzy-S^3, fuzzy-S^5 and general fuzzy odd-spheres.Comment: 35 pages, latex; v2: discussion in Appendix B on the large-N limit of the associator is modified, main results of paper unchange

On the charge density and asymptotic tail of a monopole

We propose a new definition for the abelian magnetic charge density of a nonabelian monopole, based on zero-modes of an associated Dirac operator. Unlike the standard definition of the charge density, this density is smooth in the core of the monopole. We show that this charge density induces a magnetic field whose expansion in powers of 1=r agrees with that of the conventional asymptotic magnetic field to all orders. We also show that the asymptotic field can be easily calculated from the spectral curve. Explicit examples are given for known monopole solutions

Carbonic anhydrase XII is a marker of good prognosis in invasive breast carcinoma

Hypoxia and pH influence gene expression in tumours, and it is becoming increasingly clear that the pattern of genes expressed by a tumour determines its growth and survival characteristics. Hypoxia-inducible factor-1 (HIF-1) is a key mediator of the cellular response to hypoxia and high HIF-1 expression has been identified as a poor prognostic factor in tumours. Recently, we identified the tumour-associated carbonic anhydrases (CA), CA9 and CA12 as hypoxia-inducible in tumour cell lines. Furthermore, we identified CA IX to be a poor prognostic factor in breast cancer. The aim of this study was to assess the prognostic significance of CA XII. CA XII expression was studied by immunohistochemistry in a series of 103 cases of invasive breast cancer and any association with recognised prognostic factors or relation with the outcome was examined. CA XII expression was present in 77 out of 103 (75%) cases and was associated with lower grade (P=0.001), positive estrogen receptor status (P<0.001), and negative epidermal growth factor receptor status (P<0.001). Furthermore, although CA XII expression was associated with an absence of necrosis (P<0.001), expression of CA XII in some high-grade tumours was induced in regions directly adjacent to morphological necrosis. Additionally, using univariate analysis, CA XII positive tumours were associated with a lower relapse rate (P=0.04) and a better overall survival (P=0.01). In conclusion, CA XII expression is influenced both by factors related to differentiation and hypoxia in breast cancer in vivo and CA XII expression is associated with a better prognosis in an unselected series of invasive breast carcinoma patients

QCD thermodynamics with continuum extrapolated Wilson fermions I

QCD thermodynamics is considered using Wilson fermions in the fixed scale approach. The temperature dependence of the renormalized chiral condensate, quark number susceptibility and Polyakov loop is measured at four lattice spacings allowing for a controlled continuum limit. The light quark masses are fixed to heavier than physical values in this first study. Finite volume effects are ensured to be negligible by using approriately large box sizes. The final continuum results are compared with staggered fermion simulations performed in the fixed N-t approach. The same continuum renormalization conditions are used in both approaches and the final results agree perfectly