The Free Energy of the Quantum Heisenberg Ferromagnet at Large Spin

We consider the spin-S ferromagnetic Heisenberg model in three dimensions, in the absence of an external field. Spin wave theory suggests that in a suitable temperature regime the system behaves effectively as a system of non-interacting bosons (magnons). We prove this fact at the level of the specific free energy: if $S \to \infty$ and the inverse temperature $\beta \to 0$ in such a way that $\beta S$ stays constant, we rigorously show that the free energy per unit volume converges to the one suggested by spin wave theory. The proof is based on the localization of the system in small boxes and on upper and lower bounds on the local free energy, and it also provides explicit error bounds on the remainder.Comment: 11 pages, pdfLate

Phenomenology of GUT-less Supersymmetry Breaking

We study models in which supersymmetry breaking appears at an intermediate scale, M_{in}, below the GUT scale. We assume that the soft supersymmetry-breaking parameters of the MSSM are universal at M_{in}, and analyze the morphology of the constraints from cosmology and collider experiments on the allowed regions of parameter space as M_{in} is reduced from the GUT scale. We present separate analyses of the (m_{1/2},m_0) planes for tan(beta)=10 and tan(beta)=50, as well as a discussion of non-zero trilinear couplings, A_0. Specific scenarios where the gaugino and scalar masses appear to be universal below the GUT scale have been found in mirage-mediation models, which we also address here. We demand that the lightest neutralino be the LSP, and that the relic neutralino density not conflict with measurements by WMAP and other observations. At moderate values of M_{in}, we find that the allowed regions of the (m_{1/2},m_0) plane are squeezed by the requirements of electroweak symmetry breaking and that the lightest neutralino be the LSP, whereas the constraint on the relic density is less severe. At very low M_{in}, the electroweak vacuum conditions become the dominant constraint, and a secondary source of astrophysical cold dark matter would be necessary to explain the measured relic density for nearly all values of the soft SUSY-breaking parameters and tan(beta). We calculate the neutralino-nucleon cross sections for viable scenarios and compare them with the present and projected limits from direct dark matter searches.Comment: 35 pages, 9 figures; typos corrected, references adde

Prostate cancer and Hedgehog signalling pathway

[Abstract] The Hedgehog (Hh) family of intercellular signalling proteins have come to be recognised as key mediators in many fundamental processes in embryonic development. Their activities are central to the growth, patterning and morphogenesis of many different regions within the bodies of vertebrates. In some contexts, Hh signals act as morphogens in the dose-dependent induction of distinct cell fates within a target field, in others as mitogens in the regulation of cell proliferation or as inducing factors controlling the form of a developing organ. These diverse functions of Hh proteins raise many intriguing questions about their mode of action. Various studies have now demonstrated the function of Hh signalling in the control of cell proliferation, especially for stem cells and stem-like progenitors. Abnormal activation of the Hh pathway has been demonstrated in a variety of human tumours. Hh pathway activity in these tumours is required for cancer cell proliferation and tumour growth. Recent studies have uncovered the role for Hh signalling in advanced prostate cancer and demonstrated that autocrine signalling by tumour cells is required for proliferation, viability and invasive behaviour. Thus, Hh signalling represents a novel pathway in prostate cancer that offers opportunities for prognostic biomarker development, drug targeting and therapeutic response monitoring

Evidence from peptidomic analysis of skin secretions that allopatric populations of Xenopus gilli (Anura: Pipidae) constitute distinct lineages

The International Union for Conservation of Nature (IUCN) Endangered Cape Platanna Xenopus gilli inhabits disjunct ranges at the tip of Cape Peninsula and near the town of Kleinmond on opposite sides of False Bay in the extreme southwest of Africa. Peptidomic analysis of host-defense peptides in norepinephrine-stimulated skin secretions from frogs from the Cape Peninsula range resulted in the identification of two magainins, two peptide glycine–leucine–amide (PGLa) peptides, two xenopsin-precursor fragment(XPF) peptides, nine caerulein-precursor fragment (CPF) peptides, and a peptide related to peptideglycine–glutamine (PGQ) previously found in an extract of Xenopus laevis stomach. The primary struc-tures of the peptides indicate a close phylogenetic relationship between X. gilli and X. laevis but onlymagainin-1, PGLa and one CPF peptide are identical in both species. Consistent with previous data, the CPF peptides show the greatest antimicrobial potency but are hemolytic. There are appreciable differences in the expression of host-defense peptide genes in frogs from the population of animals sampled near Kleinmond as peptides corresponding to magainin-G2, XPF-G1, XPF-G2, and four CPF peptides, present in secretions from the Cape Peninsula frogs, were not identified in the skin secretions from Kleinmond frogs. Conversely, PGLa-G3, XPF-G3, and three CPF peptides were identified in the Kleinmond frogs but not in the Cape Peninsula animals. The data support the conclusion from morphometric analyses and comparisons of the nucleotide sequences of mitochondrial genes that the disjunct populations of X. gilli have undergone appreciable genetic, morphological, and phenotypic divergence