Complex bounds for multimodal maps: bounded combinatorics

We proved the so called complex bounds for multimodal, infinitely renormalizable analytic maps with bounded combinatorics: deep renormalizations have polynomial-like extensions with definite modulus. The complex bounds is the first step to extend the renormalization theory of unimodal maps to multimodal maps.Comment: 20 pages, 3 figure

Pattern Formation of Glioma Cells: Effects of Adhesion

We investigate clustering of malignant glioma cells. \emph{In vitro} experiments in collagen gels identified a cell line that formed clusters in a region of low cell density, whereas a very similar cell line (which lacks an important mutation) did not cluster significantly. We hypothesize that the mutation affects the strength of cell-cell adhesion. We investigate this effect in a new experiment, which follows the clustering dynamics of glioma cells on a surface. We interpret our results in terms of a stochastic model and identify two mechanisms of clustering. First, there is a critical value of the strength of adhesion; above the threshold, large clusters grow from a homogeneous suspension of cells; below it, the system remains homogeneous, similarly to the ordinary phase separation. Second, when cells form a cluster, we have evidence that they increase their proliferation rate. We have successfully reproduced the experimental findings and found that both mechanisms are crucial for cluster formation and growth.Comment: 6 pages, 6 figure

Natural equilibrium states for multimodal maps

This paper is devoted to the study of the thermodynamic formalism for a class of real multimodal maps. This class contains, but it is larger than, Collet-Eckmann. For a map in this class, we prove existence and uniqueness of equilibrium states for the geometric potentials $-t \log|Df|$, for the largest possible interval of parameters $t$. We also study the regularity and convexity properties of the pressure function, completely characterising the first order phase transitions. Results concerning the existence of absolutely continuous invariant measures with respect to the Lebesgue measure are also obtained

Effective supergravity descriptions of superstring cosmology

This text is a review of aspects of supergravity theories that are relevant in superstring cosmology. In particular, it considers the possibilities and restrictions for `uplifting terms', i.e. methods to produce de Sitter vacua. We concentrate on N=1 and N=2 supergravities, and the tools of superconformal methods, which clarify the structure of these theories. Cosmic strings and embeddings of target manifolds of supergravity theories in others are discussed in short at the end.Comment: 12 pages, contribution to the proceedings of the 2nd international conference on Quantum Theories and Renormalization Group in Gravity and Cosmology, Barcelona, July 11-15, 2006, Journal of Physics

Supersymmetric Higher Spin Theories

We revisit the higher spin extensions of the anti de Sitter algebra in four dimensions that incorporate internal symmetries and admit representations that contain fermions, classified long ago by Konstein and Vasiliev. We construct the $dS_4$, Euclidean and Kleinian version of these algebras, as well as the corresponding fully nonlinear Vasiliev type higher spin theories, in which the reality conditions we impose on the master fields play a crucial role. The ${\cal N}=2$ supersymmetric higher spin theory in $dS_4$, on which we elaborate further, is included in this class of models. A subset of Konstein-Vasiliev algebras are the higher spin extensions of the $AdS_4$ superalgebras $osp(4|{\cal N})$ for ${\cal N}=1,2,4$ mod 4 and can be realized using fermionic oscillators. We tensor the higher superalgebras of the latter kind with appropriate internal symmetry groups and show that the ${\cal N}=3$ mod 4 higher spin algebras are isomorphic to those with ${\cal N}=4$ mod 4. We describe the fully nonlinear higher spin theories based on these algebras as well, and we elaborate further on the ${\cal N}=6$ supersymmetric theory, providing two equivalent descriptions one of which exhibits manifestly its relation to the ${\cal N}=8$ supersymmetric higher spin theory.Comment: 30 pages. Contribution to J. Phys. A special volume on "Higher Spin Theories and AdS/CFT" edited by M. R. Gaberdiel and M. Vasilie

Polynomial super-gl(n) algebras

We introduce a class of finite dimensional nonlinear superalgebras $L = L_{\bar{0}} + L_{\bar{1}}$ providing gradings of $L_{\bar{0}} = gl(n) \simeq sl(n) + gl(1)$. Odd generators close by anticommutation on polynomials (of degree $>1$) in the $gl(n)$ generators. Specifically, we investigate `type I' super-$gl(n)$ algebras, having odd generators transforming in a single irreducible representation of $gl(n)$ together with its contragredient. Admissible structure constants are discussed in terms of available $gl(n)$ couplings, and various special cases and candidate superalgebras are identified and exemplified via concrete oscillator constructions. For the case of the $n$-dimensional defining representation, with odd generators $Q_{a}, \bar{Q}{}^{b}$, and even generators ${E^{a}}_{b}$, $a,b = 1,...,n$, a three parameter family of quadratic super-$gl(n)$ algebras (deformations of $sl(n/1)$) is defined. In general, additional covariant Serre-type conditions are imposed, in order that the Jacobi identities be fulfilled. For these quadratic super-$gl(n)$ algebras, the construction of Kac modules, and conditions for atypicality, are briefly considered. Applications in quantum field theory, including Hamiltonian lattice QCD and space-time supersymmetry, are discussed.Comment: 31 pages, LaTeX, including minor corrections to equation (3) and reference [60

Search for non-relativistic Magnetic Monopoles with IceCube

The IceCube Neutrino Observatory is a large Cherenkov detector instrumenting $1\,\mathrm{km}^3$ of Antarctic ice. The detector can be used to search for signatures of particle physics beyond the Standard Model. Here, we describe the search for non-relativistic, magnetic monopoles as remnants of the GUT (Grand Unified Theory) era shortly after the Big Bang. These monopoles may catalyze the decay of nucleons via the Rubakov-Callan effect with a cross section suggested to be in the range of $10^{-27}\,\mathrm{cm^2}$ to $10^{-21}\,\mathrm{cm^2}$. In IceCube, the Cherenkov light from nucleon decays along the monopole trajectory would produce a characteristic hit pattern. This paper presents the results of an analysis of first data taken from May 2011 until May 2012 with a dedicated slow-particle trigger for DeepCore, a subdetector of IceCube. A second analysis provides better sensitivity for the brightest non-relativistic monopoles using data taken from May 2009 until May 2010. In both analyses no monopole signal was observed. For catalysis cross sections of $10^{-22}\,(10^{-24})\,\mathrm{cm^2}$ the flux of non-relativistic GUT monopoles is constrained up to a level of $\Phi_{90} \le 10^{-18}\,(10^{-17})\,\mathrm{cm^{-2}s^{-1}sr^{-1}}$ at a 90% confidence level, which is three orders of magnitude below the Parker bound. The limits assume a dominant decay of the proton into a positron and a neutral pion. These results improve the current best experimental limits by one to two orders of magnitude, for a wide range of assumed speeds and catalysis cross sections.Comment: 20 pages, 20 figure

Search for Relativistic Magnetic Monopoles with IceCube

We present the first results in the search for relativistic magnetic monopoles with the IceCube detector, a subsurface neutrino telescope located in the South Polar ice cap containing a volume of 1 km$^{3}$. This analysis searches data taken on the partially completed detector during 2007 when roughly 0.2 km$^{3}$ of ice was instrumented. The lack of candidate events leads to an upper limit on the flux of relativistic magnetic monopoles of \Phi_{\mathrm{90%C.L.}}\sim 3\e{-18}\fluxunits for $\beta\geq0.8$. This is a factor of 4 improvement over the previous best experimental flux limits up to a Lorentz boost $\gamma$ below $10^{7}$. This result is then interpreted for a wide range of mass and kinetic energy values.Comment: 11 pages, 11 figures. v2 is minor text edits, no changes to resul