Uncomputably noisy ergodic limits

V'yugin has shown that there are a computable shift-invariant measure on Cantor space and a simple function f such that there is no computable bound on the rate of convergence of the ergodic averages A_n f. Here it is shown that in fact one can construct an example with the property that there is no computable bound on the complexity of the limit; that is, there is no computable bound on how complex a simple function needs to be to approximate the limit to within a given epsilon

Isotopic dependence of the giant monopole resonance in the even-A ^{112-124}Sn isotopes and the asymmetry term in nuclear incompressibility

The strength distributions of the giant monopole resonance (GMR) have been measured in the even-A Sn isotopes (A=112--124) with inelastic scattering of 400-MeV $\alpha$ particles in the angular range $0^\circ$--$8.5^\circ$. We find that the experimentally-observed GMR energies of the Sn isotopes are lower than the values predicted by theoretical calculations that reproduce the GMR energies in $^{208}$Pb and $^{90}$Zr very well. From the GMR data, a value of $K_{\tau} = -550 \pm 100$ MeV is obtained for the asymmetry-term in the nuclear incompressibility.Comment: Submitted to Physical Review Letters. 10 pages; 4 figure

Complete integrability of derivative nonlinear Schr\"{o}dinger-type equations

We study matrix generalizations of derivative nonlinear Schr\"{o}dinger-type equations, which were shown by Olver and Sokolov to possess a higher symmetry. We prove that two of them are `C-integrable' and the rest of them are `S-integrable' in Calogero's terminology.Comment: 14 pages, LaTeX2e (IOP style), to appear in Inverse Problem

Pre-M Phase-promoting Factor Associates with Annulate Lamellae in Xenopus Oocytes and Egg Extracts

We have used complementary biochemical and in vivo approaches to study the compartmentalization of M phase-promoting factor (MPF) in prophase Xenopus eggs and oocytes. We first examined the distribution of MPF (Cdc2/CyclinB2) and membranous organelles in high-speed extracts of Xenopus eggs made during mitotic prophase. These extracts were found to lack mitochondria, Golgi membranes, and most endoplasmic reticulum (ER) but to contain the bulk of the pre-MPF pool. This pre-MPF could be pelleted by further centrifugation along with components necessary to activate it. On activation, Cdc2/CyclinB2 moved into the soluble fraction. Electron microscopy and Western blot analysis showed that the pre-MPF pellet contained a specific ER subdomain comprising "annulate lamellae" (AL): stacked ER membranes highly enriched in nuclear pores. Colocalization of pre-MPF with AL was demonstrated by anti-CyclinB2 immunofluorescence in prophase oocytes, in which AL are positioned close to the vegetal surface. Green fluorescent protein-CyclinB2 expressed in oocytes also localized at AL. These data suggest that inactive MPF associates with nuclear envelope components just before activation. This association may explain why nuclei and centrosomes stimulate MPF activation and provide a mechanism for targeting of MPF to some of its key substrates

Unquenched flavor and tropical geometry in strongly coupled Chern-Simons-matter theories

We study various aspects of the matrix models calculating free energies and Wilson loop observables in supersymmetric Chern-Simons-matter theories on the three-sphere. We first develop techniques to extract strong coupling results directly from the spectral curve describing the large N master field. We show that the strong coupling limit of the gauge theory corresponds to the so-called tropical limit of the spectral curve. In this limit, the curve degenerates to a planar graph, and matrix model calculations reduce to elementary line integrals along the graph. As an important physical application of these tropical techniques, we study N=3 theories with fundamental matter, both in the quenched and in the unquenched regimes. We calculate the exact spectral curve in the Veneziano limit, and we evaluate the planar free energy and Wilson loop observables at strong coupling by using tropical geometry. The results are in agreement with the predictions of the AdS duals involving tri-Sasakian manifoldsComment: 32 pages, 7 figures. v2: small corrections, added an Appendix on the relation with the approach of 1011.5487. v3: further corrections and clarifications, final version to appear in JHE

Anyonic behavior of quantum group gases

We first introduce and discuss the formalism of $SU_q(N)$-bosons and fermions and consider the simplest Hamiltonian involving these operators. We then calculate the grand partition function for these models and study the high temperature (low density) case of the corresponding gases for $N=2$. We show that quantum group gases exhibit anyonic behavior in $D=2$ and $D=3$ spatial dimensions. In particular, for a $SU_q(2)$ boson gas at $D=2$ the parameter $q$ interpolates within a wider range of attractive and repulsive systems than the anyon statistical parameter.Comment: LaTeX file, 19 pages, two figures ,uses epsf.st