Extensile actomyosin?

Living cells move thanks to assemblies of actin filaments and myosin motors that range from very organized striated muscle tissue to disordered intracellular bundles. The mechanisms powering these disordered structures are debated, and all models studied so far predict that they are contractile. We reexamine this prediction through a theoretical treatment of the interplay of three well-characterized internal dynamical processes in actomyosin bundles: actin treadmilling, the attachement-detachment dynamics of myosin and that of crosslinking proteins. We show that these processes enable an extensive control of the bundle's active mechanics, including reversals of the filaments' apparent velocities and the possibility of generating extension instead of contraction. These effects offer a new perspective on well-studied in vivo systems, as well as a robust criterion to experimentally elucidate the underpinnings of actomyosin activity.Comment: 5 pages, 5 figure

Singular spectrum of Lebesgue measure zero for one-dimensional quasicrystals

The spectrum of one-dimensional discrete Schr\"odinger operators associated to strictly ergodic dynamical systems is shown to coincide with the set of zeros of the Lyapunov exponent if and only if the Lyapunov exponent exists uniformly. This is used to obtain Cantor spectrum of zero Lebesgue measure for all aperiodic subshifts with uniform positive weights. This covers, in particular, all aperiodic subshifts arising from primitive substitutions including new examples as e.g. the Rudin-Shapiro substitution. Our investigation is not based on trace maps. Instead it relies on an Oseledec type theorem due to A. Furman and a uniform ergodic theorem due to the author.Comment: 14 page

Homotopy (Pre-)Derivators of Cofibration Categories and Quasi-Categories

We prove that the homotopy prederivator of a cofibration category is equivalent to the homotopy prederivator of its associated quasi-category of frames, as introduced by Szumi\l{}o. We use this comparison result to deduce various abstract properties of the obtained prederivators.Comment: Final version, incorporating suggestions by referee. Accepted for publication in Algebraic & Geometric Topolog

Theoretical status of the lifetime predictions: (ΔΓ/Γ)Bs,τB+/τBd(\Delta \Gamma/ \Gamma)_{B_s}, \tau_{B^+}/\tau_{B_d} and τΛb/τBd\tau_{\Lambda_b}/\tau_{B_d}

We give a review of the theoretical status of the lifetime predictions in the standard model. In case of $(\Delta \Gamma/ \Gamma)_{B_s}$ we are already in a rather advanced stage. We obtain $(\Delta\Gamma/\Gamma)_{B_s}=(9.3^{+3.4}_{-4.6})$. It seems to be difficult to improve these errors substantially. In addition now some experimental results are available. For $\tau_{B^+}/\tau_{B_d}$ and $\tau_{\Lambda_b} / \tau_{B_d}$ the theoretical status is much less advanced and the discrepancy between experiment and theory still remains. We conclude with a what-to-do-list for theorists.Comment: Invited talk given at the International Conference on Flavor Physics in Zhang-Jia-Jie City, Hunan, China, May 31 - June 6,2001. 6 page