Commutator length of annulus diffeomorphisms

We study the group of C^{r}-diffeomorphisms of the closed annulus that are isotopic to the identity. We show that, for r different from 3, the linear space of homogeneous quasi-morphisms on this group is one dimensional. Therefore, the commutator length on this group is (stably) unbounded. In particular, this provides an example of a manifold whose diffeomorphisms group is unbounded in the sense of Burago, Ivanov and Polterovich

Link Invariants for Flows in Higher Dimensions

Linking numbers in higher dimensions and their generalization including gauge fields are studied in the context of BF theories. The linking numbers associated to $n$-manifolds with smooth flows generated by divergence-free p-vector fields, endowed with an invariant flow measure are computed in different cases. They constitute invariants of smooth dynamical systems (for non-singular flows) and generalizes previous results for the 3-dimensional case. In particular, they generalizes to higher dimensions the Arnold's asymptotic Hopf invariant for the three-dimensional case. This invariant is generalized by a twisting with a non-abelian gauge connection. The computation of the asymptotic Jones-Witten invariants for flows is naturally extended to dimension n=2p+1. Finally we give a possible interpretation and implementation of these issues in the context of string theory.Comment: 21+1 pages, LaTeX, no figure

The chameleon groups of Richard J. Thompson: automorphisms and dynamics

The automorphism groups of several of Thompson's countable groups of piecewise linear homeomorphisms of the line and circle are computed and it is shown that the outer automorphism groups of these groups are relatively small. These results can be interpreted as stability results for certain structures of PL functions on the circle. Machinery is developed to relate the structures on the circle to corresponding structures on the line

Accidental parabolics and relatively hyperbolic groups

By constructing, in the relative case, objects analoguous to Rips and Sela's canonical representatives, we prove that the set of images by morphisms without accidental parabolic, of a finitely presented group in a relatively hyperbolic group, is finite, up to conjugacy.Comment: Revision, 24 pages, 4 figure

Upper bound on the density of Ruelle resonances for Anosov flows

Using a semiclassical approach we show that the spectrum of a smooth Anosov vector field V on a compact manifold is discrete (in suitable anisotropic Sobolev spaces) and then we provide an upper bound for the density of eigenvalues of the operator (-i)V, called Ruelle resonances, close to the real axis and for large real parts.Comment: 57 page

On residualizing homomorphisms preserving quasiconvexity

H is called a G-subgroup of a hyperbolic group G if for any finite subset M G there exists a homomorphism from G onto a non-elementary hyperbolic group G_1 that is surjective on H and injective on M. In his paper in 1993 A. Ol'shanskii gave a description of all G-subgroups in any given non-elementary hyperbolic group G. Here we show that for the same class of G-subgroups the finiteness assumption on M (under certain natural conditions) can be replaced by an assumption of quasiconvexity

Boundaries of Siegel Disks: Numerical Studies of their Dynamics and Regularity

Siegel disks are domains around fixed points of holomorphic maps in which the maps are locally linearizable (i.e., become a rotation under an appropriate change of coordinates which is analytic in a neighborhood of the origin). The dynamical behavior of the iterates of the map on the boundary of the Siegel disk exhibits strong scaling properties which have been intensively studied in the physical and mathematical literature. In the cases we study, the boundary of the Siegel disk is a Jordan curve containing a critical point of the map (we consider critical maps of different orders), and there exists a natural parametrization which transforms the dynamics on the boundary into a rotation. We compute numerically this parameterization and use methods of harmonic analysis to compute the global Holder regularity of the parametrization for different maps and rotation numbers. We obtain that the regularity of the boundaries and the scaling exponents are universal numbers in the sense of renormalization theory (i.e., they do not depend on the map when the map ranges in an open set), and only depend on the order of the critical point of the map in the boundary of the Siegel disk and the tail of the continued function expansion of the rotation number. We also discuss some possible relations between the regularity of the parametrization of the boundaries and the corresponding scaling exponents. (C) 2008 American Institute of Physics.NSFMathematic

The epidemiology of HIV infection in Morocco: systematic review and data synthesis.

Morocco has made significant strides in building its HIV research capacity. Based on a wealth of empirical data, the objective of this study was to conduct a comprehensive and systematic literature review and analytical synthesis of HIV epidemiological evidence in this country. Data were retrieved using three major sources of literature and data. HIV transmission dynamics were found to be focused in high-risk populations, with female sex workers (FSWs) and clients contributing the largest share of new HIV infections. There is a pattern of emerging epidemics among some high-risk populations, and some epidemics, particularly among FSWs, appear to be established and stable. The scale of the local HIV epidemics and populations affected show highly heterogeneous geographical distribution. To optimize the national HIV response, surveillance and prevention efforts need to be expanded among high-risk populations and in geographic settings where low intensity and possibly concentrated HIV epidemics are emerging or are already endemic

Entropy production in Gaussian thermostats

We show that an arbitrary Anosov Gaussian thermostat on a surface is dissipative unless the external field has a global potential

Hepatitis C viral evolution in genotype 1 treatment-naïve and treatment-experienced patients receiving telaprevir-based therapy in clinical trials

Background: In patients with genotype 1 chronic hepatitis C infection, telaprevir (TVR) in combination with peginterferon and ribavirin (PR) significantly increased sustained virologic response (SVR) rates compared with PR alone. However, genotypic changes could be observed in TVR-treated patients who did not achieve an SVR. Methods: Population sequence analysis of the NS3•4A region was performed in patients who did not achieve SVR with TVR-based treatment. Results: Resistant variants were observed after treatment with a telaprevir-based regimen in 12% of treatment-naïve patients (ADVANCE; T12PR arm), 6% of prior relapsers, 24% of prior partial responders, and 51% of prior null responder patients (REALIZE, T12PR48 arms). NS3 protease variants V36M, R155K, and V36M+R155K emerged frequently in patients with genotype 1a and V36A, T54A, and A156S/T in patients with genotype 1b. Lower-level resistance to telaprevir was conferred by V36A/M, T54A/S, R155K/T, and A156S variants; and higher-level resistance to telaprevir was conferred by A156T and V36M+R155K variants. Virologic failure during telaprevir treatment was more common in patients with genotype 1a and in prior PR nonresponder patients and was associated with higher-level telaprevir-resistant variants. Relapse was usually associated with wild-type or lower-level resistant variants. After treatment, viral populations were wild-type with a median time of 10 months for genotype 1a and 3 weeks for genotype 1b patients. Conclusions: A consistent, subtype-dependent resistance profile was observed in patients who did not achieve an SVR with telaprevir-based treatment. The primary role of TVR is to inhibit wild-type virus and variants with lower-levels of resistance to telaprevir. The complementary role of PR is to clear any remaining telaprevir-resistant variants, especially higher-level telaprevir-resistant variants. Resistant variants are detectable in most patients who fail to achieve SVR, but their levels decline over time after treatment