A new invariant on hyperbolic Dehn surgery space

In this paper we define a new invariant of the incomplete hyperbolic structures on a 1-cusped finite volume hyperbolic 3-manifold M, called the ortholength invariant. We show that away from a (possibly empty) subvariety of excluded values this invariant both locally parameterises equivalence classes of hyperbolic structures and is a complete invariant of the Dehn fillings of M which admit a hyperbolic structure. We also give an explicit formula for the ortholength invariant in terms of the traces of the holonomies of certain loops in M. Conjecturally this new invariant is intimately related to the boundary of the hyperbolic Dehn surgery space of M.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-23.abs.htm

Sexual and marital trajectories and HIV infection among ever-married women in rural Malawi.

OBJECTIVE: To explore how sexual and marital trajectories are associated with HIV infection among ever-married women in rural Malawi. METHODS: Retrospective survey data and HIV biomarker data for 926 ever-married women interviewed in the Malawi Diffusion and Ideational Change Project were used. The associations between HIV infection and four key life course transitions considered individually (age at sexual debut, premarital sexual activity, entry into marriage and marital disruption by divorce or death) were examined. These transitions were then sequenced to construct trajectories that represent the variety of patterns in the data. The association between different trajectories and HIV prevalence was examined, controlling for potentially confounding factors such as age and region. RESULTS: Although each life course transition taken in isolation may be associated with HIV infection, their combined effect appeared to be conditional on the sequence in which they occurred. Although early sexual debut, not marrying one's first sexual partner and having a disrupted marriage each increased the likelihood of HIV infection, their risk was not additive. Women who both delayed sexual debut and did not marry their first partner are, once married, more likely to experience marital disruption and to be HIV-positive. Women who marry their first partner but who have sex at a young age, however, are also at considerable risk. CONCLUSIONS: These findings identify the potential of a life course perspective for understanding why some women become infected with HIV and others do not, as well as the differentials in HIV prevalence that originate from the sequence of sexual and marital transitions in one's life. The analysis suggests, however, the need for further data collection to permit a better examination of the mechanisms that account for variations in life course trajectories and thus in lifetime probabilities of HIV infection

Ability of LISA to detect a gravitational-wave background of cosmological origin: The cosmic string case

We investigate the ability of the Laser Interferometer Space Antenna (LISA) to detect a stochastic gravitational-wave background (GWB) produced by cosmic strings, and to subsequently estimate the string tension G μ in the presence of instrument noise, an astrophysical background from compact binaries, and the galactic foreground from white dwarf binaries. Fisher Information and Markov Chain Monte Carlo methods provide estimates of the LISA noise and the parameters for the different signal sources. We demonstrate the importance of including the galactic foreground as well as the astrophysical background for LISA to detect a cosmic string produced GWB and estimate the string tension. Considering the expected astrophysical background and a galactic foreground, a cosmic string tension in the G μ ≈ 10 − 16 to G μ ≈ 10 − 15 range or bigger could be measured by LISA, with the galactic foreground affecting this limit more than the astrophysical background. The parameter estimation methods presented here can be applied to other cosmological backgrounds in the LISA observation band

Specific fluorogenic substrates for neprilysin (neutral endopeptidase, EC 3.4.24.11) which are highly resistant to serine- and metalloproteases

Two intramolecularly quenched fluorogenic peptides containing o-aminobenzoyl (Abz) and ethylenediamine 2,4-dinitrophenyl (EDDnp) groups at amino- and carboxyl-terminal amino acid residues, Abz-DArg-Arg-Leu-EDDnp (Abz-DRRL-EDDnp) and Abz-DArg-Arg-Phe-EDDnp (Abz-DRRF-EDDnp), were selectively hydrolyzed by neutral endopeptidase (NEP, enkephalinase, neprilysin, EC 3.4.24.11) at the Arg-Leu and Arg-Phe bonds, respectively. The kinetic parameters for the NEP-catalyzed hydrolysis of Abz-DRRL-EDDnp and Abz-DRRF-EDDnp were Km = 2.8 µM, kcat = 5.3 min-1, kcat/Km = 2 min-1 µM-1 and Km = 5.0 µM, kcat = 7.0 min-1, kcat/Km = 1.4 min-1 µM-1, respectively. The high specificity of these substrates was demonstrated by their resistance to hydrolysis by metalloproteases [thermolysin (EC 3.4.24.2), angiotensin-converting enzyme (ACE; EC 3.4.24.15)], serineproteases [trypsin (EC 3.4.21.4), a-chymotrypsin (EC 3.4.21.1)] and proteases present in tissue homogenates from kidney, lung, brain and testis. The blocked amino- and carboxyl-terminal amino acids protected these substrates against the action of aminopeptidases, carboxypeptidases and ACE. Furthermore, DR amino acids ensured total protection of Abz-DRRL-EDDnp and Abz-DRRF-EDDnp against the action of thermolysin and trypsin. Leu-EDDnp and Phe-EDDnp were resistant to hydrolysis by a-chymotrypsin. The high specifity of these substrates suggests their use for specific NEP assays in crude enzyme preparationsUniversidade Federal do CearáUniversité de MontréalUniversidade Federal de São Paulo (UNIFESP)UNIFESPSciEL

Collisions of particles in locally AdS spacetimes II Moduli of globally hyperbolic spaces

We investigate 3-dimensional globally hyperbolic AdS manifolds containing "particles", i.e., cone singularities of angles less than $2\pi$ along a time-like graph $\Gamma$. To each such space we associate a graph and a finite family of pairs of hyperbolic surfaces with cone singularities. We show that this data is sufficient to recover the space locally (i.e., in the neighborhood of a fixed metric). This is a partial extension of a result of Mess for non-singular globally hyperbolic AdS manifolds.Comment: 29 pages, 3 figures. v2: 41 pages, improved exposition. To appear, Comm. Math. Phys. arXiv admin note: text overlap with arXiv:0905.182

Fibered orbifolds and crystallographic groups

In this paper, we prove that a normal subgroup N of an n-dimensional crystallographic group G determines a geometric fibered orbifold structure on the flat orbifold E^n/G, and conversely every geometric fibered orbifold structure on E^n/G is determined by a normal subgroup N of G, which is maximal in its commensurability class of normal subgroups of G. In particular, we prove that E^n/G is a fiber bundle, with totally geodesic fibers, over a b-dimensional torus, where b is the first Betti number of G. Let N be a normal subgroup of G which is maximal in its commensurability class. We study the relationship between the exact sequence 1 -> N -> G -> G/N -> 1 splitting and the corresponding fibration projection having an affine section. If N is torsion-free, we prove that the exact sequence splits if and only if the fibration projection has an affine section. If the generic fiber F = Span(N)/N has an ordinary point that is fixed by every isometry of F, we prove that the exact sequence always splits. Finally, we describe all the geometric fibrations of the orbit spaces of all 2- and 3-dimensional crystallographic groups building on the work of Conway and Thurston.Comment: 26 pages, 1 Table. Some new theorems have been added to v

Sexual and marital trajectories and HIV infection among ever-married women in rural Malawi

OBJECTIVE: To explore how sexual and marital trajectories are associated with HIV infection among ever-married women in rural Malawi. METHODS: Retrospective survey data and HIV biomarker data for 926 ever-married women interviewed in the Malawi Diffusion and Ideational Change Project were used. The associations between HIV infection and four key life course transitions considered individually (age at sexual debut, premarital sexual activity, entry into marriage and marital disruption by divorce or death) were examined. These transitions were then sequenced to construct trajectories that represent the variety of patterns in the data. The association between different trajectories and HIV prevalence was examined, controlling for potentially confounding factors such as age and region. RESULTS: Although each life course transition taken in isolation may be associated with HIV infection, their combined effect appeared to be conditional on the sequence in which they occurred. Although early sexual debut, not marrying one's first sexual partner and having a disrupted marriage each increased the likelihood of HIV infection, their risk was not additive. Women who both delayed sexual debut and did not marry their first partner are, once married, more likely to experience marital disruption and to be HIV-positive. Women who marry their first partner but who have sex at a young age, however, are also at considerable risk. CONCLUSIONS: These findings identify the potential of a life course perspective for understanding why some women become infected with HIV and others do not, as well as the differentials in HIV prevalence that originate from the sequence of sexual and marital transitions in one's life. The analysis suggests, however, the need for further data collection to permit a better examination of the mechanisms that account for variations in life course trajectories and thus in lifetime probabilities of HIV infection