Ratio tauberian theorems for positive functions and sequences in banach lattices

We prove two ratio Tauberian theorems and deduce two generalized Tauberian theorems for functions and sequences with values in positive cones of Banach lattices. Two counter-examples are given to show that the hypotheses in the ratio Tauberian theorems are essential

Convergence theorems and Tauberian theorems for functions and sequences in Banach spaces and Banach lattices

We prove generalized convergence theorems and Tauberian theorems for vector-valued functions and sequences of growth order gamma - 1 with gamma > 0 and for positive functions and sequences in Banach lattices. Then the general results are applied to obtain some interesting particular Tauberian results for various examples of operator semigroups. Among them are mean ergodic theorems for Cesaro-mean-bounded semigroups (discrete and continuous) of operators and for semigroups of positive operators

Entropic Tightening of Vibrated Chains

We investigate experimentally the distribution of configurations of a ring with an elementary topological constraint, a ``figure-8'' twist. Using vibrated granular chains, which permit controlled preparation and direct observation of such a constraint, we show that configurations where one of the loops is tight and the second is large are strongly preferred. This agrees with recent predictions for equilibrium properties of topologically-constrained polymers. However, the dynamics of the tightening process weakly violate detailed balance, a signature of the nonequilibrium nature of this system.Comment: 4 pages, 4 figure

Autosis is a Na+,K+-ATPase-regulated form of cell death triggered by autophagy-inducing peptides, starvation, and hypoxia-ischemia.

A long-standing controversy is whether autophagy is a bona fide cause of mammalian cell death. We used a cell-penetrating autophagy-inducing peptide, Tat-Beclin 1, derived from the autophagy protein Beclin 1, to investigate whether high levels of autophagy result in cell death by autophagy. Here we show that Tat-Beclin 1 induces dose-dependent death that is blocked by pharmacological or genetic inhibition of autophagy, but not of apoptosis or necroptosis. This death, termed "autosis," has unique morphological features, including increased autophagosomes/autolysosomes and nuclear convolution at early stages, and focal swelling of the perinuclear space at late stages. We also observed autotic death in cells during stress conditions, including in a subpopulation of nutrient-starved cells in vitro and in hippocampal neurons of neonatal rats subjected to cerebral hypoxia-ischemia in vivo. A chemical screen of ~5,000 known bioactive compounds revealed that cardiac glycosides, antagonists of Na(+),K(+)-ATPase, inhibit autotic cell death in vitro and in vivo. Furthermore, genetic knockdown of the Na(+),K(+)-ATPase α1 subunit blocks peptide and starvation-induced autosis in vitro. Thus, we have identified a unique form of autophagy-dependent cell death, a Food and Drug Administration-approved class of compounds that inhibit such death, and a crucial role for Na(+),K(+)-ATPase in its regulation. These findings have implications for understanding how cells die during certain stress conditions and how such cell death might be prevented

Gyration radius of a circular polymer under a topological constraint with excluded volume

It is nontrivial whether the average size of a ring polymer should become smaller or larger under a topological constraint. Making use of some knot invariants, we evaluate numerically the mean square radius of gyration for ring polymers having a fixed knot type, where the ring polymers are given by self-avoiding polygons consisting of freely-jointed hard cylinders. We obtain plots of the gyration radius versus the number of polygonal nodes for the trivial, trefoil and figure-eight knots. We discuss possible asymptotic behaviors of the gyration radius under the topological constraint. In the asymptotic limit, the size of a ring polymer with a given knot is larger than that of no topological constraint when the polymer is thin, and the effective expansion becomes weak when the polymer is thick enough.Comment: 12pages,3figure

Force-Extension Relations for Polymers with Sliding Links

Topological entanglements in polymers are mimicked by sliding rings (slip-links) which enforce pair contacts between monomers. We study the force-extension curve for linear polymers in which slip-links create additional loops of variable size. For a single loop in a phantom chain, we obtain exact expressions for the average end-to-end separation: The linear response to a small force is related to the properties of the unstressed chain, while for a large force the polymer backbone can be treated as a sequence of Pincus--de Gennes blobs, the constraint effecting only a single blob. Generalizing this picture, scaling arguments are used to include self-avoiding effects.Comment: 4 pages, 5 figures; accepted to Phys. Rev. E (Brief Report

Knots in Charged Polymers

The interplay of topological constraints and Coulomb interactions in static and dynamic properties of charged polymers is investigated by numerical simulations and scaling arguments. In the absence of screening, the long-range interaction localizes irreducible topological constraints into tight molecular knots, while composite constraints are factored and separated. Even when the forces are screened, tight knots may survive as local (or even global) equilibria, as long as the overall rigidity of the polymer is dominated by the Coulomb interactions. As entanglements involving tight knots are not easy to eliminate, their presence greatly influences the relaxation times of the system. In particular, we find that tight knots in open polymers are removed by diffusion along the chain, rather than by opening up. The knot diffusion coefficient actually decreases with its charge density, and for highly charged polymers the knot's position appears frozen.Comment: Revtex4, 9 pages, 9 eps figure

Degradation and healing in a generalized neo-Hookean solid due to infusion of a fluid

The mechanical response and load bearing capacity of high performance polymer composites changes due to diffusion of a fluid, temperature, oxidation or the extent of the deformation. Hence, there is a need to study the response of bodies under such degradation mechanisms. In this paper, we study the effect of degradation and healing due to the diffusion of a fluid on the response of a solid which prior to the diffusion can be described by the generalized neo-Hookean model. We show that a generalized neo-Hookean solid - which behaves like an elastic body (i.e., it does not produce entropy) within a purely mechanical context - creeps and stress relaxes when infused with a fluid and behaves like a body whose material properties are time dependent. We specifically investigate the torsion of a generalized neo-Hookean circular cylindrical annulus infused with a fluid. The equations of equilibrium for a generalized neo-Hookean solid are solved together with the convection-diffusion equation for the fluid concentration. Different boundary conditions for the fluid concentration are also considered. We also solve the problem for the case when the diffusivity of the fluid depends on the deformation of the generalized neo-Hookean solid.Comment: 24 pages, 10 figures, submitted to Mechanics of Time-dependent Material

HIV-1 Clade D Is Associated with Increased Rates of CD4 Decline in a Kenyan Cohort

HIV-1 is grouped phylogenetically into clades, which may impact rates of HIV-1 disease progression. Clade D infection in particular has been shown to be more pathogenic. Here we confirm in a Nairobi-based prospective female sex worker cohort (1985-2004) that Clade D (n = 54) is associated with a more rapid CD4 decline than clade A1 (n = 150, 20.6% vs 13.4% decline per year, 1.53-fold increase, p = 0.015). This was independent of "protective" HLA and country of origin (p = 0.053), which in turn were also independent predictors of the rate of CD4 decline (p = 0.026 and 0.005, respectively). These data confirm that clade D is more pathogenic than clade A1. The precise reason for this difference is currently unclear, and requires further study. This is first study to demonstrate difference in HIV-1 disease progression between clades while controlling for protective HLA alleles

Measurement of νˉμ\bar{\nu}_{\mu} and νμ\nu_{\mu} charged current inclusive cross sections and their ratio with the T2K off-axis near detector

We report a measurement of cross section $\sigma(\nu_{\mu}+{\rm nucleus}\rightarrow\mu^{-}+X)$ and the first measurements of the cross section $\sigma(\bar{\nu}_{\mu}+{\rm nucleus}\rightarrow\mu^{+}+X)$ and their ratio $R(\frac{\sigma(\bar \nu)}{\sigma(\nu)})$ at (anti-)neutrino energies below 1.5 GeV. We determine the single momentum bin cross section measurements, averaged over the T2K $\bar{\nu}/\nu$-flux, for the detector target material (mainly Carbon, Oxygen, Hydrogen and Copper) with phase space restricted laboratory frame kinematics of $\theta_{\mu}$500 MeV/c. The results are $\sigma(\bar{\nu})=\left( 0.900\pm0.029{\rm (stat.)}\pm0.088{\rm (syst.)}\right)\times10^{-39}$ and $\sigma(\nu)=\left( 2.41\ \pm0.022{\rm{(stat.)}}\pm0.231{\rm (syst.)}\ \right)\times10^{-39}$in units of cm$^{2}$/nucleon and$R\left(\frac{\sigma(\bar{\nu})}{\sigma(\nu)}\right)= 0.373\pm0.012{\rm (stat.)}\pm0.015{\rm (syst.)}$.Comment: 18 pages, 8 figure