Scaling limits of a model for selection at two scales

The dynamics of a population undergoing selection is a central topic in evolutionary biology. This question is particularly intriguing in the case where selective forces act in opposing directions at two population scales. For example, a fast-replicating virus strain outcompetes slower-replicating strains at the within-host scale. However, if the fast-replicating strain causes host morbidity and is less frequently transmitted, it can be outcompeted by slower-replicating strains at the between-host scale. Here we consider a stochastic ball-and-urn process which models this type of phenomenon. We prove the weak convergence of this process under two natural scalings. The first scaling leads to a deterministic nonlinear integro-partial differential equation on the interval $[0,1]$ with dependence on a single parameter, $\lambda$. We show that the fixed points of this differential equation are Beta distributions and that their stability depends on $\lambda$ and the behavior of the initial data around $1$. The second scaling leads to a measure-valued Fleming-Viot process, an infinite dimensional stochastic process that is frequently associated with a population genetics.

Scaling limits of a model for selection at two scales

The dynamics of a population undergoing selection is a central topic in evolutionary biology. This question is particularly intriguing in the case where selective forces act in opposing directions at two population scales. For example, a fast-replicating virus strain outcompetes slower-replicating strains at the within-host scale. However, if the fast-replicating strain causes host morbidity and is less frequently transmitted, it can be outcompeted by slower-replicating strains at the between-host scale. Here we consider a stochastic ball-and-urn process which models this type of phenomenon. We prove the weak convergence of this process under two natural scalings. The first scaling leads to a deterministic nonlinear integro-partial differential equation on the interval $[0,1]$ with dependence on a single parameter, $\lambda$. We show that the fixed points of this differential equation are Beta distributions and that their stability depends on $\lambda$ and the behavior of the initial data around $1$. The second scaling leads to a measure-valued Fleming-Viot process, an infinite dimensional stochastic process that is frequently associated with a population genetics.

Jamming for a 2D granular material

This paper focuses on the nature of jamming, as seen in two-dimensional frictional granular systems consisting of photoelastic particles. The photoelastic technique is unique at this time, in its capability to provide detailed particle-scale information on forces and kinematic quantities such as particle displacements and rotations. These experiments first explore isotropic stress states near point J through measurements of the mean contact number per particle, Z, and the pressure, P as functions of the packing fraction, . In this case, the experiments show some but not all aspects of jamming, as expected on the basis of simulations and models that typically assume conservative, hence frictionless, forces between particles. Specifically, there is a rapid growth in Z, at a reasonable which we identify with as c. It is possible to fit Z and P, to power law expressions in - c above c, and to obtain exponents that are in agreement with simulations and models. However, the experiments differ from theory on several points, as typified by the rounding that is observed in Z and P near c. The application of shear to these same 2D granular systems leads to phenomena that are qualitatively different from the standard picture of jamming. In particular, there is a range of packing fractions below c, where the application of shear strain at constant leads to jammed stress-anisotropic states, i.e. they have a non-zero shear stress, τ. The application of shear strain to an initially isotropically compressed (hence jammed) state, does not lead to an unjammed state per se. Rather, shear strain at constant first leads to an increase of both τ and P. Additional strain leads to a succession of jammed states interspersed with relatively localized failures of the force network leading to other stress-anisotropic states that are jammed at typically somewhat lower stress. The locus of jammed states requires a state space that involves not only and τ, but also P. P, τ, and Z are all hysteretic functions of shear strain for fixed . However, we find that both P and τ are roughly linear functions of Z for strains large enough to jam the system. This implies that these shear-jammed states satisfy a Coulomb like-relation, τ = μP. © 2010 The Royal Society of Chemistry.

Early versus delayed fixed dose combination abacavir/lamivudine/zidovudine in patients with HIV and tuberculosis in Tanzania.

Fixed dose combination abacavir/lamivudine/zidovudine (ABC/3TC/ZDV) among HIV-1 and tuberculosis (TB)-coinfected patients was evaluated and outcomes between early vs. delayed initiation were compared. In a randomized, pilot study conducted in the Kilimanjaro Region of Tanzania, HIV-infected inpatients with smear-positive TB and total lymphocyte count <1200/mm(3) were randomized to initiate ABC/3TC/ZDV either 2 (early) or 8 (delayed) weeks after commencing antituberculosis therapy and were followed for 104 weeks. Of 94 patients screened, 70 enrolled (41% female, median CD4 count 103 cells/mm(3)), and 33 in each group completed 104 weeks. Two deaths and 12 serious adverse events (SAEs) were observed in the early arm vs. one death, one clinical failure, and seven SAEs in the delayed arm (p = 0.6012 for time to first grade 3/4 event, SAE, or death). CD4 cell increases were +331 and +328 cells/mm(3), respectively. TB-immune reconstitution inflammatory syndromes (TB-IRIS) were not observed in any subject. Using intent-to-treat (ITT), missing = failure analyses, 74% (26/35) vs. 89% (31/35) randomized to early vs. delayed therapy had HIV RNA levels <400 copies/ml at 104 weeks (p = 0.2182) and 66% (23/35) vs. 74% (26/35), respectively, had HIV RNA levels <50 copies/ml (p = 0.6026). In an analysis in which switches from ABC/3TC/ZDV = failure, those receiving early therapy were less likely to be suppressed to <400 copies/ml [60% (21/35) vs. 86% (30/35), p = 0.030]. TB-IRIS was not observed among the 70 coinfected subjects beginning antiretroviral treatment. ABC/3TC/ZDV was well tolerated and resulted in steady immunologic improvement. Rates of virologic suppression were similar between early and delayed treatment strategies with triple nucleoside regimens when substitutions were allowed.