Convergence to equilibrium for the discrete coagulation-fragmentation equations with detailed balance

Under the condition of detailed balance and some additional restrictions on the size of the coefficients, we identify the equilibrium distribution to which solutions of the discrete coagulation-fragmentation system of equations converge for large times, thus showing that there is a critical mass which marks a change in the behavior of the solutions. This was previously known only for particular cases as the generalized Becker-D\"oring equations. Our proof is based on an inequality between the entropy and the entropy production which also gives some information on the rate of convergence to equilibrium for solutions under the critical mass.Comment: 28 page

Inherited predisposition to spontaneous preterm delivery

Peer reviewedPreprin

CD4 cell responses to combination antiretroviral therapy in patients starting therapy at high CD4 cell counts

Objective: To examine CD4 cell responses to combination antiretroviral therapy (cART) in patients enrolled in the Australian HIV Observational Database who commenced cART at CD4 cell counts >350 cells per microliter. Methods: CD4 cell counts were modelled using random effects, repeated measurement models in 432 HIV-infected adults from Australian HIV Observational Database who commenced their first cART regimen and had a baseline CD4 count >350 cells per microliter. Using published AIDS and/or death incidence rates combined with the data summarized by time and predicted CD4 cell count, we calculated the expected reduction in risk of an event for different starting baseline CD4 strata. Results: Mean CD4 counts increased above 500 cells per microliter in all baseline CD4 strata by 12 months (means of 596, 717, and 881 cells/μL in baseline CD4 strata 351-500, 501-650, and >650 cells/μL, respectively) and after 72 months since initiating cART, mean CD4 cell counts (by increasing baseline CD4 strata) were 689, 746, 742 cells per microliter. The expected reduction in risk of mortality for baseline CD4 counts >650 cells per microliter relative to 351-500 cells per microliter was approximately 8%, an absolute risk reduction 0.33 per 1000 treated patient-years. Conclusions: Patients starting cART at high CD4 cell counts (>650 cells/μL) tend to maintain this immunological level over 6 years of follow-up. Patients starting from 351 to 500 CD4 cells per microliter achieve levels of >650 cells per microliter after approximately 3 years of cART. Initiating cART with a baseline CD4 count 501-650 or >650 cells per microliter relative to 351-500 cells per microliter indicated a minimal reduction in risk of AIDS incidence and/or death. Copyright © 2011 Lippincott Williams & Wilkins

Self-similar and charged spheres in the diffusion approximation

We study spherical, charged and self--similar distributions of matter in the diffusion approximation. We propose a simple, dynamic but physically meaningful solution. For such a solution we obtain a model in which the distribution becomes static and changes to dust. The collapse is halted with damped mass oscillations about the absolute value of the total charge.Comment: 15 pages, 7 figure

Rescue of the MERTK phagocytic defect in a human iPSC disease model using translational read-through inducing drugs.

Inherited retinal dystrophies are an important cause of blindness, for which currently there are no effective treatments. In order to study this heterogeneous group of diseases, adequate disease models are required in order to better understand pathology and to test potential therapies. Induced pluripotent stem cells offer a new way to recapitulate patient specific diseases in vitro, providing an almost limitless amount of material to study. We used fibroblast-derived induced pluripotent stem cells to generate retinal pigment epithelium (RPE) from an individual suffering from retinitis pigmentosa associated with biallelic variants in MERTK. MERTK has an essential role in phagocytosis, one of the major functions of the RPE. The MERTK deficiency in this individual results from a nonsense variant and so the MERTK-RPE cells were subsequently treated with two translational readthrough inducing drugs (G418 & PTC124) to investigate potential restoration of expression of the affected gene and production of a full-length protein. The data show that PTC124 was able to reinstate phagocytosis of labeled photoreceptor outer segments at a reduced, but significant level. These findings represent a confirmation of the usefulness of iPSC derived disease specific models in investigating the pathogenesis and screening potential treatments for these rare blinding disorders

Coagulation and fragmentation processes with evolving size and shape profiles : a semigroup approach

We investigate a class of bivariate coagulation-fragmentation equations. These equations describe the evolution of a system of particles that are characterised not only by a discrete size variable but also by a shape variable which can be either discrete or continuous. Existence and uniqueness of strong solutions to the associated abstract Cauchy problems are established by using the theory of substochastic semigroups of operators

First-trimester or second-trimester screening, or both, for Down's syndrome

BACKGROUND: It is uncertain how best to screen pregnant women for the presence of fetal Down's syndrome: to perform first-trimester screening, to perform second-trimester screening, or to use strategies incorporating measurements in both trimesters.METHODS: Women with singleton pregnancies underwent first-trimester combined screening (measurement of nuchal translucency, pregnancy-associated plasma protein A [PAPP-A], and the free beta subunit of human chorionic gonadotropin at 10 weeks 3 days through 13 weeks 6 days of gestation) and second-trimester quadruple screening (measurement of alpha-fetoprotein, total human chorionic gonadotropin, unconjugated estriol, and inhibin A at 15 through 18 weeks of gestation). We compared the results of stepwise sequential screening (risk results provided after each test), fully integrated screening (single risk result provided), and serum integrated screening (identical to fully integrated screening, but without nuchal translucency).RESULTS: First-trimester screening was performed in 38,167 patients; 117 had a fetus with Down's syndrome. At a 5 percent false positive rate, the rates of detection of Down's syndrome were as follows: with first-trimester combined screening, 87 percent, 85 percent, and 82 percent for measurements performed at 11, 12, and 13 weeks, respectively; with second-trimester quadruple screening, 81 percent; with stepwise sequential screening, 95 percent; with serum integrated screening, 88 percent; and with fully integrated screening with first-trimester measurements performed at 11 weeks, 96 percent. Paired comparisons found significant differences between the tests, except for the comparison between serum integrated screening and combined screening.CONCLUSIONS: First-trimester combined screening at 11 weeks of gestation is better than second-trimester quadruple screening but at 13 weeks has results similar to second-trimester quadruple screening. Both stepwise sequential screening and fully integrated screening have high rates of detection of Down's syndrome, with low false positive rates

The discrete fragmentation equations : semigroups, compactness and asynchronous exponential growth

In this paper we present a class of fragmentation semigroups which are compact in a scale of spaces defined in terms of finite higher moments. We use this compactness result to analyse the long time behaviour of such semigroups and, in particular, to prove that they have the asynchronous growth property. We note that, despite compactness, this growth property is not automatic as the fragmentation semigroups are not irreducible

Spontaneous Generation of Patient-Specific Retinal Pigment Epithelial Cells Using Induced Pluripotent Stem Cell Technology

Stem cell technology has a number potential uses when it comes to the eye, particularly disease and developmental modelling, and as potential therapeutic source. A variety of protocols have been developed that facilitate the generation of the different cell types found within the eye, as well as those that produce a facsimile of the developing eye in vitro. This chapter introduces the importance of the Retinal Pigment Epithelium (RPE) in maintaining visual function. We then focus on methods developed by our group to produce RPE from patient skin samples using human induced pluripotent stem cell technology (iPSC)