The Incidence of AIDS-Defining Illnesses at a Current CD4 Count >=200 Cells/ L in the Post-Combination Antiretroviral Therapy Era

Background. Few studies consider the incidence of individual AIDS-defining illnesses (ADIs) at higher CD4 counts, relevant on a population level for monitoring and resource allocation. Methods. Individuals from the Collaboration of Observational HIV Epidemiological Research Europe (COHERE) aged ≥14 years with ≥1 CD4 count of ≥200 µL between 1998 and 2010 were included. Incidence rates (per 1000 person-years of follow-up [PYFU]) were calculated for each ADI within different CD4 strata; Poisson regression, using generalized estimating equations and robust standard errors, was used to model rates of ADIs with current CD4 ≥500/µL. Results. A total of 12 135 ADIs occurred at a CD4 count of ≥200 cells/µL among 207 539 persons with 1 154 803 PYFU. Incidence rates declined from 20.5 per 1000 PYFU (95% confidence interval [CI], 20.0–21.1 per 1000 PYFU) with current CD4 200–349 cells/µL to 4.1 per 1000 PYFU (95% CI, 3.6–4.6 per 1000 PYFU) with current CD4 ≥ 1000 cells/µL. Persons with a current CD4 of 500–749 cells/µL had a significantly higher rate of ADIs (adjusted incidence rate ratio [aIRR], 1.20; 95% CI, 1.10–1.32), whereas those with a current CD4 of ≥1000 cells/µL had a similar rate (aIRR, 0.92; 95% CI, .79–1.07), compared to a current CD4 of 750–999 cells/µL. Results were consistent in persons with high or low viral load. Findings were stronger for malignant ADIs (aIRR, 1.52; 95% CI, 1.25–1.86) than for nonmalignant ADIs (aIRR, 1.12; 95% CI, 1.01–1.25), comparing persons with a current CD4 of 500–749 cells/µL to 750–999 cells/µL. Discussion. The incidence of ADIs was higher in individuals with a current CD4 count of 500–749 cells/µL compared to those with a CD4 count of 750–999 cells/µL, but did not decrease further at higher CD4 counts. Results were similar in patients virologically suppressed on combination antiretroviral therapy, suggesting that immune reconstitution is not complete until the CD4 increases to >750 cells/µL.

Essential spectrum of systems of singular differential equations

In this paper we develop a new method to determine the essential spectrum of coupled systems of singular differential equations. Applications to problems from magnetohydrodynamics and astrophysics are given.

Non-exponential return time distributions for vorticity extremes explained by fractional Poisson processes

Serial correlation of extreme midlatitude cyclones observed at the storm track exits is explained by deviations from a Poisson process. To model these deviations, we apply fractional Poisson processes (FPPs) to extreme midlatitude cyclones, which are defined by the 850 hPa relative vorticity of the ERA interim reanalysis during boreal winter (DJF) and summer (JJA) seasons. Extremes are defined by a 99% quantile threshold in the grid-point time series. In general, FPPs are based on long-term memory and lead to non-exponential return time distributions. The return times are described by a Weibull distribution to approximate the Mittag–Leffler function in the FPPs. The Weibull shape parameter yields a dispersion parameter that agrees with results found for midlatitude cyclones. The memory of the FPP, which is determined by detrended fluctuation analysis, provides an independent estimate for the shape parameter. Thus, the analysis exhibits a concise framework of the deviation from Poisson statistics (by a dispersion parameter), non-exponential return times and memory (correlation) on the basis of a single parameter. The results have potential implications for the predictability of extreme cyclones.

Roy-Steiner equations for piN scattering

In this talk, we present a coupled system of integral equations for the πN → πN (s-channel) and ππ → N̅N (t-channel) lowest partial waves, derived from Roy–Steiner equations for pion–nucleon scattering. After giving a brief overview of this system of equations, we present the solution of the t-channel sub-problem by means of Muskhelishvili–Omnès techniques, and solve the s-channel sub-problem after finding a set of phase shifts and subthreshold parameters which satisfy the Roy–Steiner equations.

Dichotomous Hamiltonians with unbounded entries and solutions of Riccati equations

An operator Riccati equation from systems theory is considered in the case that all entries of the associated Hamiltonian are unbounded. Using a certain dichotomy property of the Hamiltonian and its symmetry with respect to two different indefinite inner products, we prove the existence of nonnegative and nonpositive solutions of the Riccati equation. Moreover, conditions for the boundedness and uniqueness of these solutions are established.