A Massively Parallel Algorithm for the Approximate Calculation of Inverse p-th Roots of Large Sparse Matrices

We present the submatrix method, a highly parallelizable method for the approximate calculation of inverse p-th roots of large sparse symmetric matrices which are required in different scientific applications. We follow the idea of Approximate Computing, allowing imprecision in the final result in order to be able to utilize the sparsity of the input matrix and to allow massively parallel execution. For an n x n matrix, the proposed algorithm allows to distribute the calculations over n nodes with only little communication overhead. The approximate result matrix exhibits the same sparsity pattern as the input matrix, allowing for efficient reuse of allocated data structures. We evaluate the algorithm with respect to the error that it introduces into calculated results, as well as its performance and scalability. We demonstrate that the error is relatively limited for well-conditioned matrices and that results are still valuable for error-resilient applications like preconditioning even for ill-conditioned matrices. We discuss the execution time and scaling of the algorithm on a theoretical level and present a distributed implementation of the algorithm using MPI and OpenMP. We demonstrate the scalability of this implementation by running it on a high-performance compute cluster comprised of 1024 CPU cores, showing a speedup of 665x compared to single-threaded execution

Converging seasonal prevalence dynamics in experimental epidemics

Background Regular seasonal changes in prevalence of infectious diseases are often observed in nature, but the mechanisms are rarely understood. Empirical tests aiming at a better understanding of seasonal prevalence patterns are not feasible for most diseases and thus are widely lacking. Here, we set out to study experimentally the seasonal prevalence in an aquatic host-parasite system. The microsporidian parasite Hamiltosporidium tvärminnensis exhibits pronounced seasonality in natural rock pool populations of its host, Daphnia magna with a regular increase of prevalence during summer and a decrease during winter. An earlier study was, however, unable to test if different starting conditions (initial prevalence) influence the dynamics of the disease in the long term. Here, we aim at testing how the starting prevalence affects the regular prevalence changes over a 4-year period in experimental populations.Results In an outdoor experiment, populations were set up to include the extremes of the prevalence spectrum observed in natural populations: 5% initial prevalence mimicking a newly invading parasite, 100% mimicking a rock pool population founded by infected hosts only, and 50% prevalence which is commonly observed in natural populations in spring. The parasite exhibited similar prevalence changes in all treatments, but seasonal patterns in the 100% treatment differed significantly from those in the 5% and 50% treatments. Populations started with 5% and 50% prevalence exhibited strong and regular seasonality already in the first year. In contrast, the amplitude of changes in the 100% treatment was low throughout the experiment demonstrating the long-lasting effect of initial conditions on prevalence dynamics.Conclusions Our study shows that the time needed to approach the seasonal changes in prevalence depends strongly on the initial prevalence. Because individual D. magna populations in this rock pool metapopulation are mostly short lived, only few populations might ever reach a point where the initial conditions are not visible anymore

Higher steroid sulfation is linked to successful weight loss in obese children

Objective: Little information is available on the steroid sulfates profile in obese children. Therefore, we examined whether sulfated steroids are linked with weight status and associated comorbidities in obese children. Methods: We analyzed 66 obese children (mean age 10.5 ± 2.5 years, 57.6% female, 53.9% prepubertal, mean BMI 27.0 ± 4.6 kg/m2, 50% with BMI-SDS reduction >0.5, 50% without BMI-SDS reduction) who participated in an outpatient 1-year intervention program based on exercise, behavior and nutrition therapy. We measured intact sulfated steroids (cholesterol sulfate (CS), pregnenolone sulfate (PregS), 17αOH pregnenolone sulfate (17OH-PregS), 16αOH dehydroepiandrosterone sulfate (16OH-DHEAS), DHEAS, androstenediol-3-sulfate, androsterone sulfate and epiandrosterone sulfate) by LC–MS/MS, and insulin resistance index HOMA, lipids, blood pressure at baseline and 1 year later. Results: All sulfated steroids except 17OH-PregS, 16OH-DHEAS, androsterone sulfate and epiandrosterone sulfate were higher in boys compared to girls. Concentrations of CS before intervention were higher in children who lost weight. After 1 year of treatment, both groups showed increased levels of DHEAS, 16OH-DHEAS and androstenediol-3-sulfate, but PregS was only increased in children with weight loss. None of the steroid sulfates was significantly related to cardiovascular risk factors or HOMA except 17OH-PregS, which was associated with systolic blood pressure both in cross-sectional (β-coefficient: 0.09 ± 0.07, P = 0.020) and longitudinal analyses (β-coefficient: 0.06 ± 0.04, P = 0.013) in multiple linear regression analyses. Conclusions: Since higher steroid sulfation capacity was associated with successful weight intervention in children disruption of sulfation may be associated with difficulties to lose weight. Future studies are necessary to prove this hypothesis