The parabolic p-Laplacian with fractional differentiability

Breit D, Diening L, Storn J, Wichmann J. The parabolic p-Laplacian with fractional differentiability. 2020.We study the parabolic p-Laplacian system in a bounded domain. We deduce optimal convergence rates for the space-time discretization based on an implicit Euler scheme in time. Our estimates are expressed in terms of Nikolskii spaces and therefore cover situations when the (gradient of) the solution has only fractional derivatives in space and time. The main novelty is that, different to all previous results, we do not assume any coupling condition between the space and time resolution h and τ. The theoretical error analysis is complemented by numerical experiments

The parabolic p-Laplacian with fractional differentiability

We study the parabolic $p$-Laplacian system in a bounded domain. We deduce optimal convergence rates for the space-time discretization based on an implicit Euler scheme in time. Our estimates are expressed in terms of Nikolskii spaces and therefore cover situations when the (gradient of) the solution has only fractional derivatives in space and time. The main novelty is that, different to all previous results, we do not assume any coupling condition between the space and time resolution $h$ and $\tau$. The theoretical error analysis is complemented by numerical experiments.Comment: Source file for experiments included in submissio

Diagnosing Schistosomiasis by Detection of Cell-Free Parasite DNA in Human Plasma

Bilharzia (schistosomiasis) occurs in the tropics and subtropics and is one of the most important parasite diseases of humans. It is caused by flukes residing in the vessels of the gut or bladder, causing fever, pain, and bleeding. Bladder cancer or esophageal varices may follow. Diagnosis is difficult, requiring detection of parasite eggs in stool, urine, or gut/bladder biopsies. In this paper, we introduce a fundamentally new way of diagnosing bilharzia from the blood. It has been known for almost 20 years that patients with cancer have tumor-derived DNA circulating in their blood, which can be used for diagnostic purposes. During pregnancy, free DNA from the fetus can be detected in motherly blood, which can be used for diagnosing a range of fetal diseases and pregnancy-associated complications. We found that parasite DNA can be detected in the same way in the blood of patients with bilharzia. In patients with early disease, diagnosis was possible earlier than with any other test. DNA could be detected in all patients with active disease in our study. Patients after treatment had significantly lower parasite DNA concentrations and turned negative 1–2 years after treatment. Future studies should implement the method in large cohorts of patients and should define criteria for the confirmation of the success of treatment by comparing the concentration of fluke DNA before and after therapy

Genomic Relationships, Novel Loci, and Pleiotropic Mechanisms across Eight Psychiatric Disorders

Genetic influences on psychiatric disorders transcend diagnostic boundaries, suggesting substantial pleiotropy of contributing loci. However, the nature and mechanisms of these pleiotropic effects remain unclear. We performed analyses of 232,964 cases and 494,162 controls from genome-wide studies of anorexia nervosa, attention-deficit/hyper-activity disorder, autism spectrum disorder, bipolar disorder, major depression, obsessive-compulsive disorder, schizophrenia, and Tourette syndrome. Genetic correlation analyses revealed a meaningful structure within the eight disorders, identifying three groups of inter-related disorders. Meta-analysis across these eight disorders detected 109 loci associated with at least two psychiatric disorders, including 23 loci with pleiotropic effects on four or more disorders and 11 loci with antagonistic effects on multiple disorders. The pleiotropic loci are located within genes that show heightened expression in the brain throughout the lifespan, beginning prenatally in the second trimester, and play prominent roles in neurodevelopmental processes. These findings have important implications for psychiatric nosology, drug development, and risk prediction.Peer reviewe

Measurement of t(t)over-bar normalised multi-differential cross sections in pp collisions at root s=13 TeV, and simultaneous determination of the strong coupling strength, top quark pole mass, and parton distribution functions

Peer reviewe