Partial Schauder estimates for second-order elliptic and parabolic equations

We establish Schauder estimates for both divergence and non-divergence form second-order elliptic and parabolic equations involving H\"older semi-norms not with respect to all, but only with respect to some of the independent variables.Comment: CVPDE, accepted (2010)

Detection of Inconspicuous Power Quality Disturbances through Step Changes in rms Voltage Profile

Power quality disturbances commonly observed in power systems have been studied for decades, resulting in numerous algorithms for detecting the events that affect the voltage and/or current waveforms. However, a considerable amount of disturbances is not visually observable in the raw waveforms, especially switching operations. These events must be detected through an alternative feature, such as abrupt variations in the root-mean-square (rms) voltage profile. This study examines the methods commonly used for detecting power quality disturbances in the waveform or rms voltage profile domains and identifies their limitations. Afterwards, a novel step change detector is proposed based on a modified median filter and rms voltage gradient values to overcome the deficiencies of the existing methods. The effectiveness of the proposed method is assessed by applying it to both simulated and field data. This assessment shows that the method detects all switching events with no false positives for the datasets under analysis

Age at first birth in women is genetically associated with increased risk of schizophrenia

Prof. Paunio on PGC:n jäsenPrevious studies have shown an increased risk for mental health problems in children born to both younger and older parents compared to children of average-aged parents. We previously used a novel design to reveal a latent mechanism of genetic association between schizophrenia and age at first birth in women (AFB). Here, we use independent data from the UK Biobank (N = 38,892) to replicate the finding of an association between predicted genetic risk of schizophrenia and AFB in women, and to estimate the genetic correlation between schizophrenia and AFB in women stratified into younger and older groups. We find evidence for an association between predicted genetic risk of schizophrenia and AFB in women (P-value = 1.12E-05), and we show genetic heterogeneity between younger and older AFB groups (P-value = 3.45E-03). The genetic correlation between schizophrenia and AFB in the younger AFB group is -0.16 (SE = 0.04) while that between schizophrenia and AFB in the older AFB group is 0.14 (SE = 0.08). Our results suggest that early, and perhaps also late, age at first birth in women is associated with increased genetic risk for schizophrenia in the UK Biobank sample. These findings contribute new insights into factors contributing to the complex bio-social risk architecture underpinning the association between parental age and offspring mental health.Peer reviewe