Non-autonomous Lq(Lp)L^q(L^p) maximal regularity for complex systems under mixed regularity in space and time

We show non-autonomous $L^q(L^p)$ maximal regularity for families of complex second-order systems in divergence form under a mixed H{\"o}lder regularity condition in space and time.To be more precise, we let $p,q \in (1,\infty)$ and we consider coefficient functions in $C^{\beta + \varepsilon}$ with values in $C^{\alpha + \varepsilon}$ subject to the parabolic relation $2\beta + \alpha = 1$.To this end, we provide a weak $(p,q)$-solution theory with uniform constants and establish a priori higher spatial regularity.Furthermore, we show $p$-bounds for semigroups and square roots generated by complex elliptic systems under a minimal regularity assumption for the coefficients

An extrapolation result in the variational setting: improved regularity, compactness, and applications to quasilinear systems

In this paper we consider the variational setting for SPDE on a Gelfand triple $(V, H, V^*)$. Under the standard conditions on a linear coercive pair $(A,B)$, and a symmetry condition on $A$ we manage to extrapolate the classical $L^2$-estimates in time to $L^p$-estimates for some $p>2$ without any further conditions on $(A,B)$. As a consequence we obtain several other a priori regularity results of the paths of the solution. Under the assumption that $V$ embeds compactly into $H$, we derive a universal compactness result quantifying over all $(A,B)$. As an application of the compactness result we prove global existence of weak solutions to a system of second order quasi-linear equations

Off-diagonal bounds for the Dirichlet-to-Neumann operator

Let $\Omega$ be a bounded domain of $\mathbb{R}^{n+1}$ with $n \ge 1$. We assume that the boundary $\Gamma$ of $\Omega$ is Lipschitz. Consider the Dirichlet-to-Neumann operator $N_0$ associated with a system in divergence form of size $m$ with real symmetric and H\''older continuous coefficients. We prove $L^p(\Gamma)\to L^q(\Gamma)$ off-diagonal bounds of the form$$\| 1_F e^{-t N_0} 1_E f \|_q \lesssim (t \wedge 1)^{\frac{n}{q}-\frac{n}{p}} \left( 1 + \frac{dist(E,F)}{t} \right)^{-1} \| 1_E f \|_p$$for all measurable subsets $E$ and $F$ of $\Gamma$. If $\Gamma$ is $C^{1+ \kappa}$ for some $\kappa > 0$ and $m=1$, we obtain a sharp estimate in the sense that $\left( 1 + \frac{dist(E,F)}{t} \right)^{-1}$ can be replaced by$\left( 1 + \frac{dist(E,F)}{t} \right)^{-(1 + \frac{n}{p} - \frac{n}{q})}$. Such bounds are also valid for complex time. For $n=1$, we apply our off-diagonal bounds to prove that the Dirichlet-to-Neumann operator associated with a system generates an analytic semigroup on $L^p(\Gamma)$ for all $p \in (1, \infty)$. In addition, the corresponding evolution problem has $L^q(L^p)$-maximal regularity

On mixed boundary conditions, function spaces, and Kato’s square root property

In this thesis, a framework for the analytical treatment of mixed boundary conditions is given. Later, these results are applied to solve Lions' variation of the Kato square root problem

Performance of the bwHPC cluster in the production of μ -> t embedded events used for the prediction of background for H -> tt analyses

In high energy physics, a main challenge is the accurate prediction of background events at a particle detector. These events are usually estimated by simulation. As an alternative, data-driven methods use observed events to derive a background prediction and are often less computationally expensive than simulation. The lepton embedding method presents a data-driven method to estimate the background from Z ! events for Higgs boson analyses in the same final state. Z ! μμ events recorded by the CMS experiment are selected, the muons are removed from the event and replaced with simulated leptons with the same kinematic properties as the removed muons. The resulting hybrid event provides an improved description of pile-up and the underlying event compared to the simulation of the full proton-proton collision. In this paper the production of these hybrid events used by the CMS collaboration is described. The production relies on the resources made available by the bwHPC project. The data used for this purpose correspond to 65 million di-muon events collected in 2017 by CMS

Performance of the German version of the PARCA-R questionnaire as a developmental screening tool in two-year-old very preterm infants.

To validate and test a German version of the revised Parent Report of Children's Abilities questionnaire (PARCA-R). Multicentre cross-sectional study. Parents of infants born <32 gestational weeks, completed the PARCA-R within three weeks before the follow-up assessment of their child at age two years. Infants were assessed using the Mental Development Index (MDI) of the Bayley Scales of Infant Development 2nd edition (BSID-II). Pearson correlation between the Parent Report Composite (PRC) of the PARCA-R and MDI was tested. The optimal PRC cut-off for predicting moderate-to-severe mental delay, defined as MDI<70, was identified through the receiver operating characteristic (ROC) curve. PARCA-R and BSID-II data were collected from 154 consecutive infants [51% girls, mean (SD) gestational age 29.0 (2.0) weeks, birth weight 1174 (345) grams] at 23.2 (1.6) months of corrected age. The PRC score [70.5 (31.1)] correlated with the MDI [92.2 (17.3); R = 0.54; p < 0.0001]. The optimal PRC cut-off for identifying mental delay was 44 with 0.81 (0.54-0.96) sensitivity (95%-CI), 0.81 (0.74-0.87) specificity, area under the ROC curve of 0.840 (0.729-0.952). The German version of the PARCA-R had good validity with the BSID-II and PCR scores < 44 proved optimal discriminatory power for the identification of mental delay at two years of corrected age