A Sublinear Variance Bound for Solutions of a Random Hamilton Jacobi Equation

We estimate the variance of the value function for a random optimal control problem. The value function is the solution $w^\epsilon$ of a Hamilton-Jacobi equation with random Hamiltonian $H(p,x,\omega) = K(p) - V(x/\epsilon,\omega)$ in dimension $d \geq 2$. It is known that homogenization occurs as $\epsilon \to 0$, but little is known about the statistical fluctuations of $w^\epsilon$. Our main result shows that the variance of the solution $w^\epsilon$ is bounded by $O(\epsilon/|\log \epsilon|)$. The proof relies on a modified Poincar\'e inequality of Talagrand

Mechanochemical Solvent-Free Catalytic C—H Methylation

The mechanochemical, solvent-free, highly regioselective, rhodium-catalyzed C-H methylation of (hetero)arenes is reported. The reaction shows excellent functional-group compatibility and is demonstrated to work for the late-stage C-H methylation of biologically active compounds. The method requires no external heating and benefits from considerably shorter reaction times than previous solution-based C-H methylation protocols. Additionally, the mechanochemical approach is shown to enable the efficient synthesis of organometallic complexes that are difficult to generate conventionally

Correlation of computed tomography with carotid plaque transcriptomes associates calcification with lesion-stabilization

Background and aims: Unstable carotid atherosclerosis causes stroke, but methods to identify patients and lesions at risk are lacking. We recently found enrichment of genes associated with calcification in carotid plaques from asymptomatic patients. Here, we hypothesized that calcification represents a stabilising feature of plaques and investigated how macro-calcification, as estimated by computed tomography (CT), correlates with gene expression profiles in lesions. Methods: Plaque calcification was measured in pre-operative CT angiographies. Plaques were sorted into high- and lowcalcified, profiled with microarrays, followed by bioinformatic analyses. Immunohistochemistry and qPCR were performed to evaluate the findings in plaques and arteries with medial calcification from chronic kidney disease patients. Results: Smooth muscle cell (SMC) markers were upregulated in high-calcified plaques and calcified plaques from symptomatic patients, whereas macrophage markers were downregulated. The most enriched processes in high-calcified plaques were related to SMCs and extracellular matrix (ECM) organization, while inflammation, lipid transport and chemokine signaling were repressed. These findings were confirmed in arteries with high medial calcification. Proteoglycan 4 (PRG4) was identified as the most upregulated gene in association with plaque calcification and found in the ECM, SMA+ and CD68+/TRAP + cells. Conclusions: Macro-calcification in carotid lesions correlated with a transcriptional profile typical for stable plaques, with altered SMC phenotype and ECM composition and repressed inflammation. PRG4, previously not described in atherosclerosis, was enriched in the calcified ECM and localized to activated macrophages and smooth muscle-like cells. This study strengthens the notion that assessment of calcification may aid evaluation of plaque phenotype and stroke risk.The European Union’s Horizon 2020/Marie Sklodowska-Curie grant agreement No 722609 (INTRICARE);Swedish Heart and Lung FoundationSwedish Research Council (K2009-65X-2233-01-3, K2013- 65X-06816-30-4, 349-2007-8703)Uppdrag Besegra Stroke (P581/ 2011-123)Stockholm County Council (ALF2011-0260, ALF-2011- 0279)Swedish Society for Medical ResearchTore Nilsson’s FoundationMagnus Bergvall’s FoundationKarolinska Institutet FoundationEuropean Commission (722609)Publishe