On the stability of Brunn–Minkowski type inequalities

We establish the stability near a Euclidean ball of two conjectured inequalities: the dimensional Brunn–Minkowski inequality for radially symmetric log-concave measures in Rn, and of the log-Brunn–Minkowski inequality

Treatment of human lens epithelium with high levels of nanoceria leads to reactive oxygen species mediated apoptosis

Nanoceria (cerium oxide nanoparticles) have been shown to protect human lens epithelial cells (HLECs) from oxidative stress when used at low concentrations. However, there is a lack of understanding about the mechanism of the cytotoxic and genotoxic effects of nanoceria when used at higher concentrations. Here, we investigated the impact of 24-hour exposure to nanoceria in HLECs. Nanoceria’s effects on basal reactive oxygen species (ROS), mitochondrial morphology, membrane potential, ATP, genotoxicity, caspase activation and apoptotic hallmarks were investigated. Scanning electron microscopy-energy dispersive X-ray spectroscopy (SEM-EDX) studies on isolated mitochondria revealed significant uptake and localization of nanoceria in the mitochondria. At high nanoceria concentrations (400 µg mL−1), intracellular levels of ROS were increased and the HLECs exhibited classical hallmarks of apoptosis. These findings concur with the cells maintaining normal ATP levels necessary to execute the apoptotic process. These results highlight the need for nanoceria dose-effect studies on a range of cells and tissues to identify therapeutic concentrations in vitro or in viv