Neckpinch dynamics for asymmetric surfaces evolving by mean curvature flow

We study surfaces evolving by mean curvature flow (MCF). For an open set of initial data that are $C^3$-close to round, but without assuming rotational symmetry or positive mean curvature, we show that MCF solutions become singular in finite time by forming neckpinches, and we obtain detailed asymptotics of that singularity formation. Our results show in a precise way that MCF solutions become asymptotically rotationally symmetric near a neckpinch singularity.Comment: This revision corrects minor but potentially confusing misprints in Section

Ionization of Atoms in a Thermal Field

We study the stationary states of a quantum mechanical system describing an atom coupled to black-body radiation at positive temperature. The stationary states of the non-interacting system are given by product states, where the particle is in a bound state corresponding to an eigenvalue of the particle Hamiltonian, and the field is in its equilibrium state. We show that if Fermi's Golden Rule predicts that a stationary state disintegrates after coupling to the radiation field then it is unstable, provided the coupling constant is sufficiently small (depending on the temperature). The result is proven by analyzing the spectrum of the thermal Hamiltonian (Liouvillian) of the system within the framework of $W^*$-dynamical systems. A key element of our spectral analysis is the positive commutator method

Unwelcome guests – the role of gland-associated Helicobacter pylori infection in gastric carcinogenesis

Helicobacter pylori (H. pylori) are Gram-negative bacteria that cause chronic gastritis and are considered the main risk factor for the development of gastric cancer. H. pylori have evolved to survive the harsh luminal environment of the stomach and are known to cause damage and signaling aberrations in gastric epithelial cells, which can result in premalignant and malignant pathology. As well as colonizing the gastric mucus and surface epithelial cells, a subpopulation of H. pylori can invade deep into the gastric glands and directly interact with progenitor and stem cells. Gland colonization therefore bears the potential to cause direct injury to long-lived cells. Moreover, this bacterial subpopulation triggers a series of host responses that cause an enhanced proliferation of stem cells. Here, we review recent insights into how gastric gland colonization by H. pylori is established, the resulting pro-carcinogenic epithelial signaling alterations, as well as new insights into stem cell responses to infection. Together these point towards a critical role of gland-associated H. pylori in the development of gastric cancer