On the Variational Regularity of Cameron-Martin paths

It is a well-known fact that finite rho-variation of the covariance (in 2D sense) of a general Gaussian process implies finite rho-variation of Cameron-Martin paths. In the special case of fractional Brownian motion (think: 2H=1/rho), in the rougher than Brownian regime, a sharper result holds thanks to a Besov-type embedding [Friz-Victoir, JFA, 2006]. In the present note we give a general result which closes this gap. We comment on the importance of this result for various applications.Comment: The contents of this paper are now included in arXiv:1307.346

Stochastic Modified Flows, Mean-Field Limits and Dynamics of Stochastic Gradient Descent

We propose new limiting dynamics for stochastic gradient descent in the small learning rate regime called stochastic modified flows. These SDEs are driven by a cylindrical Brownian motion and improve the so-called stochastic modified equations by having regular diffusion coefficients and by matching the multi-point statistics. As a second contribution, we introduce distribution dependent stochastic modified flows which we prove to describe the fluctuating limiting dynamics of stochastic gradient descent in the small learning rate - infinite width scaling regime.Comment: 24 page

Midkine drives cardiac inflammation by promoting neutrophil trafficking and NETosis in myocarditis

Heart failure due to dilated cardiomyopathy is frequently caused by myocarditis. However, the pathogenesis of myocarditis remains incompletely understood. Here, we report the presence of neutrophil extracellular traps (NETs) in cardiac tissue of patients and mice with myocarditis. Inhibition of NET formation in experimental autoimmune myocarditis (EAM) of mice substantially reduces inflammation in the acute phase of the disease. Targeting the cytokine midkine (MK), which mediates NET formation in vitro, not only attenuates NET formation in vivo and the infiltration of polymorphonuclear neutrophils (PMNs) but also reduces fibrosis and preserves systolic function during EAM. Low-density lipoprotein receptor-related protein 1 (LRP1) acts as the functionally relevant receptor for MK-induced PMN recruitment as well as NET formation. In summary, NETosis substantially contributes to the pathogenesis of myocarditis and drives cardiac inflammation, probably via MK, which promotes PMN trafficking and NETosis. Thus, MK as well as NETs may represent novel therapeutic targets for the treatment of cardiac inflammation

Strong convergence rates for explicit space-time discrete numerical approximations of stochastic Allen-Cahn equations

Becker S, Gess B, Jentzen A, Kloeden PE. Strong convergence rates for explicit space-time discrete numerical approximations of stochastic Allen-Cahn equations. Stochastics and Partial Differential Equations : Analysis and Computations . 2022.Strong convergence rates for fuly discrete numerical approximations of space-time white noise driven SPDEs with superlinearly growing nonlinearities, such as the stochastic Allen-Cahn equation with space-time white noise, are shown. The obtained strong rates of convergence are essentially sharp

Lower and upper bounds for strong approximation errors for numerical approximations of stochastic heat equations

Becker S, Gess B, Jentzen A, Kloeden PE. Lower and upper bounds for strong approximation errors for numerical approximations of stochastic heat equations. BIT NUMERICAL MATHEMATICS. 2020.This article establishes optimal upper and lower error estimates for strong full-discrete numerical approximations of the stochastic heat equation driven by space-time white noise. Thereby, this work proves the optimality of the strong convergence rates for certain full-discrete approximations of stochastic Allen-Cahn equations with space-time white noise which have been obtained in a recent previous work of the authors of this article

Characterization of Naïve and Vitamin C-Treated Mouse Schwann Cell Line MSC80: Induction of the Antioxidative Thioredoxin Related Transmembrane Protein 1

Schwann cells (SCs) are essential in the production of the axon-wrapping myelin sheath and provide trophic function and repair mechanisms in the peripheral nerves. Consequently, well-characterized SC in vitro models are needed to perform preclinical studies including the investigation of the complex biochemical adaptations occurring in the peripheral nervous system (PNS) under different (patho)physiological conditions. MSC80 cells represent a murine SC line used as an in vitro system for neuropathological studies. Here, we introduce the most abundant 9532 proteins identified via mass spectrometry-based protein analytics, and thus provide the most comprehensive SC protein catalogue published thus far. We cover proteins causative for inherited neuropathies and demonstrate that in addition to cytoplasmic, nuclear and mitochondrial proteins and others belonging to the protein processing machinery are very well covered. Moreover, we address the suitability of MSC80 to examine the molecular effect of a drug-treatment by analyzing the proteomic signature of Vitamin C-treated cells. Proteomic findings, immunocytochemistry, immunoblotting and functional experiments support the concept of a beneficial role of Vitamin C on oxidative stress and identified TMX1 as an oxidative stress protective factor, which might represent a promising avenue for therapeutic intervention of PNS-disorders with oxidative stress burden such as diabetic neuropathy