Spectral Triples on Thermodynamic Formalism and Dixmier Trace Representations of Gibbs: theory and examples

In this paper we construct spectral triples $(A,H,D)$ on the symbolic space when the alphabet is finite. We describe some new results for the associated Dixmier trace representations for Gibbs probabilities (for potentials with less regularity than H\"older) and for a certain class of functions. The Dixmier trace representation can be expressed as the limit of a certain zeta function obtained from high order iterations of the Ruelle operator. Among other things we consider a class of examples where we can exhibit the explicit expression for the zeta function. We are also able to apply our reasoning for some parameters of the Dyson model (a potential on the symbolic space $\{-1,1\}^\mathbb{N}$) and for a certain class of observables. Nice results by R. Sharp, M.~Kesseb\"ohmer and T.~Samuel for Dixmier trace representations of Gibbs probabilities considered the case where the potential is of H\"older class. We also analyze a particular case of a pathological continuous potential where the Dixmier trace representation - via the associated zeta function - is not true.Comment: the tile was modified and there are two more author

Acute and long-term cardioprotective effects of the Traditional Chinese Medicine MLC901 against myocardial ischemia-reperfusion injury in mice

Abstract MLC901, a traditional Chinese medicine containing a cocktail of active molecules, both reduces cerebral infarction and improves recovery in patients with ischemic stroke. The aim of this study was to evaluate the acute and long-term benefits of MLC901 in ischemic and reperfused mouse hearts. Ex vivo, under physiological conditions, MLC901 did not show any modification in heart rate and contraction amplitude. However, upon an ischemic insult, MLC901 administration during reperfusion, improved coronary flow in perfused hearts. In vivo, MLC901 (4 µg/kg) intravenous injection 5 minutes before reperfusion provided a decrease in both infarct size (49.8%) and apoptosis (49.9%) after 1 hour of reperfusion. Akt and ERK1/2 survival pathways were significantly activated in the myocardium of those mice. In the 4-month clinical follow-up upon an additional continuous per os administration, MLC901 treatment decreased cardiac injury as revealed by a 45%-decrease in cTnI plasmatic concentrations and an improved cardiac performance assessed by echocardiography. A histological analysis revealed a 64%-decreased residual scar fibrosis and a 44%-increased vascular density in the infarct region. This paper demonstrates that MLC901 treatment was able to provide acute and long-term cardioprotective effects in a murine model of myocardial ischemia-reperfusion injury in vivo