Quantum metric spaces as a model for pregeometry

A new arena for the dynamics of spacetime is proposed, in which the basic quantum variable is the two-point distance on a metric space. The scaling dimension (that is, the Kolmogorov capacity) in the neighborhood of each point then defines in a natural way a local concept of dimension. We study our model in the region of parameter space in which the resulting spacetime is not too different from a smooth manifold.

Quantum metric spaces as a model for pregeometry

A new arena for the dynamics of spacetime is proposed, in which the basic quantum variable is the two-point distance on a metric space. The scaling dimension (that is, the Kolmogorov capacity) in the neighborhood of each point then defines in a natural way a local concept of dimension. We study our model in the region of parameter space in which the resulting spacetime is not too different from a smooth manifold.

Carleson Measures and Logvinenko-Sereda sets on compact manifolds

Given a compact Riemannian manifold $M$ of dimension $m \geq 2$, we study the space of functions of $L^2(M)$generated by eigenfunctions ofeigenvalues less than $L \geq 1$ associated to the Laplace-Beltrami operator on $M$. On these spaces we give a characterization of the Carleson measures and the Logvinenko-Sereda sets.

Generation of symmetric periodic orbits by a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2 in R3

In this paper we will find a continuous of periodic orbits passing near infinity for a class of polynomial vector fields in R3. We consider polynomial vector fields that are invariant under a symmetry with respect to a plane and that possess a “generalized heteroclinic loop” formed by two singular points e+ and e− at infinity and their invariant manifolds � and . � is an invariant manifold of dimension 1 formed by an orbit going from e− to e+, � is contained in R3 and is transversal to . is an invariant manifold of dimension 2 at infinity. In fact, is the 2–dimensional sphere at infinity in the Poincar´e compactification minus the singular points e+ and e−. The main tool for proving the existence of such periodic orbits is the construction of a Poincar´e map along the generalized heteroclinic loop together with the symmetry with respect to .

The differentiable chain functor is not homotopy equivalent to the continuous chain functor

Let $S_*$ and $S_*^\{infty}$ be the functors of continuous and differentiable singular chains on the category of differentiable manifolds. We prove that the natural transformation $i: S_*^\infty \rightarrow S_*$, which induces homology equivalences over each manifold, is not a natural homotopy equivalence.

Prehospital ticagrelor in ST-segment elevation myocardial infarction

Background:The direct-acting platelet P2Y receptor antagonist ticagrelor can reduce the incidence of major adverse cardiovascular events when administered at hospital admission to patients with ST-segment elevation myocardial infarction (STEMI). Whether prehospital administration of ticagrelor can improve coronary reperfusion and the clinical outcome is unknown. Methods: We conducted an international, multicenter, randomized, double-blind study involving 1862 patients with ongoing STEMI of less than 6 hours' duration, comparing prehospital (in the ambulance) versus in-hospital (in the catheterization laboratory) treatment with ticagrelor. The coprimary end points were the proportion of patients who did not have a 70% or greater resolution of ST-segment elevation before percutaneous coronary intervention (PCI) and the proportion of patients who did not have Thrombolysis in Myocardial Infarction flow grade 3 in the infarct-related artery at initial angiography. Secondary end points included the rates of major adverse cardiovascular events and definite stent thrombosis at 30 days. Results: The median time from randomization to angiography was 48 minutes, and the median time difference between the two treatment strategies was 31 minutes. The two coprimary end points did not differ significantly between the prehospital and in-hospital groups. The absence of ST-segment elevation resolution of 70% or greater after PCI (a secondary end point) was reported for 42.5% and 47.5% of the patients, respectively. The rates of major adverse cardiovascular events did not differ significantly between the two study groups. The rates of definite stent thrombosis were lower in the prehospital group than in the in-hospital group (0% vs. 0.8% in the first 24 hours; 0.2% vs. 1.2% at 30 days). Rates of major bleeding events were low and virtually identical in the two groups, regardless of the bleeding definition used