Remarks on hard Lefschetz conjectures on Chow groups

We propose two conjectures of Hard Lefschetz type on Chow groups and prove them for some special cases. For abelian varieties, we shall show they are equivalent to well-known conjectures of Beauville and Murre.Comment: to appear in Sciences in China, Ser. A Mathematic

On Damage Spreading Transitions

We study the damage spreading transition in a generic one-dimensional stochastic cellular automata with two inputs (Domany-Kinzel model) Using an original formalism for the description of the microscopic dynamics of the model, we are able to show analitically that the evolution of the damage between two systems driven by the same noise has the same structure of a directed percolation problem. By means of a mean field approximation, we map the density phase transition into the damage phase transition, obtaining a reliable phase diagram. We extend this analysis to all symmetric cellular automata with two inputs, including the Ising model with heath-bath dynamics.Comment: 12 pages LaTeX, 2 PostScript figures, tar+gzip+u

Cohomological Hasse principle and motivic cohomology for arithmetic schemes

In 1985 Kazuya Kato formulated a fascinating framework of conjectures which generalizes the Hasse principle for the Brauer group of a global field to the so-called cohomological Hasse principle for an arithmetic scheme. In this paper we prove the prime-to-characteristic part of the cohomological Hasse principle. We also explain its implications on finiteness of motivic cohomology and special values of zeta functions.Comment: 47 pages, final versio

A Class of Topological Actions

We review definitions of generalized parallel transports in terms of Cheeger-Simons differential characters. Integration formulae are given in terms of Deligne-Beilinson cohomology classes. These representations of parallel transport can be extended to situations involving distributions as is appropriate in the context of quantized fields.Comment: 41 pages, no figure

Linear and Nonlinear Rogue Wave Statistics in the Presence of Random Currents

We review recent progress in modeling the probability distribution of wave heights in the deep ocean as a function of a small number of parameters describing the local sea state. Both linear and nonlinear mechanisms of rogue wave formation are considered. First, we show that when the average wave steepness is small and nonlinear wave effects are subleading, the wave height distribution is well explained by a single "freak index" parameter, which describes the strength of (linear) wave scattering by random currents relative to the angular spread of the incoming random sea. When the average steepness is large, the wave height distribution takes a very similar functional form, but the key variables determining the probability distribution are the steepness, and the angular and frequency spread of the incoming waves. Finally, even greater probability of extreme wave formation is predicted when linear and nonlinear effects are acting together.Comment: 25 pages, 12 figure

Biocompatibility of an apical ring plug for left ventricular assist device explantation: Results of a feasibility pre-clinical study

Background Patients receiving left ventricle assist devices (LVADs) as bridge to recovery remain a minority with 1%-5% of LVADs explanted after improvement of myocardial function. Nevertheless, considering the growing population of patients supported with LVADs, an increasing demand of new explantation strategies is expected in the near future. A novel plug for LVAD explantation has been developed and its biocompatibility profile needs to be proved. This study tested the biocompatibility of this novel plug in an in vivo ovine model. Methods Six adult Blackhead Persian female sheep received plug implantation on the cardiac apex via minimally invasive approach and were clinically observed up to 90 days. Echocardiography was performed to detect thrombus formation or further plug-related complications. After the observation period, euthanasia was performed and samples including the plug and the surrounding tissues were obtained to be analyzed with correlative light and electron microscopy. Organ necrosis, ischemia and peripheral embolism were investigated. Results Three animals survived surgery and completed the follow-up time without experiencing clinical complications. Echocardiographic controls excluded the presence of an intracavitary thrombus in the left ventricle (LV). Autopsy confirmed no signs of local infection, LV thrombus or peripheral embolism. Light and electron microscopy revealed an intact epithelium covering a layer of connective tissue on the plug surface facing the heart lumen. Conclusions This novel apical plug for LVAD explantation allows for endothelial and connective tissue growth on its ventricular side within 90 days from surgery. Further studies are required to fully demonstrate the biocompatibility of this apical plug and investigate the optimal anticoagulation regimen to be applied after implantation