Large deviations for many Brownian bridges with symmetrised initial-terminal condition

Consider a large system of $N$ Brownian motions in $\mathbb{R}^d$ with some non-degenerate initial measure on some fixed time interval $[0,\beta]$ with symmetrised initial-terminal condition. That is, for any $i$, the terminal location of the $i$-th motion is affixed to the initial point of the $\sigma(i)$-th motion, where $\sigma$ is a uniformly distributed random permutation of $1,...,N$. Such systems play an important role in quantum physics in the description of Boson systems at positive temperature $1/\beta$. In this paper, we describe the large-N behaviour of the empirical path measure (the mean of the Dirac measures in the $N$ paths) and of the mean of the normalised occupation measures of the $N$ motions in terms of large deviations principles. The rate functions are given as variational formulas involving certain entropies and Fenchel-Legendre transforms. Consequences are drawn for asymptotic independence statements and laws of large numbers. In the special case related to quantum physics, our rate function for the occupation measures turns out to be equal to the well-known Donsker-Varadhan rate function for the occupation measures of one motion in the limit of diverging time. This enables us to prove a simple formula for the large-N asymptotic of the symmetrised trace of ${\rm e}^{-\beta \mathcal{H}_N}$, where $\mathcal{H}_N$ is an $N$-particle Hamilton operator in a trap

Prospective observational cohort study of the association between antiplatelet therapy, bleeding and thrombosis in patients with coronary stents undergoing noncardiac surgery

Background: The perioperative management of antiplatelet therapy in noncardiac surgery patients who have undergone previous percutaneous coronary intervention (PCI) remains a dilemma. Continuing dual antiplatelet therapy (DAPT) may carry a risk of bleeding, while stopping antiplatelet therapy may increase the risk of perioperative major adverse cardiovascular events (MACE). Methods: Occurrence of Bleeding and Thrombosis during Antiplatelet Therapy In Non-Cardiac Surgery (OBTAIN) was an international prospective multicentre cohort study of perioperative antiplatelet treatment, MACE, and serious bleeding in noncardiac surgery. The incidences of MACE and bleeding were compared in patients receiving DAPT, monotherapy, and no antiplatelet therapy before surgery. Unadjusted risk ratios were calculated taking monotherapy as the baseline. The adjusted risks of bleeding and MACE were compared in patients receiving monotherapy and DAPT using propensity score matching. Results: A total of 917 patients were recruited and 847 were eligible for inclusion. Ninety-six patients received no antiplatelet therapy, 526 received monotherapy with aspirin, and 225 received DAPT. Thirty-two patients suffered MACE and 22 had bleeding. The unadjusted risk ratio for MACE in patients receiving DAPT compared with monotherapy was 1.9 (0.93–3.88), P=0.08. There was no difference in MACE between no antiplatelet treatment and monotherapy 1.03 (0.31–3.46), P=0.96. Bleeding was more frequent with DAPT 6.55 (2.3–17.96) P=0.0002. In a propensity matched analysis of 177 patients who received DAPT and 177 monotherapy patients, the risk ratio for MACE with DAPT was 1.83 (0.69–4.85), P=0.32. The risk of bleeding was significantly greater in the DAPT group 4.00 (1.15–13.93), P=0.031. Conclusions: OBTAIN showed an increased risk of bleeding with DAPT and found no evidence for protective effects of DAPT from perioperative MACE in patients who have undergone previous PCI

Information loss in coarse-graining of stochastic particle dynamics

Recently a new class of approximating coarse-grained stochastic processes and associated Monte Carlo algorithms were derived directly from microscopic stochastic lattice models for the adsorption/desorption and diffusion of interacting particles(12,13,15). The resulting hierarchy of stochastic processes is ordered by the level of coarsening in the space/time dimensions and describes mesoscopic scales while retaining a significant amount of microscopic detail on intermolecular forces and particle fluctuations. Here we rigorously compute in terms of specific relative entropy the information loss between non-equilibrium exact and approximating coarse-grained adsorption/desorption lattice dynamics. Our result is an error estimate analogous to rigorous error estimates for finite element/finite difference approximations of Partial Differential Equations. We prove this error to be small as long as the level of coarsening is small compared to the range of interaction of the microscopic model. This result gives a first mathematical reasoning for the parameter regimes for which approximating coarse-grained Monte Carlo algorithms are expected to give errors within a given tolerance

Information loss in coarse-graining of stochastic particle dynamics

Recently a new class of approximating coarse-grained stochastic processes and associated Monte Carlo algorithms were derived directly from microscopic stochastic lattice models for the adsorption/desorption and diffusion of interacting particles(12,13,15). The resulting hierarchy of stochastic processes is ordered by the level of coarsening in the space/time dimensions and describes mesoscopic scales while retaining a significant amount of microscopic detail on intermolecular forces and particle fluctuations. Here we rigorously compute in terms of specific relative entropy the information loss between non-equilibrium exact and approximating coarse-grained adsorption/desorption lattice dynamics. Our result is an error estimate analogous to rigorous error estimates for finite element/finite difference approximations of Partial Differential Equations. We prove this error to be small as long as the level of coarsening is small compared to the range of interaction of the microscopic model. This result gives a first mathematical reasoning for the parameter regimes for which approximating coarse-grained Monte Carlo algorithms are expected to give errors within a given tolerance

Electricity sector in Mexico: Current status. Contribution of renewable energy sources

The challenge facing the world electricity sector is the cost incurred in maintaining the system and seeing to the environmental effects it causes. In Mexico the grid is supplied by thermal plants fed by oil products. Its great potential of renewable energies clearly shown in studies by national and international scholars has led the government to become more committed to take advantage of these energies. The goal is to reduce dependence on fossil fuels to generate electricity and to reduce the emission of greenhouse gases. In this article we analyse the current state of renewable energies, the conditions needed to foster them and the legislative changes already introduced to promote their greater part in the national electricity grid.Grid Biogas Renewable energy