Noncomputability Arising In Dynamical Triangulation Model Of Four-Dimensional Quantum Gravity

Computations in Dynamical Triangulation Models of Four-Dimensional Quantum Gravity involve weighted averaging over sets of all distinct triangulations of compact four-dimensional manifolds. In order to be able to perform such computations one needs an algorithm which for any given $N$ and a given compact four-dimensional manifold $M$ constructs all possible triangulations of $M$ with $\leq N$ simplices. Our first result is that such algorithm does not exist. Then we discuss recursion-theoretic limitations of any algorithm designed to perform approximate calculations of sums over all possible triangulations of a compact four-dimensional manifold.Comment: 8 Pages, LaTex, PUPT-132

Smoking cessation and risk of recurrent cardiovascular events and mortality after a first manifestation of arterial disease

Aims To quantify the relation between smoking cessation after a first cardiovascular (CV) event and risk of recurrent CV events and mortality. Methods Data were available from 4,673 patients aged 61 ± 8.7 years, with a recent (≤1 year) first manifestation of arterial disease participating in the SMART-cohort. Cox models were used to quantify the relation between smoking status and risk of recurrent major atherosclerotic cardiovascular events (MACE including stroke, MI and vascular mortality) and mortality. In addition, survival according to smoking status was plotted, taking competing risk of non-vascular mortality into account. Results A third of the smokers stopped after their first CV event. During a median of 7.4 (3.7–10.8) years of follow-up, 794 patients died and 692 MACE occurred. Compared to patients who continued to smoke, patients who quit had a lower risk of recurrent MACE (adjusted HR 0.66, 95% CI 0.49–0.88) and all-cause mortality (adjusted HR 0.63, 95% CI 0.48–0.82). Patients who reported smoking cessation on average lived 5 life years longer and recurrent MACE occurred 10 years later. In patients with a first CV event N70 years, cessation of smoking had improved survival which on average was comparable to former or never smokers. Conclusions Irrespective of age at first CV event, cessation of smoking after a first CV event is related to a substantial lower risk of recurrent vascular events and all-cause mortality. Since smoking cessation is more effective in reducing CV risk than any pharmaceutical treatment of major risk factors, it should be a key objective for patients with vascular disease. (A

In vitro accuracy and fit of milled Natural Inlays

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