On the Absence of an Exponential Bound in Four Dimensional Simplicial Gravity

We have studied a model which has been proposed as a regularisation for four dimensional quantum gravity. The partition function is constructed by performing a weighted sum over all triangulations of the four sphere. Using numerical simulation we find that the number of such triangulations containing $V$ simplices grows faster than exponentially with $V$. This property ensures that the model has no thermodynamic limit.Comment: 8 pages, 2 figure

The area of horizons and the trapped region

This paper considers some fundamental questions concerning marginally trapped surfaces, or apparent horizons, in Cauchy data sets for the Einstein equation. An area estimate for outermost marginally trapped surfaces is proved. The proof makes use of an existence result for marginal surfaces, in the presence of barriers, curvature estimates, together with a novel surgery construction for marginal surfaces. These results are applied to characterize the boundary of the trapped region.Comment: 44 pages, v3: small changes in presentatio

Insertable cardiac monitoring results in higher rates of atrial fibrillation diagnosis and oral anticoagulation prescription after ischaemic stroke

Aims: After an ischaemic stroke, atrial fibrillation (AF) detection allows for improved secondary prevention strategies. This study aimed to compare AF detection and oral anticoagulant (OAC) initiation in patients with an insertable cardiac monitor (ICM) vs. external cardiac monitor (ECM) after ischaemic stroke. Methods and results: Medicare Fee-for-Service (FFS) insurance claims and Abbott Labs device registration data were used to identify patients hospitalized with an ischaemic stroke in 2017-2019 who received an ICM or ECM within 3 months. Patients with continuous Medicare FFS insurance and prescription drug enrolment in the prior year were included. Patients with prior AF, atrial flutter, cardiac devices, or OAC were excluded. Insertable cardiac monitor and ECM patients were propensity score matched 1:4 on demographics, comorbidities, and stroke hospitalization characteristics. The outcomes of interest were AF detection and OAC initiation evaluated with Kaplan-Meier and Cox proportional hazard regression analyses. A total of 5702 Medicare beneficiaries (ICM, n = 444; ECM, n = 5258) met inclusion criteria. The matched cohort consisted of 2210 Medicare beneficiaries (ICM, n = 442; ECM, n = 1768) with 53% female, mean age 75 years, and mean CHA2DS2-VASc score 4.6 (1.6). Insertable cardiac monitor use was associated with a higher probability of AF detection [(hazard ratio (HR) 2.88, 95% confidence interval (CI) (2.31, 3.59)] and OAC initiation [HR 2.91, CI (2.28, 3.72)] compared to patients monitored only with ECM. Conclusion: Patients with an ischaemic stroke monitored with an ICM were almost three times more likely to be diagnosed with AF and to be prescribed OAC compared to patients who received ECM only

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

Discontinuity of capacitance at the onset of surface superconductivity

The effect of the magnetic field on a capacitor with a superconducting electrode is studied within the Ginzburg-Landau approach. It is shown that the capacitance has a discontinuity at the onset of the surface superconductivity $B_{\rm c3}$ which is expressed as a discontinuity in the penetration depth of the electric field into metals. Estimates show that this discontinuity is observable with recent bridges for both conventional and high-$T_{\rm c}$ superconductors of the type-II

Protein folding using contact maps

We present the development of the idea to use dynamics in the space of contact maps as a computational approach to the protein folding problem. We first introduce two important technical ingredients, the reconstruction of a three dimensional conformation from a contact map and the Monte Carlo dynamics in contact map space. We then discuss two approximations to the free energy of the contact maps and a method to derive energy parameters based on perceptron learning. Finally we present results, first for predictions based on threading and then for energy minimization of crambin and of a set of 6 immunoglobulins. The main result is that we proved that the two simple approximations we studied for the free energy are not suitable for protein folding. Perspectives are discussed in the last section.Comment: 29 pages, 10 figure

The type numbers of closed geodesics

A short survey on the type numbers of closed geodesics, on applications of the Morse theory to proving the existence of closed geodesics and on the recent progress in applying variational methods to the periodic problem for Finsler and magnetic geodesicsComment: 29 pages, an appendix to the Russian translation of "The calculus of variations in the large" by M. Mors

Lorentzian and Euclidean Quantum Gravity - Analytical and Numerical Results

We review some recent attempts to extract information about the nature of quantum gravity, with and without matter, by quantum field theoretical methods. More specifically, we work within a covariant lattice approach where the individual space-time geometries are constructed from fundamental simplicial building blocks, and the path integral over geometries is approximated by summing over a class of piece-wise linear geometries. This method of ``dynamical triangulations'' is very powerful in 2d, where the regularized theory can be solved explicitly, and gives us more insights into the quantum nature of 2d space-time than continuum methods are presently able to provide. It also allows us to establish an explicit relation between the Lorentzian- and Euclidean-signature quantum theories. Analogous regularized gravitational models can be set up in higher dimensions. Some analytic tools exist to study their state sums, but, unlike in 2d, no complete analytic solutions have yet been constructed. However, a great advantage of our approach is the fact that it is well-suited for numerical simulations. In the second part of this review we describe the relevant Monte Carlo techniques, as well as some of the physical results that have been obtained from the simulations of Euclidean gravity. We also explain why the Lorentzian version of dynamical triangulations is a promising candidate for a non-perturbative theory of quantum gravity.Comment: 69 pages, 16 figures, references adde