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

Smartphone-based cardiac implantable electronic device remote monitoring: improved compliance and connectivity

Aims: Remote monitoring (RM) is the standard of care for follow up of patients with cardiac implantable electronic devices. The aim of this study was to compare smartphone-based RM (SM-RM) using patient applications (myMerlinPulse™ app) with traditional bedside monitor RM (BM-RM). Methods and results: The retrospective study included de-identified US patients who received either SM-RM or BM-RM capable of implantable cardioverter defibrillators or cardiac resynchronization therapy defibrillators (Abbott, USA). Patients in SM-RM and BM-RM groups were propensity-score matched on age and gender, device type, implant year, and month. Compliance with RM was quantified as the proportion of patients enrolling in the RM system (Merlin.net™) and transmitting data at least once. Connectivity was measured by the median number of days between consecutive transmissions per patient. Of the initial 9714 patients with SM-RM and 26 679 patients with BM-RM, 9397 patients from each group were matched. Remote monitoring compliance was higher in SM-RM; significantly more patients with SM-RM were enrolled in RM compared with BM-RM (94.4 vs. 85.0%, P < 0.001), similar number of patients in the SM-RM group paired their device (95.1 vs. 95.0%, P = 0.77), but more SM-RM patients transmitted at least once (98.1 vs. 94.3%, P < 0.001). Connectivity was significantly higher in the SM-RM, with patients transmitting data every 1.2 (1.1, 1.7) vs. every 1.7 (1.5, 2.0) days with BM-RM (P < 0.001) and remained better over time. Significantly more SM-RM patients utilized patient-initiated transmissions compared with BM-RM (55.6 vs. 28.1%, P < 0.001). Conclusion: In this large real-world study, patients with SM-RM demonstrated improved compliance and connectivity compared with BM-RM

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

Discrete approaches to quantum gravity in four dimensions

The construction of a consistent theory of quantum gravity is a problem in theoretical physics that has so far defied all attempts at resolution. One ansatz to try to obtain a non-trivial quantum theory proceeds via a discretization of space-time and the Einstein action. I review here three major areas of research: gauge-theoretic approaches, both in a path-integral and a Hamiltonian formulation, quantum Regge calculus, and the method of dynamical triangulations, confining attention to work that is strictly four-dimensional, strictly discrete, and strictly quantum in nature.Comment: 33 pages, invited contribution to Living Reviews in Relativity; the author welcomes any comments and suggestion