Discussion on the paper “Real-Time Prediction of Clinical Trial Enrollment and Event Counts: A Review”, by DF Heitjan, Z Ge, and GS Ying

No abstract available

Symplectic Cobordism in Small Dimensions and a Series of Elements of Order Four

We present the structure of symplectic cobordism ring $MSp_{*}$ in dimensions up to 51 and give a construction of an infinite series of elements $\Gamma_i$, $i=1, 3,4, ...$, of order four in this ring, where $\operatorname{dim} \, \Gamma_i=8i+95$. The key element of the series is $\Gamma_1$ in dimension 103.Comment: 117 pages, 18 table

Modeling restricted enrollment and optimal cost-efficient design in multicenter clinical trials

Design and forecasting of patient enrollment is among the greatest challenges that the clinical research enterprize faces today, as inefficient enrollment can be a major cause of drug development delays. Therefore, the development of the innovative statistical and artificial intelligence technologies for improving the efficiency of clinical trials operation are of the imperative need. This paper is describing further developments in the innovative statistical methodology for modeling and forecasting patient enrollment. The underlying technique uses a Poisson-gamma enrollment model developed by Anisimov & Fedorov in the previous publications and is extended here to analytic modeling of the enrollment on country/region level. A new analytic technique based on the approximation of the enrollment process in country/region by a Poisson-gamma process with aggregated parameters is developed. Another innovative direction is the development of the analytic technique for modeling the enrollment under some restrictions (enrollment caps in countries). Some discussion on using historic trials for better prediction of the enrollment in the new trials is provided. These results are used for solving the problem of optimal trial cost-efficient enrollment design: find an optimal allocation of sites/countries that minimizes the global trial cost given that the probability to reach an enrollment target in time is no less than some prescribed probability. Different techniques to find an optimal solution for high dimensional optimization problem for the cases of unrestricted and restricted enrollment and for a small and large number of countries are discussed.Comment: 22 pages, 3 figure

Phantom fields: bounce solutions in the early Universe and S-branes

The cosmological model with two phantom scalar fields with the special choice of field's potential is considered. The obtained regular solution describes a bounce with a subsequent transition to the de Sitter stage of the expansion of the Universe. This solution also could be interpreted as a S-brane solution.Comment: one reference and new interpretation of the solution are added, and the title is change

Role of Coulomb correlation on magnetic and transport properties of doped manganites: La0.5Sr0.5MnO3 and LaSr2Mn2O7

Results of LSDA and LSDA+U calculations of the electronic structure and magnetic configurations of the 50% hole-doped pseudocubic perovskite La0.5Sr0.5MnO3 and double layered LaSr2Mn2O7 are presented. We demonstrate that the on-site Coulomb correlation (U) of Mn d electrons has a very different influence on the (i) band formations, (ii) magnetic ground states, (iii) interlayer exchange interactions, and (iv) anisotropy of the electrical transport in these two manganites. A possible reason why the LSDA failures in predicting observed magnetic and transport properties of the double layered compound - in contrast to the doped perovskite manganite - is considered on the basis of a p-d hybridization analysis.Comment: 11 pages, 3 figure