The incomplete beta function law for parallel tempering sampling of classical canonical systems

We show that the acceptance probability for swaps in the parallel tempering Monte Carlo method for classical canonical systems is given by a universal function that depends on the average statistical fluctuations of the potential and on the ratio of the temperatures. The law, called the incomplete beta function law, is valid in the limit that the two temperatures involved in swaps are close to one another. An empirical version of the law, which involves the heat capacity of the system, is developed and tested on a Lennard-Jones cluster. We argue that the best initial guess for the distribution of intermediate temperatures for parallel tempering is a geometric progression and we also propose a technique for the computation of optimal temperature schedules. Finally, we demonstrate that the swap efficiency of the parallel tempering method for condensed-phase systems decreases naturally to zero at least as fast as the inverse square root of the dimensionality of the physical system.Comment: 11 pages, 4 figures; minor changes; to appear in J. Chem. Phy

THE POWER’S MECHANISM OF A MONOPOLY IN A MARKET ECONOMY Antoniu Predescu, Spiru Haret University Iuliana Predescu, Romanian- American University Bucharesti Stela Aurelia Toader, Romanian- American University Bucharest Mihai Aristotel Ungureanu , Romanian- American University Bucharest

Monopolies make their presence felt in a market economy, not necessarilythrough 100% ownership control of a market, nor less, because there is a law thatsanction its existence; in most cases, the existence of a monopoly and hence its corollary,i.e. monopoly power, has as the primary cause the presence of market imperfections, thatis if those are present on the long term, become state of fact. Thus, in our approach, weconsider that to bet appropriate to release the mechanism of a monopoly, based on amathematical tool, which begins from the immutable economic concepts of monopoly.monopoly, monopolist, elasticity, demand

THE FIGHT AGAINST FRAUD AND TAX EVASION IN THE EUROPEAN UNION. THE PROTECTION OF COMMUNITY FINANCIAL INTERESTS IN ROMANIA

The European Union budget is financed by taxes paid by European taxpayers andserves for the development of projects of common interest. The European Community and itsMember States attach great importance to its protection, both in terms of proper collection of taxesand duties and also in terms of proper use of appropriations. This is one of the priorities of theinstitutions involved, as an obligation imposed by the Treaty establishing the EuropeanCommunity. The protection of European Union financial interests involve the detection, controland effective monitorising of fraud and any other illegal acts which result form the misuse of EUfunds and thus prejudicing the Community budget. Cooperation between national authorities andbetween them and EU institutions is a prerequisite for successful fight against fraud. In Romania,national coordinator of the fight against fraud, with responsibilities in control line use ofcommunity funds is European Anti-Fraud Office (OLAF).OLAF, DLAF, European funds, fraud

Sampling diffusive transition paths

We address the problem of sampling double-ended diffusive paths. The ensemble of paths is expressed using a symmetric version of the Onsager-Machlup formula, which only requires evaluation of the force field and which, upon direct time discretization, gives rise to a symmetric integrator that is accurate to second order. Efficiently sampling this ensemble requires avoiding the well-known stiffness problem associated with sampling infinitesimal Brownian increments of the path, as well as a different type of stiffness associated with sampling the coarse features of long paths. The fine-feature sampling stiffness is eliminated with the use of the fast sampling algorithm (FSA), and the coarse-feature sampling stiffness is avoided by introducing the sliding and sampling (S&S) algorithm. A key feature of the S&S algorithm is that it enables massively parallel computers to sample diffusive trajectories that are long in time. We use the algorithm to sample the transition path ensemble for the structural interconversion of the 38-atom Lennard-Jones cluster at low temperature.Comment: 13 pages 5 figure

The fast sampling algorithm for Lie-Trotter products

A fast algorithm for path sampling in path integral Monte Carlo simulations is proposed. The algorithm utilizes the Levy-Ciesielski implementation of Lie-Trotter products to achieve a mathematically proven computational cost of n*log_2(n) with the number of time slices n, despite the fact that each path variable is updated separately, for reasons of optimality. In this respect, we demonstrate that updating a group of random variables simultaneously results in loss of efficiency.Comment: 4 pages, 1 figure; fast rejection from Phys. Rev. Letts; transfered to PRE as a Rapid Communication. Eq. 6 to 10 contained some inconsistencies that have been repaired in the present version; A sample code implementing the algorithm for LJ clusters is available from the author upon reques