An "All Possible Steps" Approach to the Accelerated Use of Gillespie's Algorithm

Many physical and biological processes are stochastic in nature. Computational models and simulations of such processes are a mathematical and computational challenge. The basic stochastic simulation algorithm was published by D. Gillespie about three decades ago [D.T. Gillespie, J. Phys. Chem. {\bf 81}, 2340, (1977)]. Since then, intensive work has been done to make the algorithm more efficient in terms of running time. All accelerated versions of the algorithm are aimed at minimizing the running time required to produce a stochastic trajectory in state space. In these simulations, a necessary condition for reliable statistics is averaging over a large number of simulations. In this study I present a new accelerating approach which does not alter the stochastic algorithm, but reduces the number of required runs. By analysis of collected data I demonstrate high precision levels with fewer simulations. Moreover, the suggested approach provides a good estimation of statistical error, which may serve as a tool for determining the number of required runs.Comment: Accepted for publication at the Journal of Chemical Physics. 19 pages, including 2 Tables and 4 Figure

A note on the invariant distribution of a quasi-birth-and-death process

The aim of this paper is to give an explicit formula of the invariant distribution of a quasi-birth-and-death process in terms of the block entries of the transition probability matrix using a matrix-valued orthogonal polynomials approach. We will show that the invariant distribution can be computed using the squared norms of the corresponding matrix-valued orthogonal polynomials, no matter if they are or not diagonal matrices. We will give an example where the squared norms are not diagonal matrices, but nevertheless we can compute its invariant distribution

Досвід функціонування спеціальних економічних зон у постсоціалістичних країнах та можливості його застосування в Україні (The experience of operation of special economic zones in post-socialist countries and the possibility of its application in Ukraine)

У статті проаналізовано позитивний та негативний досвід постсоціалістичних країн щодо створення та функціонування в них різних видів спеціальних економічних зон та особливості оподаткування підприємств у вказаних зонах цих країн залежно від виду діяльності. Обґрунтовано необхідність запровадження СЕЗ в Україні. (The article analyzes the positive and negative experience of post-socialist countries on the establishment and operation of the different types of special economic zones and the features of taxation in these areas of the country depending on the activity. The necessity of introduction of SEZs in Ukraine has been proved.

Особливості фінансування соціальних видатків в умовах сучасної економічної кризи

У статті запропоновано використати новий принцип фінансування соціальних видатків у країні з недостатнім рівнем демократії в умовах економічної кризи, який пропонується назвати антиоптимум Парето. За його допомогою можна знизити соціальний ризик для кожного громадянина, незалежно від доходів та місця в суспільстві. (In the article it is suggested to use new principle of financing social charges in a country with the insufficient level of democracy in the conditions of economic crisis, which it is suggested to name аnti-optimum of Pareto. For his help it is possible to reduce a social risk for every citizen, regardless of profits and place in society.

Early appraisal of the fixation probability in directed networks

In evolutionary dynamics, the probability that a mutation spreads through the whole population, having arisen in a single individual, is known as the fixation probability. In general, it is not possible to find the fixation probability analytically given the mutant's fitness and the topological constraints that govern the spread of the mutation, so one resorts to simulations instead. Depending on the topology in use, a great number of evolutionary steps may be needed in each of the simulation events, particularly in those that end with the population containing mutants only. We introduce two techniques to accelerate the determination of the fixation probability. The first one skips all evolutionary steps in which the number of mutants does not change and thereby reduces the number of steps per simulation event considerably. This technique is computationally advantageous for some of the so-called layered networks. The second technique, which is not restricted to layered networks, consists of aborting any simulation event in which the number of mutants has grown beyond a certain threshold value, and counting that event as having led to a total spread of the mutation. For large populations, and regardless of the network's topology, we demonstrate, both analytically and by means of simulations, that using a threshold of about 100 mutants leads to an estimate of the fixation probability that deviates in no significant way from that obtained from the full-fledged simulations. We have observed speedups of two orders of magnitude for layered networks with 10000 nodes

The Need to Take into Account the Experience of U.S. Cities to Reform the Finances of Ukrainian Cities

В статті розглядаються особливості формування і використання фінансів міст в США, чий досвід доцільно використати в Україні. Насамперед це стосується податку на майно, у встановленні ставок та використанні якого міста США мають значну самостійність. The article deals with peculiarities of formation and use of finances by cities in the USA whose experience should be applied in Ukraine. It is primarily concerns the property tax whose setting and use are under the considerable autonomy of the USA cities