On angles, projections and iterations

We investigate connections between the geometry of linear subspaces and the convergence of the alternating projection method for linear projections. The aim of this article is twofold: in the first part, we show that even in Euclidean spaces the convergence of the alternating method is not determined by the principal angles between the subspaces involved. In the second part, we investigate the properties of the Oppenheim angle between two linear projections. We discuss, in particular, the question of existence and uniqueness of "consistency projections" in this context.Comment: 15 pages; published in "Linear Algebra and Its Applications". This version corrects a number of misprint

A Stochastic Process Approach of the Drake Equation Parameters

The number N of detectable (i.e. communicating) extraterrestrial civilizations in the Milky Way galaxy is usually done by using the Drake equation. This equation was established in 1961 by Frank Drake and was the first step to quantifying the SETI field. Practically, this equation is rather a simple algebraic expression and its simplistic nature leaves it open to frequent re-expression An additional problem of the Drake equation is the time-independence of its terms, which for example excludes the effects of the physico-chemical history of the galaxy. Recently, it has been demonstrated that the main shortcoming of the Drake equation is its lack of temporal structure, i.e., it fails to take into account various evolutionary processes. In particular, the Drake equation doesn't provides any error estimation about the measured quantity. Here, we propose a first treatment of these evolutionary aspects by constructing a simple stochastic process which will be able to provide both a temporal structure to the Drake equation (i.e. introduce time in the Drake formula in order to obtain something like N(t)) and a first standard error measure.Comment: 22 pages, 0 figures, 1 table, accepted for publication in the International Journal of Astrobiolog

Stochastic Differential Equations Driven by Fractional Brownian Motion and Standard Brownian Motion

We prove an existence and uniqueness theorem for solutions of multidimensional, time dependent, stochastic differential equations driven simultaneously by a multidimensional fractional Brownian motion with Hurst parameter H>1/2 and a multidimensional standard Brownian motion. The proof relies on some a priori estimates, which are obtained using the methods of fractional integration, and the classical Ito stochastic calculus. The existence result is based on the Yamada-Watanabe theorem.Comment: 21 page

A cutoff phenomenon in accelerated stochastic simulations of chemical kinetics via flow averaging (FLAVOR-SSA)

We present a simple algorithm for the simulation of stiff, discrete-space, continuous-time Markov processes. The algorithm is based on the concept of flow averaging for the integration of stiff ordinary and stochastic differential equations and ultimately leads to a straightforward variation of the the well-known stochastic simulation algorithm (SSA). The speedup that can be achieved by the present algorithm [flow averaging integrator SSA (FLAVOR-SSA)] over the classical SSA comes naturally at the expense of its accuracy. The error of the proposed method exhibits a cutoff phenomenon as a function of its speed-up, allowing for optimal tuning. Two numerical examples from chemical kinetics are provided to illustrate the efficiency of the method

Dendritic cells in plasmodium infection

Infection with Plasmodium parasites (malaria) contributes greatly to morbidity and mortality in affected areas. Interaction of the protozoan with the immune system has a critical role in the pathogenesis of the disease, but may also hold a key to containing parasite numbers through specific immune responses, which vaccine development aims to harness. A central player in the generation of such immune responses is the dendritic cell. However, Plasmodium parasites appear to have profound activating and suppressing effects on dendritic cell function, which may enhance immunopathology or facilitate the parasite’s survival by depressing beneficial immunity. Furthermore, immune responses to other infections and vaccines may be impaired. A greater understanding of the effects of the parasite on dendritic cells will contribute to insight and potential defeat of this infectious disease

Региональные экологические программы развития Болгарии 2007–2013 гг. как составляющая региональной политики ЕС

У роботі досліджуються регіональні програми розвитку Болгарії у 2007 - 2013 рр. Визначено основні напрямки європейської регіональної політики.The paper investigates the regional development programs in Bulgaria in 2007 - 2013 years. The main directions of European regional policy are determined

Особливості транскордонного управління водними ресурсами

Обґрунтовано необхідність охорони, відтворення та використання водних ресурсів у прикордонних територіях. Проаналізовано особливості здійснення управління водними ресурсами в транскордонному регіоні. The necessity of protection, reproduction and use of water resources in the border areas is substantiated. The features of water resource management in the transboundary region are analyzed

Удосконалення процесів управління транскордонними природними ресурсами

У статті автор пропонує шляхи вдосконалення управління транскордонними природними ресурсами. В даній сфері потрібно підписувати угоди про співробітництво, які повинні передбачати створення інституційної структури єврорегіону. Для того, щоб скористатися значним регіональним досвідом і знаннями, необхідно застосовувати регіональний підхід в управлінні транскордонними природними ресурсами з регіональними координаторами та створити мережу експертів в даній сфері. Важливим є створення спільного спостережного пункту для моніторингу та вимірювання змін у навколишньому середовищі з метою розробки спільного бачення в транскордонних масштабах.In the paper author suggests ways of transboundary natural resource management improvement. It is necessary to sign cooperation agreements, which should include the creation of the Euroregion institutional structure. It is necessary to apply a regional approach in the transboundary natural resource management with regional coordinators and to create a network of experts in the field. It is important to create a common observation post for the monitoring and measuring the changes in the environment in order to develop a common vision in transboundary scale

Особливості управління транскордонними водними ресурсами на території республіки Польща (на прикладі р. Західний Буг)

У роботі досліджуються особливості управління транскордонними водними ресурсами на території Республіки Польща. Автор аналізує динаміку забору та використання вод р. Західний Буг, та їх цілі.The features of the management of transboundary water resources in Poland are studied in the paper. The author analyzes the dynamics of water abstraction and use of the Western Bug, and their goals