Quasi-Monte Carlo Methods for some Linear Algebra Problems. Convergence and Complexity

We present quasi-Monte Carlo analogs of Monte Carlo methods for some linear algebra problems: solving systems of linear equations, computing extreme eigenvalues, and matrix inversion. Reformulating the problems as solving integral equations with a special kernels and domains permits us to analyze the quasi-Monte Carlo methods with bounds from numerical integration. Standard Monte Carlo methods for integration provide a convergence rate of O(N^(−1/2)) using N samples. Quasi-Monte Carlo methods use quasirandom sequences with the resulting convergence rate for numerical integration as good as O((logN)^k)N^(−1)). We have shown theoretically and through numerical tests that the use of quasirandom sequences improves both the magnitude of the error and the convergence rate of the considered Monte Carlo methods. We also analyze the complexity of considered quasi-Monte Carlo algorithms and compare them to the complexity of the analogous Monte Carlo and deterministic algorithms.

Integer Programming Approach to HP Folding

One of the most widely studied protein structure prediction models is the hydrophobic-hydrophilic (HP) model, which explains the hydrophobic interaction and tries to maximize the number of contacts among hydrophobic amino-acids. In order to find a lower bound for the number of contacts, a number of heuristics have been proposed, but finding the optimal solution is still a challenge. In this research, we focus on creating a new integer programming model which is capable to provide tractable input for mixed-integer programming solvers, is general enough and allows relaxation with provable good upper bounds. Computational experiments using benchmark problems show that our formulation achieves these goals.

A fuzzy expected value approach under generalized data envelopment analysis

Fuzzy data envelopment analysis (DEA) models emerge as another class of DEA models to account for imprecise inputs and outputs for decision making units (DMUs). Although several approaches for solving fuzzy DEA models have been developed, there are some drawbacks, ranging from the inability to provide satisfactory discrimination power to simplistic numerical examples that handles only triangular fuzzy numbers or symmetrical fuzzy numbers. To address these drawbacks, this paper proposes using the concept of expected value in generalized DEA (GDEA) model. This allows the unification of three models - fuzzy expected CCR, fuzzy expected BCC, and fuzzy expected FDH models - and the ability of these models to handle both symmetrical and asymmetrical fuzzy numbers. We also explored the role of fuzzy GDEA model as a ranking method and compared it to existing super-efficiency evaluation models. Our proposed model is always feasible, while infeasibility problems remain in certain cases under existing super-efficiency models. In order to illustrate the performance of the proposed method, it is first tested using two established numerical examples and compared with the results obtained from alternative methods. A third example on energy dependency among 23 European Union (EU) member countries is further used to validate and describe the efficacy of our approach under asymmetric fuzzy numbers.

Orthodox Christianity and Nationalism:an introduction

On the morning of January 5, 1859, at the end of the liturgy in the Orthodox cathedral in Iaşi, the capital of the principality of Moldavia, Father Neofit Scriban addressed the congregation. He had given many sermons in the cathedral; however, on this par tic u lar date Father Neofit faced an unusual audience. Among the faithful who regularly worshipped at the relics of Saint Parascheva, the protector of Moldavia, were the members of the assembly who would decide the future of the principality. They had a specific mission: to elect a new prince, a key figure in their plan to unite Moldavia with the neighboring principality of Wallachia. Father Neofit, a supporter of the unionist cause and fully aware of the significance of the moment, stated: Brethren, Jesus Christ has said that "For where two or three have gathered together in My name, I am there in their midst." You, Brethren, are not two, or three, but a real gathering in the name of God. God is in your midst. You are here in the name of the Romanian nation [and] the Romanian nation is in your midst. On the flag under which you have assembled, the flag of the Romanian nation, great events, the Romanian faith, unity, are written in large letters. The church, which is founded on faith, blesses the flag of this faith⋯. You, Brethren, through the faith of the Romanian nation, by remaining faithful to this flag, will find the same strength as the church [finds] in its own saints. The faith of the Romanian nation was not, is not, and will not be anything else, but the unity of all Romanians in a single state, the only anchor of salvation, the only port in which the national boat could be saved from surrounding waves. You, Brethren, have gathered here in the church of Stephen the Great; looking at the altar that he raised to the God of your parents, I think that, through this [altar], you will be able to enter into the wishes of this hero of our nation. You, [remember that] by leaving this place, you are leaving [in order to fulfill] a great gesture that for many centuries has been lost for us; you are about to elect a successor to this great hero; therefore, as his true sons, you could not be anything other than the true expression of his wishes. Myself, [as] last year, from this altar, I said and I will continue to say that this great hero has told us that "the God of our parents will send us a Redeemer who will heal our wounds and accomplish our wishes." May your chosen leader today be the redeemer expected by the Romanian nation. May he heal its wounds and achieve its wishes. Therefore, Brethren, may your election today be that of a real Messiah of Romania. God and the world are looking at you, the church is blessing you and the whole Romanian nation is waiting for you!1 A few hours after Father Neofit's sermon, the assembly elected Alexandru Ioan Cuza to be the prince of the principality of Moldavia; a few days later, on January 24, 1859, the assembly of the neighboring principality of Wallachia decided that Cuza should also be their prince, thus confirming the unification of the two states. A new country was inscribed on the map of Southeastern Europe, titled "The United Principalities of Wallachia and Moldavia," also known as "The United Romanian Principalities".

Nonlocal Boundary Value Problems for Two-Dimensional Potential Equation on a Rectangle

Иван Димовски, Юлиан Цанков - Предложено е разширение на принципa на Дюамел. За намиране на явно решение на нелокални гранични задачи от този тип е развито операционно смятане основано върху некласическа двумерна конволюция. Пример от такъв тип е задачата на Бицадзе-Самарски.

The Cloud Computing and Computer Virology

Евгений Николов, Димитрина Полимирова - Докладът представя текущото състояние на “облачните изчисления” и “облачните информационни атаки” в светлината на компютърната вирусология и информационната сигурност. Обсъдени са категориите “облачни възможни информационни атаки” и “облачни успешни информационни атаки”. Коментирана е архитектурата на “облачните изчисления” и основните компоненти, които изграждат тяхната инфраструктура, съответно “клиенти” (“clients”), „центрове за съхранение на данни“ (“datacenters”) и „разпределени сървъри“ (“dirstributed servers”). Коментирани са и услугите, които се предлагат от “облачните изчисления” – SaaS, HaaS и PaaS. Посочени са предимствата и недостатъците на компонентите и услугите по отношение на “облачните информационни атаки”. Направен е анализ на текущото състояние на “облачните информационни атаки” на територията на България, Балканския полуостров и Югоизточна Европа по отношение на компонентите и на услугите. Резултатите са представени под формата на 3D графични обекти. На края са направени съответните изводи и препоръки под формата на заключение.

Three-Dimensional Operational Calculi for Nonlocal Evolution Boundary Value Problems

Иван Христов Димовски, Юлиан Цанков Цанков - Построени са директни операционни смятания за функции u(x, y, t), непрекъснати в област от вида D = [0, a] × [0, b] × [0, ∞). Наред с класическата дюамелова конволюция, построението използва и две некласически конволюции за операторите ∂2x и ∂2y. Тези три едномерни конволюции се комбинират в една тримерна конволюция u ∗ v в C(D). Вместо подхода на Я. Микусински, основаващ се на конволюционни частни, се развива алтернативен подход с използване на мултипликаторните частни на конволюционната алгебра (C(D), ∗).

Couette Gas Flow Between Cylinders with Different Temperature

Петър Господинов, Добри Данков, Владимир Русинов, Стефан Стефанов - Изследвано е стационарно течение на Кует на разреден газ в случая на въртене на вътрешния цилиндър и неподвижен външен цилиндър чрез използване на DSMC метод и числено решение на уравненията на Навие–Стокс за относително малка (дозвукова) скорост на въртене. Изследвани са различни случаи при промяна на температурата на въртящият се цилиндър и числото на Кнудсен. Целта на изследването е да се установи влиянието на малки скорости на въртене върху макрохарактеристиките – плътността, скоростта и температурата на газа. Установено е добро съвпадение на резултатите получени по двата метода за Kn = 0.02. Получените резултати са важни при решаването на неравнинни, задачи от микрофлуидиката с отчитане на ефектите на кривината. Ключови думи: механика на флуидите, кинетична теория, разреден газ, DSMC.

Mobile Applications for Cultural and Historical Places

A review of free applications of smartphones working under the operation system of Android is made in the paper. The applications present users information about historical and cultural places of interest at travelling. There are three main groups of applications subject of discussion in the paper – world, national and regional. Their abilities, positive and negative characteristics are compares and described. A conclusion can be made that there is a necessity of new application that presents tourists detailed information about the Old capital of Bulgaria.

Monte Carlo Algorithm for Solving Integral Equations with Polynomial Non-Linearity. Parallel Implementation

An iterative Monte Carlo algorithm for evaluating linear functionals of the solution of integral equations with polynomial non-linearity is proposed and studied. The method uses a simulation of branching stochastic processes. It is proved that the mathematical expectation of the introduced random variable is equal to a linear functional of the solution. The algorithm uses the so-called almost optimal density function. Numerical examples are considered. Parallel implementation of the algorithm is also realized using the package ATHAPASCAN as an environment for parallel realization.The computational results demonstrate high parallel efficiency of the presented algorithm and give a good solution when almost optimal density function is used as a transition density.

A Stochastic Approach for Investigation Ultrafast Phenomena in Semiconductors

2002 Mathematics Subject Classification: 65C05

Detecting Precipitation Climate Changes: An Approach Based on a Stochastic Daily Precipitation Model

2002 Mathematics Subject Classification: 62M10.

Offspring Mean Estimators in Branching Processes with Immigration

2000 Mathematics Subject Classification: 60J80.

Estimators in Branching Processes with Immigration

2000 Mathematics Subject Classi cation: 60J80.

Option Pricing by Branching Process

2000 Mathematics Subject Classification: 60J80, 62P05.