Algorithmic Minimization of Non-zero Entries in 0,1-Matrices

In this paper we present algorithms which work on pairs of 0,1- matrices which multiply again a matrix of zero and one entries. When applied over a pair, the algorithms change the number of non-zero entries present in the matrices, meanwhile their product remains unchanged. We establish the conditions under which the number of 1s decreases. We recursively define as well pairs of matrices which product is a specific matrix and such that by applying on them these algorithms, we minimize the total number of non-zero entries present in both matrices. These matrices may be interpreted as solutions for a well known information retrieval problem, and in this case the number of 1 entries represent the complexity of the retrieve and information update operations.

Minimization of Reactive Probabilistic Automata

The problem of finite automata minimization is important for software and hardware designing. Different types of automata are used for modeling systems or machines with finite number of states. The limitation of number of states gives savings in resources and time. In this article we show specific type of probabilistic automata: the reactive probabilistic finite automata with accepting states (in brief the reactive probabilistic automata), and definitions of languages accepted by it. We present definition of bisimulation relation for automata's states and define relation of indistinguishableness of automata states, on base of which we could effectuate automata minimization. Next we present detailed algorithm reactive probabilistic automata’s minimization with determination of its complexity and analyse example solved with help of this algorithm.

Conditions of Effectiveness of Pattern Recognition Problem Solution Using Logical Level Descriptions of Classes

Earlier the authors have suggested a logical level description of classes which allows to reduce a solution of various pattern recognition problems to solution of a sequence of one-type problems with the less dimension. Here conditions of the effectiveness of the use of such a level descriptions are proposed.

Conceptual Idea of Identification of Patterns and Problem Solving in the Human’s Memory and the Possibilities to Use it in Artificial Intelligent

Given cybernetic idea is formed on the basis of neurophysiologic, neuropsychological, neurocybernetic data and verisimilar hypotheses, which fill gaps of formers, of the author as well. First of all attention is focused on general principles of a Memory organization in the brain and processes which take part in it that realize such psychical functions as perception and identification of input information about patterns and a problem solving, which is specified by the input and output conditions, as well. Realization of the second function, essentially cogitative, is discussed in the aspects of figurative and lingual thinking on the levels of intuition and understanding. The reasons of advisability and principles of bionic approach to creation of appropriate tools of artificial intelligent are proposed.

Realization of Open Addressing Hash Table in the Chained Allocated Memory

In this article, we examine a realization of an open addressing hash table in the chained allocated memory, giving us the opportunity to decrease the number of linear probing when a given element has not been inserted in the table.

Well-Posedness of the Cauchy Problem for Inhomogeneous Time-Fractional Pseudo-Differential Equations

Mathematics Subject Classification: 26A33, 45K05, 35A05, 35S10, 35S15, 33E12

Well-Posedness of Diffusion-Wave Problem with Arbitrary Finite Number of Time Fractional Derivatives in Sobolev Spaces H^s

Mathematics Subject Classification 2010: 26A33, 33E12, 35S10, 45K05.

An Analog of the Tricomi Problem for a Mixed Type Equation with a Partial Fractional Derivative

Mathematics Subject Classification 2010: 35M10, 35R11, 26A33, 33C05, 33E12, 33C20.

Explicit Solution of Bitsadze-Samarskii Problem

Иван Димовски, Юлиан Цанков - В статията е намерено точно решение на задачата на Бицадзе-Самрски (1) за уравнението на Лаплас, като е използвано операционно смятане основано на некласическа двумернa конволюция. На това точно решение може да се гледа като начин за сумиране на нехармоничния ред по синуси на решението, получен по метода на Фурие.

Education in Computer Science and the Role of the Teacher in the Environment of Open Educational Resources

Report published in the Proceedings of the National Conference on "Education in the Information Society", Plovdiv, May, 2013

Monte Carlo Study of Particle Transport Problem in Air Pollution

2002 Mathematics Subject Classification: 65C05.

Autumn Training School. Development and Promotion of Open Access to Scientific Information and Research (September 19–20, 2014, Veliko Tarnovo, Bulgaria), organized in the frame of DiPP2014

The autumn training school Development and Promotion of Open Access to Scientific Information and Research is organized in the frame of the Fourth International Conference on Digital Presentation and Preservation of Cultural and Scientific Heritage—DiPP2014 (September 18–21, 2014, Veliko Tarnovo, Bulgaria, http://dipp2014.math.bas.bg/), organized under the UNESCO patronage. The main organiser is the Institute of Mathematics and Informatics, Bulgarian Academy of Sciences with the support of EU project FOSTER (http://www.fosteropenscience.eu/) and the P. R. Slaveykov Regional Public Library in Veliko Tarnovo, Bulgaria.

Key Aspects and Approaches of Open Access, Open Data and Open Science

Overview of the key aspects and approaches to open access, open data and open science, emphasizing on sharing scientific knowledge for sustainable progress and development.

Importance and Benefits of OPEN SCIENCE for Ubiquitous Sharing, Dissemination and Impact

While openness is well applied to software development and exploitation (open sources), and successfully applied to new business models (open innovation), fundamental and applied research seems to lag behind. Even after decades of advocacy, in 2011 only 50% of the public-funded research was freely available and accessible (Archambault et al., 2013). The current research workflows, stemming from a pre-internet age, result in loss of opportunity not only for the researchers themselves (cf. extensive literature on topic at Open Access citation project, http://opcit.eprints.org/), but also slows down innovation and application of research results (Houghton & Swan, 2011). Recent studies continue to suggest that lack of awareness among researchers, rather than lack of e-infrastructure and methodology, is a key reason for this loss of opportunity (Graziotin 2014). The session will focus on why Open Science is ideally suited to achieving tenure-relevant researcher impact in a “Publish or Perish” reality. Open Science encapsulates tools and approaches for each step along the research cycle: from Open Notebook Science to Open Data, Open Access, all setting up researchers for capitalising on social media in order to promote and discuss, and establish unexpected collaborations. Incorporating these new approaches into a updated personal research workflow is of strategic beneficial for young researchers, and will prepare them for expected long term funder trends towards greater openness and demand for greater return on investment (ROI) for public funds.

On the Asymptotic Distribution of Closed Orbits for a Class of Open Billiards

2000 Mathematics Subject Classification: 37D40.