Homotopy Properties of Sphere-Like Digital Images

Recent papers have discussed digital versions of the classical fundamental group for digital images. It has been shown that for non-contractible digital simple closed curves, the digital fundamental group is isomorphic to the integers, in analogy with Euclidean simple closed curves. In this paper, we show that the digital fundamental groups of sphere-like digital images S_n, n > 1, are trivial, as are the fundamental groups of their Euclidean analogs Sⁿ. Research partially supported by a grant from the Niagara University Research Council. Laurence Boxer is Professor and past Chair of Computer and Information Sciences at Niagara University, and Research Professor of Computer Science and Engineering at the State University of New York at Buffalo. He received his Bachelor's degree in Mathematics from the University of Michigan; Master's and PhD in Mathematics from the University of Illinois at Urbana-Champaign; and Master's in Computer Science from the State University of New York at Buffalo. Dr. Boxer is coauthor of Algorithms Sequential and Parallel, an innovative textbook published by Charles River Media.     

Encouraging Citizenship in Science Education: Continuing Questions and Hopeful Possibilities

Abstract

This special issue of the Canadian Journal of Science, Mathematics and Technology Education invokes questions intended to further the discourse of citizenship in science and mathematics education, such as, How do we define citizen and democracy? Is our call for student action hypocritical? Does positioning school science through the work of Rancière present a “straw man” argument for change? To what extent does the ghost of John Dewey animate and inform a “wild pedagogy” in science education? Challenging the view of the science and mathematics curriculum as a barrier to overcome, this article argues that possibilities for developing citizenship and critical thinking can be found and developed in existing curriculum formations and practices of school science and mathematics education.     

Bounds for the number of modes of the simplest Gaussian mixture

Several theorems on sufficient unimodality conditions are formulated for a sum of k normal distributions with the same variance and with different mean values μ _i , i = 1, ..., k, 2 ≤ k < ∞, taken with their a priori probabilities π_i. On the basis of these theorems, estimates for the lower and upper bounds for the mode numbers m are obtained for k ≥ 3 in the case when the mixture contains k* components, 2 ≤ k* < k, satisfying the unimodality conditions. Aprausheva Nina Nikolaevna (b. 1940). Graduated from the Moscow State University (Department of Mechanics and Mathematics) in 1966. In 1982, defended the Cand. Sci. thesis “On the Application of Mixtures of Normal Distributions in Pattern Recognition.” Senior scientist at Dorodnicyn Computing Center, Russian Academy of Sciences. Scientific interests: mathematical statistics, computational mathematics, mathematical methods in pattern recognition, and decision theory (about 70 publications). Member of Association of Pattern Recognition. Mollaverdi Naser (b. 1967). Graduated from the Isfahan University of Technology (Iran) in 1990. In 1995, graduated from the Educational University (Teheran, Iran). Third-year scholar at Moscow State University (Department of Computational Mathematics and Cybernetics). Scientific interests: computational mathematics, pattern recognition, programming, and statistics (12 publications). Sorokin Stanislav Viktorovich (b. 1947). Graduated from Moscow State University (Department of Computational Mathematics and Cybernetics) in 1971. Programmer at Dorodnicyn Computing Center, Russian Academy of Sciences. Scientific interests: computational mathematics, system programming, and pattern recognition (15 publications).     

Stochastic filtering of approximate symmetries in dense packings of clusters

Certain questions concerning the arrangement of optimal dense packings of clusters are considered when simple routine long-term procedures are applied instead of a laborious method of direct solution. A unified approach to searching for hidden symmetries in such packings is proposed that represents a certain combination of the generalized Hough transform and the Purzen windows technique in nonparametric density estimation. All symmetries are sought via the Hough transforms adjusted to certain types of adjacent classes on the SO _N group manifold. Exact symmetries and separate solutions are filtered out by using the ergodic properties of the independent sequential choice procedure. Aleksandr Petrovich Vinogradov. Born 1951. Graduated from the Moscow Institute of Physics and Technology in 1974. Received candidates degree in physics and mathematics in the field of mathematical cybernetics. Scientific interests: pattern recognition, image analysis, application of algebraic and geometric methods to the problems of data analysis. Author of 45 papers. Jan Voracek (1962), graduated from Brno University of Technology (BUT) in 1985. Obtained his MS in Technical Cybernetics in 1985, first PhD in Technical Cybernetics in 1992, and second PhD in Manufacturing Technology in 1996, all from BUT. Since 1997 he has been working as a professor of information technology at the Laboratory of Information Processing, Lappeenranta University of Technology, Finland. Author and coauthor of more than 80 publications. Research interests include pattern recognition, image processing, and international education. Yuri I. Zhuravlev. Born 1935. Graduated from the Faculty of Mechanics and Mathematics, Moscow State University, in 1957. Received his PhD (Kandidat Nauk) degree in 1959 and Doctoral (Doktor Nauk) degree in Physics and Mathematics in 1965. Since 1969, with the Computer Center of the Russian Academy of Sciences, Moscow, first as a Laboratory Head and then as a Deputy Director. Professor at Moscow State University. Full member of the Russian Academy of Sciences (since 1992) and of the Academy of Sciences of Spain (since 1993). Scientific interests: mathematical logic; algebra; discrete optimization; pattern recognition; and the use of mathematical and computational methods for solving applied problems of data processing and research automation in industry, medicine, geology, and sociology. Author of more than 170 publications on information technology and applied mathematics. Editor-in-Chief of the journal Pattern Recognition and Image Analysis and a member of the editorial boards of several international and Russian journals on information technology and applied mathematics.     

Mathematics motivation and achievement as predictors of high school students' guessing and help‐seeking with instructional software

The study was conducted to investigate the relation of adolescent students' mathematics motivation and achievement to their appropriate help‐seeking and inappropriate guessing behaviour while using instructional software. High school students (n = 90) completed brief assessments of mathematics motivation and then worked with software for geometry instruction. Students' actions with the software were machine‐classified to identify instances of appropriate help‐seeking and inappropriate guessing. Mathematics teachers provided information about students' achievement (high, average or at risk of failing math class). Results indicated that students with low math self‐concept were most likely to engage in inappropriate guessing behaviour. Students with low math achievement were most likely to engage in appropriate help‐seeking while working with the software.     

A Review of “Technology and Literacy: 21st Century Library Programming for Children and Teens”

ABSTRACT

Given the endless volume of information available today, searchers are forced to satisfice when searching. The first satisfactory alternative is chosen over the best. Digital library search services, however, do not support satisficing users. There is no single, simple, comprehensive search service available to end-users to meet their need to gather information on alternatives from all information repositories accessible through a digital library. Federated search services bridge the gap between satisficing searchers and today's digital libraries.     

Classifying the subjects of the Russian Federation on the basis of analysis of results of Gallup polling

The problem of processing of Gallup poll results by cluster analysis methods is considered. The aim of these polls, performed in different subjects of the Russian Federation, is to extract main characteristics of the regions. Demyanov Egor A. Born 1982. Graduated from the Moscow State University in 2004. Post-graduate student of the same university. Scientific interests: discrete mathematics and mathematical methods of pattern recognition. Author of two publications. Djukova Elena V. Born 1945. Graduated from the Moscow State University in 1967. Received candidate’s degree in Physics and Mathematics in 1979, Doctoral degree in Physics and Mathematics in 1997. Dorodnicyn Computing Center, Russian Academy of Sciences, leading researcher. Moscow State University, lecturer. Moscow Pedagogical University, lecturer. Scientific interests: discrete mathematics and mathematical methods of pattern recognition. Author of 76 papers. Peskov Nikolai V. Born 1978. Graduated from the Moscow State University in 2000. Received candidate’s degree in Physics and Mathematics in 2004. Dorodnicyn Computing Center, Russian Academy of Sciences, junior researcher. Scientific interests: discrete mathematics and mathematical methods of pattern recognition. Author of 17 papers. Inyakin Andrey S. Born 1978. Graduated from the Moscow State University in 2000. Received candidate’s degree in 2006. Dorodnicyn Computing Center, Russian Academy of Sciences, junior researcher. Scientific interests: discrete mathematics and mathematical methods of pattern recognition. Author of 16 papers.     

Pre‐service secondary mathematics teachers’ beliefs about the nature of technology in the classroom

Abstract

This study investigated pre‐service secondary mathematics teachers’ (PSTs) beliefs about teaching mathematics with technology, the experiences in which those beliefs were grounded, and the organizational structure of those beliefs. In particular, this article reports on research that was designed to investigate questions beyond that of whether technology can profitably be used before mathematical content has been mastered (the question about technology most commonly reported in the literature). Beliefs were defined as dispositions to act and were viewed through what is referred to as the sensible system framework. Through the qualitative research methodology called grounded theory, four PSTs were purposefully selected and studied. The primary dimensions of the PSTs’ core beliefs with respect to technology, referred to as their beliefs about the nature of technology in the classroom, were beliefs about the availability of technology, about the purposeful use of technology, and about the importance of teacher knowledge of technology.     

On the uni- and bimodality of a two-component Gaussian mixture

Several sufficient conditions are formulated for the uni- and bimodality of a mixture of two Gaussian distributions with equal variances σ² and different expectation values μ _i , i = 1, 2. An equation governing all the degenerate critical inflection points for the probability density f(x) of the mixture is derived by a statistical method. This equation describes the boundary of the uni- and bimodality domains of f(x). Nina Nikolaevna Aprausheva was born in 1940. Graduated from the Moscow State University (Department of Mechanics and Mathematics) in 1966. In 1982, defended the Cand. Sci. thesis “On the Application of Mixtures of Normal Distributions in Pattern Recognition.” Senior scientist at Dorodnicyn Computing Center, Russian Academy of Sciences. Scientific interests: mathematical statistics, computational mathematics, mathematical methods in pattern recognition, and decision theory (about 75 publications). Member of Association of Pattern Recognition and Association of. “Women in science and education.” N.N. Aprausheva’s publications have been awarded several prizes at the scientific publications contests in Computing Center of Russian Academy of Sciences. Stanislav Viktorovich Sorokin was born in 1947. Graduated from Moscow State University (Department of Computational Mathematics and Cybernetics) in 1971. Programmer at Dorodnicyn Computing Center, Russian Academy of Sciences. Scientific interests: computational mathematics, system programming, and pattern recognition (20 publications).     

Constructing irreducible coverings of a Boolean matrix

A polynomial delay algorithm for searching for irreducible coverings of a Boolean matrix is constructed. A similar result is obtained for the problem of constructing maximal conjunctions of a monotone Boolean function specified by its conjunctive normal form. Elena V. Djukova born 1945. Graduated from Moscow State University in 1967. Candidate’s degree in Physics and Mathematics in 1979. Doctoral degree in Physics and Mathematics in 1997. Dorodnicyn Computing Center, Russian Academy of Sciences, leading researcher. Moscow State University, lecturer. Moscow Pedagogical University, lecturer. Scientific interests: discrete mathematics and mathematical methods of pattern recognition. Author of 76 papers. Andrey S. Inyakin born 1978. Graduated from Moscow State University in 2000. Candidate’s degree in Physics and Mathematics in 2000. Dorodnicyn Computing Center, Russian Academy of Sciences, junior researcher. Scientific interests: discrete mathematics and mathematical methods of pattern recognition. Author of sixteen papers.     

A Digital Start-up Project – CARM Tool as an Innovative Approach to Digital Government Transformation

The digital revolution impacts modern workplaces through constant advances in technology. This study uses a digital start-up project experience to demonstrate how a Digital Government Transformation can be beneficial. The increase of administrative requirements, compliance, and capability readiness has prompted the development of the Digital start–up project known as the CARM Tool (Compliance, Assurance and Risk Management). CARM introduces a low risk low cost and high productivity solution, which can directly and immediately benefit stakeholders in a large complex government enterprise. It aims to elevate staff performance, customer service and provide qualification between financial statements, asset management and alignment with the Digital Government Transformation strategy. The digital start-up inspired, innovative CARM tool is an original idea developed by the author to utilise emerging technologies to modernise and consolidate the manual-based business processes and legacy systems, to improve visibility and accountability within the enterprise and to advance workforce skills throughout the organisation. In this paper, the author presents a detailed start-up project approach that draws the public sector specifically Defence into the digital transformation age through the innovative CARM tool from concept, to prototype to game-changing enterprise modernisation.     

Atomic snapshots using lattice agreement

Summary Thesnapshot object is an important tool for constructing wait-free asynchronous algorithms. We relate the snapshot object to thelattice agreement decision problem. It is shown that any algorithm for solving lattice agreement can be transformed into an implementation of a snapshot object. The overhead cost of this transformation is only a linear number of read and write operations on atomic single-writer multi-reader registers. The transformation uses an unbounded amount of shared memory. We present a deterministic algorithm for lattice agreement that usedO (log² n) operations on 2-processorTest & Set registers, plusO (n) operations on atomic single-writer multi-reader registers. The shared objects are used by the algorithm in adynamic mode, that is, the identity of the processors that access each of the shared objects is determined dynamically during the execution of the algorithm. By a randomized implementation of 2-processorsTest & Set registers from atomic registers, this algorithm implies a randomized algorthm for lattice agreement that uses an expected number ofO (n) operations on (dynamic) atomic single-writer multi-reader registers. Combined with our transformation this yields implementations of atomic snapshots with the same complexity.Cambridge Research Laboratory, Digital Equipment Corporation Hagit Attiya received the B.Sc. degreeiin Mathematics and Computer Science from the Hebrew University of Jerusalem, in 1981, the M.Sc. and Ph.D. degrees in Computer Science from the Hebrew University of Jerusalem, in 1983 and 1987, respectively. She is presently a senior lecturer at the departtment of Computer Science at the Technion, Israel Institute of Technology. Prior to this, she has been a post-doctoral research associate at the Laboratory for Computer Science at M.I.T. Her general research interests are distributed computation and theoretical computer science. More specific interests include fault-tolerance, timing-based and asynchronous algorithms. Maurice Herlihy received the A.B. degree in Mathematics from Harvard University, and the M.S. and the Ph.D. degrees in Computer Science from M.I.T. From 1984 to 1989 he was a faculty member in the Computer Science Department at Carnegie Mellon University in Pittsburgh, PA. In 1989 he joined the research staff at the Digital Equipment Corporation's Cambridge Research Laboratory in Cambridge MA. Since 1994, he has been on the faculty at the Computer Science Department at Brown University. Dr. Herlihy's research interests encompass practical and theoretical aspects of distributed and concurrent computation. Ophir achman received a B.A. in computer science from the Technion, Haifa, Israel in 1989 and M.Sc. in computer science from the Technion, Haifa, Israel, in 1992. He is now studying for a D.Sc. in computer science at the Technion. His currentarea of research is distributed computing, and in particular, asynchronous shared memory systems.This work appeared in preliminary form in proceedings ofthe 6th International Workshop on Distributed Algorithms [12]. This research was partially supported by grant No. 92-0233 from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Technion V.P.R. funds — B. and G. Greenberg Research Fund (Ottawa), and the fund for the promotion of research in the TechnionPart of the work of this author was performed while visiting DEC Cambridge Research Laboratory     

Casting shadows in the science classroom

Abstract

Research in mathematics and science education frequently directs one's attention to the limited content knowledge of elementary pre‐service teachers. It is believed, however, that research of this nature leads to a deficit approach to understanding more about the teaching and learning of these subjects. In addition to focusing on the knowers of school mathematics and science, there is a call to acknowledge the problematic nature of knowing (in) mathematics and science. In this paper, the metaphor of shadows is used in a critical exploration of what it means to know and how the cultures of classrooms have shaped these images of knowing. Through the voices of pre‐service teachers, this paper directs one's attention to objects that cast shadows on the learning and knowing of mathematics and science. Three such shadow‐casting objects discussed in this paper are textbooks, teachers, and gendered ideology. The paper seeks to critically illuminate the problematic nature of what it means to know (in) mathematics and science by examining the shadowy texture of unquestioned ideologies.     

Increasing the efficiency of combinatorial logical data analysis in recognition and classification problems

Problems of increasing the efficiency of combinatorial logical data analysis in recognition problems are examined. A technique for correct conversion of initial information for reduction of its dimensionality is proposed. Results of testing this technique for problems of real medical prognoses are given. Djukova Elena V. Born 1945. Graduated from Moscow State University in 1967. Candidate’s degree in Physics and Mathematics in 1979. Doctoral degree in Physics and Mathematics in 1997. Dorodnicyn Computing Center, Russian Academy of Sciences, leading researcher. Moscow State University, lecturer. Moscow Pedagogical University, lecturer. Scientific interests: discrete mathematics and mathematical method of pattern recognition. Author of 70 papers. Peskov Nikolai V. Born 1978. Graduated from Moscow State University in 2000. Candidate’s degree in 2004. Dorodnicyn Computing Center, Russian Academy of Sciences, junior researcher. Scientific interests: discrete mathematics and mathematical methods of pattern recognition. Author of ten papers. Inyakin Andrey S. Born 1978. Graduated from Moscow State University in 2000. Dorodnicyn Computing Center, Russian Academy of Sciences, junior researcher. Scientific interests: discrete mathematics and mathematical methods of pattern recognition. Author of ten papers. Sakharov Aleksei A. Born 1980. Graduated from Moscow State University in 2003. Moscow Pedagogical University, graduate student. Scientific interests: discrete mathematics and mathematical method of pattern recognition. Author of three papers.     

A classification algorithm based on the complete decision tree

Application of decision trees in problems of classification by precedents is considered. A new model of classifier (which is called the complete decision tree) is proposed and compared with other recognition algorithms based on constructing decision trees. Elena V. Djukova born 1945. Graduated from Moscow State University in 1967. Candidate’s degree in Physics and Mathematics in 1979. Doctoral degree in Physics and Mathematics in 1997. Dorodnicyn Computing Center, Russian Academy of Sciences, leading researcher. Moscow State University, lecturer. Moscow Pedagogical University, lecturer. Scientific interests: discrete mathematics and mathematical methods of pattern recognition. Author of 76 papers. Nikolai V. Peskov born 1978. Graduated from Moscow State University in 2000. Candidate’s degree in Physics and Mathematics in 2004. Dorodnicyn Computing Center, Russian Academy of Sciences, junior researcher. Scientific interests: discrete mathematics and mathematical methods of pattern recognition. Author of seventeen papers.     

Students and applied academics: Learner agency in a changing curriculum

Abstract

Student perspectives are important, yet under‐recognized, resources for/in educational reform. This paper examines student opinions and needs with respect to curriculum reform aiming to bridge school and work. Through interviews with 20 students enrolled in applied academics courses, such as Applications of Mathematics, which attempt to integrate education, work, and life activities, we explore what matters to students and what roles they play in a changing curriculum. Findings indicate that students pursue applications courses more as a way of gaining access to curriculum and to pedagogical practices that transform their views of mathematics and of themselves as learners of mathematics than as a means toward a particular career goal. Students’ educational needs complicate and push beyond Dewey's distinction between education for and through occupations. Students became active advocates for a course taught in ways that emphasized engagement, connectedness, and collaboration where learner agency was valued and respected. Student voices provide insight into how students might participate in curriculum reform and into how such curriculum shapes them.     

Technology practices: Confirmatory factor analysis and exploration of teachers' technology integration in subject areas

It is thought that gains in student learning from the use of digital technologies are more likely to be related to teachers' practice than the technology itself. In secondary schooling, a key aspect of this is concerned with understanding how digital technologies are used to support teaching and learning in specific subject areas. Subject areas have their own conventions and expectations for learning that will influence teachers' technology use and technology-supported student tasks. The aim of this paper is to present confirmatory factor analysis of a scale considering common technology-related tasks in three subject areas. Data included in the current analysis are teacher questionnaires collected in 2010 (N = 3624), as part of a large-scale one-to-one laptop initiative in Australia. Results from the 2010 data confirm a five-factor structure revealing significant differences in teachers' professional and instructional uses of digital technologies among three core subject areas: English, Mathematics and Science. Trends are confirmed through a second teacher data set collected in 2011 for Wave 2 of the same one-on-one laptop initiative. Implications of these findings in relation to understanding and supporting effective technology integration and areas of future research are discussed.     

From truth to efficiency: Comments on some aspects of the development of mathematics education

Coray, D., Furinghetti, F., Gispert, H., Hodgson, B.R., & Schubring, G. (2003). One Hundred Years of L'Enseignement mathématique: Moments of Mathematics Education in the Twentieth Century. Monographie N° 39 de l'Enseignement mathématique. ISBN 2–940264–06–6     

Convergence of genetic algorithms

The mean convergence of various versions of a genetic algorithm are considered. A number of convergence statements are formulated and relevant estimates are obtained. A hypothesis concerning the form of these estimates under variation of the structure of a genetic algorithm is put forward. Roman Riviyanovich Sharapov. Born 1981. Graduated from the Faculty of Mechanics and Mathematics, Ural State University, in 2003. Presently, a postgraduate at the Department of Mathematical Economics at the same university. Scientific interests: genetic algorithms, neural networks, and financial mathematics. Aleksandr Vyacheslavovich Lapshin. Born 1980. Graduated from the Faculty of Mechanics and Mathematics, Ural State University, in 2003. Presently, a postgraduate at the Department of Mathematical Economics at the same university. Scientific interests: financial mathematics, genetic algorithms, and neural networks.