1,721,001 research outputs found
On an Efficient Algorithm for Big Rational Number Computations by Parallel p-adics
No full textAbstractThis paper presents an algorithm for evaluating an arithmetic expression over "big" rational numbers. The method exploits p-adic arithmetic and parallelism to achieve efficiency.Roughly, the algorithm begins by mapping the input rational numbers to the related p-adic codes for several prime bases, then the corresponding expression is evaluated over these codes and finally the rational output is recovered from the resulting codes. All these three steps are parallelized.An efficient algorithm to compute the recovery step is proposed. Let p be the maximum of the prime bases for the codes, let r be their truncation order and let k be the number of processors. The asymptotic bit-wise complexity of the proposed recovery step is O(r (k log p)log23. The previous known bound was O(r2(k log p)log23).Let n be the number of operations in the given expression: the asymptotic bitwise complexity of the proposed algorithm for evaluating arithmetic expressions is O(n r2log p)
Abstract specification of structures and methods in symbolic mathematical computation
No full textAbstractThis paper describes a methodology based on the object-oriented programming paradigm, to support the design and implementation of a symbolic computation system. The requirements of the system are related to the specification and treatment of mathematical structures. This treatment is considered from both the numerical and the symbolic points of view. The resulting programming system should be able to support the formal definition of mathematical data structures and methods at their highest level of abstraction, to perform computations on instances created from such definitions, and to handle abstract data structures through the manipulation of their logical properties. Particular consideration is given to the correctness aspects. Some examples of convenient application of the proposed design methodology are presented
Guidelines for TEL researchers on discovering and eliciting educational features in web resources
No full textThe increasing trend of sharing educational resources on the World Wide Web has attracted several contributions from the research community. Since most Technology Enhanced Learning users retrieve resources from the Web for teaching or learning, the Web is recognised as a repository of educational material. A big issue in automatic retrieval of online resources is that the Web is a huge and mostly unorganised space. Hence, there is no guarantee that items retrieved by current search engines are appropriate for educational uses. Automatically identifying Web-content suitable for education is one of the most challenging objectives because it requires extraordinary attention. Studies in Technology Enhanced Learning have proposed several solutions to support the teaching and learning needs of instructors and pupils within an enclosed platform. Other studies offer different techniques for collecting resources from the open Web that have specific characteristics. This work aims to gather findings and results from such studies for establishing a set of guidelines for researchers in education, expecting to improve the development of future proposals in this field
On Techniques to Detect Concept Maps Pedagogical Similarity
No full textIn this paper we focus on the support a teacher can have, while defining and organizing the content of a course (s)he will teach, by means of the analysis of similarity of Concept Maps. The teacher, in such an endeavor, would prepare an initial version of her/his course Concept Map, and will then seek out other maps, where the same knowledge domain is concerned, in order to find confirmations or suggestions about her/his own map. It is also conceivable that other maps would help retrieve useful learning material, possibly usable to implement the teacher's map. In particular, we show the definition of two measures, allowing to quantify the pedagogical similarity of two maps. In the analysis, we show how our measures are able to focus on the criteria they are designed for, and how they can provide assessment focused on selected pedagogical aspects (rather than providing an overall, general assessment of similarity
Retrieval of Educational Resources from the Web: A Comparison Between Google and Online Educational Repositories
No full textThe retrieval and composition of educational material are topics that attract many studies from the field of Information Retrieval and Artificial Intelligence. The Web is gradually gaining popularity among teachers and students as a source of learning resources. This transition is, however, facing skepticism from some scholars in the field of education. The main concern is about the quality and reliability of the teaching on the Web. While online educational repositories are explicitly built for educational purposes by competent teachers, web pages are designed and created for offering different services, not only education. In this study, we analyse if the Internet is a good source of teaching material compared to the currently available repositories in education. Using a collection of 50 queries related to educational topics, we compare how many useful learning resources a teacher can retrieve in Google and three popular learning object repositories. The results are very insightful and in favour of Google supported by the t-tests. For most of the queries, Google retrieves a larger number of useful web pages than the repositories p <.01, and no queries resulted in zero useful items. Instead, the repositories struggle to find even one relevant material for many queries. This study is clear evidence that even though the repositories offer a richer description of the learning resources through metadata, it is time to undertake more research towards the retrieval of web pages for educational applications
Exploiting SML for Experimenting with Algebraic Algorithms: The Example of p-adic Lifting
No full textGoing Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Linear Temporal Logic as An executable semantics for planning languages
No full textThis work presents an approach to artificial intelligence planning
based on linear temporal logic (LTL). The language PDDL-K (Planning Domain Description Language with control Knowledge), a simple and easy-to-use planning language, is described. This language allows one to specify a
planning problem together with heuristic information that can be of
help for both pruning the search space and find better plans. The
semantics of the language is given in terms of a translation into a
set of LTL formulae. Planning is then reduced to ``executing'' the
LTL encoding, i.e. to model search in LTL.
The choice of LTL is due to two main reasons. First of all, it allows
a simple and natural representation of a world that changes over time.
Secondly, it is decidable. These two features together free planning
in LTL from the above mentioned
inconveniences of planning in (either propositional or
first-order) classical logic.
Moreover, domain dependent knowledge as well as
intermediate tasks can be easily expressed both in LTL
The feasibility of the
approach has been successfully tested by means of the system Pdk,
an implementation of the proposed method.
Since expressing control knowledge correctly as LTL formulae can be quite a
delicate task, Pdk has equipped by tools
supporting the domain expert in the specification task, in particular
debugging tools, and the language PDDL-K
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