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Symbolic and Numeric Algorithms for Scientific Computing, 2006. SYNASC '06. Eighth International Symposium on

Date 26-29 Sept. 2006

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  • Eighth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing [Cover]

    Page(s): c1
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  • Eighth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing-Title

    Page(s): i - iii
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  • Eighth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing-Copyright

    Page(s): iv
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  • Eighth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing - TOC

    Page(s): v - x
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  • Preface

    Page(s): xi
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  • SYNASC 2006 Committees

    Page(s): xii
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  • ACSys 2006

    Page(s): xiii
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  • GridCAD 2006

    Page(s): xiii
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  • MTE 2006

    Page(s): xiii
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  • NCA 2006

    Page(s): xiv
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  • PN&WM 2006

    Page(s): xiv
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  • Mathematical Theory Exploration

    Page(s): 3 - 4
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (60 KB) |  | HTML iconHTML  

    Summary form only given. Mathematics is characterized by its method of gaining knowledge, namely reasoning. The automation of reasoning has seen significant advances over the past decades and, thus, the expectation was that these advances would also have significant impact on the practice of doing mathematics. However, so far, this impact is small. We think that the reason for this is the fact that automated reasoning so far concentrated on the automated proof of individual theorems whereas, in the practice of mathematics, one proceeds by building up entire theories in a step-by-step process. This process of exploring mathematical theories consists of the invention of notions, the invention and proof of propositions (lemmas, theorems), the invention of problems, and the invention and verification of methods (algorithms) that solve problems View full abstract»

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  • Emergence in Problem Solving, Classification and Machine Learning

    Page(s): 5 - 9
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    Emergence is usually the way in which a collective organisation behaves differently than the sum of its elements. We propose here an overview of different ways this paradigm is used in several fields of artificial intelligence and we propose some theoretical tracks relying on some works in the field of machine learning View full abstract»

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  • Adventures of a Logician-Engineer: A Journey through Logic, Engineering, Medicine, Biology, and Statistics

    Page(s): 10
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    Summary form only given. Whenever a programmer writes a loop, or a mathematician does a proof by induction, an invariant is involved. The discovery and understanding of invariants often underlies problem solving in many domains. The author discusses his search for powerful invariants over the past decade. This search was/is motivated by a broad spectrum of problems: understanding query languages, engineering data integration systems, optimizing disease treatments, recognizing DNA feature sites, and discovering reliable patterns View full abstract»

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  • Tiers of webOrigami Programming

    Page(s): 11
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    Summary form only given. The World Wide Web is an important knowledge repository for our daily activities, and moreover it is transforming itself to service repository. Many scientists not only publish their results on the Web but offer services that accrue from their scientific discoveries and inventions. The WebOrigami, under development by SCORE at University of Tsukuba, is one such science service portal that offers services to interested mathematicians and origamists. Its aim is to help them to explore the possibilities of computational origami as well as enjoying the origami art. In this paper the author talks about the current state of the development of the system, talking about technical problems that we encounter and solutions we came up with. The state of the art of the Web programming technology is far from our satisfaction. It often leads us into many undesired pitfalls as well as security problems. The most serious problem, in our view, is the lack of an adequate computational model with which we reason about Web programming and computing. This paper focuses on the computation model for Web computing that is based on multi-tiered programming methodology; the computation model with which we are trying to abstract from our programming efforts in constructing the portal View full abstract»

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  • Improving Pen-Based Mathematical Interfaces

    Page(s): 12
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (53 KB) |  | HTML iconHTML  

    Summary form only given. Pen-based user interfaces offer tantalizing potential for mathematical software systems. In contrast to normal text, entering and editing mathematical formulae with a digital pen can be much more natural than using a keyboard. Machine recognition of mathematical handwriting, however, is more complex than recognizing natural language text. In this context it is necessary to deal with a vast array of similar symbols and the analysis of the two-dimensional syntactic structure of formulae. This talk outlines our work in this area. We describe our architecture for a mathematical handwriting component that can be embedded in various applications. These include computer algebra systems, such as Maple, and document processing applications, such as Microsoft Word. We describe the problem of mathematical character recognition and detail how recognition rates can be enhanced using data derived from the analysis of digital libraries View full abstract»

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  • Tuning Evolutionary Algorithm Performance Using Nature Inspired Heuristics

    Page(s): 13
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    Summary form only given. Evolutionary algorithms have become an important problem solving methodology among many researchers working in the area of computational intelligence. The population based collective learning process; self adaptation and robustness are some of the key features of evolutionary algorithm when compared to other global optimization techniques. Due to its simplicity, evolutionary algorithms have been widely accepted for solving several important practical applications in engineering, business, commerce etc. However, experimental evidence had indicated cases where evolutionary algorithms are inefficient at fine tuning solutions, but better at finding global basins of attraction. The efficiency of evolutionary training can be improved significantly by hybridization of some search procedures or incorporating some heuristics into the evolution process. In this talk, we will review how particle swarm optimization algorithm and bacterial foraging algorithm could be used to optimize the performance of evolutionary algorithms. The performance of the hybridized algorithms will be illustrated using some benchmark problems View full abstract»

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  • MATHsAiD: A Mathematical Theorem Discovery Tool

    Page(s): 17 - 22
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (144 KB) |  | HTML iconHTML  

    In the field of automated reasoning, one of the most challenging (even if perhaps, somewhat overlooked) problems thus far has been to develop a means of discerning, from amongst all the truths that can be discovered and proved, those which are either useful or interesting enough to be worth recording. As for human reasoning, mathematicians are well known for their predilection towards designating certain discoveries as theorems, lemmas, corollaries, etc., whilst relegating all others as relatively unimportant. However, precisely how mathematicians determine which results to keep, and which to discard, is perhaps not so well known. Nevertheless, this practice is an essential part of the mathematical process, as it allows mathematicians to manage what would otherwise be an overwhelming amount of knowledge. MATHsAiD is a system intended for use by research mathematicians, and is designed to produce high quality theorems, as recognised by mathematicians, within a given theory. The only input required is a set of axioms and definitions for each theory. In this paper we briefly describe some of the more important methods used by MATHsAiD, most of which are based primarily on the human mathematical process View full abstract»

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  • Scheme-Based Systematic Exploration of Natural Numbers

    Page(s): 23 - 34
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (252 KB) |  | HTML iconHTML  

    In this paper, we report a case study of computer supported exploration of the theory of natural numbers, using a theory exploration model based on knowledge schemes, proposed by Bruno Buchberger. We illustrate with examples from the exploration: (i) the invention of new concepts (functions, relations) in the theory, using knowledge scheme;, (ii) the invention of new propositions, using proposition schemes; (iii) the invention of problems, using knowledge schemes; (iv) the introduction of new reasoning rules, by lifting knowledge to the inference level, after their correctness was proved View full abstract»

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  • Implementing Parameterized Type Algorithm Definitions in Mathematica

    Page(s): 35 - 40
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (243 KB) |  | HTML iconHTML  

    The paper focuses on means of defining parameterized type categories and algorithms built on such types in Mathematica. Symbolic algorithms based on category theory have the advantage of systematically dealing with domains, categories, operators over them by creating general contexts of expressing algorithms, which can be applied by parameterizing them with various domains, using the same algorithm definition. While similar approaches have been previously presented by the author, the present paper aims at a stronger focus on algorithm characteristics defined on categorical principles and giving a more general framework for implementing Mathematica algorithms based on generic principles and category theory. The paper also discusses run time efficiency aspects for these generic implementations View full abstract»

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  • A Two-Level Programming Approach to Volume Propagation in Higher-Dimensional Spaces

    Page(s): 41 - 46
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (212 KB) |  | HTML iconHTML  

    A set of algorithms designed for the analysis of phase-space perturbation propagation in dynamical systems is presented. The most important tasks are approximate volume estimation and determining the subset of the perturbation surface that is tangent to current lines. The algorithms are developed in a generic, dimension-independent fashion, but they can be partially evaluated with respect to the dimension of the space, yielding dimension specific, efficient algorithms. The MuPAD implementation of the algorithms and supporting libraries is also discussed View full abstract»

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  • Doing Numerical Cosmology with the Cactus Code

    Page(s): 47 - 54
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    The article presents some aspects concerning the construction of a new thorn for the Cactus code, a complete 3-dimensional machinery in numerical relativity. This thorn is dedicated to numerical simulations in cosmology, that means it can provide evolutions of different cosmological models, mainly based on Friedman-Robertson-Walker metric. Some numerical results are presented, testing the convergence, stability and the applicability of the code View full abstract»

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  • The Use of Maple Platform for the Study of Geodesic Motion on Curved Spacetimes

    Page(s): 55 - 62
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (272 KB) |  | HTML iconHTML  

    The article illustrates the graphical study of geodesic motion on curved space-times (mainly exact solutions of Einstein equations) using the symbolic, numerical and graphical computation facilities of Maple platform. The example of null geodesics on Schwarzschild solution is completely processed. The geodesic curves are plotted directly using DEtools package in Schwarzs child coordinates View full abstract»

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  • A Quality Measure for Multi-Level Community Structure

    Page(s): 63 - 68
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (181 KB) |  | HTML iconHTML  

    Mining relational data often boils down to computing clusters, that is finding sub-communities of data elements forming cohesive sub-units, while being well separated from one another. The clusters themselves are sometimes terms "communities" and the way clusters relate to one another is often referred to as a "community structure". We study a modularity criterion MQ introduced by Mancoridis et al. in order to infer community structure on relational data. We prove a fundamental and useful property of the modularity measure MQ, showing that it can be approximated by a Gaussian distribution, making it a prevalent choice over less focused optimization criterion for graph clustering. This makes it possible to compare two different clusterings of a same graph as well as asserting the overall quality of a given clustering relying on the fact that MQ is Gaussian. Moreover, we introduce a generalization extending MQ to hierarchical clusterings of graphs which reduces to the original MQ when the hierarchy becomes flat View full abstract»

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  • A New k-means Based Clustering Algorithm in Aspect Mining

    Page(s): 69 - 74
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (192 KB) |  | HTML iconHTML  

    Clustering is a division of data into groups of similar objects. Aspect mining is a process that tries to identify cross-cutting concerns in existing software systems. The goal is to refactor the existing systems to use aspect oriented programming, in order to make them easier to maintain and to evolve. This paper aims at presenting a new k-means based clustering algorithm used in aspect mining. Clustering is used in order to identify crosscutting concerns. We propose some quality measures in order to evaluate the results both from the clustering point of view and the aspect mining point of view, and we also report two case studies View full abstract»

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