9,628 research outputs found
ReAlM - a system to manipulate relations
Given a heterogeneous relation algebra R, it is well known that the algebra of matrices with coefficient from R is relation algebra with relational sums that is not
necessarily finite. When a relational product exists or the point axiom is given, we
can represent the relation algebra by concrete binary relations between sets, which
means the algebra may be seen as an algebra of Boolean matrices. However, it is
not possible to represent every relation algebra. It is well known that the smallest
relation algebra that is not representable has only 16 elements. Such an algebra can
not be put in a Boolean matrix form.[15]
In [15, 16] it was shown that every relation algebra R with relational sums and
sub-objects is equivalent to an algebra of matrices over a suitable basis. This basis is
given by the integral objects of R, and is, compared to R, much smaller.
Aim of my thesis is to develop a system called ReAlM - Relation Algebra Manipulator - that is capable of visualizing computations in arbitrary relation algebras
using the matrix approach
Geoscience after IT: Part F. Familiarization with quantitative analysis
Numbers, measurement and calculation extend our view of the world. Statistical methods describe the properties of sets of quantitative data, and can test models (particularly the model that observed relationships arose by chance) and help us to draw conclusions. Links between spatial and quantitative methods, through coordinate geometry and matrix algebra, lead to graphical representations for visualizing and exploring relationships. Multivariate statistics tie into visualization to look at pattern among many properties
Mining and visualizing uncertain data objects and named data networking traffics by fuzzy self-organizing map
Uncertainty is widely spread in real-world data. Uncertain data-in computer science-is typically found in the area of sensor networks where the sensors sense the environment with certain error. Mining and visualizing uncertain data is one of the new challenges that face uncertain databases. This paper presents a new intelligent hybrid algorithm that applies fuzzy set theory into the context of the Self-Organizing Map to mine and visualize uncertain objects. The algorithm is tested in some benchmark problems and the uncertain traffics in Named Data Networking (NDN). Experimental results indicate that the proposed algorithm is precise and effective in terms of the applied performance criteria.Peer ReviewedPostprint (published version
Visualizing elements of Sha[3] in genus 2 jacobians
Mazur proved that any element xi of order three in the Shafarevich-Tate group
of an elliptic curve E over a number field k can be made visible in an abelian
surface A in the sense that xi lies in the kernel of the natural homomorphism
between the cohomology groups H^1(k,E) -> H^1(k,A). However, the abelian
surface in Mazur's construction is almost never a jacobian of a genus 2 curve.
In this paper we show that any element of order three in the Shafarevich-Tate
group of an elliptic curve over a number field can be visualized in the
jacobians of a genus 2 curve. Moreover, we describe how to get explicit models
of the genus 2 curves involved.Comment: 12 page
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