2,554 research outputs found
Convergence and quantale-enriched categories
Generalising Nachbin's theory of "topology and order", in this paper we
continue the study of quantale-enriched categories equipped with a compact
Hausdorff topology. We compare these -categorical compact
Hausdorff spaces with ultrafilter-quantale-enriched categories, and show that
the presence of a compact Hausdorff topology guarantees Cauchy completeness and
(suitably defined) codirected completeness of the underlying quantale enriched
category
Mathematics in Software Reliability and Quality Assurance
This monograph concerns the mathematical aspects of software reliability and quality assurance and consists of 11 technical papers in this emerging area. Included are the latest research results related to formal methods and design, automatic software testing, software verification and validation, coalgebra theory, automata theory, hybrid system and software reliability modeling and assessment
GA-based neural fuzzy control of flexible-link manipulators
The limitations of conventional model-based control mechanisms for flexible manipulator systems have stimulated the development of intelligent control mechanisms incorporating fuzzy logic and neural networks. Problems have been encountered in applying the traditional PD-, PI-, and PID-type fuzzy controllers to flexible-link manipulators. A PD-PI-type fuzzy controller has been developed where the membership functions are adjusted by tuning the scaling factors using a neural network. Such a network needs a sufficient number of neurons in the hidden layer to approximate the nonlinearity of the system. A simple realisable network is desirable and hence a single neuron network with a nonlinear activation function is used. It has been demonstrated that the sigmoidal function and its shape can represent the nonlinearity of the system. A genetic algorithm is used to learn the weights, biases and shape of the sigmoidal function of the neural network
Theoretical Interpretations and Applications of Radial Basis Function Networks
Medical applications usually used Radial Basis Function Networks just as Artificial Neural Networks. However, RBFNs are Knowledge-Based Networks that can be interpreted in several way: Artificial Neural Networks, Regularization Networks, Support Vector Machines, Wavelet Networks, Fuzzy Controllers, Kernel Estimators, Instanced-Based Learners. A survey of their interpretations and of their corresponding learning algorithms is provided as well as a brief survey on dynamic learning algorithms. RBFNs' interpretations can suggest applications that are particularly interesting in medical domains
Topology from enrichment: the curious case of partial metrics
For any small quantaloid \Q, there is a new quantaloid \D(\Q) of
diagonals in \Q. If \Q is divisible then so is \D(\Q) (and vice versa),
and then it is particularly interesting to compare categories enriched in \Q
with categories enriched in \D(\Q). Taking Lawvere's quantale of extended
positive real numbers as base quantale, \Q-categories are generalised metric
spaces, and \D(\Q)-categories are generalised partial metric spaces, i.e.\
metric spaces in which self-distance need not be zero and with a suitably
modified triangular inequality. We show how every small quantaloid-enriched
category has a canonical closure operator on its set of objects: this makes for
a functor from quantaloid-enriched categories to closure spaces. Under mild
necessary-and-sufficient conditions on the base quantaloid, this functor lands
in the category of topological spaces; and an involutive quantaloid is
Cauchy-bilateral (a property discovered earlier in the context of distributive
laws) if and only if the closure on any enriched category is identical to the
closure on its symmetrisation. As this now applies to metric spaces and partial
metric spaces alike, we demonstrate how these general categorical constructions
produce the "correct" definitions of convergence and Cauchyness of sequences in
generalised partial metric spaces. Finally we describe the Cauchy-completion,
the Hausdorff contruction and exponentiability of a partial metric space, again
by application of general quantaloid-enriched category theory.Comment: Apart from some minor corrections, this second version contains a
revised section on Cauchy sequences in a partial metric spac
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