Spaces of valuations as quasimetric domains

AbstractWe define a natural quasimetric on the set of continuous valuations of a topological space and investigate it in the spirit of quasimetric domain theory. It turns out that the space of valuations of an (ordinary) algebraic domain D is an algebraic quasimetric domain. Moreover, it is precisely the lower powerdomain of D, where D is regarded as a quasimetric domain. The essential tool for proving these results is a generalization of the Splitting Lemma which characterizes the quasimetric for simple valuations and holds for valuations on arbitrary topological spaces

A geographic knowledge discovery approach to property valuation

This thesis involves an investigation of how knowledge discovery can be applied in the area Geographic Information Science. In particular, its application in the area of property valuation in order to reveal how different spatial entities and their interactions affect the price of the properties is explored. This approach is entirely data driven and does not require previous knowledge of the area applied. To demonstrate this process, a prototype system has been designed and implemented. It employs association rule mining and associative classification algorithms to uncover any existing inter-relationships and perform the valuation. Various algorithms that perform the above tasks have been proposed in the literature. The algorithm developed in this work is based on the Apriori algorithm. It has been however, extended with an implementation of a ‘Best Rule’ classification scheme based on the Classification Based on Associations (CBA) algorithm. For the modelling of geographic relationships a graph-theoretic approach has been employed. Graphs have been widely used as modelling tools within the geography domain, primarily for the investigation of network-type systems. In the current context, the graph reflects topological and metric relationships between the spatial entities depicting general spatial arrangements. An efficient graph search algorithm has been developed, based on the Djikstra shortest path algorithm that enables the investigation of relationships between spatial entities beyond first degree connectivity. A case study with data from three central London boroughs has been performed to validate the methodology and algorithms, and demonstrate its effectiveness for computer aided property valuation. In addition, through the case study, the influence of location in the value of properties in those boroughs has been examined. The results are encouraging as they demonstrate the effectiveness of the proposed methodology and algorithms, provided that the data is appropriately pre processed and is of high quality

Fibred contextual quantum physics

Inspired by the recast of the quantum mechanics in a toposical framework, we develop a contextual quantum mechanics via the geometric mathematics to propose a quantum contextuality adaptable in every topos. The contextuality adopted corresponds to the belief that the quantum world must only be seen from the classical viewpoints à la Bohr consequently putting forth the notion of a context, while retaining a realist understanding. Mathematically, the cardinal object is a spectral Stone bundle Σ → B (between stably-compact locales) permitting a treatment of the kinematics, fibre by fibre and fully point-free. In leading naturally to a new notion of points, the geometricity permits to understand those of the base space B as the contexts C — the commutative C*–algebras of a incommutative C*–algebras — and those of the spectral locale Σ as the couples (C, ψ), with ψ a state of the system from the perspective of such a C. The contexts are furnished with a natural order, the aggregation order which is installed as the specialization on B and Σ thanks to (one part of) the Priestley's duality adapted geometrically as well as to the effectuality of the lax descent of the Stone bundles along the perfect maps

NOTIFICATION !!!

All the content of this special edition is retrieved from the conference proceedings published by the European Scientific Institute, ESI. http://eujournal.org/index.php/esj/pages/view/books The European Scientific Journal, ESJ, after approval from the publisher re publishes the papers in a Special edition

NOTIFICATION !!!

All the content of this special edition is retrieved from the conference proceedings published by the European Scientific Institute, ESI. http://eujournal.org/index.php/esj/pages/view/books The European Scientific Journal, ESJ, after approval from the publisher re publishes the papers in a Special edition

NOTIFICATION !!!

All the content of this special edition is retrieved from the conference proceedings published by the European Scientific Institute, ESI. http://eujournal.org/index.php/esj/pages/view/books The European Scientific Journal, ESJ, after approval from the publisher re publishes the papers in a Special edition

NOTIFICATION !!!

All the content of this special edition is retrieved from the conference proceedings published by the European Scientific Institute, ESI. http://eujournal.org/index.php/esj/pages/view/books The European Scientific Journal, ESJ, after approval from the publisher re publishes the papers in a Special edition

NOTIFICATION !!!

All the content of this special edition is retrieved from the conference proceedings published by the European Scientific Institute, ESI. http://eujournal.org/index.php/esj/pages/view/books The European Scientific Journal, ESJ, after approval from the publisher re publishes the papers in a Special edition