35 research outputs found
Topological Foundations of Cognitive Science
A collection of papers presented at the First International Summer Institute in Cognitive Science, University at Buffalo, July 1994, including the following papers:
** Topological Foundations of Cognitive Science, Barry Smith
** The Bounds of Axiomatisation, Graham White
** Rethinking Boundaries, Wojciech Zelaniec
** Sheaf Mereology and Space Cognition, Jean Petitot
** A Mereotopological Definition of 'Point', Carola Eschenbach
** Discreteness, Finiteness, and the Structure of Topological Spaces, Christopher Habel
** Mass Reference and the Geometry of Solids, Almerindo E. Ojeda
** Defining a 'Doughnut' Made Difficult, N .M. Gotts
** A Theory of Spatial Regions with Indeterminate Boundaries, A.G. Cohn and N.M. Gotts
** Mereotopological Construction of Time from Events, Fabio Pianesi and Achille C. Varzi
** Computational Mereology: A Study of Part-of Relations for Multi-media Indexing, Wlodek Zadrozny and Michelle Ki
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Small scale software engineering
This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.In computing, the Software Crisis has arisen because software projects cannot meet their planned timescales, functional capabilities, reliability levels and budgets. This thesis reduces the general problem down to the Small Scale Software Engineering goal of improving the quality and tractability of the
designs of individual programs. It is demonstrated that the application of eight abstractions (set, sequence, hierarchy, h-reduction, integration, induction, enumeration, generation) can lead to a reduction in the size and complexity of and an increase in the quality of software designs when expressed via Dimensional Design, a new representational technique which uses the three spatial dimensions to represent set, sequence and hierarchy, whilst special symbols and axioms encode the other abstractions. Dimensional Designs are trees of symbols whose edges perceptually encode the relationships between the nodal symbols. They are easy to draw and manipulate both manually and mechanically. Details are given of real software projects already undertaken using Dimensional Design. Its tool kit, DD/ROOTS, produces high quality, machine drawn, detailed design documentation plus novel quality control information. A run time monitor records and animates execution, measures CPU time and
takes snapshots etc; all these results are represented according to Dimensional
Design principles to maintain conceptual integrity with the design. These techniques
are illustrated by the development of a non-trivial example program. Dimensional Design is axiomatised, compared to existing techniques and evaluated against the stated problem. It has advantages over existing techniques, mainly its clarity of expression and ease of manipulation of individual abstractions due to its graphical basis
Integrated modelling for 3D GIS
A three dimensional (3D) model facilitates the study of the real world objects it represents. A geoinformation system (GIS) should exploit the 3D model in a digital form as a basis for answering questions pertaining to aspects of the real world. With respect to the earth sciences, different kinds of objects of reality can be realized. These objects are components of the reality under study. At the present state-of-the-art different realizations are usually situated in separate systems or subsystems. This separation results in redundancy and uncertainty when different components sharing some common aspects are combined. Relationships between different kinds of objects, or between components of an object, cannot be represented adequately. This thesis aims at the integration of those components sharing some common aspects in one 3D model. This integration brings related components together, minimizes redundancy and uncertainty. Since the model should permit not only the representation of known aspects of reality, but also the derivation of information from the existing representation, the design of the model is constrained so as to afford these capabilities. The tessellation of space by the network of simplest geometry, the simplicial network, is proposed as a solution. The known aspects of the reality can be embedded in the simplicial network without degrading their quality. The model provides finite spatial units useful for the representation of objects. Relationships between objects can also be expressed through components of these spatial units which at the same time facilitate various computations and the derivation of information implicitly available in the model. Since the simplicial network is based on concepts in geoinformation science and in mathematics, its design can be generalized for n-dimensions. The networks of different dimension are said to be compatible, which enables the incorporation of a simplicial network of a lower dimension into another simplicial network of a higher dimension.The complexity of the 3D model fulfilling the requirements listed calls for a suitable construction method. The thesis presents a simple way to construct the model. The raster technique is used for the formation of the simplicial network embedding the representation of the known aspects of reality as constraints. The prototype implementation in a software package, ISNAP, demonstrates the simplicial network's construction and use. The simplicial network can facilitate spatial and non spatial queries, computations, and 2D and 3D visualizations. The experimental tests using different kinds of data sets show that the simplicial network can be used to represent real world objects in different dimensionalities. Operations traditionally requiring different systems and spatial models can be carried out in one system using one model as a basis. This possibility makes the GIS more powerful and easy to use
Chromatic polynomials
In this thesis, we shall investigate chromatic polynomials of graphs, and some related polynomials. In Chapter 1, we study the chromatic polynomial written in a modified form, and use these results to characterise the chromatic polynomials of polygon trees. In Chapter 2, we consider the chromatic polynomial written as a sum of the chromatic polynomials of complete graphs; in particular, we determine for which graphs the coefficients are symmetrical, and show that the coefficients exhibit a skewed property. In Chapter 3, we dualise many results about chromatic polynomials to flow polynomials, including the results in Chapter 1, and a result about a zero-free interval. Finally, in Chapter 4, we investigate the zeros of the Tutte Polynomial; in particular their observed proximity to certain hyperbole in the xy-plane