Summarizing level-two topological relations in large spatial datasets

Summarizing topological relations is fundamental to many spatial applications including spatial query optimization. In this article, we present several novel techniques to effectively construct cell density based spatial histograms for range (window) summarizations restricted to the four most important level-two topological relations: contains, contained, overlap, and disjoint. We first present a novel framework to construct a multiscale Euler histogram in 2D space with the guarantee of the exact summarization results for aligned windows in constant time. To minimize the storage space in such a multiscale Euler histogram, an approximate algorithm with the approximate ratio 19/12 is presented, while the problem is shown NP-hard generally. To conform to a limited storage space where a multiscale histogram may be allowed to have only k Euler histograms, an effective algorithm is presented to construct multiscale histograms to achieve high accuracy in approximately summarizing aligned windows. Then, we present a new approximate algorithm to query an Euler histogram that cannot guarantee the exact answers; it runs in constant time. We also investigate the problem of nonaligned windows and the problem of effectively partitioning the data space to support nonaligned window queries. Finally, we extend our techniques to 3D space. Our extensive experiments against both synthetic and real world datasets demonstrate that the approximate multiscale histogram techniques may improve the accuracy of the existing techniques by several orders of magnitude while retaining the cost efficiency, and the exact multiscale histogram technique requires only a storage space linearly proportional to the number of cells for many popular real datasets.

Multiscale histograms: Summarizing topological relations in large spatial datasets

Summarizing topological relations is fundamental to many spatial applications including spatial query optimization. In this paper, we present several novel techniques to eectively construct cell density based spatial histograms for range (window) summarizations restricted to the four most important topological relations: contains, contained, overlap, and disjoint. We rst present a novel framework to construct a multiscale histogram composed of multiple Euler histograms with the guarantee of the exact summarization results for aligned windows in constant time. Then we present an approximate algorithm, with the approximate ratio 19/12, to minimize the storage spaces of such multiscale Euler histograms, although the problem is generally NP-hard. To conform to a limited storage space where only k Euler histograms are allowed, an effective algorithm is presented to construct multiscale histograms to achieve high accuracy. Finally, we present a new approximate algorithm to query an Euler histogram that cannot guarantee the exact answers; it runs in constant time. Our extensive experiments against both synthetic and real world datasets demonstrated that the approximate mul- tiscale histogram techniques may improve the accuracy of the existing techniques by several orders of magnitude while retaining the cost effciency, and the exact multiscale histogram technique requires only a storage space linearly proportional to the number of cells for the real datasets.

Testing native speakers of German and Portuguese on the understanding of topological operators-line-region relations in gvSIG

Dissertation submitted in partial fulfilment of the requirements for the Degree of Master of Science in Geospatial Technologies

Cognitive assessment of topological movement Patterns and direction turns: An influence of scale

Dissertation submitted in partial fulfillment of the requirements for the Degree of Master of Science in Geospatial Technologies.

Exploratory geospatial data analysis using self-organizing maps

Dissertação apresentada como requisito parcial para obtenção do grau de Mestre em Ciência e Sistemas de Informação Geográfica

Representação e armazenamento de dados cadastrais 3D em banco de dados geográficos

Pós-graduação em Ciências Cartográficas - FCT

Derivation of Change from Sequences of Snapshots

Current research in the domain of geographic information science considers possibilities of including another dimension, time, which is generally missing to this point. Users interested in changes have few functions available to compare datasets of spatial configurations at different points in time. Such a comparison of spatial configurations requires large amounts of manual labor. An automatic derivation of changes would decrease amounts of manual labor. The thesis introduces a set of methods that allows for an automatic derivation of changes. These methods analyze identity and topological states of objects in snapshots and derive types of change for the specific configuration of data. The set of change types that can be computed by the methods presented includes continuous changes such as growing, shrinking, and moving of objects. For these continuous changes identity remains unchanged, while topological relations might be altered over time. Also discrete changes such as merging and splitting where both identity and topology are affected can be derived. Evaluation of the methods using a prototype application with simple examples suggests that the methods compute uniquely and correctly the type of change that applied in spatial scenarios captured in two snapshots.

A Topological Approach to Fuzzy Sets

This thesis presents a topological approach to studying fuzzy setsby means of modifier operators. Modifier operators are mathematical models, e.g., for hedges, and we present briefly different approaches to studying modifier operators. We are interested in compositional modifier operators, modifiers for short, and these modifiers depend on binary relations. We show that if a modifier depends on a reflexive and transitive binary relation on U, then there exists a unique topology on U such that this modifier is the closure operator in that topology. Also, if U is finite then there exists a lattice isomorphism between the class of all reflexive and transitive relations and the class of all topologies on U. We define topological similarity relation "≈" between L-fuzzy sets in an universe U, and show that the class LU/ ≈ is isomorphic with the class of all topologies on U, if U is finite and L is suitable. We consider finite bitopological spaces as approximation spaces, and we show that lower and upper approximations can be computed by means of α-level sets also in the case of equivalence relations. This means that approximations in the sense of Rough Set Theory can be computed by means of α-level sets. Finally, we present and application to data analysis: we study an approach to detecting dependencies of attributes in data base-like systems, called information systems.

The European Union and Assembling Biofuel Development – topological investigations concerning the associations between law, policy and space

Biofuels for transport are a renewable source of energy that were once heralded as a solution to multiple problems associated with poor urban air quality, the overproduction of agricultural commodities, the energy security of the European Union (EU) and climate change. It was only after the Union had implemented an incentivizing framework of legal and political instruments for the production, trade and consumption of biofuels that the problems of weakening food security, environmental degradation and increasing greenhouse gases through land-use changes began to unfold. In other words, the difference between political aims for why biofuels are promoted and their consequences has grown – which is also recognized by the EU policy-makers. Therefore, the global networks of producing, trading and consuming biofuels may face a complete restructure if the European Commission accomplishes its pursuit to sideline crop-based biofuels after 2020. My aim with this dissertation is not only to trace the manifold evolutions of the instruments used by the Union to govern biofuels but also to reveal how this evolution has influenced the dynamics of biofuel development. Therefore, I study the ways the EU’s legal and political instruments of steering biofuels are coconstitutive with the globalized spaces of biofuel development. My analytical strategy can be outlined through three concepts. I use the term ‘assemblage’ to approach the operations of the loose entity of actors and non-human elements that are the constituents of multi-scalar and -sectorial biofuel development. ‘Topology’ refers to the spatiality of this European biofuel assemblage and its parts whose evolving relations are treated as the active constituents of space, instead of simply being located in space. I apply the concept of ‘nomosphere’ to characterize the framework of policies, laws and other instruments that the EU applies and construes while attempting to govern biofuels. Even though both the materials and methods vary in the independent articles, these three concepts characterize my analytical strategy that allows me to study law, policy and space associated with each other. The results of my examinations underscore the importance of the instruments of governance of the EU constituting and stabilizing the spaces of producing and, on the other hand, how topological ruptures in biofuel development have enforced the need to reform policies. This analysis maps the vast scope of actors that are influenced by the mechanism of EU biofuel governance and, what is more, shows how they are actively engaging in the Union’s institutional policy formulation. By examining the consequences of fast biofuel development that are spatially dislocated from the established spaces of producing, trading and consuming biofuels such as indirect land use changes, I unfold the processes not tackled by the instruments of the EU. Indeed, it is these spatially dislocated processes that have pushed the Commission construing a new type of governing biofuels: transferring the instruments of climate change mitigation to land-use policies. Although efficient in mitigating these dislocated consequences, these instruments have also created peculiar ontological scaffolding for governing biofuels. According to this mode of governance, the spatiality of biofuel development appears to be already determined and the agency that could dampen the negative consequences originating from land-use practices is treated as irrelevant.

Fuzzy Topological Games and Related Topics

The main purpose of study is to extend the concept of the topological game G(K, X) and some other kinds of games into fuzzy topological games and to obtain some results regarding them. Owing to the fact that topological games have plenty of applications in covering properties, it made an attempt to explore some inter relations of games and covering properties in fuzzy topological spaces. Even though the main focus is on fuzzy para-meta compact spaces and closure preserving shading families, some brief sketches regarding fuzzy P-spaces and Shading Dimension is also provided. In a topological game players choose some objects related to the topological structure of a space such as points, closed subsets, open covers etc. More over the condition on a play to be winning for a player may also include topological notions such as closure, convergence, etc. It turns out that topological games are related to the Baire property, Baire spaces, Completeness properties, Convergence properties, Separation properties, Covering and Base properties, Continuous images, Suslin sets, Singular spaces etc.

On Chaos and Fractals in General Topological Spaces

The present study on chaos and fractals in general topological spaces. Chaos theory originated with the work of Edward Lorenz. The phenomenon which changes order into disorder is known as chaos. Theory of fractals has its origin with the frame work of Benoit Mandelbrot in 1977. Fractals are irregular objects. In this study different properties of topological entropy in chaos spaces are studied, which also include hyper spaces. Topological entropy is a measures to determine the complexity of the space, and compare different chaos spaces. The concept of fractals can’t be extended to general topological space fast it involves Hausdorff dimensions. The relations between hausdorff dimension and packing dimension. Regular sets in Metric spaces using packing measures, regular sets were defined in IR” using Hausdorff measures. In this study some properties of self similar sets and partial self similar sets. We can associate a directed graph to each partial selfsimilar set. Dimension properties of partial self similar sets are studied using this graph. Introduce superself similar sets as a generalization of self similar sets and also prove that chaotic self similar self are dense in hyper space. The study concludes some relationships between different kinds of dimension and fractals. By defining regular sets through packing dimension in the same way as regular sets defined by K. Falconer through Hausdorff dimension, and different properties of regular sets also.

Box Products in Fuzzy Topological Spaces and Related Topics

The topology as the product set with a base chosen as all products of open sets in the individual spaces. This topology is known as box topology. The main objective of this study is to extend the concept of box products to fuzzy box products and to obtain some results regarding them. Owing to the fact that box products have plenty of applications in uniform and covering properties, here made an attempt to explore some inter relations of fuzzy uniform properties and fuzzy covering properties in fuzzy box products. Even though the main focus is on fuzzy box products, some brief sketches regarding hereditarily fuzzy normal spaces and fuzzy nabla product is also provided. The main results obtained include characterization of fuzzy Hausdroffness and fuzzy regularity of box products of fuzzy topological spaces. The investigation of the completeness of fuzzy uniformities in fuzzy box products proved that a fuzzy box product of spaces is fuzzy topologically complete if each co-ordinate space is fuzzy topologically complete. The thesis also prove that the fuzzy box product of a family of fuzzy α-paracompact spaces is fuzzy topologically complete. In Fuzzy box product of hereditarily fuzzy normal spaces, the main result obtained is that if a fuzzy box product of spaces is hereditarily fuzzy normal ,then every countable subset of it is fuzzy closed. It also deals with the notion of fuzzy nabla product of spaces which is a quotient of fuzzy box product. Here the study deals the relation connecting fuzzy box product and fuzzy nabla product

Relations between two-dimensional models from dimensional reduction

In this work we explore the consequences of dimensional reduction of the 3D Maxwell-Chern-Simons and some related models. A connection between topological mass generation in 3D and mass generation according to the Schwinger mechanism in 2D is obtained. In addition, a series of relationships is established by resorting to dimensional reduction and duality interpolating transformations. Non-Abelian generalizations are also pointed out.

Topological Descriptors in Modeling the Antimalarial Activity of 4-(3’, 5’-Disubstitutedanilino)quinolines

Two series of closely related antimalarial agents, 7-chloro-4-(3’,5’-disubstitutedanilino) quinolines, have been analyzed using Combinatorial Protocol in Multiple Linear Regression (CP-MLR) for the structure-activity relations with more than 450 topological descriptors for each set. The study clearly suggested that 3’- and 5’- substituents of the anilino moiety map different domains in the activity space. While one domain favors the compact structural frames having aromatic, heterocyclic ring(s) substituted with closely spaced F, NO2 and O functional groups, the other prefers structural frames enriched with unsaturation, loops, branches, electronic content and devoid of carbonyl function. Also, this study gives an indication in favour of the electron rich centres in the aniline substituent groups for better antimalarial activity; an observation in line with several of the previous reports too. The models developed and the participating descriptors suggest that the substituent groups of the 4-anilino moiety of the 4-(3’, 5’-disubstitutedanilino)quinolines hold scope for further modification in the optimisation of the antimalarial activity.

Regular and Other Kinds of Extensions of Topological Spaces

∗ This work was partially supported by the National Foundation for Scientific Researches at the Bulgarian Ministry of Education and Science under contract no. MM-427/94.