Modelling the interdependence of spatial scales in urban systems

The multitude of interwoven spatial scales and their relevance for urban systems has been of interest to the complexity science of cities since its conception. Today, we are well aware that urban environments are being simultaneously shaped and organised through actions at all levels. However, the fundamental question of how to reveal and quantify the interdependence of processes in between various spatial and temporal scales is less often addressed. Deepening our theoretical understanding of the multiscale spatiotemporal complexity of urban systems demands a transdisciplinary framework and the deployment of novel and advanced mathematical models. This article performs a multiscale analysis of urban structures using a large dataset of rent price values in the Ruhr area, Germany. We argue that, due to their many interacting degrees of freedom, urban systems exhibit similar features as other strongly correlated systems, for example, turbulent flows, notably the occurrence of extreme small-scale fluctuations. This analogy between urban and turbulent systems, which we support by empirical evidence, allows for the modelling of spatial structures on the basis of concepts and methods from turbulence theory. We demonstrate how by identifying the main turbulence-borrowed characteristics of an arbitrary two-dimensional urban field, it can be fully reproduced with a small number of prescribed points. Our findings have theoretical implications in the way we quantify and analyse scales in urban systems, model small-scale urban structures as well as potential policy relevance on understanding the evolution and spatial organisation of cities

Analysis of the types and relations of features that people include in route sketch maps

Dissertation submitted in partial fulfilment of the requirements for the Degree of Master of Science in Geospatial TechnologiesGeographic information makes our lives easier through devices such as GPS or drones. Many technical improvements are coming up every day, but the interaction human-computer is sometimes limited. In particular, in the process of moving from the digital world to reality, how people understand this information. In this paper, I investigated what are the different features and relations of features that people include in sketch maps when they are asked to give route directions and what are the reasons for these differences. The research is based on people´s spatial knowledge using data collected among users sketch maps and spatial strategies tests. Our results show that there are differences in the features drawn and that they are related mostly due to environmental reasons. Not relevant differences are found in the spatial relation of features. From the results, it is extracted valuable information that can benefit future researchers and the creation of new navigation devices

Analysis and development of the Bees Algorithm for primitive fitting in point cloud models

This work addresses the problem of fitting a geometrical primitive to a point cloud as a numerical optimisation problem. Intelligent Optimisation Techniques like Evolutionary Algorithms and the Bees Algorithm were here adapted to select the most fit primitive out of a population of solutions, and the results compared. The necessity of understanding the dynamics of the Bees Algorithm to improve its performances and applicability led to an in-depth analysis of its key parts. A new mathematical definition of the algorithm led to the discovery and formalisation of several properties, many of which provided a mathematical answer to behaviours so far only observed in empirical tests. The implications of heuristics commonly used in the Bees Algorithm, like site abandonment and neighbourhood shrinking, were statistically analysed. The probability of a premature stalling of the local search at a site has been quantified under certain conditions. The effect of the choice of shape for the local neighbourhood on the exploitative search of the Bees Algorithm was analysed. The study revealed that this commonly overlooked aspect has profound consequences on the effectiveness of the local search, and practical applications have been suggested to address specific search problems. The results of the primitive fitting study, and the analysis of the Bees Algorithm, inspired the creation of a new algorithm for problems where multiple solutions are sought (multi-solution optimisation). This new algorithm is an ex- tension of the Bees Algorithm to multi-solution optimisation. It uses topological information on the search space gathered during the cycles of local search at a site, which is normally discarded, to alter the fitness function. The function is altered to discourage further search in already explored regions of the fitness landscape, and force the algorithm to discover new optima. This new algorithm found immediate application on the multi-shape variant of the primitive fitting problem. In a series of experimental tests, the new algorithm obtained promising results, showing its ability to find many shapes in a point cloud. It also showed its suitability as a general technique for the multi-solution optimisation problem