A 3d geoscience information system framework

Two-dimensional geographical information systems are extensively used in the geosciences to create and analyse maps. However, these systems are unable to represent the Earth's subsurface in three spatial dimensions. The objective of this thesis is to overcome this deficiency, to provide a general framework for a 3d geoscience information system (GIS), and to contribute to the public discussion about the development of an infrastructure for geological observation data, geomodels, and geoservices. Following the objective, the requirements for a 3d GIS are analysed. According to the requirements, new geologically sensible query functionality for geometrical, topological and geological properties has been developed and the integration of 3d geological modeling and data management system components in a generic framework has been accomplished. The 3d geoscience information system framework presented here is characterized by the following features: - Storage of geological observation data and geomodels in a XML-database server. According to a new data model, geological observation data can be referenced by a set of geomodels. - Functionality for querying observation data and 3d geomodels based on their 3d geometrical, topological, material, and geological properties were developed and implemented as plug-in for a 3d geomodeling user application. - For database queries, the standard XML query language has been extended with 3d spatial operators. The spatial database query operations are computed using a XML application server which has been developed for this specific purpose. This technology allows sophisticated 3d spatial and geological database queries. Using the developed methods, queries can be answered like: "Select all sandstone horizons which are intersected by the set of faults F". This request contains a topological and a geological material parameter. The combination of queries with other GIS methods, like visual and statistical analysis, allows geoscience investigations in a novel 3d GIS environment. More generally, a 3d GIS enables geologists to read and understand a 3d digital geomodel analogously as they read a conventional 2d geological map

Towards a Theory of Scale-Free Graphs: Definition, Properties, and Implications (Extended Version)

Although the ``scale-free'' literature is large and growing, it gives neither a precise definition of scale-free graphs nor rigorous proofs of many of their claimed properties. In fact, it is easily shown that the existing theory has many inherent contradictions and verifiably false claims. In this paper, we propose a new, mathematically precise, and structural definition of the extent to which a graph is scale-free, and prove a series of results that recover many of the claimed properties while suggesting the potential for a rich and interesting theory. With this definition, scale-free (or its opposite, scale-rich) is closely related to other structural graph properties such as various notions of self-similarity (or respectively, self-dissimilarity). Scale-free graphs are also shown to be the likely outcome of random construction processes, consistent with the heuristic definitions implicit in existing random graph approaches. Our approach clarifies much of the confusion surrounding the sensational qualitative claims in the scale-free literature, and offers rigorous and quantitative alternatives.Comment: 44 pages, 16 figures. The primary version is to appear in Internet Mathematics (2005

Graph Theory and Networks in Biology

In this paper, we present a survey of the use of graph theoretical techniques in Biology. In particular, we discuss recent work on identifying and modelling the structure of bio-molecular networks, as well as the application of centrality measures to interaction networks and research on the hierarchical structure of such networks and network motifs. Work on the link between structural network properties and dynamics is also described, with emphasis on synchronization and disease propagation.Comment: 52 pages, 5 figures, Survey Pape

Design and Topology Optimisation of Tissue Scaffolds

Tissue restoration by tissue scaffolding is an emerging technique with many potential applications. While it is well-known that the structural properties of tissue scaffolds play a critical role in cell regrowth, it is usually unclear how optimal tissue regeneration can be achieved. This thesis hereby presents a computational investigation of tissue scaffold design and optimisation. This study proposes an isosurface-based characterisation and optimisation technique for the design of microscopic architecture, and a porosity-based approach for the design of macroscopic structure. The goal of this study is to physically define the optimal tissue scaffold construct, and to establish any link between cell viability and scaffold architecture. Single-objective and multi-objective topology optimisation was conducted at both microscopic and macroscopic scales to determine the ideal scaffold design. A high quality isosurface modelling technique was formulated and automated to define the microstructure in stereolithography format. Periodic structures with maximised permeability, and theoretically maximum diffusivity and bulk modulus were found using a modified level set method. Microstructures with specific effective diffusivity were also created by means of inverse homogenisation. Cell viability simulation was subsequently conducted to show that the optimised microstructures offered a more viable environment than those with random microstructure. The cell proliferation outcome in terms of cell number and survival rate was also improved through the optimisation of the macroscopic porosity profile. Additionally artificial vascular systems were created and optimised to enhance diffusive nutrient transport. The formation of vasculature in the optimisation process suggests that natural vascular systems acquire their fractal shapes through self-optimisation

Design and Topology Optimisation of Tissue Scaffolds

Tissue restoration by tissue scaffolding is an emerging technique with many potential applications. While it is well-known that the structural properties of tissue scaffolds play a critical role in cell regrowth, it is usually unclear how optimal tissue regeneration can be achieved. This thesis hereby presents a computational investigation of tissue scaffold design and optimisation. This study proposes an isosurface-based characterisation and optimisation technique for the design of microscopic architecture, and a porosity-based approach for the design of macroscopic structure. The goal of this study is to physically define the optimal tissue scaffold construct, and to establish any link between cell viability and scaffold architecture. Single-objective and multi-objective topology optimisation was conducted at both microscopic and macroscopic scales to determine the ideal scaffold design. A high quality isosurface modelling technique was formulated and automated to define the microstructure in stereolithography format. Periodic structures with maximised permeability, and theoretically maximum diffusivity and bulk modulus were found using a modified level set method. Microstructures with specific effective diffusivity were also created by means of inverse homogenisation. Cell viability simulation was subsequently conducted to show that the optimised microstructures offered a more viable environment than those with random microstructure. The cell proliferation outcome in terms of cell number and survival rate was also improved through the optimisation of the macroscopic porosity profile. Additionally artificial vascular systems were created and optimised to enhance diffusive nutrient transport. The formation of vasculature in the optimisation process suggests that natural vascular systems acquire their fractal shapes through self-optimisation

A Review of Mathematical Models for the Formation of\ud Vascular Networks

Mainly two mechanisms are involved in the formation of blood vasculature: vasculogenesis and angiogenesis. The former consists of the formation of a capillary-like network from either a dispersed or a monolayered population of endothelial cells, reproducible also in vitro by specific experimental assays. The latter consists of the sprouting of new vessels from an existing capillary or post-capillary venule. Similar phenomena are also involved in the formation of the lymphatic system through a process generally called lymphangiogenesis.\ud \ud A number of mathematical approaches have analysed these phenomena. This paper reviews the different modelling procedures, with a special emphasis on their ability to reproduce the biological system and to predict measured quantities which describe the overall processes. A comparison between the different methods is also made, highlighting their specific features

A survey of statistical network models

Networks are ubiquitous in science and have become a focal point for discussion in everyday life. Formal statistical models for the analysis of network data have emerged as a major topic of interest in diverse areas of study, and most of these involve a form of graphical representation. Probability models on graphs date back to 1959. Along with empirical studies in social psychology and sociology from the 1960s, these early works generated an active network community and a substantial literature in the 1970s. This effort moved into the statistical literature in the late 1970s and 1980s, and the past decade has seen a burgeoning network literature in statistical physics and computer science. The growth of the World Wide Web and the emergence of online networking communities such as Facebook, MySpace, and LinkedIn, and a host of more specialized professional network communities has intensified interest in the study of networks and network data. Our goal in this review is to provide the reader with an entry point to this burgeoning literature. We begin with an overview of the historical development of statistical network modeling and then we introduce a number of examples that have been studied in the network literature. Our subsequent discussion focuses on a number of prominent static and dynamic network models and their interconnections. We emphasize formal model descriptions, and pay special attention to the interpretation of parameters and their estimation. We end with a description of some open problems and challenges for machine learning and statistics.Comment: 96 pages, 14 figures, 333 reference