Requirements for Topology in 3D GIS

Topology and its various benefits are well understood within the context of 2D Geographical Information Systems. However, requirements in three-dimensional (3D) applications have yet to be defined, with factors such as lack of users' familiarity with the potential of such systems impeding this process. In this paper, we identify and review a number of requirements for topology in 3D applications. The review utilises existing topological frameworks and data models as a starting point. Three key areas were studied for the purposes of requirements identification, namely existing 2D topological systems, requirements for visualisation in 3D and requirements for 3D analysis supported by topology. This was followed by analysis of application areas such as earth sciences and urban modelling which are traditionally associated with GIS, as well as others including medical, biological and chemical science. Requirements for topological functionality in 3D were then grouped and categorised. The paper concludes by suggesting that these requirements can be used as a basis for the implementation of topology in 3D. It is the aim of this review to serve as a focus for further discussion and identification of additional applications that would benefit from 3D topology. © 2006 The Authors. Journal compilation © 2006 Blackwell Publishing Ltd

A combined measure for quantifying and qualifying the topology preservation of growing self-organizing maps

The Self-OrganizingMap (SOM) is a neural network model that performs an ordered projection of a high dimensional input space in a low-dimensional topological structure. The process in which such mapping is formed is defined by the SOM algorithm, which is a competitive, unsupervised and nonparametric method, since it does not make any assumption about the input data distribution. The feature maps provided by this algorithm have been successfully applied for vector quantization, clustering and high dimensional data visualization processes. However, the initialization of the network topology and the selection of the SOM training parameters are two difficult tasks caused by the unknown distribution of the input signals. A misconfiguration of these parameters can generate a feature map of low-quality, so it is necessary to have some measure of the degree of adaptation of the SOM network to the input data model. The topologypreservation is the most common concept used to implement this measure. Several qualitative and quantitative methods have been proposed for measuring the degree of SOM topologypreservation, particularly using Kohonen's model. In this work, two methods for measuring the topologypreservation of the Growing Cell Structures (GCSs) model are proposed: the topographic function and the topology preserving ma

Toward high-content/high-throughput imaging and analysis of embryonic morphogenesis

In vivo study of embryonic morphogenesis tremendously benefits from recent advances in live microscopy and computational analyses. Quantitative and automated investigation of morphogenetic processes opens the field to high-content and high-throughput strategies. Following experimental workflow currently developed in cell biology, we identify the key challenges for applying such strategies in developmental biology. We review the recent progress in embryo preparation and manipulation, live imaging, data registration, image segmentation, feature computation, and data mining dedicated to the study of embryonic morphogenesis. We discuss a selection of pioneering studies that tackled the current methodological bottlenecks and illustrated the investigation of morphogenetic processes in vivo using quantitative and automated imaging and analysis of hundreds or thousands of cells simultaneously, paving the way for high-content/high-throughput strategies and systems analysis of embryonic morphogenesis

Foundations and modelling of dynamic networks using Dynamic Graph Neural Networks: A survey

Dynamic networks are used in a wide range of fields, including social network analysis, recommender systems, and epidemiology. Representing complex networks as structures changing over time allow network models to leverage not only structural but also temporal patterns. However, as dynamic network literature stems from diverse fields and makes use of inconsistent terminology, it is challenging to navigate. Meanwhile, graph neural networks (GNNs) have gained a lot of attention in recent years for their ability to perform well on a range of network science tasks, such as link prediction and node classification. Despite the popularity of graph neural networks and the proven benefits of dynamic network models, there has been little focus on graph neural networks for dynamic networks. To address the challenges resulting from the fact that this research crosses diverse fields as well as to survey dynamic graph neural networks, this work is split into two main parts. First, to address the ambiguity of the dynamic network terminology we establish a foundation of dynamic networks with consistent, detailed terminology and notation. Second, we present a comprehensive survey of dynamic graph neural network models using the proposed terminologyComment: 28 pages, 9 figures, 8 table