Wholeness as a Hierarchical Graph to Capture the Nature of Space

According to Christopher Alexander's theory of centers, a whole comprises numerous, recursively defined centers for things or spaces surrounding us. Wholeness is a type of global structure or life-giving order emerging from the whole as a field of the centers. The wholeness is an essential part of any complex system and exists, to some degree or other, in spaces. This paper defines wholeness as a hierarchical graph, in which individual centers are represented as the nodes and their relationships as the directed links. The hierarchical graph gets its name from the inherent scaling hierarchy revealed by the head/tail breaks, which is a classification scheme and visualization tool for data with a heavy-tailed distribution. We suggest that (1) the degrees of wholeness for individual centers should be measured by PageRank (PR) scores based on the notion that high-degree-of-life centers are those to which many high-degree-of-life centers point, and (2) that the hierarchical levels, or the ht-index of the PR scores induced by the head/tail breaks can characterize the degree of wholeness for the whole: the higher the ht-index, the more life or wholeness in the whole. Three case studies applied to the Alhambra building complex and the street networks of Manhattan and Sweden illustrate that the defined wholeness captures fairly well human intuitions on the degree of life for the geographic spaces. We further suggest that the mathematical model of wholeness be an important model of geographic representation, because it is topological oriented that enables us to see the underlying scaling structure. The model can guide geodesign, which should be considered as the wholeness-extending transformations that are essentially like the unfolding processes of seeds or embryos, for creating beautiful built and natural environments or with a high degree of wholeness.Comment: 14 pages, 7 figures, 2 table

Planetary Science Virtual Observatory architecture

In the framework of the Europlanet-RI program, a prototype of Virtual Observatory dedicated to Planetary Science was defined. Most of the activity was dedicated to the elaboration of standards to retrieve and visualize data in this field, and to provide light procedures to teams who wish to contribute with on-line data services. The architecture of this VO system and selected solutions are presented here, together with existing demonstrators

Depicting urban boundaries from a mobility network of spatial interactions: A case study of Great Britain with geo-located Twitter data

Existing urban boundaries are usually defined by government agencies for administrative, economic, and political purposes. Defining urban boundaries that consider socio-economic relationships and citizen commute patterns is important for many aspects of urban and regional planning. In this paper, we describe a method to delineate urban boundaries based upon human interactions with physical space inferred from social media. Specifically, we depicted the urban boundaries of Great Britain using a mobility network of Twitter user spatial interactions, which was inferred from over 69 million geo-located tweets. We define the non-administrative anthropographic boundaries in a hierarchical fashion based on different physical movement ranges of users derived from the collective mobility patterns of Twitter users in Great Britain. The results of strongly connected urban regions in the form of communities in the network space yield geographically cohesive, non-overlapping urban areas, which provide a clear delineation of the non-administrative anthropographic urban boundaries of Great Britain. The method was applied to both national (Great Britain) and municipal scales (the London metropolis). While our results corresponded well with the administrative boundaries, many unexpected and interesting boundaries were identified. Importantly, as the depicted urban boundaries exhibited a strong instance of spatial proximity, we employed a gravity model to understand the distance decay effects in shaping the delineated urban boundaries. The model explains how geographical distances found in the mobility patterns affect the interaction intensity among different non-administrative anthropographic urban areas, which provides new insights into human spatial interactions with urban space.Comment: 32 pages, 7 figures, International Journal of Geographic Information Scienc

Visualising the structure of document search results: A comparison of graph theoretic approaches

This is the post-print of the article - Copyright @ 2010 Sage PublicationsPrevious work has shown that distance-similarity visualisation or ‘spatialisation’ can provide a potentially useful context in which to browse the results of a query search, enabling the user to adopt a simple local foraging or ‘cluster growing’ strategy to navigate through the retrieved document set. However, faithfully mapping feature-space models to visual space can be problematic owing to their inherent high dimensionality and non-linearity. Conventional linear approaches to dimension reduction tend to fail at this kind of task, sacrificing local structural in order to preserve a globally optimal mapping. In this paper the clustering performance of a recently proposed algorithm called isometric feature mapping (Isomap), which deals with non-linearity by transforming dissimilarities into geodesic distances, is compared to that of non-metric multidimensional scaling (MDS). Various graph pruning methods, for geodesic distance estimation, are also compared. Results show that Isomap is significantly better at preserving local structural detail than MDS, suggesting it is better suited to cluster growing and other semantic navigation tasks. Moreover, it is shown that applying a minimum-cost graph pruning criterion can provide a parameter-free alternative to the traditional K-neighbour method, resulting in spatial clustering that is equivalent to or better than that achieved using an optimal-K criterion

How can heat maps of indexing vocabularies be utilized for information seeking purposes?

The ability to browse an information space in a structured way by exploiting similarities and dissimilarities between information objects is crucial for knowledge discovery. Knowledge maps use visualizations to gain insights into the structure of large-scale information spaces, but are still far away from being applicable for searching. The paper proposes a use case for enhancing search term recommendations by heat map visualizations of co-word relation-ships taken from indexing vocabulary. By contrasting areas of different "heat" the user is enabled to indicate mainstream areas of the field in question more easily.Comment: URL workshop proceedings: http://ceur-ws.org/Vol-1311

Revisiting Guerry's data: Introducing spatial constraints in multivariate analysis

Standard multivariate analysis methods aim to identify and summarize the main structures in large data sets containing the description of a number of observations by several variables. In many cases, spatial information is also available for each observation, so that a map can be associated to the multivariate data set. Two main objectives are relevant in the analysis of spatial multivariate data: summarizing covariation structures and identifying spatial patterns. In practice, achieving both goals simultaneously is a statistical challenge, and a range of methods have been developed that offer trade-offs between these two objectives. In an applied context, this methodological question has been and remains a major issue in community ecology, where species assemblages (i.e., covariation between species abundances) are often driven by spatial processes (and thus exhibit spatial patterns). In this paper we review a variety of methods developed in community ecology to investigate multivariate spatial patterns. We present different ways of incorporating spatial constraints in multivariate analysis and illustrate these different approaches using the famous data set on moral statistics in France published by Andr\'{e}-Michel Guerry in 1833. We discuss and compare the properties of these different approaches both from a practical and theoretical viewpoint.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS356 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org