Anisotropic Radial Layout for Visualizing Centrality and Structure in Graphs

This paper presents a novel method for layout of undirected graphs, where nodes (vertices) are constrained to lie on a set of nested, simple, closed curves. Such a layout is useful to simultaneously display the structural centrality and vertex distance information for graphs in many domains, including social networks. Closed curves are a more general constraint than the previously proposed circles, and afford our method more flexibility to preserve vertex relationships compared to existing radial layout methods. The proposed approach modifies the multidimensional scaling (MDS) stress to include the estimation of a vertex depth or centrality field as well as a term that penalizes discord between structural centrality of vertices and their alignment with this carefully estimated field. We also propose a visualization strategy for the proposed layout and demonstrate its effectiveness using three social network datasets.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Global brain connectivity analysis by diffusion MR tractography:algorithms, validation and applications

The human cerebral cortex consists of approximately 1010 neurons that are organized into a complex network of local circuits and long-range connections. During the past years there has been an increasing interest from the neuro-scientific community towards the study of this network, referred to as the human connectome. Due to its ability to probe the tissue microstructure in vivo and non invasively, diffusion MRI has revealed to be a helpful tool for the analysis of brain axonal pathways at the millimeter scale. Whereas the neuronal level remains unreachable, diffusion MRI enables the mapping of a low-resolution estimate of the human connectome, which should give a new breath to the study of normal or pathologic neuroanatomy. After a short introduction on diffusion MRI and tractography, the process by which fiber tracts are reconstructed from the diffusion images, we present a methodology allowing the creation of normalized whole-brain structural connection matrices derived from tractography and representing the human connectome. Based on the developed framework we then investigate the potential of front propagation algorithms in tractography. We compare their performance with classical tractography approaches on several well-known associative fiber pathways, and we discuss their advantages and limitations. Several solutions are proposed in order to evaluate and validate the connectome-related methodology. We develop a method to estimate the respective contributions of diffusion contrast versus other effects to a tractography result. Using this methodology, we show that whereas we can have a strong confidence in mid- and long-range connections, short-range connectivity has to be interpreted with care. Next, we demonstrate the strong relationship between the structural connectivity obtained from diffusion MR tractography and the functional connectivity measured with functional MRI. Then, we compare the performance of several diffusion MRI techniques through connectome-based measurements. We find that diffusion spectrum imaging is more sensitive and therefore enhances the results of tractography. Finally, we present two network-oriented applications. We use the human connectome to reveal the small-world architecture of the brain, a very efficient network topology in terms of wiring and power supply. We identify the cortical areas that belong to the core of structural connectivity. We show that these regions also belong to the default mode network, a set of dynamically coupled brain regions that are found to be more highly activated at rest. As a conclusion, we emphasize the potential of human connectome mapping for clinical applications and pathological studies

Metrics and methods for social distance

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Urban Studies and Planning, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 171-189).Distance measures are important for scientists because they illustrate the dynamics of geospatial topologies for physical and social processes. Two major types of distance are generally used for this purpose: Euclidean Distance measures the geodesic dispersion between fixed locations and Cost Distance characterizes the ease of travel between two places. This dissertation suggests that close inter-place ties may be an effect of human decisions and relationships and so embraces a third tier of distance, Social Distance, as the conceptual or physical connectivity between two places as measured by the relative or absolute frequency, volume or intensity of agent-based choices to travel, communicate or relate from one distinct place to another. In the spatial realm, Social Distance measures have not been widely developed, and since the concept is relatively new, Chapter 1 introduces and defines geo-contextual Social Distance, its operationalization, and its novelty. With similar intentions, Chapter 2 outlines the challenges facing the integration of social flow data into the Geographic Information community. The body of this dissertation consists of three separate case studies in Chapters 3, 4 and 5 whose common theme is the integration of Social Distance as models of social processes in geographic space. Each chapter addresses one aspect of this topic. Chapter 3 looks at a new visualization and classification method, called Weighted Radial Variation, for flow datasets. U.S. Migration data at the county level for 2008 is used for this case study. Chapter 4 discusses a new computational method for predicting geospatial interaction, based on social theory of trip chaining and communication. U.S. Flight, Trip and Migration data for the years 1995-2008 are used in this study. Chapter 5 presents the results of the tandem analysis for social networks and geographic clustering. Roll call vote data for the U.S. House of Representatives in the 111th Congress are used to create a social network, which is then analyzed with regards to the geographic districts of each congressperson.by Clio Andris.Ph.D