Robustness of Random Graphs Based on Natural Connectivity

Recently, it has been proposed that the natural connectivity can be used to efficiently characterise the robustness of complex networks. Natural connectivity quantifies the redundancy of alternative routes in a network by evaluating the weighted number of closed walks of all lengths and can be regarded as the average eigenvalue obtained from the graph spectrum. In this article, we explore the natural connectivity of random graphs both analytically and numerically and show that it increases linearly with the average degree. By comparing with regular ring lattices and random regular graphs, we show that random graphs are more robust than random regular graphs; however, the relationship between random graphs and regular ring lattices depends on the average degree and graph size. We derive the critical graph size as a function of the average degree, which can be predicted by our analytical results. When the graph size is less than the critical value, random graphs are more robust than regular ring lattices, whereas regular ring lattices are more robust than random graphs when the graph size is greater than the critical value.Comment: 12 pages, 4 figure

The natural connectivity of autonomous systems

The principle of biological autonomy, introduced by Francisco J. Varela, addresses the dilemma of Cartesian mind-body dualism by re-casting mind and body, or subject and object, observer and observed, not as irreconcilable categories, but as complementary perspectives on the same biological phenomena. Indeed, this distinction between self and non-self may be seen as a necessary precondition for autonomy. An autonomous system is self-governing in that it is concerned with preserving its unique character, or unity. Furthermore, an autonomous system is operationally closed in that it forms a self-referential network without reference to an external world. This paper develops these ideas in relation to thinking about embodied, enactive robotics. As well as being constructed artefacts, what is it to look at robots as truly autonomous agents? In this context we begin to explore the concept of operational closure analytically. We utilise natural connectivity as a quantitative measure of the cyclicity of these operationally closed internal processes. In doing so we discover that increased natural connectivity of an autonomous system confers a greater behavioural robustness when it is coupled with the external world

Maren Hassinger: Lives

Gettysburg College’s Schmucker Art Gallery is pleased to present Maren Hassinger: Lives, an exhibition of the artist’s films, sculptures, and installations held in conjunction with the Central Pennsylvania Consortium Africana Studies Conference, “Public Health, Human Prosperity, and Justice: Public Policy in the African Diaspora,” and co-sponsored by the Eisenhower Institute in Gettysburg, Pennsylvania February 26 and 27, 2010. Hassinger’s work provides a contemplative perspective on complicated issues of nature, culture and identity in relation to broader themes of race, gender, as well as politics, and social policy. Ethereal and evocative installations of branches, plastic bags, and twisted newspapers powerfully reveal the tenuous intersection of the mass-produced and the organic. Complimenting the coiled strands, circular forms, and ascending paths of Hassinger’s sculptures are projections and films that similarly examine notions of circularity and biological (or natural) connectivity, in addition to linearity and lineage. These installations compellingly address the various complexities of lives: personal and public identities, Hassinger’s autobiographical lineage, and the legacies of broader African-American experiences. [excerpt]https://cupola.gettysburg.edu/artcatalogs/1001/thumbnail.jp

Updating and downdating techniques for optimizing network communicability

The total communicability of a network (or graph) is defined as the sum of the entries in the exponential of the adjacency matrix of the network, possibly normalized by the number of nodes. This quantity offers a good measure of how easily information spreads across the network, and can be useful in the design of networks having certain desirable properties. The total communicability can be computed quickly even for large networks using techniques based on the Lanczos algorithm. In this work we introduce some heuristics that can be used to add, delete, or rewire a limited number of edges in a given sparse network so that the modified network has a large total communicability. To this end, we introduce new edge centrality measures which can be used to guide in the selection of edges to be added or removed. Moreover, we show experimentally that the total communicability provides an effective and easily computable measure of how "well-connected" a sparse network is.Comment: 20 pages, 9 pages Supplementary Materia

A conceptual study of connectivity elements towards successful green network / Nor Hamizah Abdul Hamid, Muhamad Ezran Zainal Abdullah and Nik Hanita Nik Mohamad

Rapid urbanization has resulted in the loss of natural setting of urban spaces. Fusing the gap between nature andthe city development can generate both common cause and conflict. Green network is a significant shift in linking urban green spaces that will lay out over the coming decades. At present, this green network is not successfully applied due to many open spaces that are not well connected. Hence, connectivity elements provided by the green network plays an important role in helping to conserve urban sustainability. Furthermore, green network is recognized as an effective urban conservation strategy to mitigate the effects of urbanization while maintaining healthy living and sustainability for urban area. However, the opportunity for green network to function as a linkage has not been optimized. Therefore, this research investigates on visitors‟ responses to different dimension of their needs for natural connectivity in the context of sustainable living. Data were collected using interviews and surveys on the scope of connectivity elements towards successful green network. This research offers input on green network by addressing visitors strong preferences towards natural connectivity elements compared to man-made landscape elements

Subdivision surface fitting to a dense mesh using ridges and umbilics

Fitting a sparse surface to approximate vast dense data is of interest for many applications: reverse engineering, recognition and compression, etc. The present work provides an approach to fit a Loop subdivision surface to a dense triangular mesh of arbitrary topology, whilst preserving and aligning the original features. The natural ridge-joined connectivity of umbilics and ridge-crossings is used as the connectivity of the control mesh for subdivision, so that the edges follow salient features on the surface. Furthermore, the chosen features and connectivity characterise the overall shape of the original mesh, since ridges capture extreme principal curvatures and ridges start and end at umbilics. A metric of Hausdorff distance including curvature vectors is proposed and implemented in a distance transform algorithm to construct the connectivity. Ridge-colour matching is introduced as a criterion for edge flipping to improve feature alignment. Several examples are provided to demonstrate the feature-preserving capability of the proposed approach