Power in the Heterogeneous Connections Model: The Emergence of Core-Periphery Networks

The heterogeneous connections model is a generalization of the homogeneous connections model of Jackson and Wolinsky (1996) in which the intrinsic value of each connection is set by a discrete, positive and symmetric function that depends solely on the types of the two end agents. Core periphery networks are defined as networks in which the agents' set can be partitioned into two subsets, one in which the members are completely connected among themselves and the other where there are no internal links. A two-type society is defined as "power based" if both types of agents prefer to connect to one of the types over the other, controlling for path length. An exhaustive analysis shows that core periphery networks, in which the "preferred" types are in the core and the "rejected" types are in the periphery, are crucial in the "power based" society. In particular, if the linking costs are not too low and not too high, at least one such network is pairwise stable. Moreover, in many cases these networks are the unique pairwise stable networks and in all cases they are the unique strongly efficient networks. The set of efficient networks often differs from the set of pairwise stable networks, hence a discussion on this issue is developed. These results suggest heterogeneity accompanied by "power based" linking preferences as a natural explanation for many core-periphery structures observed in real life social networks.Network Formation, Heterogeneity, Pairwise Stability

The Super-Eddington Nature of Super Massive Stars

Supermassive stars (SMS) are massive hydrogen objects, slowly radiating their gravitational binding energy. Such hypothetical primordial objects may have been the seed of the massive black holes (BHs) observed at the centre of galaxies. Under the standard picture, these objects can be approximately described as n=3 polytropes, and they are expected to shine extremely close to their Eddington luminosity. Once however, one considers the porosity induced by instabilities near the Eddington limit, which give rise to super-Eddington states, the standard picture should be modified. We study the structure, evolution and mass loss of these objects. We find the following. First, the evolution of SMSs is hastened due to their increased energy release. They accelerate continuum driven winds. If there is no rotational stabilization, these winds are insufficient to "evaporate" the objects, such that they can collapse to form a supermassive BHs, however, they do prevent SMSs from emitting a copious amount of ionizing radiation. If the SMSs are rotationally stabilized, the winds "evaporate" the objects until a normal sub-Eddington star remains, having a mass of a few 100Msun.Comment: 10 pages, 7 figure

Seeing the Forest for the Trees: Using the Gene Ontology to Restructure Hierarchical Clustering

Motivation: There is a growing interest in improving the cluster analysis of expression data by incorporating into it prior knowledge, such as the Gene Ontology (GO) annotations of genes, in order to improve the biological relevance of the clusters that are subjected to subsequent scrutiny. The structure of the GO is another source of background knowledge that can be exploited through the use of semantic similarity. Results: We propose here a novel algorithm that integrates semantic similarities (derived from the ontology structure) into the procedure of deriving clusters from the dendrogram constructed during expression-based hierarchical clustering. Our approach can handle the multiple annotations, from different levels of the GO hierarchy, which most genes have. Moreover, it treats annotated and unannotated genes in a uniform manner. Consequently, the clusters obtained by our algorithm are characterized by significantly enriched annotations. In both cross-validation tests and when using an external index such as protein–protein interactions, our algorithm performs better than previous approaches. When applied to human cancer expression data, our algorithm identifies, among others, clusters of genes related to immune response and glucose metabolism. These clusters are also supported by protein–protein interaction data. Contact: [email protected] Supplementary information: Supplementary data are available at Bioinformatics online.Lynne and William Frankel Center for Computer Science; Paul Ivanier center for robotics research and production; National Institutes of Health (R01 HG003367-01A1