Parameter estimators of random intersection graphs with thinned communities

This paper studies a statistical network model generated by a large number of randomly sized overlapping communities, where any pair of nodes sharing a community is linked with probability $q$ via the community. In the special case with $q=1$ the model reduces to a random intersection graph which is known to generate high levels of transitivity also in the sparse context. The parameter $q$ adds a degree of freedom and leads to a parsimonious and analytically tractable network model with tunable density, transitivity, and degree fluctuations. We prove that the parameters of this model can be consistently estimated in the large and sparse limiting regime using moment estimators based on partially observed densities of links, 2-stars, and triangles.Comment: 15 page

Correlation between clustering and degree in affiliation networks

We are interested in the probability that two randomly selected neighbors of a random vertex of degree (at least) $k$ are adjacent. We evaluate this probability for a power law random intersection graph, where each vertex is prescribed a collection of attributes and two vertices are adjacent whenever they share a common attribute. We show that the probability obeys the scaling $k^{-\delta}$ as $k\to+\infty$. Our results are mathematically rigorous. The parameter $0\le \delta\le 1$ is determined by the tail indices of power law random weights defining the links between vertices and attributes

Relationship between Nanostructure and Deformation Behavior of Microphase-Separated Styrene/Butadiene Systems

The relationship between the morphology and the mechanical properties of nanostructured blends,comprising an asymmetric styrene/butadiene star block copolymer,exhibiting cocontinuous-like morphology and low molar mass homopolymers, was studied by electron microscopy, microindentation hardness, and tensile testing methods. Results show that the deformation behavior of these systems is significantly modified by the presence of unentangled homopolymer chains, leading partly to a decrease in mechanical properties. In contrast to common polymer blends, in which usually, the hardness values do not markedly deviate from the additivity law, the H-values in the system investigated show large deviations from the linear additivity behavior. The observed anomalous behavior is discussed in terms of the enhanced local flow processes induced by the phase-separated morphology at a nanometer scale.Peer reviewe

Moment-based parameter estimation in binomial random intersection graph models

Binomial random intersection graphs can be used as parsimonious statistical models of large and sparse networks, with one parameter for the average degree and another for transitivity, the tendency of neighbours of a node to be connected. This paper discusses the estimation of these parameters from a single observed instance of the graph, using moment estimators based on observed degrees and frequencies of 2-stars and triangles. The observed data set is assumed to be a subgraph induced by a set of $n_0$ nodes sampled from the full set of $n$ nodes. We prove the consistency of the proposed estimators by showing that the relative estimation error is small with high probability for $n_0 \gg n^{2/3} \gg 1$. As a byproduct, our analysis confirms that the empirical transitivity coefficient of the graph is with high probability close to the theoretical clustering coefficient of the model.Comment: 15 pages, 6 figure

Bistable polarization switching in mutually coupled vertical-cavity surface-emitting lasers

3 pages.-- OCIS codes: 250.5270, 260.5430.-- Final full-text version of the paper available at: http://dx.doi.org/10.1364/OL.31.000996.We theoretically investigate the polarization-resolved dynamics of two vertical-cavity surface-emitting semiconductor lasers that are mutually coupled through coherent optical injection. We find a sequence of bistable polarization switchings that can be induced by either changing the coupling strength or the optical propagation phase. The successive polarization switchings are correlated to the creation of new compound-cavity modes when these parameters are continuously varied.The authors acknowledge financial support from MEC (Spain) and Feder, project FIS2004-00953. JM is supported by the CSIC (Spain) through the program I3P-PC2003. MS acknowledges support from UIB (Spain)

On plexus representation of dissimilarities

Correspondence analysis has found widespread application in analysing vegetation gradients. However, it is not clear how it is robust to situations where structures other than a simple gradient exist. The introduction of instrumental variables in canonical correspondence analysis does not avoid these difficulties. In this paper I propose to examine some simple methods based on the notion of the plexus (sensu McIntosh) where graphs or networks are used to display some of the structure of the data so that an informed choice of models is possible. I showthat two different classes of plexus model are available. These classes are distinguished by the use in one case of a global Euclidean model to obtain well-separated pair decomposition (WSPD) of a set of points which implicitly involves all dissimilarities, while in the other a Riemannian view is taken and emphasis is placed locally, i.e., on small dissimilarities. I showan example of each of these classes applied to vegetation data