Inner Disk Oscillations and QPOs in Relativistic Jet Sources

Recent results on the inner disk oscillations found in GRS 1915+105 are reviewed. QPOs during the low state are used as a marker for such oscillations and the physical picture emerging from a combined X-ray spectral and timing analysis is examined. The relationship between inner disk oscillations and synchrotron radio emission is critically evaluated.Comment: 8 pages, LaTeX, kluwer.cls, 2 figures, to be published in `Proceedings of the Third Microquasar Workshop: Granada Workshop on galactic relativistic jet sources', Eds A.J. Castro-Tirado, J. Greiner and J.M. Paredes, Astrophysics and Space Science, in pres

Extendability of quadratic modules over a polynomial extension of an equicharacteristic regular local ring

We prove that a quadratic $A[T]$-module $Q$ with Witt index ($Q/TQ$)$\geq d$, where $d$ is the dimension of the equicharacteristic regular local ring $A$, is extended from $A$. This improves a theorem of the second named author who showed it when $A$ is the local ring at a smooth point of an affine variety over an infinite field. To establish our result, we need to establish a Local-Global Principle (of Quillen) for the Dickson--Siegel--Eichler--Roy (DSER) elementary orthogonal transformations.Comment: 19 page

Predicting Item Popularity: Analysing Local Clustering Behaviour of Users

Predicting the popularity of items in rating networks is an interesting but challenging problem. This is especially so when an item has first appeared and has received very few ratings. In this paper, we propose a novel approach to predicting the future popularity of new items in rating networks, defining a new bipartite clustering coefficient to predict the popularity of movies and stories in the MovieLens and Digg networks respectively. We show that the clustering behaviour of the first user who rates a new item gives insight into the future popularity of that item. Our method predicts, with a success rate of over 65% for the MovieLens network and over 50% for the Digg network, the future popularity of an item. This is a major improvement on current results.Comment: 25 pages, 11 figure

Identifying Influential Nodes in Bipartite Networks Using the Clustering Coefficient

The identification of influential nodes in complex network can be very challenging. If the network has a community structure, centrality measures may fail to identify the complete set of influential nodes, as the hubs and other central nodes of the network may lie inside only one community. Here we define a bipartite clustering coefficient that, by taking differently structured clusters into account, can find important nodes across communities