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

Role of spatial coherence in polarization tomography

We analyze an experimental setup in which a quasi-monochromatic spatially coherent beam of light is used to probe a paraxial optical scatterer. We discuss the effect of the spatial coherence of the probe beam on the Mueller matrix representing the scatterer. We show that according to the degree of spatial coherence of the beam, the \emph{same} scattering system can be represented by \emph{different} Mueller matrices. This result should serve as a warning for experimentalists.Comment: 3 pages, 1 figur

Unsupervised Bump Hunting Using Principal Components

Principal Components Analysis is a widely used technique for dimension reduction and characterization of variability in multivariate populations. Our interest lies in studying when and why the rotation to principal components can be used effectively within a response-predictor set relationship in the context of mode hunting. Specifically focusing on the Patient Rule Induction Method (PRIM), we first develop a fast version of this algorithm (fastPRIM) under normality which facilitates the theoretical studies to follow. Using basic geometrical arguments, we then demonstrate how the PC rotation of the predictor space alone can in fact generate improved mode estimators. Simulation results are used to illustrate our findings.Comment: 24 pages, 9 figure

On the explanatory power of principal components

We show that if we have an orthogonal base ($u_1,\ldots,u_p$) in a $p$-dimensional vector space, and select $p+1$ vectors $v_1,\ldots, v_p$ and $w$ such that the vectors traverse the origin, then the probability of $w$ being to closer to all the vectors in the base than to $v_1,\ldots, v_p$ is at least 1/2 and converges as $p$ increases to infinity to a normal distribution on the interval [-1,1]; i.e., $\Phi(1)-\Phi(-1)\approx0.6826$. This result has relevant consequences for Principal Components Analysis in the context of regression and other learning settings, if we take the orthogonal base as the direction of the principal components.Comment: 10 pages, 3 figure

A search for diffuse bands in fullerene planetary nebulae: evidence of diffuse circumstellar bands

Large fullerenes and fullerene-based molecules have been proposed as carriers of diffuse interstellar bands (DIBs). The recent detection of the most common fullerenes (C60 and C70) around some planetary nebulae (PNe) now enable us to study the DIBs towards fullerene-rich space environments. We search DIBs in the optical spectra towards three fullerene-containing PNe (Tc 1, M 1-20, and IC 418). Special attention is given to DIBs which are found to be unusually intense towards these fullerene sources. In particular, an unusually strong 4428A absorption feature is a common charateristic of fullerene PNe. Similar to Tc 1, the strongest optical bands of neutral C60 are not detected towards IC 418. Our high-quality (S/N > 300) spectra for PN Tc 1, together with its large radial velocity, permit us to search for the presence of diffuse bands of circumstellar origin, which we refer to as diffuse circumstellar bands (DCBs). We report the first tentative detection of two DCBs at 4428 and 5780 A in the fullerene-rich circumstellar environment around the PN Tc 1. Laboratory and theoretical studies of fullerenes in their multifarious manifestations (carbon onions, fullerene clusters, or even complex species formed by fullerenes and other molecules like PAHs or metals) may help solve the mystery of some of the diffuse band carriers.Comment: Accepted for publication in Astronomy & Astrophysics (16 pages, 10 figures, and 7 Tables); final version (changes regarding PN M 1-20 and language corrected

Diffuse Neutron Scattering Study of Magnetic Correlations in half-doped La0.5Ca0.5-xSrxMnO3 (x = 0.1, 0.3 and 0.4) Manganites

The short range ordered magnetic correlations have been studied in half doped La0.5Ca0.5-xSrxMnO3 (x = 0.1, 0.3 and 0.4) compounds by polarized neutron scattering technique. On doping Sr2+ for Ca2+ ion, these compounds with x = 0.1, 0.3, and 0.4 exhibit CE-type, mixture of CE-type and A-type, and A-type antiferromagnetic ordering, respectively. Magnetic diffuse scattering is observed in all the compounds above and below their respective magnetic ordering temperatures and is attributed to magnetic polarons. The correlations are primarily ferromagnetic in nature above T\_N, although a small antiferromagnetic contribution is also evident. Additionally, in samples x = 0.1 and 0.3 with CE-type antiferromagnetic ordering, superlattice diffuse reflections are observed indicating correlations between magnetic polarons. On lowering temperature below T\_N the diffuse scattering corresponding to ferromagnetic correlations is suppressed and the long range ordered antiferromagnetic state is established. However, the short range ordered correlations indicated by enhanced spin flip scattering at low Q coexist with long range ordered state down to 3K. In x = 0.4 sample with A-type antiferromagnetic ordering, superlattice diffuse reflections are absent. Additionally, in comparison to x = 0.1 and 0.3 sample, the enhanced spin flip scattering at low Q is reduced at 310K, and as temperature is reduced below 200K, it becomes negligibly low. The variation of radial correlation function, g(r) with temperature indicates rapid suppression of ferromagnetic correlations at the first nearest neighbor on approaching TN. Sample x = 0.4 exhibits growth of ferromagnetic phase at intermediate temperatures (~ 200K). This has been further explored using SANS and neutron depolarization techniques.Comment: 13 pages, 12 figures, To appear in Physical Review