On the classification of quantum W-algebras

In this paper we consider the structure of general quantum W-algebras. We introduce the notions of deformability, positive-definiteness, and reductivity of a W-algebra. We show that one can associate a reductive finite Lie algebra to each reductive W-algebra. The finite Lie algebra is also endowed with a preferred $sl(2)$ subalgebra, which gives the conformal weights of the W-algebra. We extend this to cover W-algebras containing both bosonic and fermionic fields, and illustrate our ideas with the Poisson bracket algebras of generalised Drinfeld-Sokolov Hamiltonian systems. We then discuss the possibilities of classifying deformable W-algebras which fall outside this class in the context of automorphisms of Lie algebras. In conclusion we list the cases in which the W-algebra has no weight one fields, and further, those in which it has only one weight two field.Comment: 28 page

Phase transitions in Ising model on a Euclidean network

A one dimensional network on which there are long range bonds at lattice distances $l>1$ with the probability $P(l) \propto l^{-\delta}$ has been taken under consideration. We investigate the critical behavior of the Ising model on such a network where spins interact with these extra neighbours apart from their nearest neighbours for $0 \leq \delta < 2$. It is observed that there is a finite temperature phase transition in the entire range. For $0 \leq \delta < 1$, finite size scaling behaviour of various quantities are consistent with mean field exponents while for $1\leq \delta\leq 2$, the exponents depend on $\delta$. The results are discussed in the context of earlier observations on the topology of the underlying network.Comment: 7 pages, revtex4, 7 figures; to appear in Physical Review E, minor changes mad

Watch Out for the Beast: Fear Information and Attentional Bias in Children

Although valenced information about novel animals changes the implicit and explicit fear beliefs of children (Field & Lawson, 2003), how it might lead to anxiety is unknown. One possibility, based on cognitive models of anxiety, is that fear information creates attentional biases similar to those seen in anxiety disorders. Children between 7 and 9 years old were given positive information about 1 novel animal, negative information about another, and no information about the 3rd. A pictorial dot-probe task was used, immediately or with a 24-hr delay, to test for attentional biases to the different animals. The results replicated the finding that fear information changes children's fear beliefs. Regardless of whether there was a delay, children acquired an attentional bias in the left visual field toward the animal about which they held negative beliefs compared to the control animal. These results imply a possible way in which fear information might contribute to acquired fear

Identity and Search in Social Networks

Social networks have the surprising property of being "searchable": Ordinary people are capable of directing messages through their network of acquaintances to reach a specific but distant target person in only a few steps. We present a model that offers an explanation of social network searchability in terms of recognizable personal identities: sets of characteristics measured along a number of social dimensions. Our model defines a class of searchable networks and a method for searching them that may be applicable to many network search problems, including the location of data files in peer-to-peer networks, pages on the World Wide Web, and information in distributed databases.Comment: 4 page, 3 figures, revte

Scale-free networks with tunable degree distribution exponents

We propose and study a model of scale-free growing networks that gives a degree distribution dominated by a power-law behavior with a model-dependent, hence tunable, exponent. The model represents a hybrid of the growing networks based on popularity-driven and fitness-driven preferential attachments. As the network grows, a newly added node establishes $m$ new links to existing nodes with a probability $p$ based on popularity of the existing nodes and a probability $1-p$ based on fitness of the existing nodes. An explicit form of the degree distribution $P(p,k)$ is derived within a mean field approach. For reasonably large $k$, $P(p,k) \sim k^{-\gamma(p)}{\cal F}(k,p)$, where the function ${\cal F}$ is dominated by the behavior of $1/\ln(k/m)$ for small values of $p$ and becomes $k$-independent as $p \to 1$, and $\gamma(p)$ is a model-dependent exponent. The degree distribution and the exponent $\gamma(p)$ are found to be in good agreement with results obtained by extensive numerical simulations.Comment: 12 pages, 2 figures, submitted to PR

A network-based threshold model for the spreading of fads in society and markets

We investigate the behavior of a threshold model for the spreading of fads and similar phenomena in society. The model is giving the fad dynamics and is intended to be confined to an underlying network structure. We investigate the whole parameter space of the fad dynamics on three types of network models. The dynamics we discover is rich and highly dependent on the underlying network structure. For some range of the parameter space, for all types of substrate networks, there are a great variety of sizes and life-lengths of the fads -- what one see in real-world social and economical systems

Detection of K+ mesons in segmented electromagnetic calorimeters

The combination of the CrystalBall and TAPS electromagnetic calorimeters were installed in the MAMI A2 hall in 2003. Here they are able to detect the reaction products from photo-induced reactions in combination with the Glasgow photon tagger. In the last two years the MAMI facility was upgraded from 885 MeV to 1.5 GeV, the A2 photon tagger underwent a similar upgrade crossing the threshold for strangeness photoproduction. For the CrystalBall this created a new challenge, to identify K+ mesons above the large background from other charged hadrons, in a situation where the detector setup does not benefit from a magnetic field to help separate particle species. These proceedings outline a novel technique which uses the decay products of the K+ as a strangeness tag