Evolution of the clustering coefficient in growing networks
In this talk, we discuss the importance of the clustering coefficient in evolving networks. Wepropose a model for an evolving network where the attachment probability to an existing nodedepends on the number of links of the existing node and it’s age. The age of the node is modeled bya lifetime distribution whose parameters depend on the network being studied. We focus on citationnetworks and show that if the two probabilities are independent of each other, the evolution ofthe clustering coefficient depends on the lifetime distribution of the cited articles and their averagelifetime. Beyond the average citation lifetime, the clustering coefficient increases and reaches astationary value. However, in real citation networks, the citation lifetime of a paper depends onthe number of citations it has received previously. When we incorporate this in our model, wefind that the average clustering coefficient decreases. The degree distribution is always scale freeand only the power law exponent changes when the aging distribution is changed. The clusteringcoefficient is thus more sensitive to the aging pattern of the evolving network and is a bettermeasure for studying differences in the citation patterns in different disciplines over time. Thisresult can be extended to other networks where the age of a node is an important criterion forreceiving new links.PACS numbers: 89.75.Fb, 89.65.-s, 02.70.Rr
Spin observables are very useful to improve our insight into themicrosocopic dynamics of exclusive reactions, inclusive reactions andparton distributions.Each spin observable is typically normalised to vary between -1 and +1.Pairs of observables of the same reaction are often constrained to asub-domain of the square [-1,+1]^2, such as the unit disk or a triangle.For triples of observables, the domain inside the cube [-1,+1]^3 canassume a variety of shapes: sphere, cone, pyramid, tetrahedron, etc.The corresponding inequalities can be derived by purely algebraicmethods, or from the positivity of the density matrices describing theinitial or final spin states of the reaction and its crossed channels.Examples will be given for the strangeness exchange reaction antiproton+proton -> antiLambda + Lambda, the photoproduction of pseudoscalarmesons, and the Soffer inequality for transversity distributions insidethe nucleon.
