187,061 research outputs found
Exploring cooperative game mechanisms of scientific coauthorship networks
Scientific coauthorship, generated by collaborations and competitions among
researchers, reflects effective organizations of human resources. Researchers,
their expected benefits through collaborations, and their cooperative costs
constitute the elements of a game. Hence we propose a cooperative game model to
explore the evolution mechanisms of scientific coauthorship networks. The model
generates geometric hypergraphs, where the costs are modelled by space
distances, and the benefits are expressed by node reputations, i. e. geometric
zones that depend on node position in space and time. Modelled cooperative
strategies conditioned on positive benefit-minus-cost reflect the spatial
reciprocity principle in collaborations, and generate high clustering and
degree assortativity, two typical features of coauthorship networks. Modelled
reputations generate the generalized Poisson parts and fat tails appeared in
specific distributions of empirical data, e. g. paper team size distribution.
The combined effect of modelled costs and reputations reproduces the
transitions emerged in degree distribution, in the correlation between degree
and local clustering coefficient, etc. The model provides an example of how
individual strategies induce network complexity, as well as an application of
game theory to social affiliation networks
On the estimation of integrated covariance matrices of high dimensional diffusion processes
We consider the estimation of integrated covariance (ICV) matrices of high
dimensional diffusion processes based on high frequency observations. We start
by studying the most commonly used estimator, the realized covariance (RCV)
matrix. We show that in the high dimensional case when the dimension and
the observation frequency grow in the same rate, the limiting spectral
distribution (LSD) of RCV depends on the covolatility process not only through
the targeting ICV, but also on how the covolatility process varies in time. We
establish a Mar\v{c}enko--Pastur type theorem for weighted sample covariance
matrices, based on which we obtain a Mar\v{c}enko--Pastur type theorem for RCV
for a class of diffusion processes. The results explicitly
demonstrate how the time variability of the covolatility process affects the
LSD of RCV. We further propose an alternative estimator, the time-variation
adjusted realized covariance (TVARCV) matrix. We show that for processes in
class , the TVARCV possesses the desirable property that its LSD
depends solely on that of the targeting ICV through the Mar\v{c}enko--Pastur
equation, and hence, in particular, the TVARCV can be used to recover the
empirical spectral distribution of the ICV by using existing algorithms.Comment: Published in at http://dx.doi.org/10.1214/11-AOS939 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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