2,777 research outputs found
A weighted configuration model and inhomogeneous epidemics
A random graph model with prescribed degree distribution and degree dependent
edge weights is introduced. Each vertex is independently equipped with a random
number of half-edges and each half-edge is assigned an integer valued weight
according to a distribution that is allowed to depend on the degree of its
vertex. Half-edges with the same weight are then paired randomly to create
edges. An expression for the threshold for the appearance of a giant component
in the resulting graph is derived using results on multi-type branching
processes. The same technique also gives an expression for the basic
reproduction number for an epidemic on the graph where the probability that a
certain edge is used for transmission is a function of the edge weight. It is
demonstrated that, if vertices with large degree tend to have large (small)
weights on their edges and if the transmission probability increases with the
edge weight, then it is easier (harder) for the epidemic to take off compared
to a randomized epidemic with the same degree and weight distribution. A recipe
for calculating the probability of a large outbreak in the epidemic and the
size of such an outbreak is also given. Finally, the model is fitted to three
empirical weighted networks of importance for the spread of contagious diseases
and it is shown that can be substantially over- or underestimated if the
correlation between degree and weight is not taken into account
The Future of Gwydir: Community Engagement 2015-16
In mid-2015 Gwydir Shire Council engaged the Centre for Local Government at the University of Technology Sydney (UTS:CLG) to conduct workshops with Council, a deliberative panel, and a community survey exploring the financial sustainability of Council and future service delivery in the local area
Percolation in invariant Poisson graphs with i.i.d. degrees
Let each point of a homogeneous Poisson process in R^d independently be
equipped with a random number of stubs (half-edges) according to a given
probability distribution mu on the positive integers. We consider
translation-invariant schemes for perfectly matching the stubs to obtain a
simple graph with degree distribution mu. Leaving aside degenerate cases, we
prove that for any mu there exist schemes that give only finite components as
well as schemes that give infinite components. For a particular matching scheme
that is a natural extension of Gale-Shapley stable marriage, we give sufficient
conditions on mu for the absence and presence of infinite components
Non-equilibrium mean-field theories on scale-free networks
Many non-equilibrium processes on scale-free networks present anomalous
critical behavior that is not explained by standard mean-field theories. We
propose a systematic method to derive stochastic equations for mean-field order
parameters that implicitly account for the degree heterogeneity. The method is
used to correctly predict the dynamical critical behavior of some binary spin
models and reaction-diffusion processes. The validity of our non-equilibrium
theory is furtherly supported by showing its relation with the generalized
Landau theory of equilibrium critical phenomena on networks.Comment: 4 pages, no figures, major changes in the structure of the pape
Parent, Child and Public Involvement in Child Health Research: Core value not just an optional extra
Percolation transition and distribution of connected components in generalized random network ensembles
In this work, we study the percolation transition and large deviation
properties of generalized canonical network ensembles. This new type of random
networks might have a very rich complex structure, including high heterogeneous
degree sequences, non-trivial community structure or specific spatial
dependence of the link probability for networks embedded in a metric space. We
find the cluster distribution of the networks in these ensembles by mapping the
problem to a fully connected Potts model with heterogeneous couplings. We show
that the nature of the Potts model phase transition, linked to the birth of a
giant component, has a crossover from second to first order when the number of
critical colors in all the networks under study. These results shed
light on the properties of dynamical processes defined on these network
ensembles.Comment: 27 pages, 15 figure
Synchronization in Scale Free networks: The role of finite size effects
Synchronization problems in complex networks are very often studied by
researchers due to its many applications to various fields such as
neurobiology, e-commerce and completion of tasks. In particular, Scale Free
networks with degree distribution , are widely used in
research since they are ubiquitous in nature and other real systems. In this
paper we focus on the surface relaxation growth model in Scale Free networks
with , and study the scaling behavior of the fluctuations, in
the steady state, with the system size . We find a novel behavior of the
fluctuations characterized by a crossover between two regimes at a value of
that depends on : a logarithmic regime, found in previous
research, and a constant regime. We propose a function that describes this
crossover, which is in very good agreement with the simulations. We also find
that, for a system size above , the fluctuations decrease with
, which means that the synchronization of the system improves as
increases. We explain this crossover analyzing the role of the
network's heterogeneity produced by the system size and the exponent of the
degree distribution.Comment: 9 pages and 5 figures. Accepted in Europhysics Letter
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