121 research outputs found
Fluctuations in models of biological macroevolution
Fluctuations in diversity and extinction sizes are discussed and compared for
two different, individual-based models of biological coevolution. Both models
display power-law distributions for various quantities of evolutionary
interest, such as the lifetimes of individual species, the quiet periods
between evolutionary upheavals larger than a given cutoff, and the sizes of
extinction events. Time series of the diversity and measures of the size of
extinctions give rise to flicker noise. Surprisingly, the power-law behaviors
of the probability densities of quiet periods in the two models differ, while
the distributions of the lifetimes of individual species are the same.Comment: 7 pages, 5 figure
Absorbing Random Walks Interpolating Between Centrality Measures on Complex Networks
Centrality, which quantifies the "importance" of individual nodes, is among
the most essential concepts in modern network theory. As there are many ways in
which a node can be important, many different centrality measures are in use.
Here, we concentrate on versions of the common betweenness and it closeness
centralities. The former measures the fraction of paths between pairs of nodes
that go through a given node, while the latter measures an average inverse
distance between a particular node and all other nodes. Both centralities only
consider shortest paths (i.e., geodesics) between pairs of nodes. Here we
develop a method, based on absorbing Markov chains, that enables us to
continuously interpolate both of these centrality measures away from the
geodesic limit and toward a limit where no restriction is placed on the length
of the paths the walkers can explore. At this second limit, the interpolated
betweenness and closeness centralities reduce, respectively, to the well-known
it current betweenness and resistance closeness (information) centralities. The
method is tested numerically on four real networks, revealing complex changes
in node centrality rankings with respect to the value of the interpolation
parameter. Non-monotonic betweenness behaviors are found to characterize nodes
that lie close to inter-community boundaries in the studied networks
Adjustable reach in a network centrality based on current flows
Centrality, which quantifies the "importance" of individual nodes, is among
the most essential concepts in modern network theory. Most prominent centrality
measures can be expressed as an aggregation of influence flows between pairs of
nodes. As there are many ways in which influence can be defined, many different
centrality measures are in use. Parametrized centralities allow further
flexibility and utility by tuning the centrality calculation to the regime most
appropriate for a given network. Here, we identify two categories of centrality
parameters. Reach parameters control the attenuation of influence flows between
distant nodes. Grasp parameters control the centrality's potential to send
influence flows along multiple, often nongeodesic paths. Combining these
categories with Borgatti's centrality types [S. P. Borgatti, Social Networks
27, 55-71 (2005)], we arrive at a novel classification system for parametrized
centralities. Using this classification, we identify the notable absence of any
centrality measures that are radial, reach parametrized, and based on acyclic,
conservative flows of influence. We therefore introduce the ground-current
centrality, which is a measure of precisely this type. Because of its unique
position in the taxonomy, the ground-current centrality has significant
advantages over similar centralities. We demonstrate that, compared to other
conserved-flow centralities, it has a simpler mathematical description.
Compared to other reach centralities, it robustly preserves an intuitive rank
ordering across a wide range of network architectures. We also show that it
produces a consistent distribution of centrality values among the nodes,
neither trivially equally spread (delocalization), nor overly focused on a few
nodes (localization). Other reach centralities exhibit both of these behaviors
on regular networks and hub networks, respectively
Monte Carlo Studies of the Ising Antiferromagnet with a Ferromagnetic Mean-field Term
The unusual thermodynamic properties of the Ising antiferromagnet
supplemented with a ferromagnetic, mean-field term are outlined. This simple
model is inspired by more realistic models of spin-crossover materials. The
phase diagram is estimated using Metropolis Monte Carlo methods, and
differences with preliminary Wang-Landau Monte Carlo results for small systems
are noted.Comment: Four page
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