228 research outputs found
A simple person's approach to understanding the contagion condition for spreading processes on generalized random networks
We present derivations of the contagion condition for a range of spreading
mechanisms on families of generalized random networks and bipartite random
networks. We show how the contagion condition can be broken into three
elements, two structural in nature, and the third a meshing of the contagion
process and the network. The contagion conditions we obtain reflect the
spreading dynamics in a clear, interpretable way. For threshold contagion, we
discuss results for all-to-all and random network versions of the model, and
draw connections between them.Comment: 10 pages, 9 figures; chapter to appear in "Spreading Dynamics in
Social Systems"; Eds. Sune Lehmann and Yong-Yeol Ahn, Springer Natur
Packing-limited growth of irregular objects
We study growth limited by packing for irregular objects in two dimensions.
We generate packings by seeding objects randomly in time and space and allowing
each object to grow until it collides with another object. The objects we
consider allow us to investigate the separate effects of anisotropy and
non-unit aspect ratio. By means of a connection to the decay of pore-space
volume, we measure power law exponents for the object size distribution. We
carry out a scaling analysis, showing that it provides an upper bound for the
size distribution exponent. We find that while the details of the growth
mechanism are irrelevant, the exponent is strongly shape dependent. Potential
applications lie in ecological and biological environments where sessile
organisms compete for limited space as they grow.Comment: 6 pages, 4 figures, 1 table, revtex
Packing-Limited Growth
We consider growing spheres seeded by random injection in time and space.
Growth stops when two spheres meet leading eventually to a jammed state. We
study the statistics of growth limited by packing theoretically in d dimensions
and via simulation in d=2, 3, and 4. We show how a broad class of such models
exhibit distributions of sphere radii with a universal exponent. We construct a
scaling theory that relates the fractal structure of these models to the decay
of their pore space, a theory that we confirm via numerical simulations. The
scaling theory also predicts an upper bound for the universal exponent and is
in exact agreement with numerical results for d=4.Comment: 6 pages, 5 figures, 4 tables, revtex4 to appear in Phys. Rev. E, May
200
Quantitative patterns in drone wars
Attacks by drones (i.e., unmanned combat air vehicles) continue to generate
heated political and ethical debates. Here we examine the quantitative nature
of drone attacks, focusing on how their intensity and frequency compare with
that of other forms of human conflict. Instead of the power-law distribution
found recently for insurgent and terrorist attacks, the severity of attacks is
more akin to lognormal and exponential distributions, suggesting that the
dynamics underlying drone attacks lie beyond these other forms of human
conflict. We find that the pattern in the timing of attacks is consistent with
one side having almost complete control, an important if expected result. We
show that these novel features can be reproduced and understood using a
generative mathematical model in which resource allocation to the dominant side
is regulated through a feedback loop.Comment: 5 pages, 3 figure
Direct, physically-motivated derivation of the contagion condition for spreading processes on generalized random networks
For a broad range single-seed contagion processes acting on generalized
random networks, we derive a unifying analytic expression for the possibility
of global spreading events in a straightforward, physically intuitive fashion.
Our reasoning lays bare a direct mechanical understanding of an archetypal
spreading phenomena that is not evident in circuitous extant mathematical
approaches.Comment: 4 pages, 1 figure, 1 tabl
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