448 research outputs found
Slightly generalized Generalized Contagion: Unifying simple models of biological and social spreading
We motivate and explore the basic features of generalized contagion, a model
mechanism that unifies fundamental models of biological and social contagion.
Generalized contagion builds on the elementary observation that spreading and
contagion of all kinds involve some form of system memory. We discuss the three
main classes of systems that generalized contagion affords, resembling: simple
biological contagion; critical mass contagion of social phenomena; and an
intermediate, and explosive, vanishing critical mass contagion. We also present
a simple explanation of the global spreading condition in the context of a
small seed of infected individuals.Comment: 8 pages, 5 figures; chapter to appear in "Spreading Dynamics in
Social Systems"; Eds. Sune Lehmann and Yong-Yeol Ahn, Springer Natur
Percolation and Epidemic Thresholds in Clustered Networks
We develop a theoretical approach to percolation in random clustered
networks. We find that, although clustering in scale-free networks can strongly
affect some percolation properties, such as the size and the resilience of the
giant connected component, it cannot restore a finite percolation threshold. In
turn, this implies the absence of an epidemic threshold in this class of
networks extending, thus, this result to a wide variety of real scale-free
networks which shows a high level of transitivity. Our findings are in good
agreement with numerical simulations.Comment: 4 Pages and 3 Figures. Final version to appear in PR
Migration paths saturations in meta-epidemic systems
In this paper we consider a simple two-patch model in which a population
affected by a disease can freely move. We assume that the capacity of the
interconnected paths is limited, and thereby influencing the migration rates.
Possible habitat disruptions due to human activities or natural events are
accounted for. The demographic assumptions prevent the ecosystem to be wiped
out, and the disease remains endemic in both populated patches at a stable
equilibrium, but possibly also with an oscillatory behavior in the case of
unidirectional migrations. Interestingly, if infected cannot migrate, it is
possible that one patch becomes disease-free. This fact could be exploited to
keep disease-free at least part of the population
Intrinsic definitions of "relative velocity" in general relativity
Given two observers, we define the "relative velocity" of one observer with
respect to the other in four different ways. All four definitions are given
intrinsically, i.e. independently of any coordinate system. Two of them are
given in the framework of spacelike simultaneity and, analogously, the other
two are given in the framework of observed (lightlike) simultaneity. Properties
and physical interpretations are discussed. Finally, we study relations between
them in special relativity, and we give some examples in Schwarzschild and
Robertson-Walker spacetimes.Comment: 29 pages, 12 figures. New proofs in special relativity and a new open
problem in general relativity (see Remark 5.2). An Appendix has been added,
studying the relative velocities in Schwarzschild, with new figures. Some
spelling erros fixe
Analysis of Petri Net Models through Stochastic Differential Equations
It is well known, mainly because of the work of Kurtz, that density dependent
Markov chains can be approximated by sets of ordinary differential equations
(ODEs) when their indexing parameter grows very large. This approximation
cannot capture the stochastic nature of the process and, consequently, it can
provide an erroneous view of the behavior of the Markov chain if the indexing
parameter is not sufficiently high. Important phenomena that cannot be revealed
include non-negligible variance and bi-modal population distributions. A
less-known approximation proposed by Kurtz applies stochastic differential
equations (SDEs) and provides information about the stochastic nature of the
process. In this paper we apply and extend this diffusion approximation to
study stochastic Petri nets. We identify a class of nets whose underlying
stochastic process is a density dependent Markov chain whose indexing parameter
is a multiplicative constant which identifies the population level expressed by
the initial marking and we provide means to automatically construct the
associated set of SDEs. Since the diffusion approximation of Kurtz considers
the process only up to the time when it first exits an open interval, we extend
the approximation by a machinery that mimics the behavior of the Markov chain
at the boundary and allows thus to apply the approach to a wider set of
problems. The resulting process is of the jump-diffusion type. We illustrate by
examples that the jump-diffusion approximation which extends to bounded domains
can be much more informative than that based on ODEs as it can provide accurate
quantity distributions even when they are multi-modal and even for relatively
small population levels. Moreover, we show that the method is faster than
simulating the original Markov chain
The dynamics of audience applause
The study of social identity and crowd psychology looks at how and why individual people change their behaviour in response to others. Within a group, a new behaviour can emerge first in a few individuals before it spreads rapidly to all other members. A number of mathematical models have been hypothesized to describe these social contagion phenomena, but these models remain largely untested against empirical data. We used Bayesian model selection to test between various hypotheses about the spread of a simple social behaviour, applause after an academic presentation. Individuals' probability of starting clapping increased in proportion to the number of other audience members already ‘infected’ by this social contagion, regardless of their spatial proximity. The cessation of applause is similarly socially mediated, but is to a lesser degree controlled by the reluctance of individuals to clap too many times. We also found consistent differences between individuals in their willingness to start and stop clapping. The social contagion model arising from our analysis predicts that the time the audience spends clapping can vary considerably, even in the absence of any differences in the quality of the presentations they have heard
Classification of image distortions in terms of Petrov types
An observer surrounded by sufficiently small spherical light sources at a
fixed distance will see a pattern of elliptical images distributed over the
sky, owing to the distortion effect (shearing effect) of the spacetime geometry
upon light bundles. In lowest non-trivial order with respect to the distance,
this pattern is completely determined by the conformal curvature tensor (Weyl
tensor) at the observation event. In this paper we derive formulas that allow
to calculate these distortion patterns in terms of the Newman-Penrose
formalism. Then we represent the distortion patterns graphically for all Petrov
types, and we discuss their dependence on the velocity of the observer.Comment: 22 pages, 8 eps-figures; revised version, parts of Introduction and
Conclusions rewritte
Emergent spatial correlations in stochastically evolving populations
We study the spatial pattern formation and emerging long range correlations
in a model of three species coevolving in space and time according to
stochastic contact rules. Analytical results for the pair correlation
functions, based on a truncation approximation and supported by computer
simulations, reveal emergent strategies of survival for minority agents based
on selection of patterns. Minority agents exhibit defensive clustering and
cooperative behavior close to phase transitions.Comment: 11 pages, 4 figures, Adobe PDF forma
- …