2,098 research outputs found
Description of spreading dynamics by microscopic network models and macroscopic branching processes can differ due to coalescence
Spreading processes are conventionally monitored on a macroscopic level by
counting the number of incidences over time. The spreading process can then be
modeled either on the microscopic level, assuming an underlying interaction
network, or directly on the macroscopic level, assuming that microscopic
contributions are negligible. The macroscopic characteristics of both
descriptions are commonly assumed to be identical. In this work, we show that
these characteristics of microscopic and macroscopic descriptions can be
different due to coalescence, i.e., a node being activated at the same time by
multiple sources. In particular, we consider a (microscopic) branching network
(probabilistic cellular automaton) with annealed connectivity disorder, record
the macroscopic activity, and then approximate this activity by a (macroscopic)
branching process. In this framework, we analytically calculate the effect of
coalescence on the collective dynamics. We show that coalescence leads to a
universal non-linear scaling function for the conditional expectation value of
successive network activity. This allows us to quantify the difference between
the microscopic model parameter and established macroscopic estimates. To
overcome this difference, we propose a non-linear estimator that correctly
infers the model branching parameter for all system sizes.Comment: 13 page
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Spatial patterns of tree yield explained by endogenous forces through a correspondence between the Ising model and ecology.
Spatial patterning of periodic dynamics is a dramatic and ubiquitous ecological phenomenon arising in systems ranging from diseases to plants to mammals. The degree to which spatial correlations in cyclic dynamics are the result of endogenous factors related to local dynamics vs. exogenous forcing has been one of the central questions in ecology for nearly a century. With the goal of obtaining a robust explanation for correlations over space and time in dynamics that would apply to many systems, we base our analysis on the Ising model of statistical physics, which provides a fundamental mechanism of spatial patterning. We show, using 5 y of data on over 6,500 trees in a pistachio orchard, that annual nut production, in different years, exhibits both large-scale synchrony and self-similar, power-law decaying correlations consistent with the Ising model near criticality. Our approach demonstrates the possibility that short-range interactions can lead to long-range correlations over space and time of cyclic dynamics even in the presence of large environmental variability. We propose that root grafting could be the common mechanism leading to positive short-range interactions that explains the ubiquity of masting, correlated seed production over space through time, by trees
Dynamic range of hypercubic stochastic excitable media
We study the response properties of d-dimensional hypercubic excitable
networks to a stochastic stimulus. Each site, modelled either by a three-state
stochastic susceptible-infected-recovered-susceptible system or by the
probabilistic Greenberg-Hastings cellular automaton, is continuously and
independently stimulated by an external Poisson rate h. The response function
(mean density of active sites rho versus h) is obtained via simulations (for
d=1, 2, 3, 4) and mean field approximations at the single-site and pair levels
(for all d). In any dimension, the dynamic range of the response function is
maximized precisely at the nonequilibrium phase transition to self-sustained
activity, in agreement with a reasoning recently proposed. Moreover, the
maximum dynamic range attained at a given dimension d is a decreasing function
of d.Comment: 7 pages, 4 figure
Social distancing strategies against disease spreading
The recurrent infectious diseases and their increasing impact on the society
has promoted the study of strategies to slow down the epidemic spreading. In
this review we outline the applications of percolation theory to describe
strategies against epidemic spreading on complex networks. We give a general
outlook of the relation between link percolation and the
susceptible-infected-recovered model, and introduce the node void percolation
process to describe the dilution of the network composed by healthy individual,
, the network that sustain the functionality of a society. Then, we survey
two strategies: the quenched disorder strategy where an heterogeneous
distribution of contact intensities is induced in society, and the intermittent
social distancing strategy where health individuals are persuaded to avoid
contact with their neighbors for intermittent periods of time. Using
percolation tools, we show that both strategies may halt the epidemic
spreading. Finally, we discuss the role of the transmissibility, , the
effective probability to transmit a disease, on the performance of the
strategies to slow down the epidemic spreading.Comment: to be published in "Perspectives and Challenges in Statistical
Physics and Complex Systems for the Next Decade", Word Scientific Pres
Inferring collective dynamical states from widely unobserved systems
When assessing spatially-extended complex systems, one can rarely sample the
states of all components. We show that this spatial subsampling typically leads
to severe underestimation of the risk of instability in systems with
propagating events. We derive a subsampling-invariant estimator, and
demonstrate that it correctly infers the infectiousness of various diseases
under subsampling, making it particularly useful in countries with unreliable
case reports. In neuroscience, recordings are strongly limited by subsampling.
Here, the subsampling-invariant estimator allows to revisit two prominent
hypotheses about the brain's collective spiking dynamics:
asynchronous-irregular or critical. We identify consistently for rat, cat and
monkey a state that combines features of both and allows input to reverberate
in the network for hundreds of milliseconds. Overall, owing to its ready
applicability, the novel estimator paves the way to novel insight for the study
of spatially-extended dynamical systems.Comment: 7 pages + 12 pages supplementary information + 7 supplementary
figures. Title changed to match journal referenc
Critical fluctuations in epidemic models explain COVIDâ19 postâlockdown dynamics
As the COVID-19 pandemic progressed, research on mathematical modeling became imperative and
very influential to understand the epidemiological dynamics of disease spreading. The momentary
reproduction ratio r(t) of an epidemic is used as a public health guiding tool to evaluate the course of
the epidemic, with the evolution of r(t) being the reasoning behind tightening and relaxing control
measures over time. Here we investigate critical fluctuations around the epidemiological threshold,
resembling new waves, even when the community disease transmission rate β is not signifcantly
changing. Without loss of generality, we use simple models that can be treated analytically and
results are applied to more complex models describing COVID-19 epidemics. Our analysis shows that,
rather than the supercritical regime (infectivity larger than a critical value, β>βc) leading to new
exponential growth of infection, the subcritical regime (infectivity smaller than a critical value, β<βc)
with small import is able to explain the dynamic behaviour of COVID-19 spreading after a lockdown
lifting, with r(t) â 1 hovering around its threshold value.BMTF âMathematical Modeling Applied to Healthâ Project
European Unionâs Horizon 2020 research and innovation programme under the Marie SkĹodowska-Curie grant
agreement No 79249
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