97 research outputs found
Self-organization without conservation: Are neuronal avalanches generically critical?
Recent experiments on cortical neural networks have revealed the existence of
well-defined avalanches of electrical activity. Such avalanches have been
claimed to be generically scale-invariant -- i.e. power-law distributed -- with
many exciting implications in Neuroscience. Recently, a self-organized model
has been proposed by Levina, Herrmann and Geisel to justify such an empirical
finding. Given that (i) neural dynamics is dissipative and (ii) there is a
loading mechanism "charging" progressively the background synaptic strength,
this model/dynamics is very similar in spirit to forest-fire and earthquake
models, archetypical examples of non-conserving self-organization, which have
been recently shown to lack true criticality. Here we show that cortical neural
networks obeying (i) and (ii) are not generically critical; unless parameters
are fine tuned, their dynamics is either sub- or super-critical, even if the
pseudo-critical region is relatively broad. This conclusion seems to be in
agreement with the most recent experimental observations. The main implication
of our work is that, if future experimental research on cortical networks were
to support that truly critical avalanches are the norm and not the exception,
then one should look for more elaborate (adaptive/evolutionary) explanations,
beyond simple self-organization, to account for this.Comment: 28 pages, 11 figures, regular pape
Absorbing states and elastic interfaces in random media: two equivalent descriptions of self-organized criticality
We elucidate a long-standing puzzle about the non-equilibrium universality
classes describing self-organized criticality in sandpile models. We show that
depinning transitions of linear interfaces in random media and absorbing phase
transitions (with a conserved non-diffusive field) are two equivalent languages
to describe sandpile criticality. This is so despite the fact that local
roughening properties can be radically different in the two pictures, as
explained here. Experimental implications of our work as well as promising
paths for future theoretical investigations are also discussed.Comment: 4 pages. 2 Figure
Sticky grains do not change the universality class of isotropic sandpiles
We revisit the sandpile model with ``sticky'' grains introduced by Mohanty
and Dhar [Phys. Rev. Lett. {\bf 89}, 104303 (2002)] whose scaling properties
were claimed to be in the universality class of directed percolation for both
isotropic and directed models. Simulations in the so-called fixed-energy
ensemble show that this conclusion is not valid for isotropic sandpiles and
that this model shares the same critical properties of other stochastic
sandpiles, such as the Manna model. %as expected from the existence of an extra
%conservation-law, absent in directed percolation. These results are
strengthened by the analysis of the Langevin equations proposed by the same
authors to account for this problem which we show to converge, upon
coarse-graining, to the well-established set of Langevin equations for the
Manna class. Therefore, the presence of a conservation law keeps isotropic
sandpiles, with or without stickiness, away from the directed percolation
class.Comment: 4 pages. 3 Figures. Subm. to PR
Temporal Griffiths Phases
Disorder is an unavoidable ingredient of real systems. Spatial disorder
generates Griffiths phases (GPs) which, in analogy to critical points, are
characterized by a slow relaxation of the order parameter and divergences of
quantities such as the susceptibility. However, these singularities appear in
an extended region of the parameter space and not just at a (critical) point,
i.e. there is generic scale invariance. Here, we study the effects of temporal
disorder, focusing on systems with absorbing states. We show that for
dimensions there are Temporal Griffiths phases (TGPs) characterized
by generic power-law spatial scaling and generic divergences of the
susceptibility. TGPs turn out to be a counterpart of GPs, but with space and
time playing reversed roles. TGPs constitute a unifying concept, shedding light
on the non-trivial effects of temporal disorder.Comment: 4 pages, 3 figures; Accepted in PR
Quantitative Analysis of Bloggers Collective Behavior Powered by Emotions
Large-scale data resulting from users online interactions provide the
ultimate source of information to study emergent social phenomena on the Web.
From individual actions of users to observable collective behaviors, different
mechanisms involving emotions expressed in the posted text play a role. Here we
combine approaches of statistical physics with machine-learning methods of text
analysis to study emergence of the emotional behavior among Web users. Mapping
the high-resolution data from digg.com onto bipartite network of users and
their comments onto posted stories, we identify user communities centered
around certain popular posts and determine emotional contents of the related
comments by the emotion-classifier developed for this type of texts. Applied
over different time periods, this framework reveals strong correlations between
the excess of negative emotions and the evolution of communities. We observe
avalanches of emotional comments exhibiting significant self-organized critical
behavior and temporal correlations. To explore robustness of these critical
states, we design a network automaton model on realistic network connections
and several control parameters, which can be inferred from the dataset.
Dissemination of emotions by a small fraction of very active users appears to
critically tune the collective states
Universality in Bacterial Colonies
The emergent spatial patterns generated by growing bacterial colonies have
been the focus of intense study in physics during the last twenty years. Both
experimental and theoretical investigations have made possible a clear
qualitative picture of the different structures that such colonies can exhibit,
depending on the medium on which they are growing. However, there are
relatively few quantitative descriptions of these patterns. In this paper, we
use a mechanistically detailed simulation framework to measure the scaling
exponents associated with the advancing fronts of bacterial colonies on hard
agar substrata, aiming to discern the universality class to which the system
belongs. We show that the universal behavior exhibited by the colonies can be
much richer than previously reported, and we propose the possibility of up to
four different sub-phases within the medium-to-high nutrient concentration
regime. We hypothesize that the quenched disorder that characterizes one of
these sub-phases is an emergent property of the growth and division of bacteria
competing for limited space and nutrients.Comment: 12 pages, 5 figure
Absorbing state phase transitions with a non-accessible vacuum
We analyze from the renormalization group perspective a universality class of
reaction-diffusion systems with absorbing states. It describes models where the
vacuum state is not accessible, as the set of reactions together
with creation processes of the form with . This class
includes the (exactly solvable in one-dimension) {\it reversible} model as a particular example, as well as many other {\it
non-reversible} reactions, proving that reversibility is not the main feature
of this class as previously thought. By using field theoretical techniques we
show that the critical point appears at zero creation-rate (in accordance with
exact results), and it is controlled by the well known pair-coagulation
renormalization group fixed point, with non-trivial exactly computable critical
exponents in any dimension. Finally, we report on Monte-Carlo simulations,
confirming all field theoretical predictions in one and two dimensions for
various reversible and non-reversible models.Comment: 6 pages. 3 Figures. Final version as published in J.Stat.Mec
Self-organization without conservation: true or just apparent scale-invariance?
The existence of true scale-invariance in slowly driven models of
self-organized criticality without a conservation law, as forest-fires or
earthquake automata, is scrutinized in this paper. By using three different
levels of description - (i) a simple mean field, (ii) a more detailed
mean-field description in terms of a (self-organized) branching processes, and
(iii) a full stochastic representation in terms of a Langevin equation-, it is
shown on general grounds that non-conserving dynamics does not lead to bona
fide criticality. Contrarily to conserving systems, a parameter, which we term
"re-charging" rate (e.g. the tree-growth rate in forest-fire models), needs to
be fine-tuned in non-conserving systems to obtain criticality. In the infinite
size limit, such a fine-tuning of the loading rate is easy to achieve, as it
emerges by imposing a second separation of time-scales but, for any finite
size, a precise tuning is required to achieve criticality and a coherent
finite-size scaling picture. Using the approaches above, we shed light on the
common mechanisms by which "apparent criticality" is observed in non-conserving
systems, and explain in detail (both qualitatively and quantitatively) the
difference with respect to true criticality obtained in conserving systems. We
propose to call this self-organized quasi-criticality (SOqC). Some of the
reported results are already known and some of them are new. We hope the
unified framework presented here helps to elucidate the confusing and
contradictory literature in this field. In a second accompanying paper, we
shall discuss the implications of the general results obtained here for models
of neural avalanches in Neuroscience for which self-organized scale-invariance
in the absence of conservation has been claimed.Comment: 40 pages, 7 figures
Entropy estimates of small data sets
Estimating entropies from limited data series is known to be a non-trivial
task. Naive estimations are plagued with both systematic (bias) and statistical
errors. Here, we present a new 'balanced estimator' for entropy functionals
Shannon, R\'enyi and Tsallis) specially devised to provide a compromise between
low bias and small statistical errors, for short data series. This new
estimator out-performs other currently available ones when the data sets are
small and the probabilities of the possible outputs of the random variable are
not close to zero. Otherwise, other well-known estimators remain a better
choice. The potential range of applicability of this estimator is quite broad
specially for biological and digital data series.Comment: 11 pages, 2 figure
Simplest nonequilibrium phase transition into an absorbing state
We study in further detail particle models displaying a boundary-induced
absorbing state phase transition [Phys. Rev. E. {\bf 65}, 046104 (2002) and
Phys. Rev. Lett. {\bf 100}, 165701 (2008)] . These are one-dimensional systems
consisting of a single site (the boundary) where creation and annihilation of
particles occur and a bulk where particles move diffusively. We study different
versions of these models, and confirm that, except for one exactly solvable
bosonic variant exhibiting a discontinuous transition and trivial exponents,
all the others display non-trivial behavior, with critical exponents differing
from their mean-field values, representing a universality class. Finally, the
relation of these systems with a -dimensional non-Markovian process is
discussed.Comment: 9 pages, 7 figures, minor change
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