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

Predicting the energy consumption of heated plastic greenhouses in south-eastern Spain

[ENG] Measurements of heat consumption in a parral type greenhouse, equipped with an air-heating system, were carried out in south-eastern Spain (Almería) during the 1998/99 winter. From the daily values of heat consumption (Qd, MJ m-2 d-1) recorded in five identical greenhouses heated to different night temperature set-points (Tc), and data of minimum outside air temperature (Te,min), relationships between Qd and the temperature difference (ΔTmin = Tc – Te,min) were established. Linear regressions between Qd and ΔTmin gave satisfactory fits (R2 ranging from 0.75 to 0.83), considering that Te,min was the only input data for the model. When all data were pooled, the correlation was curvilinear, the best fit to a 2nd order polynomial being Qd = 0.049 ΔTmin 2 – 0.001 ΔTmin + 1.107 (R2 = 0.89). Validation of this model was performed using data obtained during other years, giving a fair agreement at the daily (R2 = 0.86), 10-day (R2 = 0.95) and yearly (R2 = 0.99) time scales. This simple model could be of interest to growers for decision-making related to the choice of set-point temperature and crop planning in heated greenhouses.[ESP] Se realizaron medidas de consumo de energía de la calefacción por aire caliente en invernaderos tipo parral durante la campaña 1998/99 en el sureste de España (Almería). Se determinaron relaciones adecuadas, para cinco invernaderos calentados a diferentes temperaturas nocturnas de consigna (Tc), entre los valores de consumos diarios de energía (Qd, MJ m-2 d-1) y la diferencia (ΔTmin) entre la temperatura de consigna de calefacción y la temperatura mínima exterior (Te,min). La regresión lineal entre Qd y ΔTmin fue satisfactoria (R2 varió entre 0,75 y 0,83), considerando que Te,min fue la única variable de entrada para el modelo. Cuando se analizaron todos los datos en conjunto, la correlación fue curvilínea, siendo el mejor ajuste para un polinomio de 2º orden, Qd = 0,049 ΔTmin 2 – 0,001 ΔTmin + 1,107 (R2 = 0,89). La validación de este modelo fue realizada utilizando datos de otros años, mostrando un ajuste adecuado para los periodos diarios (R2 = 0,86), 10-días (R2 = 0,95) y anuales (R2 = 0,99). Este sencillo modelo puede ser de interés para los agricultores a la hora de tomar decisiones sobre el mercado, escoger la temperatura de consigna y programar el periodo de calefacción del invernadero

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 $d \geq 2$ 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

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 $2 A \to A$ together with creation processes of the form $A \to n A$ with $n \geq 2$. This class includes the (exactly solvable in one-dimension) {\it reversible} model $2 A \leftrightarrow A$ 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

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

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