Average trajectory of returning walks

Avalanche shapes in the fiber bundle model

We study the temporal evolution of avalanches in the fiber bundle model of disordered solids, when the model is gradually driven towards the critical breakdown point. We use two types of loading protocols: (i) quasistatic loading and (ii) loading by a discrete amount. In the quasistatic loading, where the load is increased by the minimum amount needed to initiate an avalanche, the temporal shapes of avalanches are asymmetric away from the critical point and become symmetric as the critical point is approached. A measure of asymmetry (A) follows a universal form A∼(σ-σ_{c})^{θ}, with θ≈0.25, where σ is the load per fiber and σ_{c} is the critical load per fiber. This behavior is independent of the disorder present in the system in terms of the individual failure threshold values. Thus it is possible to use this asymmetry measure as a precursor to imminent failure. For the case of discrete loading, the load is always increased by a fixed amount. The dynamics of the model in this case can be solved in the mean field limit. It shows that the avalanche shapes always remain asymmetric. We also present a variable range load sharing version of this case, where the results remain qualitatively similar.

Mechanisms underlying pathological cortical bursts during metabolic depletion

Cortical activity depends upon a continuous supply of oxygen and other metabolic resources. Perinatal disruption of oxygen availability is a common clinical scenario in neonatal intensive care units, and a leading cause of lifelong disability. Pathological patterns of brain activity including burst suppression and seizures are a hallmark of the recovery period, yet the mechanisms by which these patterns arise remain poorly understood. Here, we use computational modeling of coupled metabolic-neuronal activity to explore the mechanisms by which oxygen depletion generates pathological brain activity. We find that restricting oxygen supply drives transitions from normal activity to several pathological activity patterns (isoelectric, burst suppression, and seizures), depending on the potassium supply. Trajectories through parameter space track key features of clinical electrophysiology recordings and reveal how infants with good recovery outcomes track toward normal parameter values, whereas the parameter values for infants with poor outcomes dwell around the pathological values. These findings open avenues for studying and monitoring the metabolically challenged infant brain, and deepen our understanding of the link between neuronal and metabolic activity.

Breakdown of Scaling and Friction Weakening in Intermittent Granular Flow

Many materials are produced, processed and stored as grains, while granularity of matter can be crucial in triggering potentially catastrophic geological events like landslides, avalanches and earthquakes. The response of grain assemblies to shear stress is therefore of utmost relevance to both human and natural environment. At low shear rate a granular system flows intermittently by distinct avalanches. In such state the avalanche velocity in time is expected to follow a symmetrical and universal average behavior, whose dependence on the slip size reduces to a scale factor. Analyzing data from long lasting experiments, we observe a breakdown of this scaling: While in short slips velocity shows indeed a self-similar and symmetric profile, it does not in long slips. The investigation of frictional response in these different regimes evidences that this breakdown can be traced back to the onset of a friction weakening, which is of dynamical origin and can amplify instabilities exactly in this critical state, the most frequent state for natural hazards.

Power-law statistics and universal scaling in the absence of criticality

Critical states are sometimes identified experimentally through power-law statistics or universal scaling functions. We show here that such features naturally emerge from networks in self-sustained irregular regimes away from criticality. In these regimes, statistical physics theory of large interacting systems predict a regime where the nodes have independent and identically distributed dynamics. We thus investigated the statistics of a system in which units are replaced by independent stochastic surrogates and found the same power-law statistics, indicating that these are not sufficient to establish criticality. We rather suggest that these are universal features of large-scale networks when considered macroscopically. These results put caution on the interpretation of scaling laws found in nature.

Transient cluster formation in sheared non-Brownian suspensions

We perform numerical simulations of non-Brownian suspensions in the laminar flow regime to study the scaling behavior of particle clusters and collisions under shear. As the particle fraction approaches the maximum packing fraction, large transient clusters appear in the system. We use methods from percolation theory to discuss the cluster size distribution. We also give a scaling relation for the percolation threshold as well as system size effects through time-dependent fluctuations of this threshold and relate them to system size. System size effects are important close to the maximum packing fraction due to the divergence of the cluster length scale. We then investigate the transient nature of the clusters through characterization of particle collisions and show that collision times exhibit scale-invariant properties. Finally, we show that particle collision times can be modeled as first-passage processes.

How we move is universal: Scaling in the average shape of human activity

Human motor activity is constrained by the rhythmicity of the 24 hours circadian cycle, including the usual 12-15 hours sleep-wake cycle. However, activity fluctuations also appear over a wide range of temporal scales, from days to a few seconds, resulting from the concatenation of a myriad of individual smaller motor events. Furthermore,  individuals present different propensity to wakefulness and thus to motor activity throughout the circadian cycle.  Are activity fluctuations across temporal scales intrinsically different, or is there a universal description encompassing them? Is this description also universal across individuals, considering the aforementioned variability?  Here we establish the presence of universality in motor activity fluctuations based on the empirical study of a month of continuous wristwatch accelerometer recordings. We study the scaling of average fluctuations across temporal scales and determine a universal law characterized by critical exponents $\alpha$, $\tau$ and $1/{ \mu}$. Results are highly reminiscent of the universality described for the average shape of avalanches in systems exhibiting crackling noise. Beyond its theoretical relevance, the present results can be important for developing objective markers of healthy  as well as pathological human motor behavior.Received: 18 October 2015,  Accepted: 10 November 2015; Edited by: E. Mizraji; Reviewed by: J. Lin, Department of Physics, Washington College, Maryland, USA.; DOI: http://dx.doi.org/10.4279/PIP.070017Cite as: D R Chialvo, A M Gonzalez Torrado, E Gudowska-Nowak, J K Ochab, P Montoya, M A Nowak, E Tagliazucchi, Papers in Physics 7, 070017 (2015)This paper, by D R Chialvo, A M Gonzalez Torrado, E Gudowska-Nowak, J K Ochab, P Montoya, M A Nowak, E Tagliazucchi, is licensed under the Creative Commons Attribution License 3.0.

Cortical burst dynamics predict clinical outcome early in extremely preterm infants

Intermittent bursts of electrical activity are a ubiquitous signature of very early brain activity. Previous studies have largely focused on assessing the amplitudes of these transient cortical bursts or the intervals between them. Recent advances in basic neuroscience have identified the presence of scale-free 'avalanche' processes in bursting patterns of cortical activity in other clinical contexts. Here, we hypothesize that cortical bursts in human preterm infants also exhibit scale-free properties, providing new insights into the nature, temporal evolution, and prognostic value of spontaneous brain activity in the days immediately following preterm birth. We examined electroencephalographic recordings from 43 extremely preterm infants (gestational age 22-28 weeks) and demonstrated that their cortical bursts exhibit scale-free properties as early as 12 h after birth. The scaling relationships of cortical bursts correlate significantly with later mental development-particularly within the first 12 h of life. These findings show that early preterm brain activity is characterized by scale-free dynamics which carry developmental significance, hence offering novel means for rapid and early clinical prediction of neurodevelopmental outcomes.

Scale-free bursting in human cortex following hypoxia at birth

The human brain is fragile in the face of oxygen deprivation. Even a brief interruption of metabolic supply at birth challenges an otherwise healthy neonatal cortex, leading to a cascade of homeostatic responses. During recovery from hypoxia, cortical activity exhibits a period of highly irregular electrical fluctuations known as burst suppression. Here we show that these bursts have fractal properties, with power-law scaling of burst sizes across a remarkable 5 orders of magnitude and a scale-free relationship between burst sizes and durations. Although burst waveforms vary greatly, their average shape converges to a simple form that is asymmetric at long time scales. Using a simple computational model, we argue that this asymmetry reflects activity-dependent changes in the excitatory-inhibitory balance of cortical neurons. Bursts become more symmetric following the resumption of normal activity, with a corresponding reorganization of burst scaling relationships. These findings place burst suppression in the broad class of scale-free physical processes termed crackling noise and suggest that the resumption of healthy activity reflects a fundamental reorganization in the relationship between neuronal activity and its underlying metabolic constraints.