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Hydraulic fracturing operations are generally associated with induced seismic events with magnitudes that are typically lower than those of tectonic-based earthquakes. Although fluid migration and the resulting pore-pressure increase appear to be the primary driving mechanisms, one must also understand fault activation and the secondary interevent triggering process(es) leading to the generation of aftershock sequences. This requires distinguishing between seismic events that are a direct consequence of fluid injections and those that predominantly arise because of secondary mechanisms such as static or dynamic stress triggering caused by preceding earthquakes. Focusing on a case study in the Montney area in western Alberta, Canada, where both surface array and borehole geophone data are available, we (1) establish the importance of secondary mechanisms and aftershock sequences in this area and (2) show that the statistical properties of the aftershock sequences can allow one to establish whether significant fault activation is at play and whether the activated fault zone was critically prestressed. Specifically, we find evidence for aftershock sequences using different statistical methodologies, although the presence of aftershocks in the studied hydraulic-fracturing-induced context is significantly less dominant compared with tectonic seismicity. The identified aftershock sequences are characterized by long-range spatial aftershock zones, setting them apart from other cases in fluid-driven settings but comparable to tectonic aftershock sequences and indicative of fault activation. Despite this observation, we find overall a strong dominance of smaller triggers for aftershock sequences and an aftershock production associated with large-magnitude events that is significantly lower than what has been observed in tectonic settings. This suggests that the activated fault zone as a whole was not critically prestressed, and the associated initial seismic hazard was significantly lower compared with tectonic cases.

We utilize a model of Wilson-Cowan oscillators to investigate structure-function relationships in the human brain by means of simulations of the spontaneous dynamics of brain networks generated through human connectome data. This allows us to establish relationships between the global excitability of such networks and global structural network quantities for connectomes of two different sizes for a number of individual subjects. We compare the qualitative behavior of such correlations between biological networks and shuffled networks, the latter generated by shuffling the pairwise connectivities of the former while preserving their distribution. Our results point towards a remarkable propensity of the brain's to achieve a trade-off between low network wiring cost and strong functionality, and highlight the unique capacity of brain network topologies to exhibit a strong transition from an inactive state to a globally excited one., 12 pages, 10 figures

Previous studies of injection-induced earthquake sequences have shown that the maximum magnitude (Mmax) of injection-induced seismicity increases with the net injected volume (V); however, different proposed seismic-hazard paradigms predict significantly different values of Mmax. Using injection and seismicity data from two project areas in northeastern British Columbia, Canada, where hydraulic fracturing induced seismicity was observed, we test the predictive power and robustness of three existing and one novel method to estimate Mmax. Due to their vastly different values of seismogenic index (Σ), these two project areas represent end-member cases of seismogenic response. Our novel method progressively adjusts the Mmax forecast under the assumption that each recorded event embodies an incremental release of fluid-induced stress. The results indicate that our method typically provides the lowest upper bound of the tested methods and it is less sensitive to site-specific calibration parameters such as Σ. This makes the novel method appealing for operational earthquake forecasting schemes as a real-time mitigation strategy to manage the risks of induced seismicity.

The frictional instability associated with earthquake initiation and earthquake dynamics is believed to be mainly controlled by the dynamics of fragmented rocks within the fault gauge. Principal features of the emerging seismicity (e.g., intermittent dynamics and broad time and/or energy scales) have been replicated by simple experimental setups, which involve a slowly driven slider on top of granular matter, for example. Yet these setups are often physically limited and might not allow one to determine the underlying nature of specific features and, hence, the universality and generality of the experimental observations. Here, we address this challenge by a numerical study of a spring-slider experiment based on two-dimensional discrete element method simulations, which allows us to control the properties of the granular matter and of the surface of the slider, for example. Upon quasistatic loading, stick-slip-type behavior emerges which is contrasted by a stable sliding regime at finite driving rates, in agreement with experimental observations. Across large parameter ranges for damping, interparticle friction, particle polydispersity, etc., the earthquake-like dynamics associated with the former regime results in several robust scale-free statistical features also observed in experiments. At first sight, these closely resemble the main empirical relations of tectonic seismicity at geological scales. This includes the Gutenberg-Richter distribution of event sizes, the Omori-Utsu-type decay of aftershock rates, as well as the aftershock productivity relation and broad recurrence time distributions. Yet, we show that the correlations associated with tectonic aftershocks are absent such that the origin of the Omori-Utsu relation, the aftershock productivity relation, and Båth's relation in the simulations is fundamentally different from the case of tectonic seismicity. This, we believe, is mainly due to a lack of macroscale relaxation processes that are closely tied to the generation of real aftershocks. We argue that the same is true for previous laboratory experiments.

Prenatal stress (PS) can impact fetal brain structure and function and contribute to higher vulnerability to neurodevelopmental and neuropsychiatric disorders. To understand how PS alters evoked and spontaneous neocortical activity and intrinsic brain functional connectivity, mesoscale voltage imaging was performed in adult C57BL/6NJ mice that had been exposed to auditory stress on gestational days 12-16, the age at which neocortex is developing. PS mice had a four-fold higher basal corticosterone level and reduced amplitude of cortical sensory-evoked responses to visual, auditory, whisker, forelimb, and hindlimb stimuli. Relative to control animals, PS led to a general reduction of resting-state functional connectivity, as well as reduced inter-modular connectivity, enhanced intra-modular connectivity, and altered frequency of auditory and forelimb spontaneous sensory motifs. These resting-state changes resulted in a cortical connectivity pattern featuring disjoint but tight modules and a decline in network efficiency. The findings demonstrate that cortical connectivity is sensitive to PS and exposed offspring may be at risk for adult stress-related neuropsychiatric disorders.

Aftershock cascades are a characteristic feature of natural seismicity, but underlying mechanisms remain debated. Here, we experimentally explore the presence or absence of aftershocks during failure of intact rock and slip on newly-created laboratory faults. We show that the overall activity increase and spatial localization of acoustic emission events during fracture nucleation occurs without temporal (Omori-type) correlations. Our analysis shows that this absence of aftershock sequences occurs even beyond peak stress and also when a macroscopic fracture has formed post peak-stress and propagates. Instead, aftershock triggering does occur during post-fracture stress relaxation along the newly-created lab-fault and in the presence of large-scale stress heterogeneities, for example, imposed by a saw-cut notch. The detected aftershocks in these cases can be described by standard seismological relationships such as a modified Omori-Utsu relation and its associated inter-event time distribution and productivity relation. Moreover, acoustic emissions within all experiments follow the Gutenberg-Richter relation, with smaller urn:x-wiley:21699313:media:jgrb55218:jgrb55218-math-0001-values for triggered events compared to non-triggered events. Performing full-moment tensor inversions, we find that seismic events with significant isotropic, compaction components play an important role for aftershock triggering. The resulting triggered events tend to have focal mechanisms similar to their trigger. Seismic events with predominant tensile components, on the other hand, show little evidence for aftershock triggering. This opens up a new perspective on aftershocks, going beyond not only the rate-and-state paradigm limited to purely frictional sliding or shear events but also the mainshock attribute paradigm where mainshock attributes control aftershock patterns.

The behavior of granular media under quasi-static loading has recently been shown to attain a stable evolution state corresponding to a manifold in the space of micromechanical variables. This state is characterized by sudden transitions between metastable jammed states, involving the partial micromechanical rearrangement of the granular medium. Using numerical simulations of two-dimensional granular media under quasistatic biaxial compression, we show that the dynamics in the stable evolution state is characterized by scale-free avalanches well before the macromechanical stationary flow regime traditionally linked to a self-organized critical state. This, together with the non-uniqueness and the non-monotony of macroscopic deformation curves, suggests that the statistical avalanche properties and the susceptibilities of the system cannot be reduced to a function of the macromechanical state. The associated scaling exponents are non-universal and depend on the interactions between particles. For stiffer particles (or samples at low confining pressure) we find distributions of avalanche properties compatible with the predictions of mean-field theory. The scaling exponents decrease below the mean-field values for softer interactions between particles. These lower exponents are consistent with observations for amorphous solids at their critical point. We specifically discuss the relationship between microscopic and macroscopic variables, including the relation between the external stress drop and the internal potential energy released during kinetic avalanches.

Spreading processes on networks are ubiquitous in both human-made and natural systems. Understanding their behavior is of broad interest; from the control of epidemics to understanding brain dynamics. While in some cases there exists a clear separation of time scales between the propagation of a single spreading cascade and the initiation of the next -- such that spreading can be modelled as directed percolation or a branching process -- there are also processes for which this is not the case, such as zoonotic diseases or spiking cascades in neural networks. For a large class of relevant network topologies, we show here that in such a scenario the nature of the overall spreading fundamentally changes. This change manifests itself in a transition between different universality classes of critical spreading, which determines the onset and the properties of an avalanche turning epidemic or neural activity turning epileptic, for example. We present analytical results in the mean-field limit giving the critical line along which scale-free spreading behaviour can be observed. The two limits of this critical line correspond to the universality classes of directed and undirected percolation, respectively. Outside these two limits, this duality manifests itself in the appearance of critical exponents from the universality classes of both directed and undirected percolation. We find that the transition between these exponents is governed by a competition between merging and propagation of activity, and identify an appropriate scaling relationship for the transition point. Finally, we show that commonly used measures, such as the branching ratio and dynamic susceptibility, fail to establish criticality in the absence of time-scale separation calling for a reanalysis of criticality in the brain., 25 pages, 17 figures, 3 tables. Update with substantial re-write to introduction and discussion, minor tweaks throughout

Within the classical eye-blink conditioning, Purkinje cells within the cerebellum are known to suppress their tonic firing rates for a well defined time period in response to the conditional stimulus after training. The temporal profile of the drop in tonic firing rate, i.e., the onset and the duration, depend upon the time interval between the onsets of the training conditional and unconditional stimulus. Direct stimulation of parallel fibers and climbing fiber by electrodes was found to be sufficient to reproduce the same characteristic drop in the firing rate of the Purkinje cell. In addition, the specific metabotropic glutamate-based receptor type 7 (mGluR7), which resides on the Purkinje cell synapses, was found responsible for the initiation of the response, suggesting an intrinsic mechanism within the Purkinje cell for the temporal learning. In an attempt to look for a mechanism for time-encoding memory formation within individual Purkinje cells, we propose a biochemical mechanism based on recent experimental findings. The proposed model tries to answer key aspects of the “Coding problem” of Neuroscience by focussing on the Purkinje cell’s ability to encode time intervals through training. According to the proposed mechanism, the time memory is encoded within the dynamics of a set of proteins — mGluR7, G-protein, G-protein coupled Inward Rectifier Potassium ion channel, Protein Kinase A and Protein Phosphatase 1 — which self-organize themselves into a protein complex. The intrinsic dynamics of these protein complexes can differ and thus can encode different time durations. Based on their amount and their collective dynamics within individual synapses, the Purkinje cell is able to suppress its own tonic firing rate for a specific time interval. The time memory is encoded within the effective rate constants of the biochemical reactions and altering these rates constants means storing a different time memory. The proposed mechanism is verified by a simplified mathematical model and corresponding dynamical simulations of the involved biomolecules, yielding testable experimental predictions.Author summaryHebbian plasticity is a widely accepted form of learning that can encode memories in our brain. Spike-timing dependent plasticity resulting in Long-term Potentiation or Depression of synapses has become the default mechanistic explanation behind memory formation within a neuronal population. However, recent experiments of conditional eyeblink response in Purkinje cells have challenged this point of view by showing that these mechanisms alone cannot account for time memory formation in the Purkinje cell. To explain the underlying mechanism behind this novel synaptic plasticity, we introduce a biochemical mechanism based on protein interactions occurring within a single synapse. These protein interactions and the associated effective rate constants are sufficient to encode time delays by auto-induced inhibition on a single excitatory synapse, suggesting that synapses are capable of storing more information than previously thought.

Prenatal stress (PS) can impact fetal brain structure and function and lead to higher vulnerability to neurodevelopmental and neuropsychiatric disorders. To understand how PS alters evoked and spontaneous cortical activity and intrinsic brain functional connectivity, mesoscale voltage imaging was performed in adult C57BL/6NJ mice who were exposed to an auditory stress paradigm on gestational days 12-16. PS mice demonstrated a four-fold higher basal corticosterone level, reduced amplitude of all cortical sensory-evoked responses (visual, auditory, whisker, forelimb, and hindlimb), decreased overall resting-state functional connectivity, declined network efficiency, reduced inter-module connectivity, enhanced intra-module connectivity, and altered frequency of auditory and forelimb spontaneous sensory motifs relative to control animals. In fact, for PS, the resting-state functional connectivity changes drastically towards an overall less connected structure that consists of largely disjoint but tight modules, leading to a declined network efficiency. The changes in structure also indicate that the posterior secondary motor, primary barrel, and secondary hindlimb cortices are cortical areas with higher susceptibility to dysfunction. Our findings highlight the PS modulation of brain functional connectivity that can pose offspring at risk for stress-related neuropsychiatric disorders.

Seismic hazard due to fluid invasion in hydraulic fracturing, wastewater disposal, and enhanced geothermal systems has become a concern for industry and nearby residents. One of the challenges associated with this seismic hazard is the estimation of the spatial effects of these industry operations. Based on a large set of real-world fluid-induced seismicity catalogs, it was recently found that the spatial decay of seismic activity with distance from injection wells exhibits two typical behaviors: short-range decay and long-range decay. The distinction between the two groups can be captured by the exponent in the seismicity density but the underlying origin remains unknown. Here, we introduce a novel conceptual model that not only can capture the observed frequency magnitude distribution of fluid-induced seismic events but also explains different spatial decay exponents observed. In particular, previous models of fluid-induced seismicity have assumed that the permeability and porosity field is either uniform or random and spatially uncorrelated. However, power-law scaling in the spatial frequency power spectrum of well-logs, S(k)∝1/k^β, has been observed for many different physical properties of rocks such as sonic velocity, porosity, and log(permeability). Our model takes advantage of this by introducing a spatially correlated field for porosity and permeability. Our analysis shows that increasing β can decrease the spatial decay exponent, leading to more seismic activity at larger distances from the injection site. In particular, our model explains the two different types of behavior in the spatial distribution of fluid-induced microseismic events as a consequence of different correlations in permeability.

We study reaction-diffusion systems beyond the Markovian approximation to take into account the effect of memory on the formation of spatiotemporal patterns. Using a non-Markovian Brusselator model as a paradigmatic example, we show how to use reductive perturbation to investigate the formation and stability of patterns. Focusing in detail on the Hopf instability and short-term memory, we derive the corresponding complex Ginzburg-Landau equation that governs the amplitude of the critical mode and we establish the explicit dependence of its parameters on the memory properties. Numerical solution of this memory-dependent complex Ginzburg-Landau equation as well as direct numerical simulation of the non-Markovian Brusselator model illustrates that memory changes the properties of the spatiotemporal patterns. Our results indicate that going beyond the Markovian approximation might be necessary to study the formation of spatiotemporal patterns even in systems with short-term memory. At the same time, our work opens up a new window into the control of these patterns using memory.

Observations of neurons in a resting brain and neurons in cultures often display spontaneous scale-free (SF) collective dynamics in the form of information cascades, also called ‘neuronal avalanches’. This has motivated the so called critical brain hypothesis which posits that the brain is self-tuned to a critical point or regime, separating exponentially-growing dynamics from quiescent states, to achieve optimality. Yet, how such optimality of information transmission is related to behavior and whether it persists under behavioral transitions has remained a fundamental knowledge gap. Here, we aim to tackle this challenge by studying behavioral transitions in mice using two-photon calcium imaging of the retrosplenial cortex (RSC)—an area of the brain well positioned to integrate sensory, mnemonic, and cognitive information by virtue of its strong connectivity with the hippocampus, medial prefrontal cortex, and primary sensory cortices. Our work shows that the response of the underlying neural population to behavioral transitions can vary significantly between different sub-populations such that one needs to take the structural and functional network properties of these sub-populations into account to understand the properties at the total population level. Specifically, we show that the RSC contains at least one sub-population capable of switching between two different SF regimes, indicating an intricate relationship between behavior and the optimality of neuronal response at the subgroup level. This asks for a potential reinterpretation of the emergence of self-organized criticality in neuronal systems.

One of the main challenges of modern physics is to provide a systematic understanding of systems far from equilibrium exhibiting emergent behavior. Prominent examples of such complex systems include, but are not limited to the cardiac electrical system, the brain, the power grid, social systems, material failure and earthquakes, and the climate system. Due to the technological advances over the last decade, the amount of observations and data available to characterize complex systems and their dynamics, as well as the capability to process that data, has increased substantially. The present issue discusses a cross section of the current research on complex systems, with a focus on novel experimental and data-driven approaches to complex systems that provide the necessary platform to model the behavior of such systems.

The total energy of acoustic emission (AE) events in externally stressed materials diverges when approaching macroscopic failure. Numerical and conceptual models explain this accelerated seismic release (ASR) as the approach to a critical point that coincides with ultimate failure. Here, we report ASR during soft uniaxial compression of three silica-based (SiO$_2$) nanoporous materials. Instead of a singular critical point, the distribution of AE energies is stationary and variations in the activity rate are sufficient to explain the presence of multiple periods of ASR leading to distinct brittle failure events. We propose that critical failure is suppressed in the AE statistics by dissipation and transient hardening. Some of the critical exponents estimated from the experiments are compatible with mean field models, while others are still open to interpretation in terms of the solution of frictional and fracture avalanche models., preprint, Main article: 7 pages, 3 figures. Supplementary material included in \anc folder: 6 pages, 3 figures

Neuronal avalanches have become an ubiquitous tool to describe the activity of large neuronal assemblies. The emergence of scale-free statistics with well-defined exponents has led to the belief that the brain might operate near a critical point. Yet not much is known in terms of how the different exponents arise or how robust they are. Using calcium imaging recordings of dissociated neuronal cultures we show that the exponents are not universal, and that significantly different exponents arise with different culture preparations, leading to the existence of different universality classes. Naturally developing cultures show avalanche statistics consistent with those of a mean-field branching process, however, cultures grown in the presence of folic acid metabolites appear to be in a distinct universality class with significantly different critical exponents. Given the increased synaptic density and number of feedback loops in folate reared cultures, our results suggest that network topology plays a leading role in shaping the avalanche dynamics. We also show that for both types of cultures pronounced correlations exist in the sizes of neuronal avalanches indicating size clustering, being much stronger in folate reared cultures.

The formation and stability of social hierarchies is a question of general relevance. Here, we propose a simple generalized theoretical model for establishing social hierarchy via pair-wise interactions between individuals and investigate its stability. In each interaction or fight, the probability of "winning" depends solely on the relative societal status of the participants, and the winner has a gain of status whereas there is an equal loss to the loser. The interactions are characterized by two parameters. The first parameter represents how much can be lost, and the second parameter represents the degree to which even a small difference of status can guarantee a win for the higher-status individual. Depending on the parameters, the resulting status distributions reach either a continuous unimodal form or lead to a totalitarian end state with one high-status individual and all other individuals having status approaching zero. However, we find that in the latter case long-lived intermediary distributions often exist, which can give the illusion of a stable society. As we show, our model allows us to make predictions consistent with animal interaction data and their evolution over a number of years. Moreover, by implementing a simple, but realistic rule that restricts interactions to sufficiently similar-status individuals, the stable or long-lived distributions acquire high-status structure corresponding to a distinct high-status class. Using household income as a proxy for societal status in human societies, we find agreement over their entire range from the low-to-middle-status parts to the characteristic high-status "tail". We discuss how the model provides a conceptual framework for understanding the origin of social hierarchy and the factors which lead to the preservation or deterioration of the societal structure., Comment: Added sections 4.1 and S2.A about agonistic interactions in animals, added sections 4.2.1 and S2.B regarding potential proxies for societal status in non-human animals, added references to sections 1 and 2. Main text: 34 pages, 11 figures. Supplementary appendices: 36 pages, 24 figures

Maximum entropy estimation is of broad interest for inferring properties of systems across many disciplines. Using a recently introduced technique for estimating the maximum entropy of a set of random discrete variables when conditioning on bivariate mutual informations and univariate entropies, we show how this can be used to estimate the direct network connectivity between interacting units from observed activity. As a generic example, we consider phase oscillators and show that our approach is typically superior to simply using the mutual information. In addition, we propose a nonparametric formulation of connected informations, used to test the explanatory power of a network description in general. We give an illustrative example showing how this agrees with the existing parametric formulation, and demonstrate its applicability and advantages for resting-state human brain networks, for which we also discuss its direct effective connectivity. Finally, we generalize to continuous random variables and vastly expand the types of information-theoretic quantities one can condition on. This allows us to establish significant advantages of this approach over existing ones. Not only does our method perform favorably in the undersampled regime, where existing methods fail, but it also can be dramatically less computationally expensive as the cardinality of the variables increases.

The acoustic emission activity associated with recent rock fracture experiments under different conditions has indicated that some features of event–event triggering are independent of the details of the experiment and the materials used and are often even indistinguishable from tectonic earthquakes. While the event–event triggering rates or aftershock rates behave pretty much identical for all rock fracture experiments at short times, this is not the case for later times. Here, we discuss how these differences can be a consequence of the aftershock identification method used and show that the true aftershock rates might have two distinct regimes. Specifically, tests on a modified Epidemic-Type Aftershock Sequence model show that the model rates cannot be correctly inferred at late times based on temporal information only if the activity rates or the branching ratio are high. We also discuss both the effect of the two distinct regimes in the aftershock rates and the effect of the background rate on the inter-event time distribution. Our findings should be applicable for inferring event–event triggering rates for many other types of triggering and branching processes as well.

We study triggering processes in triaxial compression experiments under a constant displacement rate on sandstone and granite samples using spatially located acoustic emission events and their focal mechanisms. We present strong evidence that event-event triggering plays an important role in the presence of large-scale or macrocopic imperfections, while such triggering is basically absent if no significant imperfections are present. In the former case, we recover all established empirical relations of aftershock seismicity including the Gutenberg-Richter relation, a modified version of the Omori-Utsu relation and the productivity relation-despite the fact that the activity is dominated by compaction-type events and triggering cascades have a swarmlike topology. For the Gutenberg-Richter relations, we find that the b value is smaller for triggered events compared to background events. Moreover, we show that triggered acoustic emission events have a focal mechanism much more similar to their associated trigger than expected by chance.

Hydraulic fracturing, a powerful completion technique used to enhance oil or gas production from impermeable strata, may trigger unintended earthquake activity. The primary basis for assessment of triggered and natural seismic hazard is the classic Gutenberg-Richter (G-R) relation, which expresses scale-independent behaviour of earthquake magnitudes. Here we use a stochastic approach to simulate and test magnitude-distance trends expressed by microseismic catalogues derived from three hydraulic fracture monitoring programmes in North America. We show that a widely observed rapid fall-off in large-magnitude events, almost universally quantified using the G-R b value, may in our case be an artefact of the strongly laminated character of the stimulated oil and gas reservoirs. We also show that, for the three reservoirs considered, mechanical bed thickness can be approximated by a lognormal distribution. For a stratabound fracture network, this leads asymptotically to a Gaussian decay for induced magnitudes. We show that the stratabound model provides a more significant correspondence with our observations. If applicable in general, this result has important implications for determining the energy balance of hydraulic fracture systems (i.e. radiated seismic energy versus injected energy) as well as hazard assessments based on the probability of occurrence of anomalous seismic events. Key words: Monitoring, Passive Method, Reservoir Geophysics.

Recent precision functional mapping of individual human brains has shown that individual brain organization is qualitatively different from group average estimates and that individuals exhibit distinct brain network topologies. How this variability affects the connectivity within individual resting-state networks remains an open question. This is particularly important since certain resting-state networks such as the default mode network (DMN) and the fronto-parietal network (FPN) play an important role in the early detection of neurophysiological diseases like Alzheimer&rsquo, s, Parkinson&rsquo, s, and attention deficit hyperactivity disorder. Using different types of similarity measures including conditional mutual information, we show here that the backbone of the functional connectivity and the direct connectivity within both the DMN and the FPN does not vary significantly between healthy individuals for the AAL brain atlas. Weaker connections do vary however, having a particularly pronounced effect on the cross-connections between DMN and FPN. Our findings suggest that the link topology of single resting-state networks is quite robust if a fixed brain atlas is used and the recordings are sufficiently long&mdash, even if the whole brain network topology between different individuals is variable.

For a system to exhibit spiral patterns one would expect its parts to behave synchronously, as in a Mexican wave. Proving the contrary, chemical oscillators have now been observed in a state comprising a spiral surrounding an asynchronous core.

Power grids sustain modern society by supplying electricity and thus their stability is a crucial factor for our civilization. The dynamic stability of a power grid is usually quantified by the probability of its nodes' recovery to phase synchronization of the alternating current it carries, in response to external perturbation. Intuitively, the stability of nodes in power grids is supposed to become more robust as the coupling strength between the nodes increases. However, we find a counterintuitive range of coupling strength values where the synchronization stability suddenly droops as the coupling strength increases, on a number of simple graph structures. Since power grids are designed to fulfill both local and long-range power demands, such simple graph structures or graphlets for local power transmission are indeed relevant in reality. We show that the observed nonmonotonic behavior is a consequence of transitions in multistability, which are related to changes in stability of the \emph{unsynchronized} states. Therefore, our findings suggest that a comprehensive understanding of changes in multistability are necessary to prevent the unexpected catastrophic instability in the building blocks of power grids.

Reconstructing the structural connectivity between interacting units from observed activity is a challenge across many different disciplines. The fundamental first step is to establish whether or to what extent the interactions between the units can be considered pairwise and, thus, can be modeled as an interaction network with simple links corresponding to pairwise interactions. In principle, this can be determined by comparing the maximum entropy given the bivariate probability distributions to the true joint entropy. In many practical cases, this is not an option since the bivariate distributions needed may not be reliably estimated or the optimization is too computationally expensive. Here we present an approach that allows one to use mutual informations as a proxy for the bivariate probability distributions. This has the advantage of being less computationally expensive and easier to estimate. We achieve this by introducing a novel entropy maximization scheme that is based on conditioning on entropies and mutual informations. This renders our approach typically superior to other methods based on linear approximations. The advantages of the proposed method are documented using oscillator networks and a resting-state human brain network as generic relevant examples.

While the existence of stable knotted and linked vortex lines has been established in many experimental and theoretical systems, their existence in oscillatory systems and systems with nonlocal coupling has remained elusive. Here, we present strong numerical evidence that stable knots and links such as trefoils and Hopf links do exist in simple, complex, and chaotic oscillatory systems if the coupling between the oscillators is neither too short ranged nor too long ranged. In this case, effective repulsive forces between vortex lines in knotted and linked structures stabilize curvature-driven shrinkage observed for single vortex rings. In contrast to real fluids and excitable media, the vortex lines correspond to scroll wave chimeras [synchronized scroll waves with spatially extended (tubelike) unsynchronized filaments], a prime example of spontaneous synchrony breaking in systems of identical oscillators. In the case of complex oscillatory systems, this leads to a novel topological superstructure combining knotted filaments and synchronization defect sheets., Comment: 5 figures, supplemental pdf (supplementary video at the publication website)

In many important systems exhibiting crackling noise --- intermittent avalanche-like relaxation response with power-law and, thus, self-similar distributed event sizes --- the "laws" for the rate of activity after large events are not consistent with the overall self-similar behavior expected on theoretical grounds. This is in particular true for the case of seismicity and a satisfying solution to this paradox has remained outstanding. Here, we propose a generalized description of the aftershock rates which is both self-similar and consistent with all other known self-similar features. Comparing our theoretical predictions with high resolution earthquake data from Southern California we find excellent agreement, providing in particular clear evidence for a unified description of aftershocks and foreshocks. This may offer an improved way of time-dependent seismic hazard assessment and earthquake forecasting.

For induced microseismicity associated with hydraulic fracturing, the frequency-magnitude distribution is typically characterized by a falloff with increasing magnitude that is significantly faster than for seismicity along active fault systems. This characteristic may arise from a break in scale invariance, possibly due to mechanical layering that typifies fine-grained sedimentary rocks in many shale gas and tight oil reservoirs. The latter would imply the presence of spatio-temporal magnitude correlations. Using three microseismic catalogs for well stimulations in widely separated locations with varying hydraulic-fracturing methods, we show that events with similar magnitudes indeed tend to cluster in space and time. In addition, we show that the inter-event time distribution can be described by a universal functional form characterized by two power-laws. One exponent can be related to the presence of inter-event triggering as in aftershock sequences and is a consequence of the Omori-Utsu law. The other one is a reflection of the intrinsic spatial variation in the microseismic response rates. Taken together, these features are indicative of non-trivial spatio-temporal clustering of induced microseismicity and, hence, of direct relevance for time-dependent seismic hazard assessment.

The decay of the aftershock density with distance plays an important role in the discussion of the dominant underlying cause of earthquake triggering. Here, we provide evidence that its form is more complicated than typically assumed and that in particular a transition in the power law decay occurs at length scales comparable to the thickness of the crust. This is supported by an analysis of a very recent high-resolution catalog for Southern California (SC) and surrogate catalogs generated by the Epidemic-Type Aftershock Sequence (ETAS) model, which take into account inhomogeneous background activity, short-term aftershock incompleteness, anisotropic triggering, and variations in the observational magnitude threshold. Our findings indicate specifically that the asymptotic decay in the aftershock density with distance is characterized by an exponent larger than 2, which is much bigger than the observed exponent of approximately 1.35 observed for shorter distances ranging from the main shock rupture length up to a length scale comparable to the thickness of the crust. This has also important consequences for time-dependent seismic hazard assessment based on the ETAS model.