Existence of multiple transitions of the critical state due to anesthetics.

Scale-free statistics of coordinated neuronal activity, suggesting a universal operating mechanism across spatio-temporal scales, have been proposed as a necessary condition of healthy resting-state brain activity. Recent studies have focused on anesthetic agents to induce distinct neural states in which consciousness is altered to understand the importance of critical dynamics. However, variation in experimental techniques, species, and anesthetics, have made comparisons across studies difficult. Here we conduct a survey of several common anesthetics (isoflurane, pentobarbital, ketamine) at multiple dosages, using calcium wide-field optical imaging of the mouse cortex. We show that while low-dose anesthesia largely preserves scale-free statistics, surgical plane anesthesia induces multiple dynamical modes, most of which do not maintain critical avalanche dynamics. Our findings indicate multiple pathways away from default critical dynamics associated with quiet wakefulness, not only reflecting differences between these common anesthetics but also showing significant variations in individual responses. This is suggestive of a non-trivial relationship between criticality and the underlying state of the subject.

Spatial-Temporal Analysis of Neural Desynchronization in Sleeplike States Reveals Critical Dynamics.

Sleep is characterized by nonrapid eye movement sleep, originating from widespread neuronal synchrony, and rapid eye movement sleep, with neuronal desynchronization akin to waking behavior. While these were thought to be global brain states, recent research suggests otherwise. Using time-frequency analysis of mesoscopic voltage-sensitive dye recordings of mice in a urethane-anesthetized model of sleep, we find transient neural desynchronization occurring heterogeneously across the cortex within a background of synchronized neural activity, in a manner reminiscent of a critical spreading process and indicative of an "edge-of-synchronization" phase transition.

Non-trivial relationship between behavioral avalanches and internal neuronal dynamics in a recurrent neural network.

Neuronal activity gives rise to behavior, and behavior influences neuronal dynamics, in a closed-loop control system. Is it possible then, to find a relationship between the statistical properties of behavior and neuronal dynamics? Measurements of neuronal activity and behavior have suggested a direct relationship between scale-free neuronal and behavioral dynamics. Yet, these studies captured only local dynamics in brain sub-networks. Here, we investigate the relationship between internal dynamics and output statistics in a mathematical model system where we have access to the dynamics of all network units. We train a recurrent neural network (RNN), initialized in a high-dimensional chaotic state, to sustain behavioral states for durations following a power-law distribution as observed experimentally. Changes in network connectivity due to training affect the internal dynamics of neuronal firings, leading to neuronal avalanche size distributions approximating power-laws over some ranges. Yet, randomizing the changes in network connectivity can leave these power-law features largely unaltered. Specifically, whereas neuronal avalanche duration distributions show some variations between RNNs with trained and randomized decoders, neuronal avalanche size distributions are invariant, in the total population and in output-correlated sub-populations. This is true independent of whether the randomized decoders preserve power-law distributed behavioral dynamics. This demonstrates that a one-to-one correspondence between the considered statistical features of behavior and neuronal dynamics cannot be established and their relationship is non-trivial. Our findings also indicate that statistical properties of the intrinsic dynamics may be preserved, even as the internal state responsible for generating the desired output dynamics is perturbed.

Functional brain networks in Developmental Topographical Disorientation.

Despite a decade-long study on Developmental Topographical Disorientation, the underlying mechanism behind this neurological condition remains unknown. This lifelong selective inability in orientation, which causes these individuals to get lost even in familiar surroundings, is present in the absence of any other neurological disorder or acquired brain damage. Herein, we report an analysis of the functional brain network of individuals with Developmental Topographical Disorientation ($n = 19$) compared against that of healthy controls ($n = 21$), all of whom underwent resting-state functional magnetic resonance imaging, to identify if and how their underlying functional brain network is altered. While the established resting-state networks (RSNs) are confirmed in both groups, there is, on average, a greater connectivity and connectivity strength, in addition to increased global and local efficiency in the overall functional network of the Developmental Topographical Disorientation group. In particular, there is an enhanced connectivity between some RSNs facilitated through indirect functional paths. We identify a handful of nodes that encode part of these differences. Overall, our findings provide strong evidence that the brain networks of individuals suffering from Developmental Topographical Disorientation are modified by compensatory mechanisms, which might open the door for new diagnostic tools.

MINNO: An Open Source Software for Refining Metabolic Networks and Investigating Complex Network Activity Using Empirical Metabolomics Data.

Metabolomics is a powerful tool for uncovering biochemical diversity in a wide range of organisms. Metabolic network modeling is commonly used to frame metabolomics data in the context of a broader biological system. However, network modeling of poorly characterized nonmodel organisms remains challenging due to gene homology mismatches which lead to network architecture errors. To address this, we developed the Metabolic Interactive Nodular Network for Omics (MINNO), a web-based mapping tool that uses empirical metabolomics data to refine metabolic networks. MINNO allows users to create, modify, and interact with metabolic pathway visualizations for thousands of organisms, in both individual and multispecies contexts. Herein, we illustrate the use of MINNO in elucidating the metabolic networks of understudied species, such as those of the Borrelia genus, which cause Lyme and relapsing fever diseases. Using a hybrid genomics-metabolomics modeling approach, we constructed species-specific metabolic networks for threeBorrelia species. Using these empirically refined networks, we were able to metabolically differentiate these species via their nucleotide metabolism, which cannot be predicted from genomic networks. Additionally, using MINNO, we identified 18 missing reactions from the KEGG database, of which nine were supported by the primary literature. These examples illustrate the use of metabolomics for the empirical refining of genetically constructed networks and show how MINNO can be used to study nonmodel organisms.

Changes in functional connectivity preserve scale-free neuronal and behavioral dynamics.

Does the brain optimize itself for storage and transmission of information, and if so, how? The critical brain hypothesis is based in statistical physics and posits that the brain self-tunes its dynamics to a critical point or regime to maximize the repertoire of neuronal responses. Yet, the robustness of this regime, especially with respect to changes in the functional connectivity, remains an unsolved fundamental challenge. Here, we show that both scale-free neuronal dynamics and self-similar features of behavioral dynamics persist following significant changes in functional connectivity. Specifically, we find that the psychedelic compound ibogaine that is associated with an altered state of consciousness fundamentally alters the functional connectivity in the retrosplenial cortex of mice. Yet, the scale-free statistics of movement and of neuronal avalanches among behaviorally related neurons remain largely unaltered. This indicates that the propagation of information within biological neural networks is robust to changes in functional organization of subpopulations of neurons, opening up a new perspective on how the adaptive nature of functional networks may lead to optimality of information transmission in the brain.

Physics-informed deep learning to forecast [Formula: see text] during hydraulic fracturing.

Short-term forecasting of estimated maximum magnitude ([Formula: see text]) is crucial to mitigate risks of induced seismicity during fluid stimulation. Most previous methods require real-time injection data, which are not always available. This study proposes two deep learning (DL) approaches, along with two data-partitioning methods, that rely solely on preceding patterns of seismicity. The first approach forecasts [Formula: see text] directly using DL; the second incorporates physical constraints by using DL to forecast seismicity rate, which is then used to estimate [Formula: see text]. These approaches are tested using a hydraulic-fracture monitoring dataset from western Canada. We find that direct DL learns from previous seismicity patterns to provide an accurate forecast, albeit with a time lag that limits its practical utility. The physics-informed approach accurately forecasts changes in seismicity rate, but sometimes under- (or over-) estimates [Formula: see text]. We propose that significant exceedance of [Formula: see text] may herald the onset of runaway fault rupture.

Large-scale heterogeneities can alter the characteristics of compressive failure and accelerated seismic release.

Externally stressed brittle rocks fail once the stress is sufficiently high. This failure is typically preceded by a pronounced increase in the total energy of acoustic emission (AE) events, the so-called accelerated seismic release. Yet, other characteristics of approaching the failure point such as the presence or absence of variations in the AE size distribution and, similarly, whether the failure point can be interpreted as a critical point in a statistical physics sense differs across experiments. Here, we show that large-scale stress heterogeneities induced by a notch fundamentally change the characteristics of the failure point in triaxial compression experiments under a constant displacement rate on Westerly granite samples. Specifically, we observe accelerated seismic release without a critical point and no change in power-law exponent ε of the AE size distribution. This is in contrast to intact samples, which exhibit a significant decrease in ε before failure. Our findings imply that the presence or absence of large-scale heterogeneities play a significant role in our ability to predict compressive failure in rock.

Metabolic Interactive Nodular Network for Omics (MINNO): Refining and investigating metabolic networks based on empirical metabolomics data.

Metabolomics is a powerful tool for uncovering biochemical diversity in a wide range of organisms, and metabolic network modeling is commonly used to frame results in the context of a broader homeostatic system. However, network modeling of poorly characterized, non-model organisms remains challenging due to gene homology mismatches. To address this challenge, we developed Metabolic Interactive Nodular Network for Omics (MINNO), a web-based mapping tool that takes in empirical metabolomics data to refine metabolic networks for both model and unusual organisms. MINNO allows users to create and modify interactive metabolic pathway visualizations for thousands of organisms, in both individual and multi-species contexts. Herein, we demonstrate an important application of MINNO in elucidating the metabolic networks of understudied species, such as those of the Borrelia genus, which cause Lyme disease and relapsing fever. Using a hybrid genomics-metabolomics modeling approach, we constructed species-specific metabolic networks for three Borrelia species. Using these empirically refined networks, we were able to metabolically differentiate these genetically similar species via their nucleotide and nicotinate metabolic pathways that cannot be predicted from genomic networks. These examples illustrate the use of metabolomics for the empirical refining of genetically constructed networks and show how MINNO can be used to study non-model organisms.

Global excitability and network structure in the human brain.

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 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.

Chimera patterns in conservative Hamiltonian systems and Bose-Einstein condensates of ultracold atoms.

Experimental realizations of chimera patterns, characterized by coexisting regions of phase coherence and incoherence, have so far been achieved for non-conservative systems with dissipation and exclusively in classical settings. The possibility of observing chimera patterns in quantum systems has rarely been studied and it remains an open question if chimera patterns can exist in closed, or conservative quantum systems. Here, we tackle these challenges by first proposing a conservative Hamiltonian system with nonlocal hopping, where the energy is well-defined and conserved. We show explicitly that such a system can exhibit chimera patterns. Then we propose a physical mechanism for the nonlocal hopping by using an additional mediating channel. This leads us to propose a possible experimentally realizable quantum system based on a two-component Bose-Einstein condensate (BEC) with a spin-dependent optical lattice, where an untrapped component serves as the matter-wave mediating field. In this BEC system, nonlocal spatial hopping over tens of lattice sites can be achieved and simulations suggest that chimera patterns should be observable in certain parameter regimes.

Short-term forecasting of Mmax during hydraulic fracturing.

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.

Sheared granular matter and the empirical relations of 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.

Quasistatic kinetic avalanches and self-organized criticality in deviatorically loaded granular media.

The behavior of granular media under quasistatic 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 nonuniqueness and the nonmonotony 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 nonuniversal 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.

Prenatal stress dysregulates resting-state functional connectivity and sensory motifs.

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.

A biochemical mechanism for time-encoding memory formation within individual synapses of Purkinje cells.

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 conditional and unconditional training stimuli. 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) 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 mechanism tries to answer key aspects of the "Coding problem" of Neuroscience by focusing 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, Protein Phosphatase 1 and other associated biomolecules-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 dynamics of the biochemical reactions and altering these dynamics means storing a different time memory. The proposed mechanism is verified by both a minimal and a more comprehensive mathematical model of the conditional response behavior of the Purkinje cell and corresponding dynamical simulations of the involved biomolecules, yielding testable experimental predictions.

Pattern formation in reaction-diffusion systems in the presence of non-Markovian diffusion.

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.

Self-organization and time-stability of social hierarchies.

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.

Experimental Evidence of Accelerated Seismic Release without Critical Failure in Acoustic Emissions of Compressed Nanoporous Materials.

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 mechanisms of 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.

Universal avalanche statistics and triggering close to failure in a mean-field model of rheological fracture.

The hypothesis of critical failure relates the presence of an ultimate stability point in the structural constitutive equation of materials to a divergence of characteristic scales in the microscopic dynamics responsible for deformation. Avalanche models involving critical failure have determined common universality classes for stick-slip processes and fracture. However, not all empirical failure processes exhibit the trademarks of criticality. The rheological properties of materials introduce dissipation, usually reproduced in conceptual models as a hardening of the coarse grained elements of the system. Here, we investigate the effects of transient hardening on (i) the activity rate and (ii) the statistical properties of avalanches. We find the explicit representation of transient hardening in the presence of generalized viscoelasticity and solve the corresponding mean-field model of fracture. In the quasistatic limit, the accelerated energy release is invariant with respect to rheology and the avalanche propagation can be reinterpreted in terms of a stochastic counting process. A single universality class can be defined from such analogy, and all statistical properties depend only on the distance to criticality. We also prove that interevent correlations emerge due to the hardening-even in the quasistatic limit-that can be interpreted as "aftershocks" and "foreshocks."