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Open accessJournal ArticleDOI: 10.3389/FNCIR.2021.614268

Not One, but Many Critical States: A Dynamical Systems Perspective.

02 Mar 2021-Frontiers in Neural Circuits (Frontiers Media SA)-Vol. 15, pp 614268-614268
Abstract: The past decade has seen growing support for the critical brain hypothesis, i.e., the possibility that the brain could operate at or very near a critical state between two different dynamical regimes. Such critical states are well-studied in different disciplines, therefore there is potential for a continued transfer of knowledge. Here, I revisit foundations of bifurcation theory, the mathematical theory of transitions. While the mathematics is well-known it's transfer to neural dynamics leads to new insights and hypothesis.

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Journal ArticleDOI: 10.1152/AJPCELL.00413.2020
Abstract: A patterned spread of proteinopathy represents a common characteristic of many neurodegenerative diseases. In Parkinson’s disease (PD), misfolded forms of α-synuclein proteins accumulate in hallmar...

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Topics: Alpha-synuclein (53%)

1 Citations


Open accessPosted Content
Abstract: Topological signals defined on nodes, links and higher dimensional simplices define the dynamical state of a network or of a simplicial complex. As such, topological signals are attracting increasing attention in network theory, dynamical systems, signal processing and machine learning. Topological signals defined on the nodes are typically studied in network dynamics, while topological signals defined on links are much less explored. Here we investigate topological synchronization describing locally coupled topological signals defined on the nodes and on the links of a network. The dynamics of signals defined on the nodes is affected by a phase lag depending on the dynamical state of nearby links and vice versa, the dynamics of topological signals defined on the links is affected by a phase lag depending on the dynamical state of nearby nodes. We show that topological synchronization on a fully connected network is explosive and leads to a discontinuous forward transition and a continuous backward transition. The analytical investigation of the phase diagram provides an analytical expression for the critical threshold of the discontinuous explosive synchronization. The model also displays an exotic coherent synchronized phase, also called rhythmic phase, characterized by having non-stationary order parameters which can shed light on topological mechanisms for the emergence of brain rhythms.

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1 Citations


Open accessPosted Content
Abstract: Living systems such as neuronal networks and animal groups process information about their environment via the dynamics of interacting units. These can transition between distinct macroscopic behaviors. Near such a transition (or critical point) collective computation is generally thought to be optimized, due to the associated maximal sensitivity to perturbations and fast dissemination of information. For biological systems, however, optimality depends on environmental context, making the flexible, context-dependent adoption of different distances to a critical point potentially more beneficial than its unique properties. Here, studying escape waves in schooling fish at two levels of perceived environmental risk, we investigate a) if and how distance to criticality is regulated in response to environmental changes and b) how the individual level benefits derived from special properties of the critical point compare to those achieved via regulation of the group's distance to it. We find that the observed fish schools are subcritical (not maximally responsive and sensitive to environmental cues), but decrease their distance to criticality with increased perceived risk. Considering an individual's hypothetical costs of two detection error types, we find that optimal distance to criticality depends on the riskiness and noisiness of the environment, which may explain the observed behavior. Our results highlight the benefit of evaluating biological consequences of different distances to criticality for individuals within animal collectives. This provides insights into the adaptive function of a collective system and motivates future questions about the evolutionary forces that brought the system to make this particular trade-off.

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Open accessPosted ContentDOI: 10.1101/2021.10.14.464473
Dominic R. W. Burrows1, Giovanni Diana1, B. Pimpel2, B. Pimpel3  +8 moreInstitutions (5)
16 Oct 2021-bioRxiv
Abstract: Excitation-inhibition (EI) balance may be required for the organisation of brain dynamics to a phase transition, criticality, which confers computational benefits. Brain pathology associated with EI imbalance may therefore occur due to a deviation from criticality. However, evidence linking critical dynamics with EI imbalance-induced pathology is lacking. Here, we studied the effect of EI imbalance-induced epileptic seizures on brain dynamics, using in vivo whole-brain 2-photon imaging of GCaMP6s larval zebrafish at single-neuron resolution. We demonstrate the importance of EI balance for criticality, with EI imbalance causing a loss of whole-brain critical statistics. Using network models we show that a reorganisation of network topology drives this loss of criticality. Seizure dynamics match theoretical predictions for networks driven away from a phase transition into disorder, with the emergence of chaos and a loss of network-mediated separation, dynamic range and metastability. These results demonstrate that EI imbalance drives a pathological deviation from criticality.

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35 results found


Open accessJournal ArticleDOI: 10.1523/JNEUROSCI.21-04-01370.2001
Abstract: The human brain spontaneously generates neural oscillations with a large variability in frequency, amplitude, duration, and recurrence. Little, however, is known about the long-term spatiotemporal structure of the complex patterns of ongoing activity. A central unresolved issue is whether fluctuations in oscillatory activity reflect a memory of the dynamics of the system for more than a few seconds. We investigated the temporal correlations of network oscillations in the normal human brain at time scales ranging from a few seconds to several minutes. Ongoing activity during eyes-open and eyes-closed conditions was recorded with simultaneous magnetoencephalography and electroencephalography. Here we show that amplitude fluctuations of 10 and 20 Hz oscillations are correlated over thousands of oscillation cycles. Our analyses also indicated that these amplitude fluctuations obey power-law scaling behavior. The scaling exponents were highly invariant across subjects. We propose that the large variability, the long-range correlations, and the power-law scaling behavior of spontaneous oscillations find a unifying explanation within the theory of self-organized criticality, which offers a general mechanism for the emergence of correlations and complex dynamics in stochastic multiunit systems. The demonstrated scaling laws pose novel quantitative constraints on computational models of network oscillations. We argue that critical-state dynamics of spontaneous oscillations may lend neural networks capable of quick reorganization during processing demands.

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932 Citations


Open accessJournal ArticleDOI: 10.1098/RSIF.2007.1229
Abstract: Adaptive networks appear in many biological applications. They combine topological evolution of the network with dynamics in the network nodes. Recently, the dynamics of adaptive networks has been investigated in a number of parallel studies from different fields, ranging from genomics to game theory. Here we review these recent developments and show that they can be viewed from a unique angle. We demonstrate that all these studies are characterized by common themes, most prominently: complex dynamics and robust topological self-organization based on simple local rules.

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Topics: Network dynamics (58%), Complex dynamics (52%)

874 Citations


Open accessJournal ArticleDOI: 10.1038/NPHYS1803
Dante R. Chialvo1, Dante R. Chialvo2Institutions (2)
01 Oct 2010-Nature Physics
Abstract: Is the brain on the edge of criticality? Understanding the inner workings of the brain is a task made difficult by the number of elements involved: a hundred billion neurons and a hundred trillion synapses. Viewing the brain in terms of collective dynamics is one approach now yielding some insight.

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859 Citations


Open accessJournal ArticleDOI: 10.1523/JNEUROSCI.0540-04.2004
John M. Beggs1, Dietmar PlenzInstitutions (1)
Abstract: A major goal of neuroscience is to elucidate mechanisms of cortical information processing and storage. Previous work from our laboratory (Beggs and Plenz, 2003) revealed that propagation of local field potentials (LFPs) in cortical circuits could be described by the same equations that govern avalanches. Whereas modeling studies suggested that these “neuronal avalanches” were optimal for information transmission, it was not clear what role they could play in information storage. Work from numerous other laboratories has shown that cortical structures can generate reproducible spatiotemporal patterns of activity that could be used as a substrate for memory. Here, we show that although neuronal avalanches lasted only a few milliseconds, their spatiotemporal patterns were also stable and significantly repeatable even many hours later. To investigate these issues, we cultured coronal slices of rat cortex for 4 weeks on 60-channel microelectrode arrays and recorded spontaneous extracellular LFPs continuously for 10 hr. Using correlation-based clustering and a global contrast function, we found that each cortical culture spontaneously produced 4736 ± 2769 (mean ± SD) neuronal avalanches per hour that clustered into 30 ± 14 statistically significant families of spatiotemporal patterns. In 10 hr of recording, over 98% of the mutual information shared by these avalanche patterns were retained. Additionally, jittering analysis revealed that the correlations between avalanches were temporally precise to within ±4 msec. The long-term stability, diversity, and temporal precision of these avalanches indicate that they fulfill many of the requirements expected of a substrate for memory and suggest that they play a central role in both information transmission and storage within cortical networks.

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Topics: Local field potential (51%)

562 Citations


Journal ArticleDOI: 10.1038/381610A0
R. C. deCharms1, Michael M. Merzenich1Institutions (1)
13 Jun 1996-Nature
Abstract: Cortical population coding could in principle rely on either the mean rate of neuronal action potentials, or the relative timing of action potentials, or both. When a single sensory stimulus drives many neurons to fire at elevated rates, the spikes of these neurons become tightly synchronized, which could be involved in 'binding' together individual firing-rate feature representations into a unified object percept. Here we demonstrate that the relative timing of cortical action potentials can signal stimulus features themselves, a function even more basic than feature grouping. Populations of neurons in the primary auditory cortex can coordinate the relative timing of their action potentials such that spikes occur closer together in time during continuous stimuli. In this way cortical neurons can signal stimuli even when their firing rates do not change. Population coding based on relative spike timing can systemically signal stimulus features, it is topographically mapped, and it follows the stimulus time course even where mean firing rate does not.

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Topics: Neural coding (61%), Stimulus (physiology) (56%), Auditory cortex (54%) ... read more

519 Citations