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Souza EMK, Almeida GMA. Binary Apollonian networks. Phys Rev E 2023; 107:024305. [PMID: 36932609 DOI: 10.1103/physreve.107.024305] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2022] [Accepted: 01/31/2023] [Indexed: 02/12/2023]
Abstract
There is a well-known relationship between the binary Pascal's triangle and the Sierpinski triangle, in which the latter is obtained from the former by successive modulo 2 additions starting from a corner. Inspired by that, we define a binary Apollonian network and obtain two structures featuring a kind of dendritic growth. They are found to inherit the small-world and scale-free properties from the original network but display no clustering. Other key network properties are explored as well. Our results reveal that the structure contained in the Apollonian network may be employed to model an even wider class of real-world systems.
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Affiliation(s)
- Eduardo M K Souza
- Departamento de Física, Universidade Federal de Sergipe, 49100-000 São Cristóvão, Sergipe, Brazil
| | - Guilherme M A Almeida
- Instituto de Física, Universidade Federal de Alagoas, 57072-900 Maceió, Alagoas, Brazil
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2
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Critical behaviour of the stochastic Wilson-Cowan model. PLoS Comput Biol 2021; 17:e1008884. [PMID: 34460811 PMCID: PMC8432901 DOI: 10.1371/journal.pcbi.1008884] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2021] [Revised: 09/10/2021] [Accepted: 07/31/2021] [Indexed: 11/19/2022] Open
Abstract
Spontaneous brain activity is characterized by bursts and avalanche-like dynamics, with scale-free features typical of critical behaviour. The stochastic version of the celebrated Wilson-Cowan model has been widely studied as a system of spiking neurons reproducing non-trivial features of the neural activity, from avalanche dynamics to oscillatory behaviours. However, to what extent such phenomena are related to the presence of a genuine critical point remains elusive. Here we address this central issue, providing analytical results in the linear approximation and extensive numerical analysis. In particular, we present results supporting the existence of a bona fide critical point, where a second-order-like phase transition occurs, characterized by scale-free avalanche dynamics, scaling with the system size and a diverging relaxation time-scale. Moreover, our study shows that the observed critical behaviour falls within the universality class of the mean-field branching process, where the exponents of the avalanche size and duration distributions are, respectively, 3/2 and 2. We also provide an accurate analysis of the system behaviour as a function of the total number of neurons, focusing on the time correlation functions of the firing rate in a wide range of the parameter space.
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3
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Rahimi-Majd M, Seifi MA, de Arcangelis L, Najafi MN. Role of anaxonic local neurons in the crossover to continuously varying exponents for avalanche activity. Phys Rev E 2021; 103:042402. [PMID: 34005924 DOI: 10.1103/physreve.103.042402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2020] [Accepted: 03/19/2021] [Indexed: 11/07/2022]
Abstract
Local anaxonic neurons with graded potential release are important ingredients of nervous systems, present in the olfactory bulb system of mammalians and in the human visual system, as well as in arthropods and nematodes. We develop a neuronal network model including both axonic and anaxonic neurons and monitor the activity tuned by the following parameters: the decay length of the graded potential in local neurons, the fraction of local neurons, the largest eigenvalue of the adjacency matrix, and the range of connections of the local neurons. Tuning the fraction of local neurons, we derive the phase diagram including two transition lines: a critical line separating subcritical and supercritical regions, characterized by power-law distributions of avalanche sizes and durations, and a bifurcation line. We find that the overall behavior of the system is controlled by a parameter tuning the relevance of local neuron transmission with respect to the axonal one. The statistical properties of spontaneous activity are affected by local neurons at large fractions and on the condition that the graded potential transmission dominates the axonal one. In this case the scaling properties of spontaneous activity exhibit continuously varying exponents, rather than the mean-field branching model universality class.
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Affiliation(s)
- M Rahimi-Majd
- Department of Physics, Shahid Beheshti University, 1983969411, Tehran, Iran
| | - M A Seifi
- Department of Physics, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran
| | - L de Arcangelis
- Department of Engineering, University of Campania Luigi Vanvitelli, 81031 Aversa (CE), Italy
| | - M N Najafi
- Department of Physics, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran
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4
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Heiney K, Huse Ramstad O, Fiskum V, Christiansen N, Sandvig A, Nichele S, Sandvig I. Criticality, Connectivity, and Neural Disorder: A Multifaceted Approach to Neural Computation. Front Comput Neurosci 2021; 15:611183. [PMID: 33643017 PMCID: PMC7902700 DOI: 10.3389/fncom.2021.611183] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2020] [Accepted: 01/18/2021] [Indexed: 01/03/2023] Open
Abstract
It has been hypothesized that the brain optimizes its capacity for computation by self-organizing to a critical point. The dynamical state of criticality is achieved by striking a balance such that activity can effectively spread through the network without overwhelming it and is commonly identified in neuronal networks by observing the behavior of cascades of network activity termed "neuronal avalanches." The dynamic activity that occurs in neuronal networks is closely intertwined with how the elements of the network are connected and how they influence each other's functional activity. In this review, we highlight how studying criticality with a broad perspective that integrates concepts from physics, experimental and theoretical neuroscience, and computer science can provide a greater understanding of the mechanisms that drive networks to criticality and how their disruption may manifest in different disorders. First, integrating graph theory into experimental studies on criticality, as is becoming more common in theoretical and modeling studies, would provide insight into the kinds of network structures that support criticality in networks of biological neurons. Furthermore, plasticity mechanisms play a crucial role in shaping these neural structures, both in terms of homeostatic maintenance and learning. Both network structures and plasticity have been studied fairly extensively in theoretical models, but much work remains to bridge the gap between theoretical and experimental findings. Finally, information theoretical approaches can tie in more concrete evidence of a network's computational capabilities. Approaching neural dynamics with all these facets in mind has the potential to provide a greater understanding of what goes wrong in neural disorders. Criticality analysis therefore holds potential to identify disruptions to healthy dynamics, granted that robust methods and approaches are considered.
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Affiliation(s)
- Kristine Heiney
- Department of Computer Science, Oslo Metropolitan University, Oslo, Norway
- Department of Computer Science, Norwegian University of Science and Technology (NTNU), Trondheim, Norway
| | - Ola Huse Ramstad
- Department of Neuromedicine and Movement Science, Norwegian University of Science and Technology (NTNU), Trondheim, Norway
| | - Vegard Fiskum
- Department of Neuromedicine and Movement Science, Norwegian University of Science and Technology (NTNU), Trondheim, Norway
| | - Nicholas Christiansen
- Department of Neuromedicine and Movement Science, Norwegian University of Science and Technology (NTNU), Trondheim, Norway
| | - Axel Sandvig
- Department of Neuromedicine and Movement Science, Norwegian University of Science and Technology (NTNU), Trondheim, Norway
- Department of Clinical Neuroscience, Umeå University Hospital, Umeå, Sweden
- Department of Neurology, St. Olav's Hospital, Trondheim, Norway
| | - Stefano Nichele
- Department of Computer Science, Oslo Metropolitan University, Oslo, Norway
- Department of Holistic Systems, Simula Metropolitan, Oslo, Norway
| | - Ioanna Sandvig
- Department of Neuromedicine and Movement Science, Norwegian University of Science and Technology (NTNU), Trondheim, Norway
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5
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Carroll J, Warren A, Täuber UC. Effects of inhibitory and excitatory neurons on the dynamics and control of avalanching neural networks. Phys Rev E 2019; 99:052407. [PMID: 31212542 DOI: 10.1103/physreve.99.052407] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2018] [Indexed: 06/09/2023]
Abstract
The statistical analysis of the collective neural activity known as avalanches provides insight into the proper behavior of brains across many species. We consider a neural network model based on the work of Lombardi, Herrmann, De Arcangelis et al. that captures the relevant dynamics of neural avalanches, and we show how tuning the fraction of inhibitory neurons in this model alters the connectivity of the network over time, removes exponential cut-offs present in the distributions of avalanche size and duration, and transitions the power spectral density of the network into an "epileptic" regime. We propose that the brain operates away from this power-law regime of low inhibitory fraction to protect itself from the dominating avalanches present in these extended distributions. We present control strategies that curtail these power-law distributions through either random or, more effectively, targeted disabling of excitatory neurons.
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Affiliation(s)
- Jacob Carroll
- Department of Physics (MC 0435) and Center for Soft Matter and Biological Physics, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Ada Warren
- Department of Physics (MC 0435) and Center for Soft Matter and Biological Physics, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Uwe C Täuber
- Department of Physics (MC 0435) and Center for Soft Matter and Biological Physics, Virginia Tech, Blacksburg, Virginia 24061, USA
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6
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Kinouchi O, Brochini L, Costa AA, Campos JGF, Copelli M. Stochastic oscillations and dragon king avalanches in self-organized quasi-critical systems. Sci Rep 2019; 9:3874. [PMID: 30846773 PMCID: PMC6405991 DOI: 10.1038/s41598-019-40473-1] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2018] [Accepted: 01/28/2019] [Indexed: 12/04/2022] Open
Abstract
In the last decade, several models with network adaptive mechanisms (link deletion-creation, dynamic synapses, dynamic gains) have been proposed as examples of self-organized criticality (SOC) to explain neuronal avalanches. However, all these systems present stochastic oscillations hovering around the critical region that are incompatible with standard SOC. Here we make a linear stability analysis of the mean field fixed points of two self-organized quasi-critical systems: a fully connected network of discrete time stochastic spiking neurons with firing rate adaptation produced by dynamic neuronal gains and an excitable cellular automata with depressing synapses. We find that the fixed point corresponds to a stable focus that loses stability at criticality. We argue that when this focus is close to become indifferent, demographic noise can elicit stochastic oscillations that frequently fall into the absorbing state. This mechanism interrupts the oscillations, producing both power law avalanches and dragon king events, which appear as bands of synchronized firings in raster plots. Our approach differs from standard SOC models in that it predicts the coexistence of these different types of neuronal activity.
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Affiliation(s)
- Osame Kinouchi
- Universidade de São Paulo, Departamento de Física-FFCLRP, Ribeirão Preto, SP, Brazil.
| | - Ludmila Brochini
- Universidade de São Paulo, Instituto de Matemática e Estatística, São Paulo, SP, Brazil
| | - Ariadne A Costa
- Universidade Federal de Goiás, Unidade Acadêmica Especial de Ciências Exatas, Jataí, GO, Brazil
| | | | - Mauro Copelli
- Universidade de São Paulo, Departamento de Física-FFCLRP, Ribeirão Preto, SP, Brazil.,Universidade Federal de Pernambuco, Departamento de Física, Recife, PE, Brazil
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7
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Self-Organized Supercriticality and Oscillations in Networks of Stochastic Spiking Neurons. ENTROPY 2017. [DOI: 10.3390/e19080399] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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8
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Michiels van Kessenich L, de Arcangelis L, Herrmann HJ. Synaptic plasticity and neuronal refractory time cause scaling behaviour of neuronal avalanches. Sci Rep 2016; 6:32071. [PMID: 27534901 PMCID: PMC4989193 DOI: 10.1038/srep32071] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2016] [Accepted: 08/02/2016] [Indexed: 11/09/2022] Open
Abstract
Neuronal avalanches measured in vitro and in vivo in different cortical networks consistently exhibit power law behaviour for the size and duration distributions with exponents typical for a mean field self-organized branching process. These exponents are also recovered in neuronal network simulations implementing various neuronal dynamics on different network topologies. They can therefore be considered a very robust feature of spontaneous neuronal activity. Interestingly, this scaling behaviour is also observed on regular lattices in finite dimensions, which raises the question about the origin of the mean field behavior observed experimentally. In this study we provide an answer to this open question by investigating the effect of activity dependent plasticity in combination with the neuronal refractory time in a neuronal network. Results show that the refractory time hinders backward avalanches forcing a directed propagation. Hebbian plastic adaptation plays the role of sculpting these directed avalanche patterns into the topology of the network slowly changing it into a branched structure where loops are marginal.
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Affiliation(s)
- L Michiels van Kessenich
- ETH Zürich, Computational Physics for Engineering Materials, IfB, Wolfgang-Pauli-Strasse 27, CH-8093 Zürich, Switzerland
| | - L de Arcangelis
- Dept. of Industrial and Information Engineering, Second University of Naples, Aversa (CE), Italy.,INFN sez. Naples, Gr. Coll. Salerno (Italy)
| | - H J Herrmann
- ETH Zürich, Computational Physics for Engineering Materials, IfB, Wolfgang-Pauli-Strasse 27, CH-8093 Zürich, Switzerland
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9
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Harris NG, Verley DR, Gutman BA, Thompson PM, Yeh HJ, Brown JA. Disconnection and hyper-connectivity underlie reorganization after TBI: A rodent functional connectomic analysis. Exp Neurol 2016; 277:124-138. [PMID: 26730520 PMCID: PMC4761291 DOI: 10.1016/j.expneurol.2015.12.020] [Citation(s) in RCA: 65] [Impact Index Per Article: 8.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2015] [Revised: 12/01/2015] [Accepted: 12/22/2015] [Indexed: 10/22/2022]
Abstract
While past neuroimaging methods have contributed greatly to our understanding of brain function after traumatic brain injury (TBI), resting state functional MRI (rsfMRI) connectivity methods have more recently provided a far more unbiased approach with which to monitor brain circuitry compared to task-based approaches. However, current knowledge on the physiologic underpinnings of the correlated blood oxygen level dependent signal, and how changes in functional connectivity relate to reorganizational processes that occur following injury is limited. The degree and extent of this relationship remain to be determined in order that rsfMRI methods can be fully adapted for determining the optimal timing and type of rehabilitative interventions that can be used post-TBI to achieve the best outcome. Very few rsfMRI studies exist after experimental TBI and therefore we chose to acquire rsfMRI data before and at 7, 14 and 28 days after experimental TBI using a well-known, clinically-relevant, unilateral controlled cortical impact injury (CCI) adult rat model of TBI. This model was chosen since it has widespread axonal injury, a well-defined time-course of reorganization including spine, dendrite, axonal and cortical map changes, as well as spontaneous recovery of sensorimotor function by 28 d post-injury from which to interpret alterations in functional connectivity. Data were co-registered to a parcellated rat template to generate adjacency matrices for network analysis by graph theory. Making no assumptions about direction of change, we used two-tailed statistical analysis over multiple brain regions in a data-driven approach to access global and regional changes in network topology in order to assess brain connectivity in an unbiased way. Our main hypothesis was that deficits in functional connectivity would become apparent in regions known to be structurally altered or deficient in axonal connectivity in this model. The data show the loss of functional connectivity predicted by the structural deficits, not only within the primary sensorimotor injury site and pericontused regions, but the normally connected homotopic cortex, as well as subcortical regions, all of which persisted chronically. Especially novel in this study is the unanticipated finding of widespread increases in connection strength that dwarf both the degree and extent of the functional disconnections, and which persist chronically in some sensorimotor and subcortically connected regions. Exploratory global network analysis showed changes in network parameters indicative of possible acutely increased random connectivity and temporary reductions in modularity that were matched by local increases in connectedness and increased efficiency among more weakly connected regions. The global network parameters: shortest path-length, clustering coefficient and modularity that were most affected by trauma also scaled with the severity of injury, so that the corresponding regional measures were correlated to the injury severity most notably at 7 and 14 days and especially within, but not limited to, the contralateral cortex. These changes in functional network parameters are discussed in relation to the known time-course of physiologic and anatomic data that underlie structural and functional reorganization in this experiment model of TBI.
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Affiliation(s)
- N G Harris
- UCLA Brain Research Center, Department of Neurosurgery, University of California, Los Angeles, USA.
| | - D R Verley
- UCLA Brain Research Center, Department of Neurosurgery, University of California, Los Angeles, USA
| | - B A Gutman
- Imaging Genetics Center, Institute for Neuroimaging and Informatics, Department of Neurology, Keck/USC School of Medicine, University of Southern California, Los Angeles, CA, USA
| | - P M Thompson
- Departments of Psychiatry, Engineering, Radiology, & Ophthalmology, Keck/USC School of Medicine, University of Southern California, Los Angeles, CA, USA
| | - H J Yeh
- Department of Neurology, University of California, Los Angeles, USA
| | - J A Brown
- Department of Neurology, University of California at San Francisco School of Medicine, San Francisco, CA, USA
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10
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Zorick T, Mandelkern MA. Discrete Scale Invariance of Human Large EEG Voltage Deflections is More Prominent in Waking than Sleep Stage 2. Front Hum Neurosci 2015; 9:638. [PMID: 26696860 PMCID: PMC4667071 DOI: 10.3389/fnhum.2015.00638] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2015] [Accepted: 11/09/2015] [Indexed: 11/24/2022] Open
Abstract
Electroencephalography (EEG) is typically viewed through the lens of spectral analysis. Recently, multiple lines of evidence have demonstrated that the underlying neuronal dynamics are characterized by scale-free avalanches. These results suggest that techniques from statistical physics may be used to analyze EEG signals. We utilized a publicly available database of fourteen subjects with waking and sleep stage 2 EEG tracings per subject, and observe that power-law dynamics of critical-state neuronal avalanches are not sufficient to fully describe essential features of EEG signals. We hypothesized that this could reflect the phenomenon of discrete scale invariance (DSI) in EEG large voltage deflections (LVDs) as being more prominent in waking consciousness. We isolated LVDs, and analyzed logarithmically transformed LVD size probability density functions (PDF) to assess for DSI. We find evidence of increased DSI in waking, as opposed to sleep stage 2 consciousness. We also show that the signatures of DSI are specific for EEG LVDs, and not a general feature of fractal simulations with similar statistical properties to EEG. Removing only LVDs from waking EEG produces a reduction in power in the alpha and beta frequency bands. These findings may represent a new insight into the understanding of the cortical dynamics underlying consciousness.
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Affiliation(s)
- Todd Zorick
- Greater Los Angeles Veterans Administration Healthcare System, Departments of Psychiatry, (TZ) and Imaging (MM), University of California Los Angeles, CA, USA ; Department of Psychiatry and Biobehavioral Sciences, University of California Los Angeles, CA, USA
| | - Mark A Mandelkern
- Greater Los Angeles Veterans Administration Healthcare System, Departments of Psychiatry, (TZ) and Imaging (MM), University of California Los Angeles, CA, USA ; Department of Physics, University of California Irvine, CA, USA
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11
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Capano V, Herrmann HJ, de Arcangelis L. Optimal percentage of inhibitory synapses in multi-task learning. Sci Rep 2015; 5:9895. [PMID: 25898781 PMCID: PMC4405698 DOI: 10.1038/srep09895] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2014] [Accepted: 02/16/2015] [Indexed: 11/11/2022] Open
Abstract
Performing more tasks in parallel is a typical feature of complex brains. These are characterized by the coexistence of excitatory and inhibitory synapses, whose percentage in mammals is measured to have a typical value of 20-30%. Here we investigate parallel learning of more Boolean rules in neuronal networks. We find that multi-task learning results from the alternation of learning and forgetting of the individual rules. Interestingly, a fraction of 30% inhibitory synapses optimizes the overall performance, carving a complex backbone supporting information transmission with a minimal shortest path length. We show that 30% inhibitory synapses is the percentage maximizing the learning performance since it guarantees, at the same time, the network excitability necessary to express the response and the variability required to confine the employment of resources.
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Affiliation(s)
- Vittorio Capano
- Physics Department, University of Naples Federico II, Napoli, Italy
| | - Hans J. Herrmann
- Institute Computational Physics for Engineering Materials, ETH, Zürich, CH
- Departamento de Fisica, Universidade Federal do Ceará, 60451-970 Fortaleza, Ceará, Brazil
| | - Lucilla de Arcangelis
- Department of Industrial and Information Engineering, Second University of Naples and INFN Gr. Coll. Salerno, Aversa (CE), Italy
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12
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Lombardi F, Herrmann HJ, Plenz D, De Arcangelis L. On the temporal organization of neuronal avalanches. Front Syst Neurosci 2014; 8:204. [PMID: 25389393 PMCID: PMC4211381 DOI: 10.3389/fnsys.2014.00204] [Citation(s) in RCA: 37] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/26/2014] [Accepted: 10/01/2014] [Indexed: 11/13/2022] Open
Abstract
Spontaneous activity of cortex in vitro and in vivo has been shown to organize as neuronal avalanches. Avalanches are cascades of neuronal activity that exhibit a power law in their size and duration distribution, typical features of balanced systems in a critical state. Recently it has been shown that the distribution of quiet times between consecutive avalanches in rat cortex slice cultures displays a non-monotonic behavior with a power law decay at short time scales. This behavior has been attributed to the slow alternation between up and down-states. Here we further characterize the avalanche process and investigate how the functional behavior of the quiet time distribution depends on the fine structure of avalanche sequences. By systematically removing smaller avalanches from the experimental time series we show that size and quiet times are correlated and highlight that avalanche occurrence exhibits the characteristic periodicity of θ and β/γ oscillations, which jointly emerge in most of the analyzed samples. Furthermore, our analysis indicates that smaller avalanches tend to be associated with faster β/γ oscillations, whereas larger ones are associated with slower θ and 1-2 Hz oscillations. In particular, large avalanches corresponding to θ cycles trigger cascades of smaller ones, which occur at β/γ frequency. This temporal structure follows closely the one of nested θ - β/γ oscillations. Finally we demonstrate that, because of the multiple time scales characterizing avalanche dynamics, the distributions of quiet times between avalanches larger than a certain size do not collapse onto a unique function when rescaled by the average occurrence rate. However, when considered separately in the up-state and in the down-state, these distributions are solely controlled by the respective average rate and two different unique function can be identified.
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Affiliation(s)
- Fabrizio Lombardi
- Institute of Computational Physics for Engineering Materials, ETH Zurich, Switzerland
| | - Hans J Herrmann
- Institute of Computational Physics for Engineering Materials, ETH Zurich, Switzerland ; Departamento de Física, Universitade Federal do Ceará Fortaleza, Brazil
| | - Dietmar Plenz
- Section on Critical Brain Dynamics, National Institute of Mental Health, National Institute of Health Bethesda, MD, USA
| | - Lucilla De Arcangelis
- Department of Industrial and Information Engineering, Second University of Naples, National Institute for Nuclear Physics Gr. Coll. Salerno Aversa, Italy
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13
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Tomen N, Rotermund D, Ernst U. Marginally subcritical dynamics explain enhanced stimulus discriminability under attention. Front Syst Neurosci 2014; 8:151. [PMID: 25202240 PMCID: PMC4142542 DOI: 10.3389/fnsys.2014.00151] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2014] [Accepted: 08/04/2014] [Indexed: 11/27/2022] Open
Abstract
Recent experimental and theoretical work has established the hypothesis that cortical neurons operate close to a critical state which describes a phase transition from chaotic to ordered dynamics. Critical dynamics are suggested to optimize several aspects of neuronal information processing. However, although critical dynamics have been demonstrated in recordings of spontaneously active cortical neurons, little is known about how these dynamics are affected by task-dependent changes in neuronal activity when the cortex is engaged in stimulus processing. Here we explore this question in the context of cortical information processing modulated by selective visual attention. In particular, we focus on recent findings that local field potentials (LFPs) in macaque area V4 demonstrate an increase in γ-band synchrony and a simultaneous enhancement of object representation with attention. We reproduce these results using a model of integrate-and-fire neurons where attention increases synchrony by enhancing the efficacy of recurrent interactions. In the phase space spanned by excitatory and inhibitory coupling strengths, we identify critical points and regions of enhanced discriminability. Furthermore, we quantify encoding capacity using information entropy. We find a rapid enhancement of stimulus discriminability with the emergence of synchrony in the network. Strikingly, only a narrow region in the phase space, at the transition from subcritical to supercritical dynamics, supports the experimentally observed discriminability increase. At the supercritical border of this transition region, information entropy decreases drastically as synchrony sets in. At the subcritical border, entropy is maximized under the assumption of a coarse observation scale. Our results suggest that cortical networks operate at such near-critical states, allowing minimal attentional modulations of network excitability to substantially augment stimulus representation in the LFPs.
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Affiliation(s)
- Nergis Tomen
- Institute for Theoretical Physics, University of Bremen Bremen, Germany
| | - David Rotermund
- Institute for Theoretical Physics, University of Bremen Bremen, Germany
| | - Udo Ernst
- Institute for Theoretical Physics, University of Bremen Bremen, Germany
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14
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Rybarsch M, Bornholdt S. Avalanches in self-organized critical neural networks: a minimal model for the neural SOC universality class. PLoS One 2014; 9:e93090. [PMID: 24743324 PMCID: PMC3990531 DOI: 10.1371/journal.pone.0093090] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2013] [Accepted: 03/02/2014] [Indexed: 11/21/2022] Open
Abstract
The brain keeps its overall dynamics in a corridor of intermediate activity and it has been a long standing question what possible mechanism could achieve this task. Mechanisms from the field of statistical physics have long been suggesting that this homeostasis of brain activity could occur even without a central regulator, via self-organization on the level of neurons and their interactions, alone. Such physical mechanisms from the class of self-organized criticality exhibit characteristic dynamical signatures, similar to seismic activity related to earthquakes. Measurements of cortex rest activity showed first signs of dynamical signatures potentially pointing to self-organized critical dynamics in the brain. Indeed, recent more accurate measurements allowed for a detailed comparison with scaling theory of non-equilibrium critical phenomena, proving the existence of criticality in cortex dynamics. We here compare this new evaluation of cortex activity data to the predictions of the earliest physics spin model of self-organized critical neural networks. We find that the model matches with the recent experimental data and its interpretation in terms of dynamical signatures for criticality in the brain. The combination of signatures for criticality, power law distributions of avalanche sizes and durations, as well as a specific scaling relationship between anomalous exponents, defines a universality class characteristic of the particular critical phenomenon observed in the neural experiments. Thus the model is a candidate for a minimal model of a self-organized critical adaptive network for the universality class of neural criticality. As a prototype model, it provides the background for models that may include more biological details, yet share the same universality class characteristic of the homeostasis of activity in the brain.
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Affiliation(s)
- Matthias Rybarsch
- Institut für Theoretische Physik, Universität Bremen, Bremen, Germany
| | - Stefan Bornholdt
- Institut für Theoretische Physik, Universität Bremen, Bremen, Germany
- * E-mail:
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15
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Russo R, Herrmann HJ, de Arcangelis L. Brain modularity controls the critical behavior of spontaneous activity. Sci Rep 2014; 4:4312. [PMID: 24621482 PMCID: PMC3952147 DOI: 10.1038/srep04312] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/24/2013] [Accepted: 02/19/2014] [Indexed: 11/29/2022] Open
Abstract
The human brain exhibits a complex structure made of scale-free highly connected modules loosely interconnected by weaker links to form a small-world network. These features appear in healthy patients whereas neurological diseases often modify this structure. An important open question concerns the role of brain modularity in sustaining the critical behaviour of spontaneous activity. Here we analyse the neuronal activity of a model, successful in reproducing on non-modular networks the scaling behaviour observed in experimental data, on a modular network implementing the main statistical features measured in human brain. We show that on a modular network, regardless the strength of the synaptic connections or the modular size and number, activity is never fully scale-free. Neuronal avalanches can invade different modules which results in an activity depression, hindering further avalanche propagation. Critical behaviour is solely recovered if inter-module connections are added, modifying the modular into a more random structure.
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Affiliation(s)
- R. Russo
- Physics Department, University of Naples Federico II, Napoli, Italy
| | - H. J. Herrmann
- Institute Computational Physics for Engineering Materials, ETH, Zürich, CH
- Departamento de Física, Universidade Federal do Ceará, 60451-970 Fortaleza, Ceará, Brazil
| | - L. de Arcangelis
- Department of Industrial and Information Engineering, Second University of Naples and INFN Gr. Coll. Salerno, Aversa (CE), Italy
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Boonstra TW, He BJ, Daffertshofer A. Scale-free dynamics and critical phenomena in cortical activity. Front Physiol 2013; 4:79. [PMID: 23596422 PMCID: PMC3622032 DOI: 10.3389/fphys.2013.00079] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2013] [Accepted: 03/23/2013] [Indexed: 11/13/2022] Open
Affiliation(s)
- Tjeerd W Boonstra
- School of Psychiatry, University of New South Wales Sydney, NSW, Australia ; Black Dog Institute Sydney, NSW, Australia ; Research Institute MOVE, VU University Amsterdam Netherlands
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Time-varying functional network information extracted from brief instances of spontaneous brain activity. Proc Natl Acad Sci U S A 2013; 110:4392-7. [PMID: 23440216 DOI: 10.1073/pnas.1216856110] [Citation(s) in RCA: 438] [Impact Index Per Article: 39.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Recent functional magnetic resonance imaging studies have shown that the brain is remarkably active even in the absence of overt behavior, and this activity occurs in spatial patterns that are reproducible across subjects and follow the brain's established functional subdivision. Investigating the distribution of these spatial patterns is an active area of research with the goal of obtaining a better understanding of the neural networks underlying brain function. One intriguing aspect of spontaneous activity is an apparent nonstationarity, or variability of interaction between brain regions. It was recently proposed that spontaneous brain activity may be dominated by brief traces of activity, possibly originating from a neuronal avalanching phenomenon. Such traces may involve different subregions in a network at different times, potentially reflecting functionally relevant relationships that are not captured with conventional data analysis. To investigate this, we examined publicly available functional magnetic resonance imaging data with a dedicated analysis method and found indications that functional networks inferred from conventional correlation analysis may indeed be driven by activity at only a few critical time points. Subsequent analysis of the activity at these critical time points revealed multiple spatial patterns, each distinctly different from the established functional networks. The spatial distribution of these patterns suggests a potential functional relevance.
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