Self-Organization Toward Criticality by Synaptic Plasticity

Self-organized criticality has been proposed to be a universal mechanism for the emergence of scale-free dynamics in many complex systems, and possibly in the brain. While such scale-free patterns were identified experimentally in many different types of neural recordings, the biological principles behind their emergence remained unknown. Utilizing different network models and motivated by experimental observations, synaptic plasticity was proposed as a possible mechanism to self-organize brain dynamics toward a critical point. In this review, we discuss how various biologically plausible plasticity rules operating across multiple timescales are implemented in the models and how they alter the network’s dynamical state through modification of number and strength of the connections between the neurons. Some of these rules help to stabilize criticality, some need additional mechanisms to prevent divergence from the critical state. We propose that rules that are capable of bringing the network to criticality can be classified by how long the near-critical dynamics persists after their disabling. Finally, we discuss the role of self-organization and criticality in computation. Overall, the concept of criticality helps to shed light on brain function and self-organization, yet the overall dynamics of living neural networks seem to harnesses not only criticality for computation, but also deviations thereof.

[1]  Oren Shriki,et al.  Deviations from Critical Dynamics in Interictal Epileptiform Activity , 2016, The Journal of Neuroscience.

[2]  Karl W. Birkeland,et al.  Power‐laws and snow avalanches , 2002 .

[3]  H. Stanley,et al.  Introduction to Phase Transitions and Critical Phenomena , 1972 .

[4]  F. Lombardi,et al.  Temporal correlations in neuronal avalanche occurrence , 2016, Scientific Reports.

[5]  R. Kanzaki,et al.  Development of neural population activity toward self-organized criticality , 2017, Neuroscience.

[6]  Charles F. Richter,et al.  Earthquake magnitude, intensity, energy, and acceleration(Second paper) , 1956 .

[7]  G. Davis Homeostatic control of neural activity: from phenomenology to molecular design. , 2006, Annual review of neuroscience.

[8]  James P. Gleeson,et al.  Emergence of power laws in noncritical neuronal systems , 2019, Physical review. E.

[9]  D. Turcotte,et al.  Forest fires: An example of self-organized critical behavior , 1998, Science.

[10]  J. Michael Herrmann,et al.  Criticality of avalanche dynamics in adaptive recurrent networks , 2006, Neurocomputing.

[11]  P. Bak,et al.  Self-organized criticality. , 1988, Physical review. A, General physics.

[12]  Characterizing spreading dynamics of subsampled systems with nonstationary external input. , 2020, Physical review. E.

[13]  Gustavo Deco,et al.  Spontaneous cortical activity is transiently poised close to criticality , 2017, PLoS Comput. Biol..

[14]  Jorge Stolfi,et al.  Phase transitions and self-organized criticality in networks of stochastic spiking neurons , 2016, Scientific Reports.

[15]  M. A. Muñoz Colloquium: Criticality and dynamical scaling in living systems , 2017, Reviews of Modern Physics.

[16]  Michael J. Berry,et al.  Thermodynamics and signatures of criticality in a network of neurons , 2015, Proceedings of the National Academy of Sciences.

[17]  Viola Priesemann,et al.  Subsampling effects in neuronal avalanche distributions recorded in vivo , 2009, BMC Neuroscience.

[18]  S. Nelson,et al.  Homeostatic plasticity in the developing nervous system , 2004, Nature Reviews Neuroscience.

[19]  P. Bak,et al.  Adaptive learning by extremal dynamics and negative feedback. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Satu Palva,et al.  Critical dynamics of endogenous fluctuations predict cognitive flexibility in the Go/NoGo task , 2017, Scientific Reports.

[21]  John M Beggs,et al.  Critical branching captures activity in living neural networks and maximizes the number of metastable States. , 2005, Physical review letters.

[22]  Leonardo L. Gollo Coexistence of critical sensitivity and subcritical specificity can yield optimal population coding , 2017, Journal of The Royal Society Interface.

[23]  Narayan Srinivasa,et al.  Synaptic Plasticity Enables Adaptive Self-Tuning Critical Networks , 2015, PLoS Comput. Biol..

[24]  Stefan Bornholdt,et al.  Self-organized criticality in neural networks from activity-based rewiring. , 2020, Physical review. E.

[25]  L. de Arcangelis,et al.  Self-organized criticality model for brain plasticity. , 2006, Physical review letters.

[26]  Jochen Triesch,et al.  Fading Memory, Plasticity, and Criticality in Recurrent Networks , 2019 .

[27]  Osame Kinouchi,et al.  Self-Organized Supercriticality and Oscillations in Networks of Stochastic Spiking Neurons , 2017, Entropy.

[28]  Fabrizio Lombardi,et al.  Effects of Poisson noise in a IF model with STDP and spontaneous replay of periodic spatiotemporal patterns, in absence of cue stimulation , 2013, Biosyst..

[29]  Maurizio Corbetta,et al.  Homeostatic plasticity and emergence of functional networks in a whole-brain model at criticality , 2018, Scientific Reports.

[30]  Woodrow L. Shew,et al.  Adaptation to sensory input tunes visual cortex to criticality , 2015, Nature Physics.

[31]  H. Markram,et al.  The neural code between neocortical pyramidal neurons depends on neurotransmitter release probability. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[32]  Joao Pinheiro Neto,et al.  MR. Estimator, a toolbox to determine intrinsic timescales from subsampled spiking activity , 2020, PloS one.

[33]  H J Herrmann,et al.  Critical neural networks with short- and long-term plasticity. , 2017, Physical review. E.

[34]  Wulfram Gerstner,et al.  SPIKING NEURON MODELS Single Neurons , Populations , Plasticity , 2002 .

[35]  Danielle Smith Bassett,et al.  Small-World Brain Networks , 2006, The Neuroscientist : a review journal bringing neurobiology, neurology and psychiatry.

[36]  Arjen van Ooyen,et al.  Homeostatic Structural Plasticity Can Build Critical Networks , 2019, Springer Series on Bio- and Neurosystems.

[37]  K. Linkenkaer-Hansen,et al.  Critical-State Dynamics of Avalanches and Oscillations Jointly Emerge from Balanced Excitation/Inhibition in Neuronal Networks , 2012, The Journal of Neuroscience.

[38]  J. Wilting,et al.  25 years of criticality in neuroscience — established results, open controversies, novel concepts , 2019, Current Opinion in Neurobiology.

[39]  K. McClements,et al.  Solar flares as cascades of reconnecting magnetic loops. , 2002, Physical review letters.

[40]  Florentin Wörgötter,et al.  Self-Organized Criticality in Developing Neuronal Networks , 2010, PLoS Comput. Biol..

[41]  B. Drossel,et al.  Self-organized criticality in a forest-fire model , 1992 .

[42]  G. Deco,et al.  Ongoing Cortical Activity at Rest: Criticality, Multistability, and Ghost Attractors , 2012, The Journal of Neuroscience.

[43]  Nergis Tomen,et al.  Marginally subcritical dynamics explain enhanced stimulus discriminability under attention , 2014, Front. Syst. Neurosci..

[44]  Tawan T. A. Carvalho,et al.  Synaptic balance due to homeostatically self-organized quasicritical dynamics , 2020, Physical Review Research.

[45]  H. Markram,et al.  Dendritic calcium transients evoked by single back‐propagating action potentials in rat neocortical pyramidal neurons. , 1995, The Journal of physiology.

[46]  S. Carpenter,et al.  Early-warning signals for critical transitions , 2009, Nature.

[47]  Thilo Gross,et al.  Adaptive self-organization in a realistic neural network model. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[48]  Biyu J. He Scale-free brain activity: past, present, and future , 2014, Trends in Cognitive Sciences.

[49]  S. Bornholdt,et al.  Avalanches in Self-Organized Critical Neural Networks: A Minimal Model for the Neural SOC Universality Class , 2012, PloS one.

[50]  A Vespignani,et al.  Avalanche and spreading exponents in systems with absorbing states. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[51]  F. Mormann,et al.  No evidence that epilepsy impacts criticality in pre-seizure single-neuron activity of human cortex , 2020, 2004.10642.

[52]  Woodrow L. Shew,et al.  Neuronal Avalanches Imply Maximum Dynamic Range in Cortical Networks at Criticality , 2009, The Journal of Neuroscience.

[53]  N. Brunel,et al.  Astrocytes: Orchestrating synaptic plasticity? , 2015, Neuroscience.

[54]  B. Gutenberg,et al.  Seismicity of the Earth , 1941 .

[55]  J. Sethna Statistical Mechanics: Entropy, Order Parameters, and Complexity , 2021 .

[56]  Shan Yu,et al.  Maintained avalanche dynamics during task-induced changes of neuronal activity in nonhuman primates , 2017, eLife.

[57]  Woodrow L. Shew,et al.  State-dependent intrinsic predictability of cortical network dynamics , 2015, PLoS Comput. Biol..

[58]  L. Abbott,et al.  Synaptic plasticity: taming the beast , 2000, Nature Neuroscience.

[59]  S. Scarpetta,et al.  Neural Avalanches at the Critical Point between Replay and Non-Replay of Spatiotemporal Patterns , 2013, PloS one.

[60]  Shan Yu,et al.  Short-term synaptic plasticity expands the operational range of long-term synaptic changes in neural networks , 2019, Neural Networks.

[61]  M. Newman Power laws, Pareto distributions and Zipf's law , 2005 .

[62]  M. A. Muñoz,et al.  Time-series thresholding and the definition of avalanche size. , 2019, Physical review. E.

[63]  S. Scarpetta,et al.  Hysteresis, neural avalanches, and critical behavior near a first-order transition of a spiking neural network. , 2018, Physical review. E.

[64]  Julijana Gjorgjieva,et al.  Homeostatic Activity-Dependent Tuning of Recurrent Networks for Robust Propagation of Activity , 2015, The Journal of Neuroscience.

[65]  J Wilting,et al.  Between Perfectly Critical and Fully Irregular: A Reverberating Model Captures and Predicts Cortical Spike Propagation , 2018, Cerebral cortex.

[66]  M. Nicolelis,et al.  Spike Avalanches Exhibit Universal Dynamics across the Sleep-Wake Cycle , 2010, PloS one.

[67]  L. Abbott,et al.  A simple growth model constructs critical avalanche networks. , 2007, Progress in brain research.

[68]  P. J. Sjöström,et al.  Dendritic excitability and synaptic plasticity. , 2008, Physiological reviews.

[69]  Edward Ott,et al.  Feedback control stabilization of critical dynamics via resource transport on multilayer networks: How glia enable learning dynamics in the brain. , 2016, Physical review. E.

[70]  V. Priesemann,et al.  Subsampling scaling , 2017, Nature Communications.

[71]  M. Farries,et al.  Reinforcement learning with modulated spike timing dependent synaptic plasticity. , 2007, Journal of neurophysiology.

[72]  Kristopher T Kahle,et al.  The GABA Excitatory/Inhibitory Shift in Brain Maturation and Neurological Disorders , 2012, The Neuroscientist : a review journal bringing neurobiology, neurology and psychiatry.

[73]  John M. Beggs,et al.  Attaining and maintaining criticality in a neuronal network model , 2013 .

[74]  M. Poo,et al.  Calcium stores regulate the polarity and input specificity of synaptic modification , 2000, Nature.

[75]  B. Cessac,et al.  Effects of Cellular Homeostatic Intrinsic Plasticity on Dynamical and Computational Properties of Biological Recurrent Neural Networks , 2013, The Journal of Neuroscience.

[76]  Martin A. Riedmiller,et al.  Modeling effects of intrinsic and extrinsic rewards on the competition between striatal learning systems , 2013, Front. Psychol..

[77]  Stefan Mihalas,et al.  Self-organized criticality occurs in non-conservative neuronal networks during Up states , 2010, Nature physics.

[78]  Woodrow L. Shew,et al.  Adaptation towards scale-free dynamics improves cortical stimulus discrimination at the cost of reduced detection , 2017, PLoS Comput. Biol..

[79]  Maya Paczuski,et al.  A heavenly example of scale-free networks and self-organized criticality , 2004 .

[80]  H. Markram,et al.  Regulation of Synaptic Efficacy by Coincidence of Postsynaptic APs and EPSPs , 1997, Science.

[81]  James G. King,et al.  Cortical reliability amid noise and chaos , 2018, Nature Communications.

[82]  H. Laufs,et al.  The avalanche-like behaviour of large-scale haemodynamic activity from wakefulness to deep sleep , 2019, Journal of the Royal Society Interface.

[83]  R. Nicoll,et al.  Activity differentially regulates the surface expression of synaptic AMPA and NMDA glutamate receptors. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[84]  V. Priesemann,et al.  Description of spreading dynamics by microscopic network models and macroscopic branching processes can differ due to coalescence. , 2019, Physical review. E.

[85]  M. Tsodyks,et al.  Synaptic Theory of Working Memory , 2008, Science.

[86]  Nils Bertschinger,et al.  Real-Time Computation at the Edge of Chaos in Recurrent Neural Networks , 2004, Neural Computation.

[87]  Mauro Copelli,et al.  Stochastic oscillations and dragon king avalanches in self-organized quasi-critical systems , 2019, Scientific Reports.

[88]  Minoru Asada,et al.  Information processing in echo state networks at the edge of chaos , 2011, Theory in Biosciences.

[89]  Viola Priesemann,et al.  A unified picture of neuronal avalanches arises from the understanding of sampling effects , 2019, bioRxiv.

[90]  K. Linkenkaer-Hansen,et al.  Long-Range Temporal Correlations and Scaling Behavior in Human Brain Oscillations , 2001, The Journal of Neuroscience.

[91]  Amos Maritan,et al.  Scaling and criticality in a phenomenological renormalization group , 2020 .

[92]  Rui Ponte Costa,et al.  Unified pre- and postsynaptic long-term plasticity enables reliable and flexible learning , 2015, eLife.

[93]  Ilya Nemenman,et al.  Latent dynamical variables produce signatures of spatiotemporal criticality in large biological systems , 2020, bioRxiv.

[94]  D. Feldman,et al.  Timing-Based LTP and LTD at Vertical Inputs to Layer II/III Pyramidal Cells in Rat Barrel Cortex , 2000, Neuron.

[95]  William Bialek,et al.  Coarse Graining, Fixed Points, and Scaling in a Large Population of Neurons. , 2018, Physical review letters.

[96]  Dietmar Plenz,et al.  Critical Slowing Down Governs the Transition to Neuron Spiking , 2015, PLoS Comput. Biol..

[97]  M. A. Muñoz,et al.  Neutral Theory and Scale-Free Neural Dynamics , 2017, 1703.05079.

[98]  E. Bienenstock,et al.  Theory for the development of neuron selectivity: orientation specificity and binocular interaction in visual cortex , 1982, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[99]  Carla Perrone-Capano,et al.  Activity-dependent neural network model on scale-free networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[100]  Woodrow L. Shew,et al.  Inhibition causes ceaseless dynamics in networks of excitable nodes. , 2013, Physical review letters.

[101]  A. V. Ooyen,et al.  Complex periodic behaviour in a neural network model with activity-dependent neurite outgrowth. , 1996 .

[102]  Henry Markram,et al.  Neural Networks with Dynamic Synapses , 1998, Neural Computation.

[103]  Edward T. Bullmore,et al.  Failure of Adaptive Self-Organized Criticality during Epileptic Seizure Attacks , 2011, PLoS Comput. Biol..

[104]  Anirban Das,et al.  Critical Neuronal Models with Relaxed Timescale Separation , 2018, Physical Review X.

[105]  A. Fronczak,et al.  Interplay between network structure and self-organized criticality , 2005, cond-mat/0509043.

[106]  M. A. Muñoz,et al.  Paths to self-organized criticality , 1999, cond-mat/9910454.

[107]  O. Sporns,et al.  Complex brain networks: graph theoretical analysis of structural and functional systems , 2009, Nature Reviews Neuroscience.

[108]  A. Gemignani,et al.  Self-organized dynamical complexity in human wakefulness and sleep: different critical brain-activity feedback for conscious and unconscious states. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[109]  J. M. Herrmann,et al.  Dynamical synapses causing self-organized criticality in neural networks , 2007, 0712.1003.

[110]  Bruno Cessac,et al.  Effects of Hebbian learning on the dynamics and structure of random networks with inhibitory and excitatory neurons , 2007, Journal of Physiology-Paris.

[111]  O. Kinouchi,et al.  Optimal dynamical range of excitable networks at criticality , 2006, q-bio/0601037.

[112]  L. Abbott,et al.  Redundancy Reduction and Sustained Firing with Stochastic Depressing Synapses , 2002, The Journal of Neuroscience.

[113]  J. M. Herrmann,et al.  Phase transitions towards criticality in a neural system with adaptive interactions. , 2009, Physical review letters.

[114]  Jae Woo Lee,et al.  Avalanche size distribution of an integrate-and-fire neural model on complex networks. , 2020, Chaos.

[115]  L. Abbott,et al.  Synaptic Depression and Cortical Gain Control , 1997, Science.

[116]  Mark C. W. van Rossum,et al.  Stable Hebbian Learning from Spike Timing-Dependent Plasticity , 2000, The Journal of Neuroscience.

[117]  S. S. Manna Two-state model of self-organized criticality , 1991 .

[118]  Baktash Babadi,et al.  Intrinsic Stability of Temporally Shifted Spike-Timing Dependent Plasticity , 2010, PLoS Comput. Biol..

[119]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[120]  H. Stanley,et al.  Common scale-invariant patterns of sleep-wake transitions across mammalian species. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[121]  Ginestra Bianconi,et al.  Clogging and self-organized criticality in complex networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[122]  Tang,et al.  Self-Organized Criticality: An Explanation of 1/f Noise , 2011 .

[123]  D. Plenz,et al.  Spontaneous cortical activity in awake monkeys composed of neuronal avalanches , 2009, Proceedings of the National Academy of Sciences.

[124]  W. Regehr,et al.  Short-term synaptic plasticity. , 2002, Annual review of physiology.

[125]  M. E. J. Newman,et al.  Power laws, Pareto distributions and Zipf's law , 2005 .

[126]  Kevin Murphy,et al.  Neural correlates of the LSD experience revealed by multimodal neuroimaging , 2016, Proceedings of the National Academy of Sciences.

[127]  Viola Priesemann,et al.  Sequence memory in recurrent neuronal network can develop without structured input , 2020, bioRxiv.

[128]  Viola Priesemann,et al.  Neuronal Avalanches Differ from Wakefulness to Deep Sleep – Evidence from Intracranial Depth Recordings in Humans , 2013, PLoS Comput. Biol..

[129]  J. Hopfield,et al.  Earthquake cycles and neural reverberations: Collective oscillations in systems with pulse-coupled threshold elements. , 1995, Physical review letters.

[130]  Olaf Sporns,et al.  Neurobiologically Realistic Determinants of Self-Organized Criticality in Networks of Spiking Neurons , 2011, PLoS Comput. Biol..

[131]  H. Markram,et al.  Redistribution of synaptic efficacy between neocortical pyramidal neurons , 1996, Nature.

[132]  Silvia Scarpetta,et al.  Alternation of up and down states at a dynamical phase-transition of a neural network with spatiotemporal attractors , 2014, Front. Syst. Neurosci..

[133]  Johannes Zierenberg,et al.  Tailored ensembles of neural networks optimize sensitivity to stimulus statistics , 2019, Physical Review Research.

[134]  John M. Beggs,et al.  Neuronal Avalanches in Neocortical Circuits , 2003, The Journal of Neuroscience.

[135]  A. Scheidegger A COMPLETE THERMODYNAMIC ANALOGY FOR LANDSCAPE EVOLUTION , 1967 .

[136]  J. Michael Herrmann,et al.  Critical dynamics in associative memory networks , 2013, Front. Comput. Neurosci..

[137]  H. Herrmann,et al.  Self-organized criticality on small world networks , 2001, cond-mat/0110239.

[138]  Jens Wilting,et al.  Assessing Criticality in Experiments , 2019, Springer Series on Bio- and Neurosystems.

[139]  J. Michael Herrmann,et al.  Self-organized Criticality via Retro-Synaptic Signals , 2017, Front. Phys..

[140]  S. Bornholdt,et al.  Topological evolution of dynamical networks: global criticality from local dynamics. , 2000, Physical review letters.

[141]  R. Huganir,et al.  Activity-Dependent Modulation of Synaptic AMPA Receptor Accumulation , 1998, Neuron.

[142]  Wulfram Gerstner,et al.  A neuronal learning rule for sub-millisecond temporal coding , 1996, Nature.

[143]  J. Michael Herrmann,et al.  Critical branching processes in neural networks , 2007 .

[144]  Dan-Mei Chen,et al.  Self-organized criticality in a cellular automaton model of pulse-coupled integrate-and-fire neurons , 1995 .

[145]  Min Lin,et al.  Self-organized criticality in a simple model of neurons based on small-world networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[146]  Johannes Zierenberg,et al.  Operating in a Reverberating Regime Enables Rapid Tuning of Network States to Task Requirements , 2018, Front. Syst. Neurosci..

[147]  Zhang,et al.  Scaling theory of self-organized criticality. , 1989, Physical review letters.

[148]  Jochen Triesch,et al.  Criticality meets learning: Criticality signatures in a self-organizing recurrent neural network , 2017, PloS one.

[149]  I. Mastromatteo,et al.  On the criticality of inferred models , 2011, 1102.1624.

[150]  D. Plenz,et al.  Neuronal Avalanches in the Resting MEG of the Human Brain , 2012, The Journal of Neuroscience.

[151]  W. Gerstner,et al.  Hebbian plasticity requires compensatory processes on multiple timescales , 2017, Philosophical Transactions of the Royal Society B: Biological Sciences.

[152]  Johannes Zierenberg,et al.  Homeostatic plasticity and external input shape neural network dynamics , 2018, bioRxiv.

[153]  Niraj S. Desai,et al.  Activity-dependent scaling of quantal amplitude in neocortical neurons , 1998, Nature.

[154]  C. Saper,et al.  Critical Dynamics and Coupling in Bursts of Cortical Rhythms Indicate Non-Homeostatic Mechanism for Sleep-Stage Transitions and Dual Role of VLPO Neurons in Both Sleep and Wake , 2019, The Journal of Neuroscience.

[155]  T. E. Harris,et al.  The Theory of Branching Processes. , 1963 .

[156]  L. de Arcangelis,et al.  Learning as a phenomenon occurring in a critical state , 2010, Proceedings of the National Academy of Sciences.

[157]  J. Touboul,et al.  Power-law statistics and universal scaling in the absence of criticality. , 2015, Physical review. E.

[158]  Thilo Gross,et al.  Analytical investigation of self-organized criticality in neural networks , 2012, Journal of The Royal Society Interface.

[159]  Y. Goda,et al.  Unraveling Mechanisms of Homeostatic Synaptic Plasticity , 2010, Neuron.

[160]  Naoki Sugimoto,et al.  A-T base pairs are more stable than G-C base pairs in a hydrated ionic liquid. , 2012, Angewandte Chemie.

[161]  Ralf Wessel,et al.  Cortical Circuit Dynamics Are Homeostatically Tuned to Criticality In Vivo , 2019, Neuron.

[162]  Wulfram Gerstner,et al.  Spiking Neuron Models , 2002 .

[163]  Viola Priesemann,et al.  Can a time varying external drive give rise to apparent criticality in neural systems? , 2018, PLoS Comput. Biol..

[164]  Wulfram Gerstner,et al.  Spike-timing dependent plasticity , 2010, Scholarpedia.

[165]  G. Cecchi,et al.  Scale-free brain functional networks. , 2003, Physical review letters.

[166]  Rufin van Rullen,et al.  Neurons Tune to the Earliest Spikes Through STDP , 2005, Neural Computation.

[167]  Everton J. Agnes,et al.  Inhibitory Plasticity: Balance, Control, and Codependence. , 2017, Annual review of neuroscience.

[168]  Arenas,et al.  Self-organized criticality and synchronization in a lattice model of integrate-and-fire oscillators. , 1994, Physical review letters.

[169]  J. M. Herrmann,et al.  Finite-size effects of avalanche dynamics. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[170]  Gordon Pipa,et al.  SORN: A Self-Organizing Recurrent Neural Network , 2009, Front. Comput. Neurosci..

[171]  M. A. Muñoz,et al.  Self-organization without conservation: are neuronal avalanches generically critical? , 2010, 1001.3256.

[172]  Eve Marder,et al.  Homeostatic Regulation of Neuronal Excitability , 2013, Scholarpedia.

[173]  Kenneth D. Miller,et al.  The Role of Constraints in Hebbian Learning , 1994, Neural Computation.

[174]  P. J. Sjöström,et al.  Rate, Timing, and Cooperativity Jointly Determine Cortical Synaptic Plasticity , 2001, Neuron.

[175]  J. M. Herrmann,et al.  The Functional Role of Critical Dynamics in Neural Systems , 2019, Springer Series on Bio- and Neurosystems.

[176]  G. Curio,et al.  Temporal Signatures of Criticality in Human Cortical Excitability as Probed by Early Somatosensory Responses , 2020, The Journal of Neuroscience.

[177]  Georg Martius,et al.  The dynamical regime and its importance for evolvability, task performance and generalization , 2021, ALIFE.

[178]  Patrick D. Roberts,et al.  Computational Consequences of Temporally Asymmetric Learning Rules: II. Sensory Image Cancellation , 2000, Journal of Computational Neuroscience.

[179]  Jochen Triesch,et al.  Spike avalanches in vivo suggest a driven, slightly subcritical brain state , 2014, Front. Syst. Neurosci..

[180]  Dhar,et al.  Exactly solved model of self-organized critical phenomena. , 1989, Physical review letters.

[181]  Leonardo L. Gollo,et al.  Criticality in the brain: A synthesis of neurobiology, models and cognition , 2017, Progress in Neurobiology.

[182]  Takayasu,et al.  New type of self-organized criticality in a model of erosion. , 1992, Physical review letters.

[183]  J. Michael Herrmann,et al.  Dynamical Synapses Give Rise to a Power-Law Distribution of Neuronal Avalanches , 2005, NIPS.

[184]  Claudia Clopath,et al.  Local inhibitory plasticity tunes macroscopic brain dynamics and allows the emergence of functional brain networks , 2016, NeuroImage.

[185]  W. Wildman,et al.  Theoretical Neuroscience , 2014 .

[186]  S. Bornholdt,et al.  Self-organized critical neural networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[187]  Roxana Zeraati,et al.  A flexible Bayesian framework for unbiased estimation of timescales , 2020, Nature Computational Science.

[188]  Steve M. Potter,et al.  Upward synaptic scaling is dependent on neurotransmission rather than spiking , 2015, Nature Communications.

[189]  A flexible Bayesian framework for unbiased estimation of timescales , 2020 .

[190]  Raoul-Martin Memmesheimer,et al.  Growing Critical: Self-Organized Criticality in a Developing Neural System. , 2018, Physical review letters.

[191]  M. Alexander,et al.  Principles of Neural Science , 1981 .

[192]  Martin Gerlach,et al.  Testing Statistical Laws in Complex Systems. , 2019, Physical review letters.

[193]  S. Nelson,et al.  Hebb and homeostasis in neuronal plasticity , 2000, Current Opinion in Neurobiology.

[194]  A. Montakhab,et al.  Spike-Timing-Dependent Plasticity With Axonal Delay Tunes Networks of Izhikevich Neurons to the Edge of Synchronization Transition With Scale-Free Avalanches , 2019, Front. Syst. Neurosci..

[195]  R. Kempter,et al.  Hebbian learning and spiking neurons , 1999 .

[196]  Viola Priesemann,et al.  Control of criticality and computation in spiking neuromorphic networks with plasticity , 2020, Nature Communications.

[197]  Seunghwan Kim,et al.  Self-organized criticality and scale-free properties in emergent functional neural networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[198]  A. V. Ooyen,et al.  Activity-dependent outgrowth of neurons and overshoot phenomena in developing neural networks , 1994 .

[199]  Changsong Zhou,et al.  Hierarchical modular structure enhances the robustness of self-organized criticality in neural networks , 2012 .

[200]  G. Bi,et al.  Synaptic Modifications in Cultured Hippocampal Neurons: Dependence on Spike Timing, Synaptic Strength, and Postsynaptic Cell Type , 1998, The Journal of Neuroscience.

[201]  H. Laufs,et al.  Breakdown of long-range temporal dependence in default mode and attention networks during deep sleep , 2013, Proceedings of the National Academy of Sciences.

[202]  Wulfram Gerstner,et al.  Synaptic Plasticity in Neural Networks Needs Homeostasis with a Fast Rate Detector , 2013, PLoS Comput. Biol..

[203]  Wulfram Gerstner,et al.  Integrating Hebbian and homeostatic plasticity: the current state of the field and future research directions , 2017, Philosophical Transactions of the Royal Society B: Biological Sciences.

[204]  John M. Beggs,et al.  Universal critical dynamics in high resolution neuronal avalanche data. , 2012, Physical review letters.

[205]  C. Meisel Antiepileptic drugs induce subcritical dynamics in human cortical networks , 2019, Proceedings of the National Academy of Sciences.

[206]  Woodrow L. Shew,et al.  The Functional Benefits of Criticality in the Cortex , 2013, The Neuroscientist : a review journal bringing neurobiology, neurology and psychiatry.

[207]  Jorge Hidalgo,et al.  Information-based fitness and the emergence of criticality in living systems , 2013, Proceedings of the National Academy of Sciences.

[208]  M. A. Muñoz,et al.  Griffiths phases and the stretching of criticality in brain networks , 2013, Nature Communications.