Colloquium: Criticality and dynamical scaling in living systems

Close to a transition between different phases a substance can show universal behavior that is independent of the microscopic details and is characterized by power law correlations and critical exponents. In this Colloquium the concepts of criticality and universality are discussed when applied to biological systems and suggest that in some cases these systems can extract functional advantages close to criticality.

[1]  F. Galton,et al.  On the Probability of the Extinction of Families , 1875 .

[2]  G. Yule,et al.  A Mathematical Theory of Evolution, Based on the Conclusions of Dr. J. C. Willis, F.R.S. , 1925 .

[3]  M. Kleiber Body size and metabolism , 1932 .

[4]  E. Schrödinger What Is Life , 1946 .

[5]  Thomas Gold,et al.  Hearing. II. The Physical Basis of the Action of the Cochlea , 1948, Proceedings of the Royal Society of London. Series B - Biological Sciences.

[6]  A. Turing The chemical basis of morphogenesis , 1952, Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences.

[7]  H. Simon,et al.  ON A CLASS OF SKEW DISTRIBUTION FUNCTIONS , 1955 .

[8]  W. Ashby,et al.  Design for a brain: The origin of adaptive behaviour (2nd ed. rev.). , 1960 .

[9]  L. R. Taylor,et al.  Aggregation, Variance and the Mean , 1961, Nature.

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

[11]  B. Mandelbrot,et al.  RANDOM WALK MODELS FOR THE SPIKE ACTIVITY OF A SINGLE NEURON. , 1964, Biophysical journal.

[12]  S. Kauffman Metabolic stability and epigenesis in randomly constructed genetic nets. , 1969, Journal of theoretical biology.

[13]  F. Crick Central Dogma of Molecular Biology , 1970, Nature.

[14]  Douglas Poland,et al.  Theory of helix-coil transitions in biopolymers , 1970 .

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

[16]  D. Thouless Introduction to Phase Transitions and Critical Phenomena , 1972 .

[17]  Shun-ichi Amari,et al.  Learning Patterns and Pattern Sequences by Self-Organizing Nets of Threshold Elements , 1972, IEEE Transactions on Computers.

[18]  P. Anderson More is different. , 1972, Science.

[19]  K. Wilson,et al.  The Renormalization group and the epsilon expansion , 1973 .

[20]  Michael E. Fisher,et al.  The renormalization group in the theory of critical behavior , 1974 .

[21]  Huzihiro Araki,et al.  International Symposium on Mathematical Problems in Theoretical Physics , 1975 .

[22]  Shang‐keng Ma Modern Theory of Critical Phenomena , 1976 .

[23]  P. Hohenberg,et al.  Theory of Dynamic Critical Phenomena , 1977 .

[24]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[25]  M. Kimura,et al.  The neutral theory of molecular evolution. , 1983, Scientific American.

[26]  Professor Dr. Manfred Eigen,et al.  The Hypercycle , 1979, Springer Berlin Heidelberg.

[27]  P. Gennes Scaling Concepts in Polymer Physics , 1979 .

[28]  K. Wilson Problems in Physics with many Scales of Length , 1979 .

[29]  K. Binder Finite size scaling analysis of ising model block distribution functions , 1981 .

[30]  N. Kampen,et al.  Stochastic processes in physics and chemistry , 1981 .

[31]  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.

[32]  H. Berg Random Walks in Biology , 2018 .

[33]  D. Sherrington Stochastic Processes in Physics and Chemistry , 1983 .

[34]  J. Kelso Phase transitions and critical behavior in human bimanual coordination. , 1984, The American journal of physiology.

[35]  Geoffrey E. Hinton,et al.  A Learning Algorithm for Boltzmann Machines , 1985, Cogn. Sci..

[36]  A Portrait of Twenty-five Years , 1985 .

[37]  T. Liggett Interacting Particle Systems , 1985 .

[38]  J. Kelso,et al.  Nonequilibrium phase transitions in coordinated biological motion: critical fluctuations , 1986 .

[39]  B. Derrida,et al.  Random networks of automata: a simple annealed approximation , 1986 .

[40]  J. Kelso,et al.  Nonequilibrium phase transitions in coordinated biological motion: Critical slowing down and switching time , 1987 .

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

[42]  G. Yarrington Molecular Cell Biology , 1987, The Yale Journal of Biology and Medicine.

[43]  H. Haken,et al.  Synergetics , 1988, IEEE Circuits and Devices Magazine.

[44]  D. Amit Modelling Brain Function: The World of Attractor Neural Networks , 1989 .

[45]  Antonio Coniglio,et al.  Exact Relations Between Damage Spreading and Thermodynamical Properties , 1989 .

[46]  P. Bak,et al.  Earthquakes as a self‐organized critical phenomenon , 1989 .

[47]  Ming Li,et al.  Kolmogorov Complexity and its Applications , 1991, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.

[48]  P. Bak,et al.  A forest-fire model and some thoughts on turbulence , 1990 .

[49]  Christopher G. Langton,et al.  Computation at the edge of chaos: Phase transitions and emergent computation , 1990 .

[50]  A. M. Turing,et al.  Computing Machinery and Intelligence , 1950, The Philosophy of Artificial Intelligence.

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

[52]  D. Baylor,et al.  Synchronous bursts of action potentials in ganglion cells of the developing mammalian retina. , 1991, Science.

[53]  Stuart A. Kauffman,et al.  The origins of order , 1993 .

[54]  G. Forgacs,et al.  Phase transition and morphogenesis in a model biological system. , 1991, Physical review letters.

[55]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[56]  Wentian Li,et al.  Transition phenomena in cellular automata rule space , 1991 .

[57]  G. Grinstein Generic scale invariance in classical nonequilibrium systems (invited) , 1991 .

[58]  Bruce J. West,et al.  Fractal physiology , 1994, IEEE Engineering in Medicine and Biology Magazine.

[59]  A. Fisher,et al.  The Theory of critical phenomena , 1992 .

[60]  Christensen,et al.  Self-organized criticality in a continuous, nonconservative cellular automaton modeling earthquakes. , 1992, Physical review letters.

[61]  Drossel,et al.  Self-organized critical forest-fire model. , 1992, Physical review letters.

[62]  T. Ikegami,et al.  Homeochaos: dynamic stability of a symbiotic network with population dynamics and evolving mutation rates , 1992 .

[63]  A. Goldberger Fractal mechanisms in the electrophysiology of the heart , 1992, IEEE Engineering in Medicine and Biology Magazine.

[64]  Bak,et al.  Punctuated equilibrium and criticality in a simple model of evolution. , 1993, Physical review letters.

[65]  Giorgio Parisi,et al.  Statistical Physics and biology , 1993 .

[66]  Abbott,et al.  Asynchronous states in networks of pulse-coupled oscillators. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[67]  M. Steriade,et al.  A novel slow (< 1 Hz) oscillation of neocortical neurons in vivo: depolarizing and hyperpolarizing components , 1993, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[68]  G. Cowan,et al.  Complexity Metaphors, Models, and Reality , 1994 .

[69]  R. Palmer,et al.  Introduction to the theory of neural computation , 1994, The advanced book program.

[70]  J. Hopfield Physics, Computation, and Why Biology Looks so Different , 1994 .

[71]  D. Sornette Sweeping of an instability : an alternative to self-organized criticality to get powerlaws without parameter tuning , 1994 .

[72]  G. Edelman,et al.  A measure for brain complexity: relating functional segregation and integration in the nervous system. , 1994, Proceedings of the National Academy of Sciences of the United States of America.

[73]  T. Lubensky,et al.  Principles of condensed matter physics , 1995 .

[74]  Peter Grassberger,et al.  Are damage spreading transitions generically in the universality class of directed percolation? , 1994, cond-mat/9409068.

[75]  Stanley,et al.  Self-organized branching processes: Mean-field theory for avalanches. , 1995, Physical review letters.

[76]  S. Strogatz Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering , 1995 .

[77]  Tu,et al.  Long-Range Order in a Two-Dimensional Dynamical XY Model: How Birds Fly Together. , 1995, Physical review letters.

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

[79]  W. Bialek,et al.  Naturalistic stimuli increase the rate and efficiency of information transmission by primary auditory afferents , 1995, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[80]  Stassinopoulos,et al.  Democratic reinforcement: A principle for brain function. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[81]  C. Adami,et al.  Self-organized criticality in living systems , 1994, adap-org/9401001.

[82]  B. Biswal,et al.  Functional connectivity in the motor cortex of resting human brain using echo‐planar mri , 1995, Magnetic resonance in medicine.

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

[84]  Ricard V. Solé,et al.  Information at the edge of chaos in fluid neural networks , 1995 .

[85]  Vicsek,et al.  Novel type of phase transition in a system of self-driven particles. , 1995, Physical review letters.

[86]  P. Bak,et al.  Evolution as a self-organized critical phenomenon. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[87]  S. Kauffman At Home in the Universe: The Search for the Laws of Self-Organization and Complexity , 1995 .

[88]  Arantxa Etxeverria The Origins of Order , 1993 .

[89]  Losa Ga Fractals in pathology: are they really useful? , 1995 .

[90]  Ricard V. Solé,et al.  Phase transitions and complex systems: Simple, nonlinear models capture complex systems at the edge of chaos , 1996, Complex..

[91]  D. Sornette,et al.  Convergent Multiplicative Processes Repelled from Zero: Power Laws and Truncated Power Laws , 1996, cond-mat/9609074.

[92]  V. Frette,et al.  Avalanche dynamics in a pile of rice , 1996, Nature.

[93]  Moreira,et al.  Critical dynamics of the contact process with quenched disorder. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[94]  Per Bak,et al.  How Nature Works , 1996 .

[95]  D. Contreras,et al.  Synchronization of fast (30-40 Hz) spontaneous cortical rhythms during brain activation , 1996, The Journal of neuroscience : the official journal of the Society for Neuroscience.

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

[97]  A. Grinvald,et al.  Dynamics of Ongoing Activity: Explanation of the Large Variability in Evoked Cortical Responses , 1996, Science.

[98]  J. D. Burgos,et al.  Zipf-scaling behavior in the immune system. , 1996, Bio Systems.

[99]  H. Sompolinsky,et al.  Chaos in Neuronal Networks with Balanced Excitatory and Inhibitory Activity , 1996, Science.

[100]  Christensen,et al.  Tracer Dispersion in a Self-Organized Critical System. , 1996, Physical review letters.

[101]  James H. Brown,et al.  A General Model for the Origin of Allometric Scaling Laws in Biology , 1997, Science.

[102]  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.

[103]  Eytan Domany,et al.  Damage spreading in the Ising model , 1997 .

[104]  G. Ermentrout Principles of brain functioning: A synergetic approach to brain activity, behavior, and cognition , 1997 .

[105]  E. Novikov,et al.  Scale-similar activity in the brain , 1997 .

[106]  D. Amit,et al.  Model of global spontaneous activity and local structured activity during delay periods in the cerebral cortex. , 1997, Cerebral cortex.

[107]  M O Magnasco,et al.  A model for amplification of hair-bundle motion by cyclical binding of Ca2+ to mechanoelectrical-transduction channels. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[108]  M. Marsili,et al.  Interacting Individuals Leading to Zipf's Law , 1998, cond-mat/9801289.

[109]  Daniel Lehmann,et al.  Regulated Criticality in the Brain? , 1998, Adv. Complex Syst..

[110]  M. A. Muñoz,et al.  DRIVING, CONSERVATION, AND ABSORBING STATES IN SANDPILES , 1998, cond-mat/9806249.

[111]  Henrik Jeldtoft Jensen,et al.  Self-Organized Criticality: Emergent Complex Behavior in Physical and Biological Systems , 1998 .

[112]  Henrik Jeldtoft Jensen,et al.  Self-Organized Criticality , 1998 .

[113]  D. Sornette Multiplicative processes and power laws , 1997, cond-mat/9708231.

[114]  Andrea Gabrielli,et al.  Disordered one-dimensional contact process , 1998 .

[115]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[116]  L. Amaral,et al.  Multifractality in human heartbeat dynamics , 1998, Nature.

[117]  J. Drake,et al.  Mutation rates among RNA viruses. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[118]  D. Turcotte,et al.  Self-organized criticality , 1999 .

[119]  R. Dickman,et al.  Nonequilibrium Phase Transitions in Lattice Models , 1999 .

[120]  D. Botstein,et al.  Exploring the new world of the genome with DNA microarrays , 1999, Nature Genetics.

[121]  Amos Maritan,et al.  Size and form in efficient transportation networks , 1999, Nature.

[122]  P. Bak,et al.  Learning from mistakes , 1997, Neuroscience.

[123]  Deepak Dhar The Abelian sandpile and related models , 1999 .

[124]  Benton,et al.  Criticality and scaling in evolutionary ecology. , 1997, Trends in ecology & evolution.

[125]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[126]  J. Hopfield,et al.  From molecular to modular cell biology , 1999, Nature.

[127]  Doyle,et al.  Highly optimized tolerance: robustness and design in complex systems , 2000, Physical review letters.

[128]  A. Hudspeth,et al.  Essential nonlinearities in hearing. , 2000, Physical review letters.

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

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

[131]  Yudong D. He,et al.  Functional Discovery via a Compendium of Expression Profiles , 2000, Cell.

[132]  Maria V. Sanchez-Vives,et al.  Cellular and network mechanisms of rhythmic recurrent activity in neocortex , 2000, Nature Neuroscience.

[133]  F. Jülicher,et al.  Auditory sensitivity provided by self-tuned critical oscillations of hair cells. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[134]  Lubeck,et al.  Scaling of waves in the bak-tang-wiesenfeld sandpile model , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[135]  S. Rose,et al.  The future of the brain. , 2000, Biologist.

[136]  H. Hinrichsen Non-equilibrium critical phenomena and phase transitions into absorbing states , 2000, cond-mat/0001070.

[137]  Zapperi,et al.  Absorbing-state phase transitions in fixed-energy sandpiles , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[138]  J. Sethna,et al.  Crackling noise , 2001, Nature.

[139]  Alessandro Vespignani,et al.  Explaining the uneven distribution of numbers in nature: the laws of Benford and Zipf , 2001 .

[140]  M. Magnasco,et al.  Evidence of a Hopf bifurcation in frog hair cells. , 2001, Biophysical journal.

[141]  Sidney Redner,et al.  A guide to first-passage processes , 2001 .

[142]  Peter Dayan,et al.  Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems , 2001 .

[143]  Sorin Solomon,et al.  POWER LAWS ARE DISGUISED BOLTZMANN LAWS , 2001 .

[144]  G L Shulman,et al.  INAUGURAL ARTICLE by a Recently Elected Academy Member:A default mode of brain function , 2001 .

[145]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.

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

[147]  R. Segev,et al.  Spontaneous synchronized bursting in 2D neural networks , 2001 .

[148]  B. Kendall Nonlinear Dynamics and Chaos , 2001 .

[149]  T. Gisiger Scale invariance in biology: coincidence or footprint of a universal mechanism? , 2001, Biological reviews of the Cambridge Philosophical Society.

[150]  C. Cameron,et al.  RNA virus error catastrophe: Direct molecular test by using ribavirin , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[151]  H. Hinrichsen,et al.  Critical coarsening without surface tension: the universality class of the voter model. , 2001, Physical review letters.

[152]  Hiroaki Kitano,et al.  Foundations of systems biology , 2001 .

[153]  J. Martinerie,et al.  The brainweb: Phase synchronization and large-scale integration , 2001, Nature Reviews Neuroscience.

[154]  A J Hudspeth,et al.  Comparison of a hair bundle's spontaneous oscillations with its response to mechanical stimulation reveals the underlying active process , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[155]  D. Sumpter,et al.  Phase transition between disordered and ordered foraging in Pharaoh's ants , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[156]  Y Shapira,et al.  Observations and modeling of synchronized bursting in two-dimensional neural networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[157]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[158]  Vinod Menon,et al.  Functional connectivity in the resting brain: A network analysis of the default mode hypothesis , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[159]  S. N. Dorogovtsev,et al.  Evolution of networks , 2001, cond-mat/0106144.

[160]  Vittorio Loreto,et al.  Language trees and zipping. , 2002, Physical review letters.

[161]  Manfred Eigen,et al.  Error catastrophe and antiviral strategy , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[162]  R. R. Krausz Living in Groups , 2013 .

[163]  R. Solé,et al.  Selection, Tinkering, and Emergence in Complex Networks - Crossing the Land of Tinkering , 2002 .

[164]  S. Bornholdt,et al.  Criticality in random threshold networks: annealed approximation and beyond , 2002, cond-mat/0201079.

[165]  Jeffrey M. Hausdorff,et al.  Fractal dynamics in physiology: Alterations with disease and aging , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[166]  A. Barabasi,et al.  Hierarchical Organization of Modularity in Metabolic Networks , 2002, Science.

[167]  Hidde de Jong,et al.  Modeling and Simulation of Genetic Regulatory Systems: A Literature Review , 2002, J. Comput. Biol..

[168]  W. Reed,et al.  From gene families and genera to incomes and internet file sizes: why power laws are so common in nature. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[169]  Ricard V Solé,et al.  Self-organized instability in complex ecosystems. , 2002, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[170]  Henry Markram,et al.  Real-Time Computing Without Stable States: A New Framework for Neural Computation Based on Perturbations , 2002, Neural Computation.

[171]  Katherine C. Chen,et al.  Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell. , 2003, Current opinion in cell biology.

[172]  J. Stoyanov A Guide to First‐passage Processes , 2003 .

[173]  C. Furusawa,et al.  Zipf's law in gene expression. , 2002, Physical review letters.

[174]  Luc Moreau,et al.  Balancing at the border of instability. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[175]  W. Freeman,et al.  Spatial spectra of scalp EEG and EMG from awake humans , 2003, Clinical Neurophysiology.

[176]  Michael Mitzenmacher,et al.  A Brief History of Generative Models for Power Law and Lognormal Distributions , 2004, Internet Math..

[177]  I. Couzin,et al.  Self-Organization and Collective Behavior in Vertebrates , 2003 .

[178]  Joël Tabak,et al.  Analysis of spontaneous bursting activity in random neural networks , 2003, Neuroreport.

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

[180]  Carsten Peterson,et al.  Random Boolean network models and the yeast transcriptional network , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[181]  R. Stoop,et al.  Essential Role of Couplings between Hearing Nonlinearities. , 2003, Physical review letters.

[182]  Ricard V. Solé,et al.  Phase transitions in unstable cancer cell populations , 2003 .

[183]  Marcelo O Magnasco A wave traveling over a Hopf instability shapes the cochlear tuning curve. , 2003, Physical review letters.

[184]  Frank Jülicher,et al.  Active traveling wave in the cochlea. , 2003, Physical review letters.

[185]  M. Aldana Boolean dynamics of networks with scale-free topology , 2003 .

[186]  U. Alon Biological Networks: The Tinkerer as an Engineer , 2003, Science.

[187]  H. Othmer,et al.  The topology of the regulatory interactions predicts the expression pattern of the segment polarity genes in Drosophila melanogaster. , 2003, Journal of theoretical biology.

[188]  A. Pikovsky,et al.  Synchronization: Theory and Application , 2003 .

[189]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[190]  Short-period attractors and non-ergodic behavior in the deterministic fixed-energy sandpile model , 2002, cond-mat/0207674.

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

[192]  S. Cortassa,et al.  Percolation and criticality in a mitochondrial network. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[193]  Dante R. Chialvo Critical brain networks , 2004 .

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

[195]  Q. Ouyang,et al.  The yeast cell-cycle network is robustly designed. , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[196]  Ricard V Solé,et al.  An error catastrophe in cancer? , 2004, Journal of theoretical biology.

[197]  Junichiro Hayano,et al.  Critical scale invariance in a healthy human heart rate. , 2004, Physical review letters.

[198]  P. Alstrøm,et al.  COMPLEXITY AND CRITICALITY , 2004 .

[199]  E. Sackmann,et al.  Phase transformations in a model mesenchymal tissue , 2004, Physical biology.

[200]  Nicolas Brunel,et al.  Dynamics of Sparsely Connected Networks of Excitatory and Inhibitory Spiking Neurons , 2000, Journal of Computational Neuroscience.

[201]  M Villani,et al.  Genetic network models and statistical properties of gene expression data in knock-out experiments. , 2004, Journal of theoretical biology.

[202]  O. Sporns,et al.  Organization, development and function of complex brain networks , 2004, Trends in Cognitive Sciences.

[203]  Eugene M. Izhikevich,et al.  Which model to use for cortical spiking neurons? , 2004, IEEE Transactions on Neural Networks.

[204]  C. Espinosa-Soto,et al.  A Gene Regulatory Network Model for Cell-Fate Determination during Arabidopsis thaliana Flower Development That Is Robust and Recovers Experimental Gene Expression Profilesw⃞ , 2004, The Plant Cell Online.

[205]  John M. Beggs,et al.  Behavioral / Systems / Cognitive Neuronal Avalanches Are Diverse and Precise Activity Patterns That Are Stable for Many Hours in Cortical Slice Cultures , 2004 .

[206]  Alvaro Corral Long-term clustering, scaling, and universality in the temporal occurrence of earthquakes. , 2004, Physical review letters.

[207]  H. Chaté,et al.  Onset of collective and cohesive motion. , 2004, Physical review letters.

[208]  H. Haken,et al.  A theoretical model of phase transitions in human hand movements , 2004, Biological Cybernetics.

[209]  M. Elowitz,et al.  Modeling a synthetic multicellular clock: repressilators coupled by quorum sensing. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[210]  A. Wagner Robustness and Evolvability in Living Systems , 2005 .

[211]  L. Trefethen,et al.  Spectra and pseudospectra : the behavior of nonnormal matrices and operators , 2005 .

[212]  Olaf Sporns,et al.  The Human Connectome: A Structural Description of the Human Brain , 2005, PLoS Comput. Biol..

[213]  A. Lansner,et al.  The cortex as a central pattern generator , 2005, Nature Reviews Neuroscience.

[214]  Zbigniew R Struzik,et al.  Phase transition in a healthy human heart rate. , 2005, Physical review letters.

[215]  Stephen M. Smith,et al.  Investigations into resting-state connectivity using independent component analysis , 2005, Philosophical Transactions of the Royal Society B: Biological Sciences.

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

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

[218]  R. Spigler,et al.  The Kuramoto model: A simple paradigm for synchronization phenomena , 2005 .

[219]  Walter J. Freeman,et al.  Metastability, instability, and state transition in neocortex , 2005, Neural Networks.

[220]  I. Couzin,et al.  Effective leadership and decision-making in animal groups on the move , 2005, Nature.

[221]  Albert-László Barabási,et al.  The origin of bursts and heavy tails in human dynamics , 2005, Nature.

[222]  David E. Goldberg,et al.  Genetic algorithms and Machine Learning , 1988, Machine Learning.

[223]  Stefan Bornholdt,et al.  Less Is More in Modeling Large Genetic Networks , 2005, Science.

[224]  S. Leibler,et al.  Phenotypic Diversity, Population Growth, and Information in Fluctuating Environments , 2005, Science.

[225]  Gabriel S. Eichler,et al.  Cell fates as high-dimensional attractor states of a complex gene regulatory network. , 2005, Physical review letters.

[226]  Ilya Shmulevich,et al.  Eukaryotic cells are dynamically ordered or critical but not chaotic. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[227]  A. Arkin,et al.  Diversity in times of adversity: probabilistic strategies in microbial survival games. , 2005, Journal of theoretical biology.

[228]  J. Toner,et al.  Hydrodynamics and phases of flocks , 2005 .

[229]  Kim Christensen,et al.  Complexity and Criticality , 2005 .

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

[231]  Kevin E Bassler,et al.  Emergent criticality from coevolution in random Boolean networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[232]  Michael J. Berry,et al.  Weak pairwise correlations imply strongly correlated network states in a neural population , 2005, Nature.

[233]  O. Yli-Harja,et al.  Perturbation avalanches and criticality in gene regulatory networks. , 2006, Journal of theoretical biology.

[234]  A. Selverston,et al.  Dynamical principles in neuroscience , 2006 .

[235]  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.

[236]  G. Buzsáki Rhythms of the brain , 2006 .

[237]  Joseph J. Hale,et al.  From Disorder to Order in Marching Locusts , 2006, Science.

[238]  D. Chialvo Are our senses critical? , 2006 .

[239]  Thomas Vojta,et al.  TOPICAL REVIEW: Rare region effects at classical, quantum and nonequilibrium phase transitions , 2006 .

[240]  Jordi Soriano,et al.  Hydra molecular network reaches criticality at the symmetry-breaking axis-defining moment. , 2006, Physical review letters.

[241]  Misha Tsodyks,et al.  The Emergence of Up and Down States in Cortical Networks , 2006, PLoS Comput. Biol..

[242]  Eugene V. Koonin,et al.  Power Laws, Scale-Free Networks and Genome Biology , 2006 .

[243]  P. Ivanov Scale-invariant Aspects of Cardiac Dynamics Across Sleep Stages and Circadian Phases , 2007, 2006 International Conference of the IEEE Engineering in Medicine and Biology Society.

[244]  D. Retzloff,et al.  Phase transition as a mechanism of DNA opening for replication and transcription. , 2006, Mathematical biosciences.

[245]  Danny Eytan,et al.  Dynamics and Effective Topology Underlying Synchronization in Networks of Cortical Neurons , 2006, The Journal of Neuroscience.

[246]  C. Bédard,et al.  Does the 1/f frequency scaling of brain signals reflect self-organized critical states? , 2006, Physical review letters.

[247]  Eugene M. Izhikevich,et al.  Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting , 2006 .

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

[249]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

[250]  S. Platek,et al.  Evolutionary Cognitive Neuroscience , 2006 .

[251]  Kunihiko Kaneko,et al.  Life: An Introduction to Complex Systems Biology , 2006 .

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

[253]  Samuel Litwin,et al.  Examining The Theory of Error Catastrophe , 2006, Journal of Virology.

[254]  T. Geisel,et al.  The scaling laws of human travel , 2006, Nature.

[255]  H. Markram The Blue Brain Project , 2006, Nature Reviews Neuroscience.

[256]  Introduction To Genomics , 2007 .

[257]  Herbert Jaeger,et al.  Echo state network , 2007, Scholarpedia.

[258]  T. Rohlf,et al.  Damage spreading and criticality in finite random dynamical networks. , 2007, Physical review letters.

[259]  D. Plenz,et al.  The organizing principles of neuronal avalanches: cell assemblies in the cortex? , 2007, Trends in Neurosciences.

[260]  S. Kauffman,et al.  Robustness and evolvability in genetic regulatory networks. , 2007, Journal of theoretical biology.

[261]  V. Torre,et al.  On the Dynamics of the Spontaneous Activity in Neuronal Networks , 2007, PloS one.

[262]  I. Couzin Collective minds , 2007, Nature.

[263]  M. Fox,et al.  Spontaneous fluctuations in brain activity observed with functional magnetic resonance imaging , 2007, Nature Reviews Neuroscience.

[264]  I. Shmulevich,et al.  Basin entropy in Boolean network ensembles. , 2007, Physical review letters.

[265]  K. Gawrisch,et al.  Critical fluctuations in domain-forming lipid mixtures , 2007, Proceedings of the National Academy of Sciences.

[266]  Gerhard Werner,et al.  Metastability, criticality and phase transitions in brain and its models , 2007, Biosyst..

[267]  I. Aranson,et al.  Concentration dependence of the collective dynamics of swimming bacteria. , 2007, Physical review letters.

[268]  Robert A. Legenstein,et al.  2007 Special Issue: Edge of chaos and prediction of computational performance for neural circuit models , 2007 .

[269]  Néstor Parga,et al.  Network Model of Spontaneous Activity Exhibiting Synchronous Transitions Between Up and Down States , 2007, Front. Neurosci..

[270]  S. Kauffman,et al.  Why a simple model of genetic regulatory networks describes the distribution of avalanches in gene expression data. , 2007, Journal of theoretical biology.

[271]  Sergey N. Dorogovtsev,et al.  Critical phenomena in complex networks , 2007, ArXiv.

[272]  John M Beggs,et al.  The criticality hypothesis: how local cortical networks might optimize information processing , 2008, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

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

[274]  Guido Caldarelli,et al.  Scale-Free Networks , 2007 .

[275]  Thilo Gross,et al.  Adaptive coevolutionary networks: a review , 2007, Journal of The Royal Society Interface.

[276]  Thomas C G Bosch,et al.  Why polyps regenerate and we don't: towards a cellular and molecular framework for Hydra regeneration. , 2007, Developmental biology.

[277]  Guido Caldarelli,et al.  Scale-Free Networks , 2007 .

[278]  A. J. McKane,et al.  Stochastic models of evolution in genetics, ecology and linguistics , 2007, cond-mat/0703478.

[279]  W. Maass,et al.  Self-tuning of neural circuits through short-term synaptic plasticity. , 2007, Journal of neurophysiology.

[280]  S. Kauffman,et al.  Measures for information propagation in Boolean networks , 2007 .

[281]  U. Sauer,et al.  Getting Closer to the Whole Picture , 2007, Science.

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

[283]  Heinz Georg Schuster,et al.  Reviews of nonlinear dynamics and complexity , 2008 .

[284]  Thimo Rohlf,et al.  Self-organization of heterogeneous topology and symmetry breaking in networks with adaptive thresholds and rewiring , 2007, 0708.1637.

[285]  Giorgio Parisi,et al.  The STARFLAG handbook on collective animal behaviour: Part I, empirical methods , 2008, 0802.1668.

[286]  Cristóbal López,et al.  Crystallization and melting of bacteria colonies and Brownian bugs. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[287]  Viktor K. Jirsa,et al.  Noise during Rest Enables the Exploration of the Brain's Dynamic Repertoire , 2008, PLoS Comput. Biol..

[288]  H. Stanley,et al.  Phase Transitions and Critical Phenomena , 2008 .

[289]  Gerald H. Pollack,et al.  Phase Transitions in Cell Biology , 2008 .

[290]  Line tensions, correlation lengths, and critical exponents in lipid membranes near critical points. , 2008, Biophysical journal.

[291]  Alessandro Vespignani,et al.  Dynamical Processes on Complex Networks , 2008 .

[292]  Jason Lloyd-Price,et al.  Mutual information in random Boolean models of regulatory networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[293]  D. Plenz,et al.  Homeostasis of neuronal avalanches during postnatal cortex development in vitro , 2008, Journal of Neuroscience Methods.

[294]  S. Kauffman,et al.  Critical Dynamics in Genetic Regulatory Networks: Examples from Four Kingdoms , 2008, PloS one.

[295]  Claudius Gros,et al.  Complex and Adaptive Dynamical Systems: A Primer , 2008 .

[296]  H. Chaté,et al.  Collective motion of self-propelled particles interacting without cohesion. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[297]  David A. Winkler,et al.  Critical-like self-organization and natural selection: Two facets of a single evolutionary process? , 2008, Biosyst..

[298]  L. Hood,et al.  Gene expression dynamics in the macrophage exhibit criticality , 2008, Proceedings of the National Academy of Sciences.

[299]  Géza Ódor,et al.  Universality in Nonequilibrium Lattice Systems: Theoretical Foundations , 2008 .

[300]  B. Duchaine Evolutionary Cognitive Neuroscience , 2008 .

[301]  L. L. Bologna,et al.  Self-organization and neuronal avalanches in networks of dissociated cortical neurons , 2008, Neuroscience.

[302]  R. Hanel,et al.  Inflation of the edge of chaos in a simple model of gene interaction networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[303]  H. Chaté,et al.  Modeling collective motion: variations on the Vicsek model , 2008 .

[304]  Valery Tereshko,et al.  Phase Transitions and Bistability in Honeybee Foraging Dynamics , 2008, Artificial Life.

[305]  Albert Y. Zomaya,et al.  Local information transfer as a spatiotemporal filter for complex systems. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[306]  Giorgio Parisi,et al.  The STARFLAG handbook on collective animal behaviour: 1. Empirical methods , 2008, Animal Behaviour.

[307]  Ilya Shmulevich,et al.  Critical networks exhibit maximal information diversity in structure-dynamics relationships. , 2008, Physical review letters.

[308]  Stefan Bornholdt,et al.  Boolean network models of cellular regulation: prospects and limitations , 2008, Journal of The Royal Society Interface.

[309]  O. Sporns,et al.  Mapping the Structural Core of Human Cerebral Cortex , 2008, PLoS biology.

[310]  G. Parisi,et al.  Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study , 2007, Proceedings of the National Academy of Sciences.

[311]  Prabuddha Sengupta,et al.  Critical fluctuations in plasma membrane vesicles. , 2008, ACS chemical biology.

[312]  D. Chialvo,et al.  The Brain: What is Critical About It? , 2008, 0804.0032.

[313]  Nicolas Brunel,et al.  Sparsely synchronized neuronal oscillations. , 2008, Chaos.

[314]  O. Kuipers,et al.  Bistability, epigenetics, and bet-hedging in bacteria. , 2008, Annual review of microbiology.

[315]  D. Plenz,et al.  Neuronal avalanches organize as nested theta- and beta/gamma-oscillations during development of cortical layer 2/3 , 2008, Proceedings of the National Academy of Sciences.

[316]  Jurgen Kurths,et al.  Synchronization in complex networks , 2008, 0805.2976.

[317]  Dante R Chialvo,et al.  Emergent self-organized complex network topology out of stability constraints. , 2008, Physical review letters.

[318]  Michael J. Berry,et al.  Spin glass models for a network of real neurons , 2009, 0912.5409.

[319]  Sten Rüdiger,et al.  Mechanogenetic coupling of Hydra symmetry breaking and driven Turing instability model. , 2009, Biophysical journal.

[320]  K. Miller,et al.  Balanced Amplification: A New Mechanism of Selective Amplification of Neural Activity Patterns , 2009, Neuron.

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

[322]  M. A. Muñoz,et al.  Self-organization without conservation: true or just apparent scale-invariance? , 2009, 0905.1799.

[323]  Florian Greil,et al.  Critical Boolean networks with scale-free in-degree distribution. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[325]  Alain Destexhe,et al.  Self-sustained Asynchronous Irregular States and Up–down States in Thalamic, Cortical and Thalamocortical Networks of Nonlinear Integrate-and-fire Neurons , 2022 .

[326]  Mark E. J. Newman,et al.  Power-Law Distributions in Empirical Data , 2007, SIAM Rev..

[327]  J. C. Phillips Scaling and self-organized criticality in proteins I , 2009, Proceedings of the National Academy of Sciences.

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

[329]  Barak A. Pearlmutter,et al.  A New Hypothesis for Sleep: Tuning for Criticality , 2009, Neural Computation.

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

[331]  I. Couzin Collective cognition in animal groups , 2009, Trends in Cognitive Sciences.

[332]  M. Magnasco,et al.  Self-tuned critical anti-Hebbian networks. , 2009, Physical review letters.

[333]  X. Illa,et al.  The effect of thresholding on temporal avalanche statistics , 2008, 0810.0948.

[334]  S. Leibler,et al.  Neuronal couplings between retinal ganglion cells inferred by efficient inverse statistical physics methods , 2009, Proceedings of the National Academy of Sciences.

[335]  D. Chialvo,et al.  Ising-like dynamics in large-scale functional brain networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[336]  F. Burden,et al.  Stem cell decision making and critical-like exploratory networks. , 2009, Stem cell research.

[337]  D. Chialvo Emergent complex neural dynamics , 2010, 1010.2530.

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

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

[340]  J. Touboul,et al.  Can Power-Law Scaling and Neuronal Avalanches Arise from Stochastic Dynamics? , 2009, PloS one.

[341]  Allon M Klein,et al.  Intestinal Stem Cell Replacement Follows a Pattern of Neutral Drift , 2010, Science.

[342]  G. Parisi,et al.  Scale-free correlations in starling flocks , 2009, Proceedings of the National Academy of Sciences.

[343]  Hilbert J. Kappen,et al.  Irregular Dynamics in Up and Down Cortical States , 2010, PloS one.

[344]  O. Sporns Networks of the Brain , 2010 .

[345]  W. Bialek,et al.  Maximum entropy models for antibody diversity , 2009, Proceedings of the National Academy of Sciences.

[346]  R. Hanel,et al.  Living on the edge of chaos: minimally nonlinear models of genetic regulatory dynamics , 2010, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[347]  Arend Hintze,et al.  Critical Dynamics in the Evolution of Stochastic Strategies for the Iterated Prisoner's Dilemma , 2010, PLoS Comput. Biol..

[348]  Olli Yli-Harja,et al.  Information propagation within the Genetic Network of Saccharomyces cerevisiae , 2010, BMC Systems Biology.

[349]  Marc Benayoun,et al.  Avalanches in a Stochastic Model of Spiking Neurons , 2010, PLoS Comput. Biol..

[350]  Angelo Gemignani,et al.  Fractal Complexity in Spontaneous EEG Metastable-State Transitions: New Vistas on Integrated Neural Dynamics , 2010, Front. Physiology.

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

[352]  Edward T. Bullmore,et al.  Modular and Hierarchically Modular Organization of Brain Networks , 2010, Front. Neurosci..

[353]  T. Vicsek,et al.  Collective Motion , 1999, physics/9902023.

[354]  G. Deco,et al.  Emerging concepts for the dynamical organization of resting-state activity in the brain , 2010, Nature Reviews Neuroscience.

[355]  James H. Brown,et al.  A general basis for quarter-power scaling in animals , 2010, Proceedings of the National Academy of Sciences.

[356]  Bruce J. West,et al.  Complex webs : anticipating the improbable , 2010 .

[357]  M. Buchanan,et al.  Networks in cell biology , 2010 .

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

[359]  Avi Ma'ayan,et al.  Microdynamics and criticality of adaptive regulatory networks. , 2009, Physical review letters.

[360]  A. Maritan,et al.  Applications of the principle of maximum entropy: from physics to ecology , 2010, Journal of physics. Condensed matter : an Institute of Physics journal.

[361]  M. Shanahan Metastable chimera states in community-structured oscillator networks. , 2009, Chaos.

[362]  Filippo Simini,et al.  Self-similarity and scaling in forest communities , 2010, Proceedings of the National Academy of Sciences.

[363]  V. Roychowdhury,et al.  Re-inventing Willis , 2006, physics/0601192.

[364]  Christopher T. Kello,et al.  Scaling laws in cognitive sciences , 2010, Trends in Cognitive Sciences.

[365]  D. Sumpter Collective Animal Behavior , 2010 .

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

[367]  Frank Jülicher,et al.  A critique of the critical cochlea: Hopf--a bifurcation--is better than none. , 2010, Journal of neurophysiology.

[368]  John M. Beggs,et al.  Aberrant Neuronal Avalanches in Cortical Tissue Removed From Juvenile Epilepsy Patients , 2010, Journal of clinical neurophysiology : official publication of the American Electroencephalographic Society.

[369]  S. Ramaswamy The Mechanics and Statistics of Active Matter , 2010, 1004.1933.

[370]  Mark Newman,et al.  Networks: An Introduction , 2010 .

[371]  W. Singer,et al.  Neuronal avalanches in spontaneous activity in vivo. , 2010, Journal of neurophysiology.

[372]  M. A. Muñoz,et al.  Griffiths phases on complex networks. , 2010, Physical review letters.

[373]  Edward R. Dougherty,et al.  Probabilistic Boolean Networks - The Modeling and Control of Gene Regulatory Networks , 2010 .

[374]  Maria V. Sanchez-Vives,et al.  Exploring the spectrum of dynamical regimes and timescales in spontaneous cortical activity , 2012, Cognitive Neurodynamics.

[375]  A. Kamenev Field Theory of Non-Equilibrium Systems , 2011 .

[376]  Marcus E. Raichle,et al.  The Restless Brain , 2011, Brain Connect..

[377]  X. Rosalind Wang,et al.  Fisher Information at the Edge of Chaos in Random Boolean Networks , 2011, Artificial Life.

[378]  J. Tuszynski,et al.  Cancer as a dynamical phase transition , 2011, Theoretical Biology and Medical Modelling.

[379]  Carlos Gershenson,et al.  Guiding the self-organization of random Boolean networks , 2010, Theory in Biosciences.

[380]  Andrew T. Hartnett,et al.  This PDF file includes: Materials and Methods SOM Text Figs. S1 to S12 Table S1 Full Reference List , 2022 .

[381]  Shan Yu,et al.  Higher-Order Interactions Characterized in Cortical Activity , 2011, The Journal of Neuroscience.

[382]  Fabio Vanni,et al.  Criticality and transmission of information in a swarm of cooperative units. , 2011, Physical review letters.

[383]  Marcus Kaiser,et al.  A tutorial in connectome analysis: Topological and spatial features of brain networks , 2011, NeuroImage.

[384]  W. Bialek,et al.  Are Biological Systems Poised at Criticality? , 2010, 1012.2242.

[385]  E. Koonin The Logic of Chance: The Nature and Origin of Biological Evolution , 2011 .

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

[387]  Biyu J. He Scale-Free Properties of the Functional Magnetic Resonance Imaging Signal during Rest and Task , 2011, The Journal of Neuroscience.

[388]  M. A. Muñoz,et al.  Quasi-Neutral Theory of Epidemic Outbreaks , 2011, PloS one.

[389]  L. Arcangelis Neuronal avalanches and learning , 2011 .

[390]  W. Ashby,et al.  Design for a brain; the origin of adaptive behavior , 2011 .

[391]  N. Goldenfeld,et al.  Life is Physics: Evolution as a Collective Phenomenon Far From Equilibrium , 2010, 1011.4125.

[392]  Carlos Gershenson,et al.  Modular Random Boolean Networks1 , 2011, Artificial Life.

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

[394]  D. Long Networks of the Brain , 2011 .

[395]  Jordi Garcia-Ojalvo,et al.  Physical approaches to the dynamics of genetic circuits: a tutorial , 2011, 1105.4335.

[396]  P. Schwille,et al.  Near-critical fluctuations and cytoskeleton-assisted phase separation lead to subdiffusion in cell membranes. , 2010, Biophysical journal.

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

[398]  Gustavo Deco,et al.  Role of local network oscillations in resting-state functional connectivity , 2011, NeuroImage.

[399]  L. Abbott,et al.  Beyond the edge of chaos: amplification and temporal integration by recurrent networks in the chaotic regime. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[400]  Sebastian Bernhardsson,et al.  Zipf's law unzipped , 2011, ArXiv.

[401]  S. Hubbell The Unified Neutral Theory of Biodiversity and Biogeography (MPB-32) , 2011 .

[402]  Hermann Haken Principles of Brain Functioning: A Synergetic Approach to Brain Activity, Behavior and Cognition , 2012 .

[403]  W. Bialek,et al.  Statistical mechanics for natural flocks of birds , 2011, Proceedings of the National Academy of Sciences.

[404]  Vojkan Jaksic,et al.  Field Theory of Non-Equilibrium Systems , 2012 .

[405]  Benjamin Schrauwen,et al.  Reservoir Computing Trends , 2012, KI - Künstliche Intelligenz.

[406]  C. Kuehn Time-scale and noise optimality in self-organized critical adaptive networks. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[407]  M. Porter,et al.  Critical Truths About Power Laws , 2012, Science.

[408]  G. Pruessner Self-Organised Criticality: Theory, Models and Characterisation , 2012 .

[409]  Miao‐kun Sun,et al.  Trends in cognitive sciences , 2012 .

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

[411]  M. Kikuchi,et al.  Robustness Leads Close to the Edge of Chaos in Coupled Map Networks: toward the understanding of biological networks , 2012, 1205.3944.

[412]  Meng Xu,et al.  Allometric scaling of population variance with mean body size is predicted from Taylor’s law and density-mass allometry , 2012, Proceedings of the National Academy of Sciences.

[413]  Pablo Balenzuela,et al.  Criticality in Large-Scale Brain fMRI Dynamics Unveiled by a Novel Point Process Analysis , 2012, Front. Physio..

[414]  C. Furusawa,et al.  A Dynamical-Systems View of Stem Cell Biology , 2012, Science.

[415]  Matt Visser,et al.  Zipf's law, power laws and maximum entropy , 2012, 1212.5567.

[416]  J. Crutchfield Between order and chaos , 2011, Nature Physics.

[417]  Jayanth R Banavar,et al.  Scale invariance in the dynamics of spontaneous behavior , 2012, Proceedings of the National Academy of Sciences.

[418]  W. Bialek Biophysics: Searching for Principles , 2012 .

[419]  Critical behavior and axis defining symmetry breaking in Hydra embryonic development. , 2012, Physical review letters.

[420]  H. Swinney,et al.  Scale-invariant correlations in dynamic bacterial clusters. , 2012, Physical review letters.

[421]  L. de Arcangelis,et al.  Are dragon-king neuronal avalanches dungeons for self-organized brain activity? , 2012 .

[422]  Karl J. Friston,et al.  Perception and self-organized instability , 2012, Front. Comput. Neurosci..

[423]  Sui Huang,et al.  Criticality Is an Emergent Property of Genetic Networks that Exhibit Evolvability , 2012, PLoS Comput. Biol..

[424]  Andreas Deutsch,et al.  Collective motion and nonequilibrium cluster formation in colonies of gliding bacteria. , 2012, Physical review letters.

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

[426]  Hans J. Herrmann,et al.  Activity-Dependent Neuronal Model on Complex Networks , 2012, Front. Physio..

[427]  A. Hyman,et al.  Beyond Oil and Water—Phase Transitions in Cells , 2012, Science.

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

[429]  Woodrow L. Shew,et al.  Maximal Variability of Phase Synchrony in Cortical Networks with Neuronal Avalanches , 2012, The Journal of Neuroscience.

[430]  F. Scheer,et al.  Fractal Patterns of Neural Activity Exist within the Suprachiasmatic Nucleus and Require Extrinsic Network Interactions , 2012, PloS one.

[431]  Julián Candia,et al.  Criticality and the onset of ordering in the standard Vicsek model , 2012, Interface Focus.

[432]  E. Aurell,et al.  Inverse Ising inference using all the data. , 2011, Physical review letters.

[433]  Kunihiko Kaneko,et al.  Evolution of Robustness and Plasticity under Environmental Fluctuation: Formulation in Terms of Phenotypic Variances , 2012, 1305.0366.

[434]  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.

[435]  M. A. Muñoz,et al.  Stochastic Amplification of Fluctuations in Cortical Up-States , 2012, PloS one.

[436]  Christof Teuscher,et al.  Emergent Criticality Through Adaptive Information Processing in Boolean Networks , 2011, Physical review letters.

[437]  Michael J. Berry,et al.  Mapping a Complete Neural Population in the Retina , 2012, The Journal of Neuroscience.

[438]  Kunihiko Kaneko,et al.  Adaptation to optimal cell growth through self-organized criticality. , 2012, Physical review letters.

[439]  J. García-Ojalvo,et al.  Towards a statistical mechanics of cell fate decisions. , 2012, Current opinion in genetics & development.

[440]  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.

[441]  Gustavo Deco,et al.  Resting brains never rest: computational insights into potential cognitive architectures , 2013, Trends in Neurosciences.

[442]  Joaquín Goñi,et al.  On the origins of hierarchy in complex networks , 2013, Proceedings of the National Academy of Sciences.

[443]  I. Couzin,et al.  Emergent Sensing of Complex Environments by Mobile Animal Groups , 2013, Science.

[444]  Richard F. Betzel,et al.  Multi-scale community organization of the human structural connectome and its relationship with resting-state functional connectivity , 2013, Network Science.

[445]  Dietmar Plenz,et al.  The Critical Brain , 2013 .

[446]  Matteo Marsili,et al.  The effect of nonstationarity on models inferred from neural data , 2012, 1203.5673.

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

[448]  Andrea Cavagna,et al.  Superfluid transport of information in turning flocks of starlings , 2013, 1303.7097.

[449]  F. MacKintosh,et al.  Molecular motors robustly drive active gels to a critically connected state , 2013, Nature Physics.

[450]  T. Bossomaier,et al.  Information flow in a kinetic Ising model peaks in the disordered phase. , 2013, Physical review letters.

[451]  B. Bassler,et al.  Cutting through the complexity of cell collectives , 2013, Proceedings of the Royal Society B: Biological Sciences.

[452]  Michael J. Berry,et al.  The simplest maximum entropy model for collective behavior in a neural network , 2012, 1207.6319.

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

[454]  Douglas H. Kelley,et al.  Emergent dynamics of laboratory insect swarms , 2013, Scientific Reports.

[455]  Maurizio Corbetta,et al.  Resting-State Functional Connectivity Emerges from Structurally and Dynamically Shaped Slow Linear Fluctuations , 2013, The Journal of Neuroscience.

[456]  S. Rosenfeld Global Consensus Theorem and Self-Organized Criticality: Unifying Principles for Understanding Self-Organization, Swarm Intelligence and Mechanisms of Carcinogenesis , 2013, Gene regulation and systems biology.

[457]  Shimon Marom,et al.  Self-organized criticality in single-neuron excitability. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[459]  Dante R Chialvo,et al.  Brain organization into resting state networks emerges at criticality on a model of the human connectome. , 2012, Physical review letters.

[460]  Leonardo L. Gollo,et al.  Single-neuron criticality optimizes analog dendritic computation , 2013, Scientific Reports.

[461]  A. Hyman,et al.  Spatial organization of the cell cytoplasm by position-dependent phase separation. , 2013, Physical review letters.

[462]  A. Maritan,et al.  Emergence of structural and dynamical properties of ecological mutualistic networks , 2013, Nature.

[463]  O. Shriki,et al.  Fading Signatures of Critical Brain Dynamics during Sustained Wakefulness in Humans , 2013, The Journal of Neuroscience.

[464]  Matteo Marsili,et al.  On sampling and modeling complex systems , 2013, 1301.3622.

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

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

[467]  K. Linkenkaer-Hansen,et al.  Neuronal long-range temporal correlations and avalanche dynamics are correlated with behavioral scaling laws , 2013, Proceedings of the National Academy of Sciences.

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

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

[470]  M. A. Muñoz,et al.  Insect Swarms Go Critical , 2014 .

[471]  David J Schwab,et al.  Zipf's law and criticality in multivariate data without fine-tuning. , 2013, Physical review letters.

[472]  Yves Laberge Self-organised criticality: theory, models and characterisation , 2014 .

[473]  Michael J. Berry,et al.  Searching for Collective Behavior in a Large Network of Sensory Neurons , 2013, PLoS Comput. Biol..

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

[475]  A. Hudspeth Integrating the active process of hair cells with cochlear function , 2014, Nature Reviews Neuroscience.

[476]  W. Bialek,et al.  Social interactions dominate speed control in poising natural flocks near criticality , 2013, Proceedings of the National Academy of Sciences.

[477]  M. Corbetta,et al.  How Local Excitation–Inhibition Ratio Impacts the Whole Brain Dynamics , 2014, The Journal of Neuroscience.

[478]  D. Marković,et al.  Power laws and Self-Organized Criticality in Theory and Nature , 2013, 1310.5527.

[479]  Piet Van Mieghem,et al.  Epidemic processes in complex networks , 2014, ArXiv.

[480]  Andrea Rinaldo,et al.  Form, function, and evolution of living organisms , 2014, Proceedings of the National Academy of Sciences.

[481]  M. A. Muñoz,et al.  Frustrated hierarchical synchronization and emergent complexity in the human connectome network , 2014, Scientific Reports.

[482]  Andreas Klaus,et al.  Scale-Invariant Neuronal Avalanche Dynamics and the Cut-Off in Size Distributions , 2014, PloS one.

[483]  Indrani Bose,et al.  Non-genetic heterogeneity, criticality and cell differentiation , 2014, Physical biology.

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

[485]  Jesse Tinker,et al.  Power law scaling in synchronization of brain signals depends on cognitive load , 2014, Front. Syst. Neurosci..

[486]  B. Doiron,et al.  Balanced Networks of Spiking Neurons with Spatially Dependent Recurrent Connections , 2013, 1308.6014.

[487]  J Anthony Movshon,et al.  Putting big data to good use in neuroscience , 2014, Nature Neuroscience.

[488]  Tamás Vicsek,et al.  Collective motion of cells: from experiments to models. , 2014, Integrative biology : quantitative biosciences from nano to macro.

[489]  Julien O. Dubuis,et al.  Morphogenesis at criticality , 2013, Proceedings of the National Academy of Sciences.

[490]  Hans J. Herrmann,et al.  Criticality in the brain , 2014 .

[491]  Miguel A Muñoz,et al.  Quenched disorder forbids discontinuous transitions in nonequilibrium low-dimensional systems. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[492]  M. Shen,et al.  From blastocyst to gastrula: gene regulatory networks of embryonic stem cells and early mouse embryogenesis , 2014, Philosophical Transactions of the Royal Society B: Biological Sciences.

[493]  Stefan Bornholdt,et al.  Self‐Organized Criticality in Neural Network Models , 2012, 1212.3106.

[494]  David J. Schwab,et al.  An exact mapping between the Variational Renormalization Group and Deep Learning , 2014, ArXiv.

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

[496]  Uwe C. Täuber,et al.  Critical Dynamics: A Field Theory Approach to Equilibrium and Non-Equilibrium Scaling Behavior , 2014 .

[497]  A. Cavagna,et al.  Finite-size scaling as a way to probe near-criticality in natural swarms. , 2014, Physical review letters.

[498]  James G. Puckett,et al.  Determining asymptotically large population sizes in insect swarms , 2014, Journal of The Royal Society Interface.

[499]  John M. Beggs,et al.  Quasicritical brain dynamics on a nonequilibrium Widom line. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[500]  A. Keller,et al.  Humans Can Discriminate More than 1 Trillion Olfactory Stimuli , 2014, Science.

[501]  H. Frauenfelder Ask not what physics can do for biology—ask what biology can do for physics , 2014, Physical biology.

[502]  Theodore H. Schwartz,et al.  Dynamical criticality during induction of anesthesia in human ECoG recordings , 2014, Front. Neural Circuits.

[503]  D. Plenz,et al.  Criticality in neural systems , 2014 .

[504]  J. Kurths,et al.  Chaos–order transition in foraging behavior of ants , 2014, Proceedings of the National Academy of Sciences.

[505]  Tamás Vicsek,et al.  Collective foraging in heterogeneous landscapes , 2013, Journal of The Royal Society Interface.

[506]  J. Michael Herrmann,et al.  CriPS: Critical Particle Swarm Optimisation , 2015, ECAL.

[507]  Jorge Hidalgo,et al.  Cooperation, competition and the emergence of criticality in communities of adaptive systems , 2015 .

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

[509]  Marco Fiorucci,et al.  The Search for Candidate Relevant Subsets of Variables in Complex Systems , 2015, Artificial Life.

[510]  Ofer Feinerman,et al.  Ant groups optimally amplify the effect of transiently informed individuals , 2015, Nature Communications.

[511]  A. Maritan,et al.  Sample and population exponents of generalized Taylor’s law , 2014, Proceedings of the National Academy of Sciences.

[512]  Paolo Massobrio,et al.  Criticality as a signature of healthy neural systems , 2015, Front. Syst. Neurosci..

[513]  Konstantinos C Zygalakis,et al.  Entropy, Ergodicity, and Stem Cell Multipotency. , 2015, Physical review letters.

[514]  A. Giuliani,et al.  Emergent Self-Organized Criticality in Gene Expression Dynamics: Temporal Development of Global Phase Transition Revealed in a Cancer Cell Line , 2015, PloS one.

[515]  Andreas Klaus,et al.  Irregular spiking of pyramidal neurons organizes as scale-invariant neuronal avalanches in the awake state , 2015, eLife.

[516]  Gunnar Pruessner,et al.  25 Years of Self-organized Criticality: Concepts and Controversies , 2015, 1504.04991.

[517]  Matteo Marsili,et al.  Criticality of mostly informative samples: a Bayesian model selection approach , 2015, 1502.00356.

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

[519]  A. Deluca,et al.  The perils of thresholding , 2014, 1410.6048.

[520]  Hopf-type neurons increase input-sensitivity by forming forcing-coupled ensembles , 2015, 1510.03241.

[521]  I. Csabai,et al.  Quantum criticality at the origin of life , 2015, 1502.06880.

[522]  James G. King,et al.  Reconstruction and Simulation of Neocortical Microcircuitry , 2015, Cell.

[523]  Error catastrophe and phase transition in the empirical fitness landscape of HIV. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[524]  H. Chaté,et al.  Intermittent collective dynamics emerge from conflicting imperatives in sheep herds , 2015, Proceedings of the National Academy of Sciences.

[525]  Stefan Thurner,et al.  Physiologically motivated multiplex Kuramoto model describes phase diagram of cortical activity , 2014, Scientific Reports.

[526]  Ricard V. Sol'e,et al.  Systems poised to criticality through Pareto selective forces , 2015, 1510.08697.

[527]  Geoffrey E. Hinton,et al.  Deep Learning , 2015, Nature.

[528]  Christian A Yates,et al.  Onset of collective motion in locusts is captured by a minimal model. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[529]  Jürgen Jost,et al.  Self-organization in Balanced State Networks by STDP and Homeostatic Plasticity , 2015, PLoS Comput. Biol..

[530]  John Porrill,et al.  At the Edge of Chaos: How Cerebellar Granular Layer Network Dynamics Can Provide the Basis for Temporal Filters , 2015, PLoS Comput. Biol..

[531]  Henrik Jeldtoft Jensen,et al.  Criticality as a signature of healthy neural systems: multi-scale experimental and computational studies , 2015 .

[532]  M. A. Muñoz,et al.  A novel brain partition highlights the modular skeleton shared by structure and function , 2014, Scientific Reports.

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

[534]  M. Goodell,et al.  Somatic stem cell heterogeneity: diversity in the blood, skin and intestinal stem cell compartments , 2015, Nature Reviews Molecular Cell Biology.

[535]  Mauro Copelli,et al.  Can dynamical synapses produce true self-organized criticality? , 2014, 1405.7740.

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

[537]  Thierry Mora,et al.  Dynamical criticality in the collective activity of a population of retinal neurons. , 2014, Physical review letters.

[538]  M. Bethge,et al.  Signatures of criticality arise in simple neural population models with correlations , 2016, 1603.00097.

[539]  John M. Beggs,et al.  Unveiling causal activity of complex networks , 2016, 1603.05659.

[540]  R. Stoop,et al.  Auditory Power-Law Activation Avalanches Exhibit a Fundamental Computational Ground State. , 2016, Physical review letters.

[541]  Steven Laureys,et al.  Large-scale signatures of unconsciousness are consistent with a departure from critical dynamics , 2015, Journal of The Royal Society Interface.

[542]  Oren Shriki,et al.  Optimal Information Representation and Criticality in an Adaptive Sensory Recurrent Neuronal Network , 2016, PLoS Comput. Biol..

[543]  F. Ginelli The Physics of the Vicsek model , 2015, 1511.01451.

[544]  M. A. Muñoz,et al.  Self-Organized Bistability Associated with First-Order Phase Transitions. , 2016, Physical review letters.

[545]  Yrjö H. Roos,et al.  Introduction to phase transitions , 2016 .

[546]  Fabio Rinaldi,et al.  RegulonDB version 9.0: high-level integration of gene regulation, coexpression, motif clustering and beyond , 2015, Nucleic Acids Res..

[547]  Eric Smith,et al.  The Origin and Nature of Life on Earth: The Emergence of the Fourth Geosphere , 2016 .

[548]  Jérémie Barral,et al.  Synaptic scaling rule preserves excitatory–inhibitory balance and salient neuronal network dynamics , 2016, Nature Neuroscience.

[549]  Jorge Hidalgo,et al.  Intrinsic noise and deviations from criticality in Boolean gene-regulatory networks , 2016, Scientific Reports.

[550]  Mitochondria poised at a fission-fusion balance?: A quantitative assessment of mitochondrial network complexity , 2016, 1609.02133.

[551]  A. Maritan,et al.  Statistical mechanics of ecological systems: Neutral theory and beyond , 2015, 1506.01721.

[552]  A. Giuliani,et al.  Self-Organizing Global Gene Expression Regulated through Criticality: Mechanism of the Cell-Fate Change , 2016, bioRxiv.

[553]  J. Fortrat,et al.  Self-Organization of Blood Pressure Regulation: Clinical Evidence , 2016, Front. Physiol..

[554]  Max Tegmark,et al.  Criticality in Formal Languages and Statistical Physics∗ , 2017 .

[555]  Thierry Mora,et al.  Local equilibrium in bird flocks , 2015, Nature Physics.

[556]  Peter E. Latham,et al.  Zipf’s Law Arises Naturally When There Are Underlying, Unobserved Variables , 2016, PLoS Comput. Biol..

[557]  M. Alava,et al.  Interevent Correlations from Avalanches Hiding Below the Detection Threshold. , 2016, Physical review letters.

[558]  Junghyo Jo,et al.  Emergence and Relevance of Criticality in Deep Learning , 2017, ArXiv.

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

[560]  Dante R Chialvo,et al.  Critical Fluctuations in the Native State of Proteins. , 2017, Physical review letters.

[561]  Robert G. Endres,et al.  A critical-like collective state leads to long-range cell communication in Dictyostelium discoideum aggregation , 2017, bioRxiv.

[562]  I. Bose,et al.  Criticality in cell differentiation , 2016, bioRxiv.

[563]  Amos Korman,et al.  Individual versus collective cognition in social insects , 2017, Journal of Experimental Biology.

[564]  Peter Toth,et al.  Criticality & Deep Learning II: Momentum Renormalisation Group , 2017, ArXiv.

[565]  Fred Wolf,et al.  Flexible information routing by transient synchrony , 2017, Nature Neuroscience.

[566]  Daniel M. Conti,et al.  Dynamic scaling in natural swarms , 2016, Nature Physics.

[567]  M. Breakspear Dynamic models of large-scale brain activity , 2017, Nature Neuroscience.

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

[569]  Takahiro Sagawa,et al.  Dynamical crossover in a stochastic model of cell fate decision. , 2016, Physical review. E.

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

[571]  M. A. Muñoz,et al.  Simple unified view of branching process statistics: Random walks in balanced logarithmic potentials. , 2016, Physical review. E.

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

[573]  Models of Life , 2017 .

[574]  Ilaria Giannoccaro,et al.  Criticality triggers the emergence of collective intelligence in groups. , 2017, Physical review. E.

[575]  Peter Toth,et al.  Criticality & Deep Learning I: Generally Weighted Nets , 2017 .

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

[577]  William Bialek,et al.  Perspectives on theory at the interface of physics and biology , 2015, Reports on progress in physics. Physical Society.

[578]  Hovering stochastic oscillations in self-organized critical systems , 2018 .

[579]  Riccardo Gallotti,et al.  How ants move: individual and collective scaling properties , 2017, Journal of The Royal Society Interface.

[580]  G. Biroli,et al.  Marginally stable equilibria in critical ecosystems , 2017, New Journal of Physics.

[581]  M. A. Muñoz,et al.  Non-normality, reactivity, and intrinsic stochasticity in neural dynamics: a non-equilibrium potential approach , 2018, Journal of Statistical Mechanics: Theory and Experiment.

[582]  Zohar Ringel,et al.  Critical Percolation as a Framework to Analyze the Training of Deep Networks , 2018, ICLR.

[583]  Robert M. Vogel,et al.  Universality of biochemical feedback and its application to immune cells. , 2017, Physical review. E.

[584]  U. Alon An introduction to systems biology : design principles of biological circuits , 2019 .

[585]  Cortical Activity , 2020, Encyclopedia of Behavioral Medicine.

[586]  Physics Reports , 2022 .

[587]  October I Physical Review Letters , 2022 .

[588]  Gene Regulation and Systems Biology , 2022 .