The criticality hypothesis: how local cortical networks might optimize information processing

2007 ◽  
Vol 366 (1864) ◽  
pp. 329-343 ◽  
Author(s):  
John M Beggs
Keyword(s):  
Phase Transition ◽  
Information Processing ◽  
Experimental Evidence ◽  
Critical Point ◽  
Cortical Neurons ◽  
Simulation Studies ◽  
Computational Power ◽  
Cortical Networks ◽  
Edge Of Chaos ◽  
Near Future

Early theoretical and simulation work independently undertaken by Packard, Langton and Kauffman suggested that adaptability and computational power would be optimized in systems at the ‘edge of chaos’, at a critical point in a phase transition between total randomness and boring order. This provocative hypothesis has received much attention, but biological experiments supporting it have been relatively few. Here, we review recent experiments on networks of cortical neurons, showing that they appear to be operating near the critical point. Simulation studies capture the main features of these data and suggest that criticality may allow cortical networks to optimize information processing. These simulations lead to predictions that could be tested in the near future, possibly providing further experimental evidence for the criticality hypothesis.

scholarly journals Computational Power of Asynchronously Tuned Automata Enhancing the Unfolded Edge of Chaos

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1376
Author(s):  
Yukio-Pegio Gunji ◽  
Daisuke Uragami
Keyword(s):  
Phase Transition ◽  
Cellular Automata ◽  
Dissipative Structure ◽  
Quantitative Measure ◽  
Computational Power ◽  
Critical Property ◽  
Edge Of Chaos ◽  
Computational Universality ◽  
Asynchronous Updating ◽  
The Relationship

Asynchronously tuned elementary cellular automata (AT-ECA) are described with respect to the relationship between active and passive updating, and that spells out the relationship between synchronous and asynchronous updating. Mutual tuning between synchronous and asynchronous updating can be interpreted as the model for dissipative structure, and that can reveal the critical property in the phase transition from order to chaos. Since asynchronous tuning easily makes behavior at the edge of chaos, the property of AT-ECA is called the unfolded edge of chaos. The computational power of AT-ECA is evaluated by the quantitative measure of computational universality and efficiency. It shows that the computational efficiency of AT-ECA is much higher than that of synchronous ECA and asynchronous ECA.

scholarly journals Mechanisms of Self-Organized Quasicriticality in Neuronal Network Models

2020 ◽  
Vol 8 ◽  
Author(s):  
Osame Kinouchi ◽  
Renata Pazzini ◽  
Mauro Copelli
Keyword(s):  
Phase Transition ◽  
Information Processing ◽  
Critical Point ◽  
Neuronal Network ◽  
Critical Region ◽  
Critical State ◽  
Neuronal Networks ◽  
Network Models ◽  
Biological Mechanisms ◽  
Self Organized

The critical brain hypothesis states that there are information processing advantages for neuronal networks working close to the critical region of a phase transition. If this is true, we must ask how the networks achieve and maintain this critical state. Here, we review several proposed biological mechanisms that turn the critical region into an attractor of a dynamics in network parameters like synapses, neuronal gains, and firing thresholds. Since neuronal networks (biological and models) are not conservative but dissipative, we expect not exact criticality but self-organized quasicriticality, where the system hovers around the critical point.

Dynamic simulation of sludge blanket movements in a full-scale rectangular sedimentation basin

1996 ◽  
Vol 33 (1) ◽  
pp. 89-99 ◽  
Author(s):  
F. Göhle ◽  
A. Finnson ◽  
B. Hultman
Keyword(s):  
Dynamic Simulation ◽  
Sewage Treatment ◽  
Sewage Treatment Plant ◽  
Treatment Plant ◽  
Full Scale ◽  
Simulation Studies ◽  
Separation Processes ◽  
Sedimentation Basin ◽  
Near Future ◽  
Sludge Concentration

Bromma sewage treatment plant in Stockholm is the second largest plant in Stockholm and will in the near future have requirements for nitrogen removal. This means that a higher sludge age must be used in the aeration basin. This may be accomplished by an increase of the sludge concentration up to values until the limiting solids flux is exceeded. Measurement of the sludge blanket level is a possibility for better control of the sedimentation basin. Different measurements were performed to evaluate the main factors influencing the level. Dynamic simulation studies were performed at Bromma sewage treatment plant in Stockholm of the sludge blanket level and the return sludge concentration in a full-scale sedimentation basin. The simulations were performed with the help of a Danish simulation package, EFOR (1992), in which both reactions in the aeration basin (mainly based on the IAWPRC model) and separation processes in the sedimentation basin (both clarification and thickening) can be studied. The thickening model is based on the solids flux theory and the Vesilind formula (1979). Different methods were compared for determination and use of characteristic parameters in the Vesilind formula.

scholarly journals Solving the 2D SUSY Gross-Neveu-Yukawa model with conformal truncation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
A. Liam Fitzpatrick ◽  
Emanuel Katz ◽  
Matthew T. Walters ◽  
Yuan Xin
Keyword(s):  
Phase Transition ◽  
Critical Point ◽  
Fine Tuning ◽  
Yukawa Model ◽  
Spectral Functions ◽  
Scalar Superfield ◽  
Local Operators ◽  
Dimensionless Coupling ◽  
Zumino Model ◽  
Yukawa Theory

Abstract We use Lightcone Conformal Truncation to analyze the RG flow of the two-dimensional supersymmetric Gross-Neveu-Yukawa theory, i.e. the theory of a real scalar superfield with a ℤ2-symmetric cubic superpotential, aka the 2d Wess-Zumino model. The theory depends on a single dimensionless coupling $$ \overline{g} $$ g ¯ , and is expected to have a critical point at a tuned value $$ {\overline{g}}_{\ast } $$ g ¯ ∗ where it flows in the IR to the Tricritical Ising Model (TIM); the theory spontaneously breaks the ℤ2 symmetry on one side of this phase transition, and breaks SUSY on the other side. We calculate the spectrum of energies as a function of $$ \overline{g} $$ g ¯ and see the gap close as the critical point is approached, and numerically read off the critical exponent ν in TIM. Beyond the critical point, the gap remains nearly zero, in agreement with the expectation of a massless Goldstino. We also study spectral functions of local operators on both sides of the phase transition and compare to analytic predictions where possible. In particular, we use the Zamolodchikov C-function to map the entire phase diagram of the theory. Crucial to this analysis is the fact that our truncation is able to preserve supersymmetry sufficiently to avoid any additional fine tuning.

scholarly journals Finite-size transitions in complex membranes

2020 ◽  
Author(s):  
M. Girard ◽  
T. Bereau
Keyword(s):  
Experimental Evidence ◽  
Critical Point ◽  
Finite Size ◽  
Underlying Mechanism ◽  
Large Temperature ◽  
Strong Argument ◽  
Biological Regulation ◽  
Critical Manifold ◽  
Critical Composition ◽  
Dynamics Simulations

ABSTRACTThe lipid raft hypothesis postulates that cell membranes possess some degree of lateral organization. The last decade has seen a large amount of experimental evidence for rafts. Yet, the underlying mechanism remains elusive. One hypothesis that supports rafts relies on the membrane to lie near a critical point. While supported by experimental evidence, the role of regulation is unclear. Using both a lattice model and molecular dynamics simulations, we show that lipid regulation of a many-component membrane can lead to critical behavior over a large temperature range. Across this range, the membrane displays a critical composition due to finite-size effects. This mechanism provides a rationale as to how cells tune their composition without the need for specific sensing mechanisms. It is robust and reproduces important experimentally verified biological trends: membrane-demixing temperature closely follows cell growth temperature, and the composition evolves along a critical manifold. The simplicity of the mechanism provides a strong argument in favor of the critical membrane hypothesis.SIGNIFICANCEWe show that biological regulation of a large amount of phospholipids in membranes naturally leads to a critical composition for finite-size systems. This suggests that regulating a system near a critical point is trivial for cells. These effects vanish logarithmically and therefore can be present in micron-sized systems.

scholarly journals Variational procedure leading from Davidson potentials to the E(5)and X(5) critical point symmetries

2020 ◽  
Vol 13 ◽  
pp. 10
Author(s):  
Dennis Bonatsos ◽  
D. Lenis ◽  
N. Minkov ◽  
D. Petrellis ◽  
P. P. Raychev ◽  
...  
Keyword(s):  
Phase Transition ◽  
Critical Point ◽  
Ground State ◽  
Nuclear Energy ◽  
Energy Spectra ◽  
Variational Procedure ◽  
Ground State Band ◽  
Sharp Maximum ◽  
State Band ◽  
Shape Phase Transition

Davidson potentials of the form β^2 + β0^4/β^2, when used in the original Bohr Hamiltonian for γ-independent potentials bridge the U(5) and 0(6) symmetries. Using a variational procedure, we determine for each value of angular momentum L the value of β0 at which the derivative of the energy ratio RL = E(L)/E(2) with respect to β0 has a sharp maximum, the collection of RL values at these points forming a band which practically coincides with the ground state band of the E(5) model, corresponding to the critical point in the shape phase transition from U(5) to Ο(6). The same potentials, when used in the Bohr Hamiltonian after separating variables as in the X(5) model, bridge the U(5) and SU(3) symmetries, the same variational procedure leading to a band which practically coincides with the ground state band of the X(5) model, corresponding to the critical point of the U(5) to SU(3) shape phase transition. A new derivation of the Holmberg-Lipas formula for nuclear energy spectra is obtained as a by-product.

scholarly journals Dendrites enable a robust mechanism for neuronal stimulus selectivity

2015 ◽  
Author(s):  
Romain D. Cazé ◽  
Sarah Jarvis ◽  
Amanda J. Foust ◽  
Simon R. Schultz
Keyword(s):  
Spatial Distribution ◽  
Information Processing ◽  
Linear Model ◽  
Cortical Neurons ◽  
General Mechanism ◽  
Starting Point ◽  
Dendritic Processing ◽  
Non Linear ◽  
Equivalent Linear Model ◽  
Preferred Stimulus

AbstractHearing, vision, touch-underlying all of these senses is stimulus selectivity, a robust information processing operation in which cortical neurons respond more to some stimuli than to others. Previous models assume that these neurons receive the highest weighted input from an ensemble encoding the preferred stimulus, but dendrites enable other possibilities. Non-linear dendritic processing can produce stimulus selectivity based on the spatial distribution of synapses, even if the total preferred stimulus weight does not exceed that of non-preferred stimuli. Using a multi-subunit non-linear model, we demonstrate that stimulus selectivity can arise from the spatial distribution of synapses. We propose this as a general mechanism for information processing by neurons possessing dendritic trees. Moreover, we show that this implementation of stimulus selectivity increases the neuron's robustness to synaptic and dendritic failure. Importantly, our model can maintain stimulus selectivity for a larger range of synapses or dendrites loss than an equivalent linear model. We then use a layer 2/3 biophysical neuron model to show that our implementation is consistent with two recent experimental observations: (1) one can observe a mixture of selectivities in dendrites, that can differ from the somatic selectivity, and (2) hyperpolarization can broaden somatic tuning without affecting dendritic tuning. Our model predicts that an initially non-selective neuron can become selective when depolarized. In addition to motivating new experiments, the model's increased robustness to synapses and dendrites loss provides a starting point for fault-resistant neuromorphic chip development.

scholarly journals The Size of the Giant Joint Component in a Binomial Random Double Graph

10.37236/8846 ◽  
2021 ◽  
Vol 28 (1) ◽  
Author(s):  
Mark Jerrum ◽  
Tamás Makai
Keyword(s):  
Phase Transition ◽  
Critical Point ◽  
Random Graphs ◽  
Spanning Tree ◽  
Branching Process ◽  
Graph Model ◽  
First Order ◽  
Blue Edge ◽  
Critical Pairs

We study the joint components in a random 'double graph' that is obtained by superposing red and blue binomial random graphs on $n$~vertices.  A joint component is a maximal set of vertices that supports both a red and a blue spanning tree.  We show that there are critical pairs of red and blue edge densities at which a giant joint component appears.  In contrast to the standard binomial graph model, the phase transition is first order:  the size of the largest joint component jumps from $O(1)$ vertices to $\Theta(n)$ at the critical point.  We connect this phenomenon to the properties of a certain bicoloured branching process. 

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