Avalanche size distribution of an integrate-and-fire neural model on complex networks

2020 ◽  
Vol 30 (6) ◽  
pp. 063118
Author(s):  
Nam Jung ◽  
Quang Anh Le ◽  
Kyoung-Eun Lee ◽  
Jae Woo Lee
Keyword(s):  
Complex Networks ◽  
Size Distribution ◽  
Neural Model ◽  
Avalanche Size ◽  
Integrate And Fire

A SIMPLE NEURON NETWORK BASED ON HEBB'S RULE

2011 ◽  
Vol 22 (07) ◽  
pp. 755-763
Author(s):  
GUI-QING ZHANG ◽  
ZI YU ◽  
QIU-YING YANG ◽  
TIAN-LUN CHEN
Keyword(s):  
Finite Size ◽  
Neural Model ◽  
Fat Tails ◽  
Neuron Network ◽  
Finite Size Effects ◽  
Gaussian Shape ◽  
Avalanche Size ◽  
Self Organized ◽  
Self Organized Criticality ◽  
The Stability

A weighted mechanism in neural networks is studied. This paper focuses on the neuron's behaviors in an area of brain. Our model could regenerate the power-law behaviors and finite size effects of neural avalanche. The probability density functions (PDFs) for the neural avalanche size differing at different times (lattice size) have fat tails with a q-Gaussian shape and the same parameter value of q in the thermodynamical limit. Above two kinds of behaviors show that our neural model can well present self-organized critical behavior. The robustness of PDFs shows the stability of self-organized criticality. Meanwhile, the avalanche scaling relation of the waiting time has been found.

scholarly journals Analysis of the one-dimensional Yut-Nori game: Winning strategy and avalanche-size distribution

2013 ◽  
Vol 63 (8) ◽  
pp. 1497-1502
Author(s):  
Hye Jin Park ◽  
Hasung Sim ◽  
Hang-Hyun Jo ◽  
Beom Jun Kim
Keyword(s):  
Size Distribution ◽  
Winning Strategy ◽  
Avalanche Size ◽  
One Dimensional ◽  
The One

scholarly journals A Generalized Linear Integrate-and-Fire Neural Model Produces Diverse Spiking Behaviors

2009 ◽  
Vol 21 (3) ◽  
pp. 704-718 ◽  
Author(s):  
Ştefan Mihalaş ◽  
Ernst Niebur
Keyword(s):  
Differential Equations ◽  
Biological Significance ◽  
Polynomial Equation ◽  
Neural Model ◽  
Fire Model ◽  
Variable Threshold ◽  
Integrate And Fire ◽  
Linear Differential ◽  
Update Rules ◽  
Parameter Values

For simulations of neural networks, there is a trade-off between the size of the network that can be simulated and the complexity of the model used for individual neurons. In this study, we describe a generalization of the leaky integrate-and-fire model that produces a wide variety of spiking behaviors while still being analytically solvable between firings. For different parameter values, the model produces spiking or bursting, tonic, phasic or adapting responses, depolarizing or hyperpolarizing after potentials and so forth. The model consists of a diagonalizable set of linear differential equations describing the time evolution of membrane potential, a variable threshold, and an arbitrary number of firing-induced currents. Each of these variables is modified by an update rule when the potential reaches threshold. The variables used are intuitive and have biological significance. The model's rich behavior does not come from the differential equations, which are linear, but rather from complex update rules. This single-neuron model can be implemented using algorithms similar to the standard integrate-and-fire model. It is a natural match with event-driven algorithms for which the firing times are obtained as a solution of a polynomial equation.

Unravelling the size distribution of social groups with information theory in complex networks

2010 ◽  
Vol 76 (1) ◽  
pp. 87-97 ◽  
Author(s):  
A. Hernando ◽  
D. Villuendas ◽  
C. Vesperinas ◽  
M. Abad ◽  
A. Plastino
Keyword(s):  
Information Theory ◽  
Complex Networks ◽  
Size Distribution ◽  
Social Groups

AVALANCHES IN THE DIRECTED PERCOLATION DEPINNING AND SELF-ORGANIZED DEPINNING MODELS OF INTERFACE ROUGHENING

Fractals ◽  
1996 ◽  
Vol 04 (03) ◽  
pp. 307-319 ◽  
Author(s):  
S. V. BULDYREV ◽  
L. A. N. AMARAL ◽  
A. -L. BARABÁSI ◽  
S. T. HARRINGTON ◽  
S. HAVLIN ◽  
...  
Keyword(s):  
Size Distribution ◽  
Quenched Disorder ◽  
Directed Percolation ◽  
Invasion Process ◽  
Avalanche Size ◽  
Scaling Properties ◽  
Self Organized ◽  
Interface Roughening

We review the recently introduced Directed Percolation Depinning (DPD) and Self-Organized Depinning (SOD) models for interface roughening with quenched disorder. The differences in the dynamics of the invasion process in these two models are discussed and different avalanche definitions are presented. The scaling properties of the avalanche size distribution and the properties of active cells are discussed.

scholarly journals Macroscopic Quantum Tunneling and Avalanche Size Distribution of 4He Crystallization in Aerogel

2011 ◽  
Vol 80 (12) ◽  
pp. 123601 ◽  
Author(s):  
Ryuji Nomura ◽  
Hirofumi Matsuda ◽  
Ryota Masumoto ◽  
Ken-ichi Ueno ◽  
Yuichi Okuda
Keyword(s):  
Size Distribution ◽  
Quantum Tunneling ◽  
Avalanche Size ◽  
Macroscopic Quantum ◽  
Macroscopic Quantum Tunneling
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