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.

Multifractal Aspects for a Self Organized Critical Model

2003 ◽  
Vol 17 (16) ◽  
pp. 3065-3073 ◽  
Author(s):  
S. T. R. Pinho ◽  
R. F. S. Andrade ◽  
E. Nogueira
Keyword(s):  
Probability Distribution ◽  
Potential Energy ◽  
Finite Size ◽  
Finite Size Scaling ◽  
Avalanche Size ◽  
Clear Cut ◽  
Size Scaling ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Critical Model

We investigate multifractal properties for an Abelian directed model of self-organized criticality that describes the growth of droplets inside a cloud and the subsequent rainfall. The probability distribution of events of the model satisfies finite-size scaling. We obtain the singularity spectra f(α) associated with temporal records for avalanche size and for the potential energy, defined by the total sum of the product between mass and height of each site. The measure defined by avalanche size has a clear cut multifractal character, while the obtained f(α) for potential energy may include a spurious branch.

Crowd Evacuation Stability Based on Self-Organized Criticality Theory

2014 ◽  
Vol 501-504 ◽  
pp. 2403-2406 ◽  
Author(s):  
Rong Yong Zhao ◽  
Jian Wang ◽  
Wei Qing Ling
Keyword(s):  
Stability Analysis ◽  
Complex Problem ◽  
Unstable State ◽  
Sand Pile ◽  
Mapping Model ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Crowd Evacuation ◽  
Crowd Motion ◽  
The Stability

In emergency, the crowd evacuation from public buildings is the most important issue to save human lives. Panic generation and spread normally can lead to the unstable state -stampede during the crowd motion. The stability of crowd evacuation is a complex problem being researched for decades. This paper introduces self-organized criticality(SOC) theory to build the mapping model from a collective crowd into a sand pile with SOC. Therefore, the complex problem of stability analysis for crowd evacuation is converted into sandpiper stability analysis in a relatively simpler way.

SELF-ORGANIZED CRITICALITY IN AN EARTHQUAKE MODEL BASED ON ASSORTATIVE SCALE-FREE NETWORKS

2011 ◽  
Vol 22 (05) ◽  
pp. 483-493 ◽  
Author(s):  
MIN LIN ◽  
GANG WANG
Keyword(s):  
Stress Evolution ◽  
Scale Invariant ◽  
Avalanche Size ◽  
Scale Free ◽  
Self Organized ◽  
Dynamical Behaviors ◽  
Period Distribution ◽  
Scale Free Networks ◽  
Earthquake Model ◽  
Self Organized Criticality

A modified Olami–Feder–Christensen (OFC) earthquake model on scale-free networks with assortative mixing is introduced. In this model, the distributions of avalanche sizes and areas display power-law behaviors. It is found that the period distribution of avalanches displays a scale-invariant law with the increment of range parameter d. More importantly, different assortative topologies lead to different dynamical behaviors, such as the distribution of avalanche size, the stress evolution process, and period distribution.

THE AVERAGE AVALANCHE SIZE IN THE MANNA MODEL AND OTHER MODELS OF SELF-ORGANIZED CRITICALITY

2013 ◽  
Vol 27 (05) ◽  
pp. 1350009 ◽  
Author(s):  
GUNNAR PRUESSNER
Keyword(s):  
Field Theory ◽  
Boundary Conditions ◽  
Higher Dimensions ◽  
One Dimension ◽  
Leading Order ◽  
Numerical Work ◽  
Avalanche Size ◽  
Self Organized ◽  
Self Organized Criticality ◽  
External Driving

The average avalanche size can be calculated exactly in a number of models of self-organized criticality (SOC). While the calculation is straight-forward in one dimension, it is more involved in higher dimensions and further complicated by the presence of different boundary conditions and different forms of external driving. Amplitudes of the leading order are determined analytically and evaluated to obtain analytical references for numerical work. A subtle link exists between the procedure to calculate the average avalanche size and the field theory of SOC.

scholarly journals STABILITY OF COLOR-FLAVOR LOCKED STRANGELETS

2006 ◽  
Vol 21 (13n14) ◽  
pp. 3021-3030 ◽  
Author(s):  
O. KIRIYAMA
Keyword(s):  
Size Effects ◽  
Thermodynamic Potential ◽  
Finite Size ◽  
Baryon Number ◽  
Critical Value ◽  
Coupling Constant ◽  
Finite Size Effects ◽  
Quark Coupling ◽  
The Stability ◽  
Quark Flavors

The stability of color-flavor locked (CFL) strangelets is studied in the three-flavor Nambu–Jona-Lasinio model. We consider all quark flavors to be massless, for simplicity. By making use of the multiple reflection expansion, we explicitly take into account finite size effects and formulate the thermodynamic potential for CFL strangelets. We find that the CFL gap could be large enough so that the energy per baryon number of CFL strangelets is greatly affected. In addition, if the quark–quark coupling constant is larger than a certain critical value, there is a possibility of finding absolutely stable CFL strangelets.

Self-organized criticality of a simple integrate-and-fire neural model

2012 ◽  
Vol 60 (4) ◽  
pp. 657-659 ◽  
Author(s):  
Hyung Wooc Choi ◽  
Seong Eun Maeng ◽  
Jae Woo Lee
Keyword(s):  
Neural Model ◽  
Integrate And Fire ◽  
Self Organized ◽  
Self Organized Criticality

THE EVIDENCE FOR SELF-ORGANIZED CRITICALITY IN SANDPILE DYNAMICS

Fractals ◽  
1995 ◽  
Vol 03 (03) ◽  
pp. 431-443 ◽  
Author(s):  
J. FEDER
Keyword(s):  
Characteristic Size ◽  
Size Distributions ◽  
Exponential Distributions ◽  
Avalanche Size ◽  
Stretched Exponential ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Stretched Exponential Distribution ◽  
Rotating Drums ◽  
Low Rate

Self-organized criticality (SOC) is thought to describe avalanche dynamics in sandpiles. Experiments on the dynamics of “sandpiles” fall in two broad categories. Sandpiles in rotating drums exhibit periodic large avalanches, which is inconsistent with SOC. Other experiments study sandpiles on a circular support driven by the addition of grains of sand at a low rate from above and centered with respect to the support. The mass of avalanches that drop sand off the support is typically measured by a balance. It has been claimed that the observed avalanche statistics is consistent with SOC. However, I find that experiments described in the literature all have avalanche-size distributions that can be very well described by stretched-exponential distributions. Since the stretched-exponential distribution has a characteristic size, I conclude that the experiments described in the literature are inconsistent with SOC.

Finite Size Effects in Field-Induced Transitions in Magnetic Multilayers

2009 ◽  
Vol 152-153 ◽  
pp. 245-248 ◽  
Author(s):  
Victor V. Kostyuchenko
Keyword(s):  
Size Effects ◽  
Uniaxial Anisotropy ◽  
Finite Size ◽  
Exchange Interactions ◽  
Magnetic Multilayers ◽  
Analytical Investigation ◽  
Finite Size Effects ◽  
Biquadratic Exchange ◽  
Finite Difference Equations ◽  
The Stability

The technique of finite difference equations is used for an analytical investigation of field-induced transitions in magnetic multilayers. Heisenberg and biquadratic exchange interactions and uniaxial anisotropy are taken into account. The analytical dependencies of critical field values determining the stability of ferromagnetic and antiferromagnetic phases on the layers number are obtained.

Sign in / Sign up

Export Citation Format

Share Document