Damage spreading on two-dimensional trivalent structures with Glauber dynamics: Hierarchical and random lattices

Guo, Zizheng; Szeto, Kwok Yip; Fu, Xiujun

doi:10.1103/physreve.70.016105

Cited by 18 publications

(11 citation statements)

References 16 publications

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“…These features have positive correlation with the clustering coefficients of the network. Our results appear to be general, within the confine of the two-dimensional hexagonal lattices of various sizes, hierarchical lattice [15], Voronoi diagrams, as well as some high-dimensional random networks [21]. Extension to the problem of more than two competing companies has been addressed in a model Hamiltonian similar to the Potts model [22].…”

Section: Resultsmentioning

confidence: 84%

“…Although our numerical works are performed on the hexagonal lattice, we expect our findings to be generally applicable to the Voronoi diagrams constructed from random point patterns in two-dimension. This expectation is based on our recent work on damage spreading in various kinds of two-dimensional cellular structures [13][14][15].…”

Section: Model In Two-dimensionmentioning

confidence: 98%

“…The results are similar to the ones shown in section 2. Other than hexagonal lattice, the simulation was also performed on 3-12 lattice [15], 70 sites two-dimensional Voronoi pattern and 8x8 square lattice. The above five features for the 8 x 8 hexagonal lattice are observed in these lattice.…”

Section: General Measures Of Topological Featuresmentioning

confidence: 99%

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Topology for Dominance for Network of Multi-Agent System

Szeto¹

2007

AIP Conference Proceedings

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The resource allocation problem in evolving two-dimensional point patterns is investigated for the existence of good strategies for the construction of initial configuration that leads to fast dominance of the pattern by one single species, which can be interpreted as market dominance by a company in the context of multi-agent systems in econophysics. For hexagonal lattice, certain special topological arrangements of the resource in two-dimensions, such as rings, lines and clusters have higher probability of dominance, compared to random pattern. For more complex networks, a systematic way to search for a stable and dominant strategy of resource allocation in the changing environment is found by means of genetic algorithm. Five typical features can be summarized by means of the distribution function for the local neighborhood of friends and enemies as well as the local clustering coefficients: (l)The winner has more triangles than the loser has.(2) The winner likes to form clusters as the winner tends to connect with other winner rather than with losers; while the loser tends to connect with winners rather than losers. (3) The distribution function of friends as well as enemies for the winner is broader than the corresponding distribution function for the loser. (4) The connectivity at which the peak of the distribution of friends for the winner occurs is larger than that of the loser ; while the peak values for friends for winners is lower. (5) The connectivity at which the peak of the distribution of enemies for the winner occurs is smaller than that of the loser ; while the peak values for enemies for winners is lower. These five features appear to be general, at least in the context of two-dimensional hexagonal lattices of various sizes, hierarchical lattice, Voronoi diagrams, as well as high-dimensional random networks. These general local topological properties of networks are relevant to strategists aiming at dominance in evolving patterns when the interaction between the agents is local.

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Section: Resultsmentioning

confidence: 84%

Section: Model In Two-dimensionmentioning

confidence: 98%

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Topology for Dominance for Network of Multi-Agent System

Szeto¹

2007

AIP Conference Proceedings

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“…promote its service to the relatives, friends and acquaintances of the existing clients since this would enhance the interconnectedness among its client and they will tend to be loyal customers. This strategy to market dominance can also be viewed as a way to produce the maximum damage to other companies [10]. K.Y.…”

Section: Results Of the Simulationmentioning

confidence: 99%

Efficient Search of Winning Strategies in Multi-agent Systems on Random Network: Importance of Local Solidarity

Pang

Szeto

2006

Intelligent Data Engineering and Automated Learning – IDEAL 2006

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Abstract. Multi-agent systems defined on a network can be used for modelling the competition between companies in terms of market dominance. In view of the enormous size of the search space for winning strategies of initial configuration of resource allocation on network, we focus our search on the subspace defined by special local clustering effects, using the recently developed evolutionary computational algorithm. Strategies that emphasize local solidarity, measured by the formation of clusters in the form of triangles linkage between members of the same company, prove to be effective in winning both the market share with high probability and high speed. The result provides a good guideline to improve the collective competitiveness in a network of agents. The formulation is based on the Ising model in statistical physics and the evolutionary game is based on Monte Carlo simulation. Significance and the application of the algorithm in the context of econophysics and damage spreading in network are discussed.

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“…Here is where the DS method comes in: its operational side amounts to an algorithm designed to study how small perturbations spread within the system by working in detail how each of the system's components react to the changes. The method has been applied to many different dynamical systems such as Ising systems [2,3,4,5,6,9,10,11], Kauffman networks [12,13,14], spin glasses [15,16], cellular automata [17] amongst others, yielding in many cases useful information about their evolution and stability. Succinctly speaking, the algorithm analyzes the evolution of two almost identical states of the system.…”

Section: Introductionmentioning

confidence: 99%

Self-overlap as a method of analysis in Ising models

et al. 2007

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The damage spreading method (DS) provided a useful tool to obtain analytical results of the thermodynamics and stability of the 2D Ising model -amongst many others-, but it suffered both from ambiguities in its results and from large computational costs. In this paper we propose an alternative method, the so called self-overlap method, based on the study of correlation functions measured at subsequent time steps as the system evolves towards its equilibrium. Applying markovian and mean field approximations to a 2D Ising system we obtain both analytical and numerical results on the thermodynamics that agree with the expected behavior. We also provide some analytical results on the stability of the system. Since only a single replica of the system needs to be studied, this method would seem to be free from the ambiguities that afflicted DS. It also seems to be numerically more efficient and analytically simpler.

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Damage spreading on two-dimensional trivalent structures with Glauber dynamics: Hierarchical and random lattices

Cited by 18 publications

References 16 publications

Topology for Dominance for Network of Multi-Agent System

Topology for Dominance for Network of Multi-Agent System

Efficient Search of Winning Strategies in Multi-agent Systems on Random Network: Importance of Local Solidarity

Self-overlap as a method of analysis in Ising models

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