Stationary efficiency of co-evolutionary networks: an inverse voter model Chen-Ping Zhu12, Hui Kong1, Li Li3 Zhi-Ming Gul, Shi-Jie Xiong4
Stationary efficiency of co-evolutionary networks: an inverse voter model Chen-Ping Zhu12 ，Hui Kong1 ，Li Li3 ， Zhi-Ming Gu1 ， Shi-Jie Xiong4
Outline 1. Motivations of our work 2. Inverse voter model (vM)for Co-evolutionary networks 3. Analytic and numerical results 4. Discussion and conclusions
Outline 1. Motivations of our work 2. Inverse voter model (IVM) for co-evolutionary networks 3. Analytic and numerical results 4. Discussion and Conclusions
Motivations (1)A sort of real networks composed of nodes with binary states (a)sIS epidemic networks: susceptible/infected (b Stock market: buyers/sellers ( c) Neural networks abstracted with firing and quiescent nodes ( d) Communication networks with transmitters and receivers Generalized information-flow yields between linked pairs of nodes in two opposite states The function of such networks is to produce generalized information flow So we call them flow networks Only links between the nodes in the opposite states are effective for the function of a specific network
Motivations (1) A sort of real networks composed of nodes with binary states: (a) SIS epidemic networks: susceptible/infected (b) Stock market: buyers /sellers (c) Neural networks abstracted with firing and quiescent nodes (d) Communication networks with transmitters and receivers. Generalized information-flow yields between linked pairs of nodes in two opposite states. The function of such networks is to produce generalized information flow. So we call them flow networks. Only links between the nodes in the opposite states are effective for the function of a specific network
Motivations (1)An edge linking two nodes: correlation/interaction between them. Effective/ineffective for realizing the function of a network? In a co-evolutionary network, node states vary with time, it changes the efficacy of links between them, even cause links to rewire correspondingly Two actions feed back with each other We advocate Global efficiency should be the ratio of income/ pay-off It should refers to the density of effective links among all Links which may be time-dependent and arrives at dynamic equilibrium by co-evolution
Motivations (1) An edge linking two nodes: correlation/interaction between them. Effective/ineffective for realizing the function of a network? In a co-evolutionary network, node states vary with time, it changes the efficacy of links between them, even cause links to rewire correspondingly. Two actions feed back with each other. We advocate : Global efficiency should be the ratio of income/pay-off. It should refers to the density of effective links among all Links which may be time-dependent and arrives at dynamic equilibrium by co-evolution
The primitive definition of global efficiency for a complex network 2 b (N-1)分l It is irrelevant to either the function of a network or to the state of any node, which is abnormal from the viewpoint of statistical physICS
• The primitive definition of global efficiency for a complex network • It is irrelevant to either the function of a network or to the state of any node, which is abnormal from the viewpoint of statistical physics 2 1 ( 1) glob i j ij E N N l = −