Motivations (3)Most practically existing networks are sparse k << Inx<< m O k≤lnN<<N Rarely could I find papers interpreting sparseness
Motivations (3) Most practically existing networks are sparse: Rarely could I find papers interpreting sparseness。 ln ln k N N or k N N
3. Inverse voter model(IVM) Flow of generalized message, and coevolution Flow networks: SIS epidemics, stock markets, mAnET and neural networks Nodes with binary states( t) Effective links:+<> The flow-producing efficiency of dynamic networks with binary node states p,p=p+p p++ tp+tp Define the efficiency of a flow-network E
3. Inverse voter model (IVM) • Flow of generalized message, and coevolution • Flow networks: SIS epidemics, stock markets, MANET, and neural networks. • Nodes with binary states( ) • Effective links: • The flow-producing efficiency of dynamic networks with binary node states: + − , E 1 + − +− ++ −− ++ +− −− + − = = + + + = = − Define the efficiency of a flow-network:
3. Inverse voter model --n inert links n-1 inert links k-n active links k-n+l active links rewire e k-n inert links n active links flir 2(k-2n) FIG. 1: Flipping or rewiring and associated changes in the global density of inert links in the inverse voter model
3. Inverse voter model
3. Inverse voter model(IVM) Define the ratio of edges linking both nodes in the same state as p, then master equation describing its evolution reads =2Ph)k ∑B B"2 dt k=11/N n=0 , k )(k-2m) N where n and k represent the number of links connecting the same state from any node and the degree of it, respectively u is average degree under the distribution p(k), and Bnk is binary distribution. Adjustable parameter BE(0, 1.0) controls average rewiring probability of nodes, reflecting randomness of interaction among nodes which modifies the deterministic nearest neighbor correlations
3. Inverse voter model (IVM) , 1 0 ( ) 2 [(1 )( 2 ) ] 1 / (1) n n k k k n k k n d p k n B e k n e dt N k N − − = = = − − − n,k where n and k represent the number of links connecting the same state from any node and the degree of it, respectively, is average degree under the distribution p(k), and B is binary distributi on. Adjustable parameter (0,1.0) controls average rewiring probability of nodes, reflecting randomness of interaction among nodes which modifies the deterministic nearest neighbor correlations. Define the ratio of edges linking both nodes in the same state as , then master equation describin g its evolution reads
3. Inverse voter model(VM dual meanings of parameter p probabilistic modifying factor to decide flipping/rewiring Random factor describing effects caused by non-deterministic factors other nearest interactions ie normalized inverse-temperature β=1/(T+1
3. Inverse voter model (IVM) • dual meanings of parameter : • probabilistic modifying factor to decide flipping/rewiring; • Random factor describing effects caused by non-deterministic factors other nearest interactions, i.e., normalized inverse-temperature, =1/(T+1)