Mean-field Theory for Some Bus Transport Networks with Random Overlapping Clique Structure

Transport networks, such as railway networks and airport networks, are a kind of random network with complex topology. Recently, more and more scholars paid attention to various kinds of transport networks and try to explore their inherent characteristics. Here we study the exponential properties of a recently introduced Bus Transport Networks （BTNs） evolution model with random overlapping clique structure, which gives a possible explanation for the observed exponential distribution of the connectivities of some BTNs of three major cities in China. Applying mean-field theory, we analyze the BTNs model and prove that this model has the character of exponential distribution of the connectivities, and develop a method to predict the growth dynamics of the individual vertices, and use this to calculate analytically the connectivity distribution and the exponents. By comparing mean-field based theoretic results with the statistical data of real BTNs, we observe that, as a whole, both of their data show similar character of exponential distribution of the connectivities, and their exponents have same order of magnitude, which show the availability of the analytical result of this paper.     

Weighted Scaling in Non-growth Random Networks

We propose a weighted model to explain the self-organizing formation of scale-free phenomenon in nongrowth random networks.In this model,we use multiple-edges to represent the connections between vertices and define the weight of a multiple-edge as the total weights of all single-edges within it and the strength of a vertex as the sum of weights for those multiple-edges attached to it.The network evolves according to a vertex strength preferential selection mechanism.During the evolution process,the network always holds its total number of vertices and its total number of single-edges constantly.We show analytically and numerically that a network will form steady scale-free distributions with our model.The results show that a weighted non-growth random network can evolve into scale-free state.It is interesting that the network also obtains the character of an exponential edge weight distribution.Namely,coexistence of scale-free distribution and exponential distribution emerges.     

Synthesization of high-capacity auto-associative memories using complex-valued neural networks

In this paper, a novel design procedure is proposed for synthesizing high-capacity auto-associative memories based on complex-valued neural networks with real-imaginary-type activation functions and constant delays. Stability criteria dependent on external inputs of neural networks are derived. The designed networks can retrieve the stored patterns by external inputs rather than initial conditions. The derivation can memorize the desired patterns with lower-dimensional neural networks than real-valued neural networks, and eliminate spurious equilibria of complex-valued neural networks.One numerical example is provided to show the effectiveness and superiority of the presented results.