Scale-free topology and high clustering coexist in some real networks, and keep invariant for growing sizes of the systems. Previous models could hardly give out size-independent clustering with self- organized mechan...Scale-free topology and high clustering coexist in some real networks, and keep invariant for growing sizes of the systems. Previous models could hardly give out size-independent clustering with self- organized mechanism when succeeded in producing power-law degree distributions. Always ignored, some empirical statistic results display flat-head power-law behaviors. We modify our recent coevo- lutionary model to explain such phenomena with the inert property of nodes to retain small portion of unfavorable links in self-organized rewiring process. Flat-head power-law and size-independent clustering are induced as the new characteristics by this modification. In addition, a new scaling relation is found as the result of interplay between node state growth and adaptive variation of connections.展开更多
The distribution of the geometric distances of connected neurons is a practical factor underlying neural networks in the brain. It can affect the brain＇s dynamic properties at the ground level. Karbowski derived a po...The distribution of the geometric distances of connected neurons is a practical factor underlying neural networks in the brain. It can affect the brain＇s dynamic properties at the ground level. Karbowski derived a power-law decay distribution that has not yet been verified by experiment. In this work, we check its validity using simulations with a phenomenological model. Based on the in vitro two- dimensional development of neural networks in culture vessels by Ito, we match the synapse number saturation time to obtain suitable parameters for the development process, then determine the distri-bution of distances between connected neurons under such conditions. Our simulations obtain a clear exponential distribution instead of a power-law one, which indicates that Karbowski＇s conclusion is invalid, at least for the case of in vitro neural network development in two-dimensional culture vessels.展开更多
基金Acknowledgements We acknowledge the financial suppor~ from the National Basic Science Program of China Project No. 2006CB705500 and the National Natural Science Foundation of China under the grant Nos. 70471084, 10775071, 10635040, and 60676056. C. P. Zhu thanks the hospitable accommodation of Bao- Wen Li at NUS and Visitors Program of MPIPKS in Dresden, Germany.
文摘Scale-free topology and high clustering coexist in some real networks, and keep invariant for growing sizes of the systems. Previous models could hardly give out size-independent clustering with self- organized mechanism when succeeded in producing power-law degree distributions. Always ignored, some empirical statistic results display flat-head power-law behaviors. We modify our recent coevo- lutionary model to explain such phenomena with the inert property of nodes to retain small portion of unfavorable links in self-organized rewiring process. Flat-head power-law and size-independent clustering are induced as the new characteristics by this modification. In addition, a new scaling relation is found as the result of interplay between node state growth and adaptive variation of connections.
文摘The distribution of the geometric distances of connected neurons is a practical factor underlying neural networks in the brain. It can affect the brain＇s dynamic properties at the ground level. Karbowski derived a power-law decay distribution that has not yet been verified by experiment. In this work, we check its validity using simulations with a phenomenological model. Based on the in vitro two- dimensional development of neural networks in culture vessels by Ito, we match the synapse number saturation time to obtain suitable parameters for the development process, then determine the distri-bution of distances between connected neurons under such conditions. Our simulations obtain a clear exponential distribution instead of a power-law one, which indicates that Karbowski＇s conclusion is invalid, at least for the case of in vitro neural network development in two-dimensional culture vessels.
