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Exponential distance distribution of connected neurons in simulations of two-dimensional in vitro neural network development

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Frontiers of physics 2017年第3期12卷 133-138页

作者： Zhi-Song Lv Chen-Ping Zhu Pei Nie Jing Zhao Hui-Jie Yang Yan-Jun Wang Chin-Kun Hu Department of Physics in Science College Nanjing University of Aeronautics and Astronautics Nanjing 210016 Research Center of Complex Systems Science University of Shanghai for Science and Technology Shanghai 200093 Department of Mathematics College-of Logistic-Engineering of PLANanjing 210016 College of Civil Aviation Nanjing University of Aeronautics and Astronautics Nanjing 210016 Institute of Physics Academia Sinica Nankang Taipei 11529 National Center for Theoretical Sciences Tsing Hua University Hsinchu 30013

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.

关键词： distance distribution connected neurons development exponential power-law neuralnetworks complex systems

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EXTENDED CLUSTERING COEFFICIENTS：GENERALIZATION OF CLUSTERING COEFFICIENTS IN SMALL-WORLD NETWORKS

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Journal of Systems Science and Systems Engineering 2007年第3期16卷 370-382页

作者： Wenjun XIAO Wenhong WEI Weidong CHEN Yong QIN Behrooz PARHAMI Department of Computer Science South China University of Technology Guangzhou 510641 China Department of Electrical & ComputerEngineering University of California Santa Barbara CA 93106-9560 USA

The clustering coefficient C of a network, which is a measure of direct connectivity between neighbors of the various nodes, ranges from 0 （for no connectivity） to 1 （for full connectivity）. We define extended clustering coefficients C（h） of a small-world network based on nodes that are at distance h from a source node, thus generalizing distance-1 neighborhoods employed in computing the ordinary clustering coefficient C = C（1）. Based on known results about the distance distribution Pδ（h） in a network, that is, the probability that a randomly chosen pair of vertices have distance h, we derive and experimentally validate the law Pδ（h）C（h） ≤ c log N / N, where c is a small constant that seldom exceeds 1. This result is significant because it shows that the product Pδ（h）C（h） is upper-bounded by a value that is considerably smaller than the product of maximum values for Pδ（h） and C（h）. Extended clustering coefficients and laws that govern them offer new insights into the structure of small-world networks and open up avenues for further exploration of their properties.

关键词： Clustering coefficient small-world extended clustering coefficient distance distribution

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On the ErdÖs distance Conjecture in Geometry

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Open Journal of Discrete Mathematics 2016年第3期6卷 109-160页

作者： Amir Jafari Amin Najafi Amin Department of Mathematics Sharif University of Technology Tehran Iran

ErdÖs asks if it is possible to have n points in general position in the plane (no three on a line or four on a circle) such that for every i (1≤i≤n-1 ) there is a distance determined by the points that occur exactly i times. So far some examples have been discovered for 2≤n≤8 [1] [2]. A solution for the 8 point is provided by I. Palasti [3]. Here two other possible solutions for the 8 point case as well as all possible answers to 4 - 7 point cases are provided and finally a brief discussion on the generalization of the problem to higher dimensions is given.

关键词： ErdÖs distance Problem General Position Graph Pattern distance distribution

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Shenzhen Mobility Research for Different Travel Scenes

Shenzhen Mobility Research for Different Travel Scenes

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2019中国汽车工程学会年会

作者： Liu Zongwei Li Zan Zhao Fuquan Tsinghua Automotive Strategy Research Institute State Key Laboratory of Automotive Safety and EnergyTsinghua University

As an emerging city that has developed rapidly alter China’s reform and opening up,Shenzhen’s urban appearance can not only reflect the general situation of China’s vast cities,but also have certain historical *** on the introduction of the status quo of Shenzhen’s urban development,this paper qualitatively studies the distance distribution and traffic structure characteristics of Shenzhen residents in the four travel scenarios of commuting,shopping,leisure and pick-up,and makes a portrait discussion on the current status of mobility in *** predicted the future development direction of Shenzhen’s transportation.

关键词： urban mobility commuting distance distribution traffic structure

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