A simple stochastic mechanism that produces exact and approximate power-law distributions is presented. The model considers radially symmetric Gaussian, exponential and power-law functions inn= 1, 2, 3 dimensions. Ran...A simple stochastic mechanism that produces exact and approximate power-law distributions is presented. The model considers radially symmetric Gaussian, exponential and power-law functions inn= 1, 2, 3 dimensions. Randomly sampling these functions with a radially uniform sampling scheme produces heavy-tailed distributions. For two-dimensional Gaussians and one-dimensional exponential functions, exact power-laws with exponent –1 are obtained. In other cases, densities with an approximate power-law behaviour close to the origin arise. These densities are analyzed using Padé approximants in order to show the approximate power-law behaviour. If the sampled function itself follows a power-law with exponent –α, random sampling leads to densities that also follow an exact power-law, with exponent -n/a – 1. The presented mechanism shows that power-laws can arise in generic situations different from previously considered specialized systems such as multi-particle systems close to phase transitions, dynamical systems at bifurcation points or systems displaying self-organized criticality. Thus, the presented mechanism may serve as an alternative hypothesis in system identification problems.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
In software engineering, class diagrams are often used to describe the system＇s class structures in Unified Modelling Language （UML）. A class diagram, as a graph, is a collection of static declarative model element...In software engineering, class diagrams are often used to describe the system＇s class structures in Unified Modelling Language （UML）. A class diagram, as a graph, is a collection of static declarative model elements, such as classes, interfaces, and the relationships of their connections with each other. In this paper, class graphs axe examined within several Java software systems provided by Sun and IBM, and some new features are found. For a large-scale Java software system, its in-degree distribution tends to an exponential distribution, while its out-degree and degree distributions reveal the power-law behaviour. And then a directed preferential-random model is established to describe the corresponding degree distribution features and evolve large-scale Java software systems.展开更多
Truncated elliptical distributions occur naturally in theoretical and applied statistics and are essential for the study of other classes of multivariate distributions.Two members of this class are the multivariate tr...Truncated elliptical distributions occur naturally in theoretical and applied statistics and are essential for the study of other classes of multivariate distributions.Two members of this class are the multivariate truncated normal and multivariate truncated t distributions.We derive statistical properties of the truncated elliptical distributions.Applications of our results establish new properties of the multivariate truncated slash and multivariate truncated power exponential distributions.展开更多
文摘A simple stochastic mechanism that produces exact and approximate power-law distributions is presented. The model considers radially symmetric Gaussian, exponential and power-law functions inn= 1, 2, 3 dimensions. Randomly sampling these functions with a radially uniform sampling scheme produces heavy-tailed distributions. For two-dimensional Gaussians and one-dimensional exponential functions, exact power-laws with exponent –1 are obtained. In other cases, densities with an approximate power-law behaviour close to the origin arise. These densities are analyzed using Padé approximants in order to show the approximate power-law behaviour. If the sampled function itself follows a power-law with exponent –α, random sampling leads to densities that also follow an exact power-law, with exponent -n/a – 1. The presented mechanism shows that power-laws can arise in generic situations different from previously considered specialized systems such as multi-particle systems close to phase transitions, dynamical systems at bifurcation points or systems displaying self-organized criticality. Thus, the presented mechanism may serve as an alternative hypothesis in system identification problems.
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.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 60374057 and 50575204）.
文摘In software engineering, class diagrams are often used to describe the system＇s class structures in Unified Modelling Language （UML）. A class diagram, as a graph, is a collection of static declarative model elements, such as classes, interfaces, and the relationships of their connections with each other. In this paper, class graphs axe examined within several Java software systems provided by Sun and IBM, and some new features are found. For a large-scale Java software system, its in-degree distribution tends to an exponential distribution, while its out-degree and degree distributions reveal the power-law behaviour. And then a directed preferential-random model is established to describe the corresponding degree distribution features and evolve large-scale Java software systems.
基金Conselho Nacional de Desenvolvi-mento Cientifico e Tecnologico-CNPq(Grant No.305963-2018-0).
文摘Truncated elliptical distributions occur naturally in theoretical and applied statistics and are essential for the study of other classes of multivariate distributions.Two members of this class are the multivariate truncated normal and multivariate truncated t distributions.We derive statistical properties of the truncated elliptical distributions.Applications of our results establish new properties of the multivariate truncated slash and multivariate truncated power exponential distributions.
基金Supported by Major Program of National Natural Science Foundation of China(71490725)National Key Basic Research Program of China(2013CB329600)+1 种基金National Science Foundation of China(9154611,71371062)Key Project of Natural Science of Anhui Province Education Department(KJ2015A348)
