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
In this paper, without recourse to the nonlinear dynamical equations of the waves, the nonlinear random waves are retrieved from the non-Gaussian characteristic of the sea surface elevation distribution. The question ...In this paper, without recourse to the nonlinear dynamical equations of the waves, the nonlinear random waves are retrieved from the non-Gaussian characteristic of the sea surface elevation distribution. The question of coincidence of the nonlinear wave profile, spectrum and its distributions of maximum (or minimum) values of the sea surface elevation with results derived from some existing nonlinear theories is expounded under the narrow-band spectrum condition. Taking the shoaling sea wave as an example, the nonlinear random wave process and its spectrum in shallow water are retrieved from both the non-Gaussian characteristics of the sea surface elevation distribution in shallow water and the normal sea waves in deep water and compared with the values actually measured. Results show that they can coincide with the actually measured values quite well, thus, this can confirm that the method proposed in this paper is feasible.展开更多
A new algorithm is suggested based on the central limit theorem for generating pseudo-random numbers with a specified normal or Gaussian probability density function. The suggested algorithm is very simple but highly ...A new algorithm is suggested based on the central limit theorem for generating pseudo-random numbers with a specified normal or Gaussian probability density function. The suggested algorithm is very simple but highly accurate, with an efficiency that falls between those of the Box-Muller and von Neumann rejection methods.展开更多
This work applies non-stationary random processes to resilience of power distribution under severe weather. Power distribution, the edge of the energy infrastructure, is susceptible to external hazards from severe wea...This work applies non-stationary random processes to resilience of power distribution under severe weather. Power distribution, the edge of the energy infrastructure, is susceptible to external hazards from severe weather. Large-scale power failures often occur, resulting in millions of people without electricity for days. However, the problem of large-scale power failure, recovery and resilience has not been formulated rigorously nor studied systematically. This work studies the resilience of power distribution from three aspects. First, we derive non-stationary random processes to model large-scale failures and recoveries. Transient Little’s Law then provides a simple approximation of the entire life cycle of failure and recovery through a queue at the network-level. Second, we define time-varying resilience based on the non-stationary model. The resilience metric characterizes the ability of power distribution to remain operational and recover rapidly upon failures. Third, we apply the non-stationary model and the resilience metric to large-scale power failures caused by Hurricane Ike. We use the real data from the electric grid to learn time-varying model parameters and the resilience metric. Our results show non-stationary evolution of failure rates and recovery times, and how the network resilience deviates from that of normal operation during the hurricane.展开更多
The famous de Moivre’s Laplace limit theorem proved the probability density function of Gaussian distribution from binomial probability mass function under specified conditions. De Moivre’s Laplace approach is cumbe...The famous de Moivre’s Laplace limit theorem proved the probability density function of Gaussian distribution from binomial probability mass function under specified conditions. De Moivre’s Laplace approach is cumbersome as it relies heavily on many lemmas and theorems. This paper invented an alternative and less rigorous method of deriving Gaussian distribution from basic random experiment conditional on some assumptions.展开更多
The collective behavior of a ring of coupled identical van der Pol oscillators is numerically studied in this work. Constant, gaussian and random distributions of the coupling parameter along the ring are considered. ...The collective behavior of a ring of coupled identical van der Pol oscillators is numerically studied in this work. Constant, gaussian and random distributions of the coupling parameter along the ring are considered. Three values of the oscillators constant are assumed in order to cover from quasilinear to nonlinear dynamic performance. Single and multiple coupled frequencies are obtained using power spectra of the long term time series. Phase portraits are obtained from numerical simulations, and the coupled behavior is analyzed, compared and discussed.展开更多
目的针对数据中心网络(Data Center Network,DCN)中数据流量多导致大象流与老鼠流识别精确度低的问题,提出一种基于软件定义网络(Software Defined Networking,SDN)下两阶段大象流识别算法。方法将SDN与DCN结合,第一阶段,采用高斯分布...目的针对数据中心网络(Data Center Network,DCN)中数据流量多导致大象流与老鼠流识别精确度低的问题,提出一种基于软件定义网络(Software Defined Networking,SDN)下两阶段大象流识别算法。方法将SDN与DCN结合,第一阶段,采用高斯分布动态阈值优化算法,通过对数据包阈值的设定,计算大象流误检率与漏检率,不断优化得到最优阈值,以此识别出可疑大象流;第二阶段,在依据流传输速率与流持续时间精确得到大象流的基础上,提出阈值约束、流量检测机制、Count计数器等三方面改进对大象流识别阈值下限的约束,将网络中大象流的数据量与流持续时间进行周期内阈值计算,提高大象流的识别精确度。结果实验结果表明:算法与已有相关算法相比,第一阶段可疑大象流平均字节数比网络流平均字节数多11.3%;不同阈值下的算法准确度提高1.7%,不同网络流量下的大象流平均检测时间降低至6 ms以内。结论软件定义网络下两阶段大象流识别算法在第一阶段具有较强的大象流识别能力,同时算法的精确度有所提高,大象流的平均检测时间降低,提高了网络质量,能为进行网络流量调度策略的进一步研究提供相关性条件。展开更多
In this paper,we construct random two-faced families of matrices with non-Gaussian entries to approximate a bi-free central limit distribution with a positive definite covariance matrix.We prove that,under modest cond...In this paper,we construct random two-faced families of matrices with non-Gaussian entries to approximate a bi-free central limit distribution with a positive definite covariance matrix.We prove that,under modest conditions weaker than independence,a family of random two-faced families of matrices with non-Gaussian entries is asymptotically bi-free from a two-faced family of constant diagonal matrices.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.
基金This work is funded by National Natural Science Foundation of China
文摘In this paper, without recourse to the nonlinear dynamical equations of the waves, the nonlinear random waves are retrieved from the non-Gaussian characteristic of the sea surface elevation distribution. The question of coincidence of the nonlinear wave profile, spectrum and its distributions of maximum (or minimum) values of the sea surface elevation with results derived from some existing nonlinear theories is expounded under the narrow-band spectrum condition. Taking the shoaling sea wave as an example, the nonlinear random wave process and its spectrum in shallow water are retrieved from both the non-Gaussian characteristics of the sea surface elevation distribution in shallow water and the normal sea waves in deep water and compared with the values actually measured. Results show that they can coincide with the actually measured values quite well, thus, this can confirm that the method proposed in this paper is feasible.
文摘A new algorithm is suggested based on the central limit theorem for generating pseudo-random numbers with a specified normal or Gaussian probability density function. The suggested algorithm is very simple but highly accurate, with an efficiency that falls between those of the Box-Muller and von Neumann rejection methods.
文摘This work applies non-stationary random processes to resilience of power distribution under severe weather. Power distribution, the edge of the energy infrastructure, is susceptible to external hazards from severe weather. Large-scale power failures often occur, resulting in millions of people without electricity for days. However, the problem of large-scale power failure, recovery and resilience has not been formulated rigorously nor studied systematically. This work studies the resilience of power distribution from three aspects. First, we derive non-stationary random processes to model large-scale failures and recoveries. Transient Little’s Law then provides a simple approximation of the entire life cycle of failure and recovery through a queue at the network-level. Second, we define time-varying resilience based on the non-stationary model. The resilience metric characterizes the ability of power distribution to remain operational and recover rapidly upon failures. Third, we apply the non-stationary model and the resilience metric to large-scale power failures caused by Hurricane Ike. We use the real data from the electric grid to learn time-varying model parameters and the resilience metric. Our results show non-stationary evolution of failure rates and recovery times, and how the network resilience deviates from that of normal operation during the hurricane.
文摘The famous de Moivre’s Laplace limit theorem proved the probability density function of Gaussian distribution from binomial probability mass function under specified conditions. De Moivre’s Laplace approach is cumbersome as it relies heavily on many lemmas and theorems. This paper invented an alternative and less rigorous method of deriving Gaussian distribution from basic random experiment conditional on some assumptions.
文摘The collective behavior of a ring of coupled identical van der Pol oscillators is numerically studied in this work. Constant, gaussian and random distributions of the coupling parameter along the ring are considered. Three values of the oscillators constant are assumed in order to cover from quasilinear to nonlinear dynamic performance. Single and multiple coupled frequencies are obtained using power spectra of the long term time series. Phase portraits are obtained from numerical simulations, and the coupled behavior is analyzed, compared and discussed.
文摘目的针对数据中心网络(Data Center Network,DCN)中数据流量多导致大象流与老鼠流识别精确度低的问题,提出一种基于软件定义网络(Software Defined Networking,SDN)下两阶段大象流识别算法。方法将SDN与DCN结合,第一阶段,采用高斯分布动态阈值优化算法,通过对数据包阈值的设定,计算大象流误检率与漏检率,不断优化得到最优阈值,以此识别出可疑大象流;第二阶段,在依据流传输速率与流持续时间精确得到大象流的基础上,提出阈值约束、流量检测机制、Count计数器等三方面改进对大象流识别阈值下限的约束,将网络中大象流的数据量与流持续时间进行周期内阈值计算,提高大象流的识别精确度。结果实验结果表明:算法与已有相关算法相比,第一阶段可疑大象流平均字节数比网络流平均字节数多11.3%;不同阈值下的算法准确度提高1.7%,不同网络流量下的大象流平均检测时间降低至6 ms以内。结论软件定义网络下两阶段大象流识别算法在第一阶段具有较强的大象流识别能力,同时算法的精确度有所提高,大象流的平均检测时间降低,提高了网络质量,能为进行网络流量调度策略的进一步研究提供相关性条件。
文摘In this paper,we construct random two-faced families of matrices with non-Gaussian entries to approximate a bi-free central limit distribution with a positive definite covariance matrix.We prove that,under modest conditions weaker than independence,a family of random two-faced families of matrices with non-Gaussian entries is asymptotically bi-free from a two-faced family of constant diagonal matrices.
