Smoothed Bagging with Kernel Bandwidth Selectors

Recently, a combined approach of bagging (bootstrap aggregating) and noise addition was proposed and shown to result in a significantly improved generalization performance. But, the level of noise introduced, a crucial factor, was determined by trial and error. The procedure is not only ad hoc but also time consuming since bagging involves training a committee of networks. Here we propose a principled procedure of computing the level of noise, which is also computationally less expensive. The idea comes from kernel density estimation (KDE), a non-parametric probability density estimation method where appropriate kernel functions such as Gaussian are imposed on data. The kernel bandwidth selector is a numerical method for finding the width of a kernel function (called bandwidth). The computed bandwidth can be used as the variance of added noise. The proposed approach makes the trial and error procedure unnecessary, and thus provides a much faster way of finding an appropriate level of noise. In addition, experimental results show that the proposed approach results in an improved performance over bagging, particularly for noisy data.     

Computing ruin probability in the classical risk model

We consider the classical risk model with discrete time and loss distribution with heavy tails. When computing the ruin probability, a region of medium values of the argument, which is most interesting in practice, arises. In this region, known asymptotic formulas do not work yet, while direct solutions of the corresponding linear integral equations do not work already. We construct sufficiently accurate and efficient algorithms for computing the ruin probability in this region, which are based on approximating the loss distribution with a family of exponential distributions. To test the results, we have conducted a numerical experiment.     

油藏数值模拟有限元并行计算方法研究

针对目前油藏数值模拟普遍采用的有限差分法计算精度低的问题,提出了兼顾计算精度、计算速度问题的有限元油藏数值模拟方法,即在建立了油藏数值模拟数学模型的基础上通过有限元数值分析方法建立有限元数值模型,但有限元在油藏数值模拟时存在单机计算困难、计算时间长的问题,为此提出了利用区域分解技术的油藏数值模拟并行计算方法,最后将该方法通过实例进行检验,取得了良好的加速比和并行效率。     

含时滞项的双稳系统中平均首次穿越时间的研究

研究了含时滞项的非对称双稳系统中的平均首次穿越时间问题.应用小时滞近似方法,得到了系统的Fokker-Planck方程及稳态概率密度函数,进而得到了系统的平均首次穿越时间的表达式,最后对理论结果做了数值模拟.数值计算结果表明:(1)时滞量的大小对系统的稳态概率密度函数的影响是不一样的,当0<τ<0.175时,系统的稳态概率密度函数曲线仍然为双峰形状;当τ>0.175时,系统的稳态概率密度函数曲线呈现出阱状.(2)在0<τ<0.175时,讨论了系统的乘性和加性噪声强度对系统的平均首次穿越时间的影响,发现平均首次穿越时间T -乘性噪声强度曲线上有最小值出现,而T -加性噪声强度曲线是单调的.     

An efficient and high-order sliding mesh method for computational aeroacoustics

This paper presents an efficient sliding mesh method to simulate the noise emission from aero-engines. The vortexes shed from the rotating blade and interact with the downstream stationary outlet guide vanes (OGVs), producing noise. The challenges in simulating the problem are the accurate modelling of the wake turbulence, and the capabilities to capture the acoustic waves, the energy of which is several orders lower than the turbulent components. To model the relative motion between the rotors and OGVs, a sliding mesh method is developed to account for the rotation of the rotor blades and wakes, which can lead to efficiency and accuracy challenges. In this work, an advanced treatment is developed for efficient and high-accuracy interpolation by combining both patch and sliding interfaces. The grid along the sliding interface is uniformly distributed taking advantage of the patch interface, providing huge benefits to the overall performance by reusing data and omitting repeated calculation. The algorithm using message passing interface is well designed for maintaining ideal performance of the code. The fan–OGV geometry is represented as unwrapped two-dimensional cascades with isotropic and anisotropic turbulence synthesised and injected to simulate the fan-wake. The numerical results are compared to analytical solutions for accuracy validation. The simulations numerically reveal the effect of turbulence intensity, length scale and anisotropy in the fan wake on the noise emission due to the turbulence-OGV interaction. Also the blockage effect of rotating blades on the noise propagation and its impact on the hearing of observers are discussed. Moreover, it is shown that the new method is able to maintain a high accuracy for acoustic computation and an ideal performance is obtained from the numerical code using a parallel computing algorithm.

     

Determination of firing times for the stochastic Fitzhugh-Nagumo neuronal model

We present for the first time an analytical approach for determining the time of firing of multicomponent nonlinear stochastic neuronal models. We apply the theory of first exit times for Markov processes to the Fitzhugh-Nagumo system with a constant mean gaussian white noise input, representing stochastic excitation and inhibition. Partial differential equations are obtained for the moments of the time to first spike. The observation that the recovery variable barely changes in the prespike trajectory leads to an accurate one-dimensional approximation. For the moments of the time to reach threshold, this leads to ordinary differential equations that may be easily solved. Several analytical approaches are explored that involve perturbation expansions for large and small values of the noise parameter. For ranges of the parameters appropriate for these asymptotic methods, the perturbation solutions are used to establish the validity of the one-dimensional approximation for both small and large values of the noise parameter. Additional verification is obtained with the excellent agreement between the mean and variance of the firing time found by numerical solution of the differential equations for the one-dimensional approximation and those obtained by simulation of the solutions of the model stochastic differential equations. Such agreement extends to intermediate values of the noise parameter. For the mean time to threshold, we find maxima at small noise values that constitute a form of stochastic resonance. We also investigate the dependence of the mean firing time on the initial values of the voltage and recovery variables when the input current has zero mean.     

Approximation of event probabilities in noisy cellular processes

Molecular noise, which arises from the randomness of the discrete events in the cell, significantly influences fundamental biological processes. Discrete-state continuous-time stochastic models (CTMC) can be used to describe such effects, but the calculation of the probabilities of certain events is computationally expensive.We present a comparison of two analysis approaches for CTMC. On one hand, we estimate the probabilities of interest using repeated Gillespie simulation and determine the statistical accuracy that we obtain. On the other hand, we apply a numerical reachability analysis that approximates the probability distributions of the system at several time instances. We use examples of cellular processes to demonstrate the superiority of the reachability analysis if accurate results are required.     

基于MPI的不可压缩N-S方程并行计算方法

在目前的流体计算中,当雷诺数较高时,计算量非常巨大,存在耗时长的问题,需要采用并行计算,对此提出一种基于MPI(Message Passing Interface)的并行计算方法。通过实例验证,该方法准确、易行、稳健,并且可以大幅提高计算速度,节省计算时间,对于大型科学计算问题具有很好的适用性。     

Helmholtz共振腔气动噪声数值仿真

为探究出一套完整、准确的气动噪声仿真方法,用FLUENT和Actran仿真Helmholtz共振腔旁接管道系统模型.针对流场仿真,采用六面体网格建模,分析选择合适的网格密度,明确网格及边界条件的影响,以获得准确的声源信息;运用Lighthill声类比方法对声场进行仿真,采用数值计算、传声损失仿真和气动噪声仿真计算等3种方法提取管道内部场点声压级频谱曲线,分析曲线峰值频率特征,包括共振频率分析和声模态分析等.采用CFD软件与声学仿真软件相结合的方法,可以有效进行流场和声场的仿真.     

谱方法求解水声传播问题的优化与并行

水声传播数值计算的效率是各类水声学应用关心的核心因素之一,谱方法作为求解微分方程的一种数值方法,具有精度高、收敛速度快等优点,因此,近年来利用简正波-谱方法求解水声传播方程引起了许多学者的关注;然而,谱方法计算量更大,计算时间更长,在求解大范围海域声传播问题时,难以满足实时性的需求.因此,需要借助现代高性能计算机系统,...     

二维复杂向量场可视化方法研究及应用

向量场数据广泛存在于科学和工程计算中,面当前缺少和有效的复杂向量场可视化方法,使得在一些研究领域中计算出来的数据无法得到很好的理解和使用。通过分析点噪声方法和非定常网格数据场的特点,提出适用于二维非定常网格数据折可视化方法;非定常点噪声方法。该方法主要解决变化网格及数据时间精度不足带来的问题,通过对惯性约束聚变的数值模拟数据进行可视化,取得了令人满意的结果,结果表明该方法是一种对复杂向量场有效的可视化方法。     

Comment on "Characterization of subthreshold voltage fluctuations in neuronal membranes," by M. Rudolph and A. Destexhe

In two recent articles, Rudolph and Destexhe (2003, 2005) studied a leaky integrator model (an RC-circuit) driven by correlated ("colored") gaussian conductance noise and Gaussian current noise. In the first article, they derived an expression for the stationary probability density of the membrane voltage; in the second, they modified this expression to cover a larger parameter regime. Here we show by standard analysis of solvable limit cases (white noise limit of additive and multiplicative noise sources; only slow multiplicative noise; only additive noise) and by numerical simulations that their first result does not hold for the general colored-noise case and uncover the errors made in the derivation of a Fokker-Planck equation for the probability density. Furthermore, we demonstrate analytically (including an exact integral expression for the time-dependent mean value of the voltage) and by comparison to simulation results that the extended expression for the probability density works much better but still does not exactly solve the full colored-noise problem. We also show that at stronger synaptic input, the stationary mean value of the linear voltage model may diverge and give an exact condition relating the system parameters for which this takes place.     

回归神经网络中样本特征记忆的反馈控制方法研究

分析了具有遗忘特性及信息锁存能力的状态回归神经网络的计算方法。针对多输入多输出时序样本,提出了更能反映网络短时记忆能力以及时序样本数据物理特性的同时刻反馈控制和计算方法。实验结果显示,该文提出的方法对时序样本的学习和记忆不但具有更高的准确性,而且不增加计算的复杂性。     

The spectral density of the nonlinear damping model: single DOFcase

An analytical method of computing the frequency response of single degree of freedom (DOF) oscillators with nonlinear damping is described. The author proposes an energy-type nonlinear damping model and the corresponding stationary probability density with white noise input can be obtained explicitly. A theorem is presented which gives an interesting result, in terms of the Krylov-Bogoliubov approximation, concerning the modeling and identification of nonlinear internal damping in flexible structures. This analysis also serves as a contribution to random vibration theory by providing a method of computing the first- and second-order statistics (steady-state probability density, correlation function, and spectral density) of nonlinearity damped oscillators with white noise input     

接地网接地电阻的优化算法

基于对称复镜象法提出了一种模拟计算接地网接地电阻的优化算法。对称复镜象法是一种适用于非均匀土壤中任意结构接地网接地参数精确计算的新方法。对于多层媒质模型,利用对称复镜象法计算接地电阻时,需要假定总的泄漏电流,由此得到每个单元的泄漏电流和地网电位升,进而得到地网接地电阻。本文对此进行了较简便的优化,不必假设总的泄漏电流,而是通过矩阵变换直接求出接地电阻,从而大大提高了计算精度和计算时间。文中给出了两层大地模型中接地网接地电阻的优化算法并给出了任意放置的两导体间互阻的解析计算公式,且应用所介绍的方法分析计算了实际接地网系统,得到了满意的结果。     

基于算术平均数粒度计算的人形特征约简

为将基于粒度计算的属性约简方法应用于人形特征的筛选,避免传统方法难以准确消除冗余的缺点,提出一种基于算术平均数的粒度计算方法。采用支持向量机对目标图片进行人形识别,记录不同特征参数下的识别率,求出其算术平均数,并与单个数据做比较,简化决策表后通过粒度计算的方法约简人形特征。将得到的约简特征与原始特征在相同测试集下做性能比较,实验结果表明,该方法能消除冗余,提高识别的性能,且鲁棒性较好。     

基于MPI的伪谱法DNS并行计算方法研究

使用伪谱方法的直接数值模拟准确、高效,但在高雷诺数情况下,计算量非常巨大,需要采用并行方法,但是快速傅里叶变换的并行算法在实际应用中有很大的困难。针对这一问题,提出了一种新的基于MPI的伪谱法直接数值模拟的并行计算方法。通过实例验证,该方法准确、易行、稳健,并且可以大幅提高计算速度,节省计算时间,这对直接模拟在科学研究和工程实际中的广泛应用都具有重要意义。     

Flexible distributed heterogeneous computing in traffic noise mapping

In China, fast city rebuilding poses the challenge of frequent refresh cycle of urban traffic noise mapping. Computational complexity and lack of resources are the primary bottleneck in traffic noise mapping. In this paper, we present a flexible distributed heterogeneous computing method based on GPU-CPU cooperation, which reduces the overhead, improves the efficiency of parallel computing and consistently generates good quality results for traffic noise mapping. A genetic algorithm based large-scale task partition algorithm is employed to solve load balancing problem in distributed noise mapping calculation. The methodology is evaluated by an example, whose results show that the proposed task partition method can significantly improve running efficiency. Parallel efficiency increases from 54% to 78%. In addition, test speed is further improved by 21% with the GPU-CPU collaborative computing, even with only low-end type GPUs.     

A new class of Zernike moments for computer vision applications

A Modified Direct Method for the computation of the Zernike moments is presented in this paper. The presence of many factorial terms, in the direct method for computing the Zernike moments, makes their computation process a very time consuming task. Although the computational power of the modern computers is impressively increasing, the calculation of the factorial of a big number is still an inaccurate numerical procedure. The main concept of the present paper is that, by using Stirling’s Approximation formula for the factorial and by applying some suitable mathematical properties, a novel, factorial-free direct method can be developed. The resulted moments are not equal to those computed by the original direct method, but they are a sufficiently accurate approximation of them. Besides, their variability does not affect their ability to describe uniquely and distinguish the objects they represent. This is verified by pattern recognition simulation examples.     

色噪声激励的时滞非线性系统瞬态响应研究

建立了色噪声与时滞联合作用的非线性系统模型,提出求解其瞬态概率密度的高效近似算法。利用等价变换将时滞系统简化为非时滞系统;通过线性化方法和随机平均原理得到原系统振幅过程的平均It?随机微分方程和相应的Fokker-Planck-Kolmogorov（FPK）方程。基于退化线性系统导出一组正交基,在该基空间内进行Galerkin变分得到近似瞬态概率密度。将该方法应用到受色噪声激励的双时滞Duffing-Van Der Pol振子得到理论解,采用蒙特卡罗模拟（MCS）验证理论解的正确性。分析了色噪声参数和时滞参数对瞬态响应的影响。研究结果表明：所提理论方法可有效求解受色噪声激励的时滞非线性系统的瞬态概率密度;算法求解效率高于MCS;色噪声和时滞均明显影响了系统瞬态响应。