A stochastic Kaczmarz algorithm for network tomography

We develop a stochastic approximation version of the classical Kaczmarz algorithm that is incremental in nature and takes as input noisy real time data. Our analysis shows that with probability one it mimics the behavior of the original scheme: starting from the same initial point, our algorithm and the corresponding deterministic Kaczmarz algorithm converge to precisely the same point. The motivation for this work comes from network tomography where network parameters are to be estimated based upon end-to-end measurements. Numerical examples via Matlab based simulations demonstrate the efficacy of the algorithm.     

广义Mamdani模糊系统依K-积分模的泛逼近及其实现过程

首先,通过引入拟减法算子给出K-积分模定义,并针对广义Mamdani模糊系统实施等距剖分其输入空间. 其次,应用分片线性函数（Piecewise linear function,PLF）的性质构造性地证明了广义Mamdani模糊系统在K-积分模意义下具有泛逼近性,从而将该模糊系统对连续函数空间的逼近能力扩展到一类可积函数类空间上. 最后,通过模拟实例给出该广义Mamdani模糊系统对给定可积函数的泛逼近及实现过程.     

Nonlinear time series forecasting with Bayesian neural networks

The Bayesian learning provides a natural way to model the nonlinear structure as the artificial neural networks due to their capability to cope with the model complexity. In this paper, an evolutionary Monte Carlo (MC) algorithm is proposed to train the Bayesian neural networks (BNNs) for the time series forecasting. This approach called as Genetic MC is based on Gaussian approximation with recursive hyperparameter. Genetic MC integrates MC simulations with the genetic algorithms and the fuzzy membership functions. In the implementations, Genetic MC is compared with the traditional neural networks and time series techniques in terms of their forecasting performances over the weekly sales of a Finance Magazine.     

Effects of neutral solvent addition on the body-centered cubic spheres of block copolymers

We employ self-consistent mean-field (SCMF) theory in studying the body-centered cubic (bcc) spheres of block copolymers in the presence of a neutral solvent. First we examine the accuracy of the dilution approximation then analyze the dependence of the bcc structural sizes with copolymer volume fraction ?, the interaction parameter χ_AB, and degree of copolymerization N. Our results reveal that both distribution of each component and the micro-structural length scales are greatly influenced by each parameter ?, χ_AB, and N. As expected, with decreasing ?, more solvent distributes non-uniformally in the segregated domains, therefore deviation from the dilution approximation increases. This also suggests that when the effective segregation parameter ?χ_ABN is fixed, a larger deviation is expected as χ_ABN increases (i.e. ? decreases). Although when both χ_ABN and ? are fixed, decreasing N (i.e. increasing χ_AB) enlarges the deviation from the dilution approximation. Furthermore, this solvent non-uniformity behavior is so significant that it even affects the dependence of the domain spacing L^* and the matrix length Λ^* with respect to (χ_AB)_effN=?χ_ABN near the ODT. When the systems are in molten state and/or in the concentrated regime, both L^* and Λ^* exhibit a sharp increase behavior as ODT is approached, due to many of the minority blocks being pulled from the spherical domains and swelling the matrix. With increasing solvent amount and/or χ_ABN, we observe that the increase of the degree for the minority blocks pulled from the spheres into the matrix near the ODT is not as significant as that in the melt. As such, the sharp increase behavior in L^* as well as Λ^* near the ODT smoothens and even disappears.     

State space approximation for general fractional order dynamic systems

Approximations for general fractional order dynamic systems are of much theoretical and practical interest. In this paper, a new approximate method for fractional order integrator is proposed. The poles of the approximate model are unrelated to the order of integrator. This feature shows benefits on extending the algorithm to the systems containing various fractional orders. Then a unified approximate method is derived for general fractional order linear or nonlinear dynamic systems via combining the proposed new method with the distributed frequency model approach. Numerical examples are given to show the wide applicability of our method and to illustrate the acceptable accuracy for approximations as well.     

Bayesian estimation of Dirichlet mixture model with variational inference

In statistical modeling, parameter estimation is an essential and challengeable task. Estimation of the parameters in the Dirichlet mixture model (DMM) is analytically intractable, due to the integral expressions of the gamma function and its corresponding derivatives. We introduce a Bayesian estimation strategy to estimate the posterior distribution of the parameters in DMM. By assuming the gamma distribution as the prior to each parameter, we approximate both the prior and the posterior distribution of the parameters with a product of several mutually independent gamma distributions. The extended factorized approximation method is applied to introduce a single lower-bound to the variational objective function and an analytically tractable estimation solution is derived. Moreover, there is only one function that is maximized during iterations and, therefore, the convergence of the proposed algorithm is theoretically guaranteed. With synthesized data, the proposed method shows the advantages over the EM-based method and the previously proposed Bayesian estimation method. With two important multimedia signal processing applications, the good performance of the proposed Bayesian estimation method is demonstrated.     

Multilevel microwave design optimization with automated model fidelity adjustment

A computationally efficient algorithm for electromagnetic (EM)‐simulation‐driven design optimization of microwave structures is proposed. Our technique exploits variable‐fidelity EM simulations and the multilevel design approach where an approximate optimum of the lower accuracy but faster EM model of the structure under design is used as a starting point for optimizing a more accurate model. Several enhancements of the basic multifidelity method are introduced, including an efficient algorithm of optimizing EM models that is based on local response surface approximations, as well as automated adjustment of model fidelity. Convergence of the procedure to the optimum design is ensured by defaulting to the higher fidelity model whenever the prediction given by the lower fidelity fails to improve the design. Distribution of the computational effort between the models of different fidelity allows for making larger steps in the design space at a low cost, as well as substantial reduction of the number of high‐fidelity model evaluations, because the high‐fidelity model is only referred to in the last design stage. The article provides comprehensive numerical verification of our technique. Substantial computational savings are demonstrated in comparison to the benchmark methods: over 40% on average as compared to a basic version of the multifidelity optimization approach and over 95% as compared to direct optimization of the high‐fidelity model. © 2013 Wiley Periodicals, Inc. Int J RF and Microwave CAE 24:281–288, 2014.     

Integral approximation—an approach to reduced models for particulate processes

In this contribution, a model reduction technique for population balance systems describing particulate processes is presented. This technique is based on integral approximation and allows the derivation of highly accurate moment models. In contrast to other model reduction methods which can be found in literature, this integral approximation technique can be applied for arbitrarily complex phenomena specifications. The applicability of the presented method will be demonstrated for different example processes by comparing the dynamic behavior of the original population balance models with those of the derived reduced models of moments.