用于混沌时间序列预测的组合核函数最小二乘支持向量机

针对混沌时间序列的预测问题,考虑到单一核函数的最小二乘支持向量机无法明显提高预测精度,提出了一种组合核函数的最小二乘支持向量机预测模型,模型中采用多项式函数与径向基函数组合构建核函数.同时,还对遗传算法进行了改进,使之具有更快的收敛速度和更高的精度,改进的遗传算法适用于解决预测模型中的参数优化问题.通过典型的Lorenz时间序列、Mackey-Glass时间序列、太阳黑子数时间序列以及具有混沌特性的网络流量时间序列对该模型进行了验证.仿真结果表明所提出的模型是有效的.     

On a Theorem of Høegh-Krohn

A theorem proved by R. Høegh-Krohn in Comm. Math. Phys. 38(1974), 195–224, which yields a possibility to define states of systems of quantum particles by their values on the products , where \mathfraka _t , t are time automorphisms and F _j are multiplication operators, is generalized and extended. In particular, it is shown that the algebras generated by such products with F _j taken from the families of multiplication operators satisfying certain conditions are dense in the algebras of observables in the -weak topology, in which normal states are continuous. This result was obtained for the systems with two types of kinetic energy: the usual one expressed by means of the Laplacian; the relativistic kinetic energy defined by a pseudo-differential operator.     

Approximate Homotopy Symmetry Reduction Method： Infinite Series Reductions to Kawahara Equation

The Kawahara equation is studied through the approximate homotopy symmetry method. Under this method we get the similarity reduction solutions of the Kawahara equation, leading to the corresponding homotopy series solutions. Furthermore, the similarity solutions of the corresponding reduced linear ordinary differential equations are also considered.     

Approximate Homotopy Symmetry Reduction Method: Infinite Series Reductions to Kawahara Equation

The Kawahara equation is studied through the approximate homotopy symmetry method. Under this method we get the similarity reduction solutions of the Kawahara equation, leading to the corresponding homotopy series solutions. Furthermore, the similarity solutions of the corresponding reduced linear ordinary differential equations are also considered.     

John Bell and the Identical Twins

I present a biographical profile of John S. Bell based upon extensive interviews I had with him. I present Bell‘s views on the quantum theory along with a simple explanation of his identity. Jeremy Bernstein is Professor Emeritus of Physics at the Stevens Institute of Technology and a former staff writer for The New Yorker.     

Sequential estimation of velocity fields using episodic proper orthogonal decomposition

In this paper, the problem of approximating velocity fields at future and past times based on information available at the current time is addressed. A novel method called “episodic POD” is described and developed that enables us to achieve our objective. Application of episodic POD to an ensemble of flow data results in a set of spatio-temporal eigenfunctions and a set of coefficients associated with the eigenfunctions. From these eigenfunctions, we develop two models called the “forward model” and “inverse model” that enable us to approximate the velocity fields at future and past times, based on information provided at the current time. A second set of models, the forward and inverse sequential models are also developed that enable the dynamic update of approximated velocity fields when new information is made available, making these models more adept at on-line estimation. The various properties associated with these models are described in detail, and four different examples are used to validate the models and show the different properties associated with episodic POD. It is shown through numerical validation, that the episodic POD model has a form that is dynamically consistent with the original system. It is also shown that episodic POD outperforms linear Kalman filters in the presence of noise.     

基于X射线断层成像的逆向工程中轮廓序列分割算法的原理及实现

为了实现基于X射线断层成像(CT)的逆向工程中具有参数识别的三维图像重构, 提出了一种分割轮廓序列的新算法. 首先通过一定角度的射线法来得到轮廓间的嵌套关系,然后采用扫描一次关系矩阵生成轮廓树的方法实现层内轮廓定位, 最后运用轮廓间定量、定性的属性判定来完成层间的轮廓匹配. 通过实例, 本文提供的算法可以准确、快速地分割CT零件中的轮廓序列.     

Molecular dynamics calculations of the hard-sphere equation of state

The equation of state of the hard-sphere fluid is studied by a Monte Carlomolecular dynamics method for volumes ranging from 25V ₀ to 1.6V ₀ , whereV ₀ is the close-packed volume, and for system sizes from 108 to 4000 particles. TheN dependence of the equation of state is compared to the theoretical dependence given by Salsburg for theNPT ensemble, after correction for the ensemble difference, in order to obtain estimates for the thermodynamic limit. The observed values of the pressure are compared with both the [3/2] and the [2/3] Padé approximants to the virial series, using Kratky's value for the fifth virial coefficientB ₅ and choosingB ₆ andB ₇, to obtain a least-squares fit. The resulting values ofB ₆ andB ₇ lie within the uncertainties of the Ree-Hoover-Kratky Monte Carlo estimates for these virial coefficients. The values ofB ₈,B ₉, andB ₁₀ predicted by our optimal [3/2] approximant are also reported. Finally, the Monte Carlo-molecular dynamics equation of state is compared with a number of analytic expressions for the hard-sphere equation of state.Work supported by the Office of Basic Energy Sciences, U.S. Department of Energy.     

Exact expressions for row correlation functions in the isotropicd=2 ising model

We present exact explicit expressions for the row spin-spin correlation functions _{00 n}0 in the isotropicd= 2 Ising model, in terms of elliptic integrals, forn 5. We also give a general structural formula for _{00 n}0.