Small-world and the growing properties of the Chinese railway network

By using the tools of statistical physics and recent investigations of the scaling properties of different complex networks, the structural and evolving properties of the Chinese railway network (CRN) is studied. It has been verified that the CRN has the same small-world properties of the Indian railway network (IRN). According to the class of small-world networks, we believe the CRN is a single scale. In addition, a novel result is obtained. Measurements on the CRN indicate that the rate at which nodes acquire links depends on the node’s degree and follows a power law.      

Refraction of light in media

The roles of the magnetic field and electric field of the light are investigated when the light is refracted in the medium. The model of the electron cloud conductor is presented. Electron cloud in a molecule is treated as a conductor and the Faraday’s Law is applied to this conductor that is in the alternating magnetic field of the light. dB _M/dt of the light gives rise to an alternating induced current on the electron cloud conductor, and the light exchanges energy, i.e. the refractive energy, with the electron cloud conductor. Formulas of refractive index, which is the ratio of light speed in vacuum to that in the medium, are derived with this model. These formulas are tested with several mediums and Langevin’s diamagnetic susceptibility of helium gas, and the results are in good agreement with the measured data. The anisotropy and the nonlinearity of the refractive index are explained with the theory described in this work. Supported by Beijing Science and Technology New Star Program (Grant No. 952870400), the Beijing Municipal Commission of Education and the Excellent Young Teachers Program of Ministry of Education of China     

A novel approach based on recurrent neural networks applied to nonlinear systems optimization

This paper presents an efficient approach based on recurrent neural network for solving nonlinear optimization. More specifically, a modified Hopfield network is developed and its internal parameters are computed using the valid subspace technique. These parameters guarantee the convergence of the network to the equilibrium points that represent an optimal feasible solution. The main advantage of the developed network is that it treats optimization and constraint terms in different stages with no interference with each other. Moreover, the proposed approach does not require specification of penalty and weighting parameters for its initialization. A study of the modified Hopfield model is also developed to analyze its stability and convergence. Simulation results are provided to demonstrate the performance of the proposed neural network.     

The Problem of Capacity Addition in Multi-user Elastic Demand Communication Networks

In this paper we consider some properties on prices under flow control in a network that is to be shared by noncooperative users. Each user is faced with an optimization problem which is formulated as the minimization of its own criterion subject to constraint on the flows of the other users. The operating points of the network are the Nash equilibria of the underlying routing game. Our objective is to study the behavior of prices of all users when the network designer needs to allocate capacities to network links. For parallel links topologies, we show that degradation of the performances such as prices will not take place, as well as the users may find it beneficial to improve their requests     

Parking Capacity and Pricing in Park'n Ride Trips: A Continuous Equilibrium Network Design Problem

In this paper we consider the problem of designing parking facilities for park'n ride trips. We present a new continuous equilibrium network design problem to decide the capacity and fare of these parking lots at a tactical level. We assume that the parking facilities have already been located and other topological decisions have already been taken.The modeling approach proposed is mathematical programming with equilibrium constraints. In the outer optimization problem, a central Authority evaluates the performance of the transport network for each network design decision. In the inner problem a multimodal traffic assignment with combined modes, formulated as a variational inequality problem, generates the share demand for modes of transportation, and for parking facilities as a function of the design variables of the parking lots. The objective is to make optimal parking investment and pricing decisions in order to minimize the total travel cost in a subnetwork of the multimodal transportation system.We present a new development in model formulation based on the use of generalized parking link cost as a design variable.The bilevel model is solved by a simulated annealing algorithm applied to the continuous and non-negative design decision variables. Numerical tests are reported in order to illustrate the use of the model, and the ability of the approach to solve applications of moderate size.     

Comparative Study on Large and Small Signal Theory for Intensity Modulation Response of Semiconductor Lasers Including Higher-Order Dispersion Terms

In this article, the comparison of large signal theory and small signal theory has been done with dispersive propagation of optical signal with IMDD (Intensity Modulation Direct Detection) systems for semiconductor lasers with higher-order dispersion terms. The expressions for an exact large signal theory and small signal theory including higher-order dispersion terms for propagation of an optical wave with sinusoidal amplitude and frequency modulation in a dispersive fiber have been derived. It is observed that small signal theory is more sensitive compared to large signal theory in terms of intensity modulation/direct detection systems. Also, it is reported that for large signal analysis the higher-order effects of dispersion can be ignored, whereas for small signal theory, the higher-order effects can be ignored for lower modulation frequencies only. The variation in the transfer function for various values of modulation indices are greater for small signal analysis than for large signal analysis. Also, as the intensity modulation index is increased, there is a decrease in the value of transfer function. The large signal model approximates the small signal model for lower values of the intensity modulation index.     

Approximating the single source unsplittable min-cost flow problem

In the single source unsplittable min-cost flow problem, commodities must be routed simultaneously from a common source vertex to certain destination vertices in a given graph with edge capacities and costs; the demand of each commodity must be routed along a single path so that the total flow through any edge is at most its capacity. Moreover, the total cost must not exceed a given budget. This problem has been introduced by Kleinberg [7] and generalizes several NP-complete problems from various areas in combinatorial optimization such as packing, partitioning, scheduling, load balancing, and virtual-circuit routing. Kolliopoulos and Stein [9] and Dinitz, Garg, and Goemans [4] developed algorithms improving the first approximation results of Kleinberg for the problem of minimizing the violation of edge capacities and for other variants. However, known techniques do not seem to be capable of providing solutions without also violating the cost constraint. We give the first approximation results with hard cost constraints. Moreover, all our results dominate the best known bicriteria approximations. Finally, we provide results on the hardness of approximation for several variants of the problem. Received: August 23, 2000 / Accepted: April 20, 2001?Published online October 2, 2001     

不确定非线性系统的鲁棒自适应控制器

在ｂａｃｋｓｔｅｐｐｉｎｇ程序中，把非线性自适应控制和鲁棒控制连接起来，为参数化的严格反馈系统在不确定性存在的情况下，建立了一种鲁棒自适应控制方案．非线性自适应控制被用来处理系统的线性参数化部分，而鲁棒控制通过引进非线性阻尼项被用来处理不确定性部分．与现有的方案不同，作者给出了非线性阻尼项的无限种选择，而不是仅仅一种选择．通过使用一种合适的选择，能够设计一个鲁棒自适应控制器．它不仅能够保证对不确定性的鲁棒性，而且能够使输出误差任意小，以及用较小的控制努力取得较好的性能．     

On Numerical Solution of Shape Inverse Problems

The new method is proposed for the numerical solution of a class of shape inverse problems. The size and the location of a small opening in the domain of integration of an elliptic equation is identified on the basis of an observation. The observation includes the finite number of shape functionals. The approximation of the shape functionals by using the so-called topological derivatives is used to perform the learning process of an artificial neural network. The results of computations for 2D examples show, that the method allows to determine an approximation of the global solution to the inverse problem, sufficiently closed to the exact solution. The proposed method can be extended to the problems with an opening of general shape and to the identification problems of small inclusions. However, the mathematical theory of the proposed approach still requires futher research. In particular, the proof of global convergence of the method is an open problem.     

神经网络在工程爆破应力波规律探讨中的应用

采用BP（Back Propagation)前馈人工神经网络模型，对工程爆破中柱状震源的自由场应力波传播规律进行了探讨。结果表明：利用人神经网络模型的非线性映射功能，可以较好地给出工程爆破引起的近区自由场力学规律，对于同类型问题的研究，也有着很重要的意义。