On the hardness of approximating label-cover

The Label-Cover problem, defined by S. Arora, L. Babai, J. Stern, Z. Sweedyk [Proceedings of 34th IEEE Symposium on Foundations of Computer Science, 1993, pp. 724-733], serves as a starting point for numerous hardness of approximation reductions. It is one of six ‘canonical’ approximation problems in the survey of Arora and Lund [Hardness of Approximations, in: Approximation Algorithms for NP-Hard Problems, PWS Publishing Company, 1996, Chapter 10]. In this paper we present a direct combinatorial reduction from low error-probability PCP [Proceedings of 31st ACM Symposium on Theory of Computing, 1999, pp. 29-40] to Label-Cover showing it NP-hard to approximate to within 2^{(logn)1−o(1)}. This improves upon the best previous hardness of approximation results known for this problem.We also consider the Minimum-Monotone-Satisfying-Assignment (MMSA) problem of finding a satisfying assignment to a monotone formula with the least number of 1's, introduced by M. Alekhnovich, S. Buss, S. Moran, T. Pitassi [Minimum propositional proof length is NP-hard to linearly approximate, 1998]. We define a hierarchy of approximation problems obtained by restricting the number of alternations of the monotone formula. This hierarchy turns out to be equivalent to an AND/OR scheduling hierarchy suggested by M.H. Goldwasser, R. Motwani [Lecture Notes in Comput. Sci., Vol. 1272, Springer-Verlag, 1997, pp. 307-320]. We show some hardness results for certain levels in this hierarchy, and place Label-Cover between levels 3 and 4. This partially answers an open problem from M.H. Goldwasser, R. Motwani regarding the precise complexity of each level in the hierarchy, and the place of Label-Cover in it.     

低云中短波红外表观辐射模型研究

在对空红外系统的多光谱探测和红外仿真中，云的干扰不可忽略，所以，对云的辐射特性的研究至关重要。在不同的波段，云的辐射特性会有很大的差异，为了研究各个不同波段云的表现辐射特性．需要计算云的光谱辐射量。在典型观测模式下建立了低云的表观光谱辐射模型，研究了对云背景辐射有贡献的各个辐射分量的计算方法。基于传统的二流近似模型获取各个参数，引入云的光谱光学厚度的经验公式。进而获得了低云在中短波段的光谱辐射特性，有效地计算出了云背景在1-5μm的中短波段内的表现光谱辐亮度数据，并且节省了计算时间。经过比较发现，该模型的计算结果与实测结果有较好的一致性。可以为云背景多光谱分析、探测及仿真提供背景数据。     

EM procedures using mean field-like approximations for Markov model-based image segmentation

Image segmentation using Markov random fields involves parameter estimation in hidden Markov models for which the EM algorithm is widely used. In practice, difficulties arise due to the dependence structure in the models and approximations are required. Using ideas from the mean field approximation principle, we propose a class of EM-like algorithms in which the computation reduces to dealing with systems of independent variables. Within this class, the simulated field algorithm is a new stochastic algorithm which appears to be the most promising for its good performance and speed, on synthetic and real image experiments.     

Coordinating production and distribution of jobs with bundling operations

We consider an integrated scheduling and distribution model in which jobs completed by two different machines must be bundled together for delivery. The objective is to minimize the sum of the delivery cost and customers' waiting costs. Such a model not only attempts to coordinate the job schedules on both machines, but also aims to coordinate the machine schedules with the delivery plan. Polynomial-time heuristics and approximation schemes are developed for the model with only direct shipments as well as the general model with milk-run deliveries.     

WKB近似下的Fourier衍射成象方法

对于介质目标微波衍射成象，本文引入了ＷＫＢ近似来模拟目标内部总场。基于这种近似，我们导出了Ｆｏｕｒｉｅｒ衍射公式，并采用了广义滤波逆传播方法由目标空间谱实现目标特性的重建。计算机模拟结果表明采用ＷＫＢ近似重建目标特性较Ｂｏｒｎ近似有明显改善。     

The Continuous Interpolating Self-organizing Map

The self-organizing map (SOM) [5] provides a general data approximation method which is suitable for several application domains. The topology preservation is an important feature in data-analysis and may also be advantageous for the evaluation of the data in a function approximation or regression task. For this reason the interpolated self-organizing map (I-SOM) adds an output layer to the SOM architecture which computes a real valued output vector. This paper presents an extension of I-SOM towards a continuous interpolation. It is compared to RBF and to the parametrized self-organizing map.     

Best L1 Piecewise Monotonic Data Modelling

Let us consider n data measurements of a univariate process that have been altered by random errors. We assume that an underlying model function has a substantially smaller number of turning points than the observed ones. We propose algorithms that make least the sum of the moduli of the errors by requiring k monotonic sections, alternately increasing and decreasing, in the sequence of the smoothed values. The main difficulty in this calculation is that the optimal positions of the joins of the monotonic sections have to be found automatically among so many combinations that it is impossible to test each one separately. Moreover, the calculation seems to be very intractable to general optimization techniques because O(n^k) local minima can occur. It is shown that dynamic programming can be used for separating the data into optimal disjoint sections of adjacent data, where each section requires a single L₁ monotonic calculation. This procedure is highly efficient, requiring at most O(kn²) computer operations and O(n) best L₁ monotonic calculations to subranges of data for a global minimum.     

符号运算在求解车辆传动系扭振中的应用

介绍符号运算方法在用拉普拉斯变换方法求解车辆传动系扭振过程中的作用．针对弹性联轴器的匹配计算，给出了具体求解实例．实践表明，与传统的纯数值计算方法相比，符号运算方法可以方便准确地处理车辆传动系统扭振分析中的非线性等复杂问题，具有推广应用价值．     

Practical method for generation expansion planning based on dynamic programming

This paper presents an efficient method which provides the optimal generation mix and the optimal generation construction process. The approximation method in which the dynamic programming technique and gradient method are combined is applied to determine the optimal generation mix with hydropower generation technologies. The successive approximations dynamic programming (SADP) technique, which is very suitable for high-dimensional multistage decision process problems, is used for obtaining the optimal generation construction process. The effectiveness and feasibility of the developed technique are demonstrated on a practical power system model which has five types of generation technologies including a hydropower generation technology.