关键词： LATTICE dynamics   FOURIER transforms   MATHEMATICAL analysis  

摘要： It is with great sadness that the authors contribute this paper to this special issue in memory of their former PhD advisor Thomas Beth. Beth was an extremely versatile researcher with contributions in a wide range of disciplines. However, one pervading theme can be identified in all of his work: the belief that mathematics, and in particular abstract algebra, was the language and key to uncovering the structure in many real world problems. One testament to this vision is his seminal habilitation thesis on the theory of Fourier transform algorithms, which ingeniously connects one of the principal tools in signal processing with group theory to open up an entirely new field of research. The authors deeply regret that Beth's untimely death prevented him from seeing the Algebraic Signal Processing Theory, a body of work, including the present paper, that develops an axiomatic approach to and generalization of signal processing based on the representation theory of algebras. The theory is a logical continuation of Beth's ideas and would not exist without him and his influence as PhD advisor. The authors like to think that he would have approved of this work and wish to dedicate this paper to him and his memory.

关键词： system planning   tabu search   genetic algorithm   mathematical programming   artificial intelligence   iterative improvement methods  

摘要： In this paper, system network planning expansion is formulated for mixed integer programming, a genetic algorithm (GA) and tabu search (TS). Compared with other optimization methods, GAs are suitable for traversing large search spaces, since they can do this relatively rapidly and because the use of mutation diverts the method away from local minima, which will tend to become more common as the search space increases in size. GA's give an excellent trade off between solution quality and computing time and flexibility for taking into account specific constraints in real situations. TS has emerged as a new, highly efficient, search paradigm for finding quality solutions to combinatorial problems. It is characterized by gathering knowledge during the search and subsequently profiting from this knowledge. The attractiveness of the technique comes from its ability to escape local optimality. The cost function of this problem consists of the capital investment cost in discrete form, the cost of transmission losses and the power generation costs. The DC load flow equations for the network are embedded in the constraints of the mathematical model to avoid sub-optimal solutions that can arise if the enforcement of such constraints is done in an indirect way. The solution of the model gives the best line additions and also provides information regarding the optimal generation at each generation point. This method of solution is demonstrated on the expansion of a 10 bus bar system to 18 bus bars. Finally, a steady-state genetic algorithm is employed rather than generational replacement, also uniform crossover is used. (C) 2007 Elsevier Ltd. All rights reserved.

关键词： Reinforcement learning   Galois lattices  

摘要： The generalization of policies in reinforcement learning is a main issue, both from the theoretical model point of view and for their applicability. However, generalizing from a set of examples or searching for regularities is a problem which has already been intensively studied in machine learning. Thus, existing domains such as Inductive Logic Programming have already been linked with reinforcement learning. Our work uses techniques in which generalizations are constrained by a language bias, in order to regroup similar states. Such generalizations are principally based on the properties of concept lattices. To guide the possible groupings of similar states of the environment, we propose a general algebraic framework, considering the generalization of policies through a partition of the set of states and using a language bias as an a priori knowledge. We give a practical application as an example of our theoretical approach by proposing and experimenting a bottom-up algorithm. (c) 2008 Published by Elsevier Ltd

关键词： Correctness criteria   algebraic closures   Estimate-Calculating Algorithm Model   accuracy class   Algebra   algorithms  

摘要： This paper presents correctness criteria for algebraic closures of the estimate-calculating algorithm (ECA) model. It is shown that a correct algorithm of minimal power complexity can be sought in a special form and criteria for the realization of a particular classification of a control sample are found. A metric is constructed that contains the entire information on the algebraic closures of the model.

摘要： Recently, strapdown gyro navigation systems have become widely used. In such systems, sensors, gyros, and accelerometers are placed directly aboard the object and an imaginary analytic trihedral is used instead of a stabilized gyroplatform. The object orientation with respect to the analytic trihedral is calculated by numerically solving the Poisson equations taking into account the readings of gyro sensors measuring the object angular velocities. The mutual orientation parameters permit recalculating the apparent acceleration measured by the accelerometers on the object axes for the axes of the analytic trihedral. In the analytic trihedral, the navigation problem is solved in the same way as it is solved in platform systems but, in the whole, the functions of the onboard algorithms of strapdown systems are significantly more complicated than those of platform systems. The possibility of detailed processing of on-board algorithms is of great importance for ensuring the accuracy of the entire navigation system. In the present paper, we state algorithms for reproducing the exact readings of ideal gyro sensors and the exact readings of ideal accelerometers under bench operating conditions of the system under an angular motion imitating the object orientation evolution and the possible angular vibration. Simultaneously, we calculate the exact position and orientation parameters, which can be compared with the results produced by the on-board algorithm.

关键词： 遗传算法   时间窗   定位路线问题   物流集成化   物流中心  

摘要： 随着社会经济的不断发展，人民生活水平的不断提高，产业化、信息化的不断加速，产品生产成本的降低空间已越来越小，而物流作为一个新兴产业，其发展空间十分可观。美国、日本等发达国家的物流集成化已发展到一定水平，而我国的物流仅处于初级发展阶段，为了更好的适应我国经济发展的需要，就必须尽快提高我国物流集成化水平。\n 物流中心的选址作为物流运作中的基础要素，其优化和求解意义重大，对此问题的研究即为定位配给问题(Location Association Problem，LAP)；而物流配送作为物流系统的重要组成部分，对物流系统成本也有较大影响，综合考虑这两个方面并对其进行优化求解设计就可以大大降低物流系统总成本；随着物流集成化水平的不断提高，人们对物流服务的要求也越来越高，因此就要考虑物流服务中的时间约束问题，即时间窗约束，综合考虑以上三个方面的因素，即为本文所要研究的带时间窗的定位路线问题(LocationRouting Problems With Time－Windows，LRPTW)。\n 在结合定位配给问题和车辆路线问题数学模型的基础上，本文建立了带时间窗的定位一路线问题的数学模型，并用Lingo10.0软件对其进行检验，证明了本文建立的数学模型的正确性。因其NP-hard属性，当节点数较多时精确解不宜得到，本文设计了启发式算法进行求解，先用空间填充曲线(Space Filling Curves，SFC)求解定位配给问题，再用遗传算法求解带时间窗的车辆路线问题。遗传算法采用自然数编码的方法使得交叉和变异操作更加简便，利用随机构造初始解的方法产生初始种群，可以使解更具有遍历性，避免了“早熟”现象的发生。用本文设计的遗传算法对小规模数据进行测算，其结果与Lingo10.0所得优化解十分接近，说明本文设计的遗传启发式算法的有效性；对于一定规模的LRPTW模型，通过实例仿真测算并与有关文献进行对比显示：本文所采用的遗传算法在求解一定规模的LRPTW模型时其求解速度较快，解的精度较高，说明本文设计的算法求解该问题具有一定的有效性，这对实际环境下的物流系统集成理论应用研究和发展具有重要意义。

关键词： electrostatic self-assembly   enzyme electrodes   relaxation method   simplex algorithm  

摘要： A description of the implementation of the relaxation method with automatic mesh point allocation for. immobilized enzyme electrodes is presented. The advantages of this method for the solution of coupled reaction-diffusion problems are discussed. The relaxation numerical simulation technique is combined with the Simplex fitting algorithm to extract kinetic parameters from experimental data. The results of the simulations are compared to experimental data from self-assembled multilayered electrodes comprised of glucose oxidase (GOx) and an Os modified redox mediator and found to be in excellent agreement. (c) 2008 Elsevier B.V. All rights reserved.

关键词： 数据挖掘   离群点检测   算法循环   数学形态学  

摘要： 数据挖掘是在海量的数据中提取隐含的、未知的、潜在有用的知识或信息模式的决策支持方法。在信息爆炸的今天，数据挖掘显得尤为重要。\n 一个人的噪声可能是另一个人的信号，忽视或降低离群点的存在性都将可能导致重要隐藏信息的丢失。在一些从数据库中发现知识(KDD)的应用实践中，发掘特别的实例，不具备一般数据特性的数据对象或离群点比找出普通模式更加令人感兴趣。因此，离群点本身可能是非常重要的，例如在欺诈探测中，离群点可能预示着欺诈行为。总之，离群点检测是数据挖掘领域一个重要的研究方向。\n 本文在分析已有离群点算法的基础上，提出了一种基于数学形态学的离群点检测算法。该算法首次把数学形态学的理论引入到离群点检测中，采用启发式方法自动检测离群点，无论是点状、线状，还是各种复杂的面状(凸面形状、非凸面形状、环面形状等)数据集，算法都能正确和精确地找出离群点，而对于非均匀密度数据集、多密度的数据集，算法也同样地能找出离群点。算法考虑了离群点“局部”的概念。无论与怎样的方式输入感兴趣的数据，对算法确定离群点都没有任何影响。此外，由于使用的是启发式的方法检测，用户只需要输入感兴趣的数据作为输入，而无需输入其它参数即能自动确定出离群点。同时，该算法既适用于栅格系统又适用于矢量系统，且便于进行并行高速处理。\n 算法循环地用半径由小到大递增变化的圆形结构元对数据库中的各数据点作闭运算，具体地说是半径由0开始，以增幅为1进行变化，这一过程中非邻接点个数以不同速度逐渐减少，当半径为0时所有的数据点都为非邻接点，当半径增大到一定程度时，非邻接点个数为0。随着结构元半径的不断增大，找出非邻接点个数与半径之间存在的关系，最终检测出数据库中存在的离群点。\n 大量实验和理论分析表明该算法是可行的和有效的，能从数据库中正确并且精确无误地找出离群点。

关键词： 数学形态学   小波变换   小电流接地系统   配电网   接地故障   选线算法   选线判据  

摘要： 我国配电网广泛采用中性点不接地或经消弧线圈接地系统,即小电流接地系统。在配电网中,单相接地故障率最高,但由于故障后接地电流小,故障特征不明显,因此小电流接地系统单相接地故障选线问题虽已经研究多年却一直未能很好解决,严重阻碍了配电网供电可靠性和自动化水平的提高。\n 本文首先对以往的各种稳态选线算法和暂态选线算法进行综述并指出各种算法存在的缺陷,然后对小电流接地系统单相接地故障特征进行了深入的理论研究和实验分析,研究结果表明故障后暂态过程中含有大量的高频特征信息,对这些特征信息进行分析提取,可构成选线判据。由于小波分析具有时频同时局部化的特点,可以将信号分解到不同的频率带,因此特别适合分析非平稳信号和暂态信号。本文对小波理论进行了深入的理论研究,从而为故障特征的提取提供了理论依据。虽然小波分析算法能很好的滤除白噪声,但是对于脉冲噪声却无能为力,如果不滤除脉冲噪声,就会影响选线时刻的判断造成选线不正确。因此本文提出了一种基于数学形态学及小波变换综合的选线算法,该算法利用数学形态学滤波器对采集到的电压电流信号进行滤波,而后利用小波变换的奇异性理论和模极大值理论来构成接地选线算法,本算法很好地体现了形态学滤波器的噪声抑制能力和小波分解的奇异点检测能力。Matlab仿真结果表明,该算法不受中性点接地方式、故障时刻和线路参数的影响,且具有较强的承受过渡电阻的能力。同时本文还讨论了小波分析用于故障选线所碰到的一些问题,如小波函数的选取,分解尺度的选取依据和采样频率的选择等。

关键词： 超声传感器   T靶   声学定位   弹着点  

摘要： 建立一种基于超声测量法的开放式T靶的数学模型.弹丸在空气中飞行时产生声波,利用超声传感器测出T型阵列传感器接收到声波时的相对时间差,通过建立相应T靶的数学解算模型可求出弹丸穿过靶面的精确位置以实现弹丸的自动定位.分析了影响定位精度的诸因素及提高定位精度的办法.