城市、分形与空间复杂性探索

首先阐明空间复杂性的来龙去脉，包括复杂系统与复杂性的关系，空间复杂性与自组织临界性的等价性等。其次论证分形是刻画空间复杂性的有效工具：由于城市系统是一种具有分形性质的复杂空间系统，而分雏则是联系复杂性度量的重要参量，借助分形思想探索城市地理系统的复杂性和奇异性顺理成章。最后阐述城市系统空间复杂性的临界判据和研究方法。3大判据(分形结构、1/f噪声和位序-规模分布)对应着城市系统的3类空间结构，空间复杂性和复杂化研究必须将数学模式、理论探讨和模拟实验乃至计算方法有效结合才能取得实质性的理论进展。     

算法复杂性研究历史述评

主要讨论了算法复杂性的产生、内容及其意义。     

赛程问题分治算法

对于单循环赛的比赛日程安排问题，给出了可读性较好，时空复杂度仅为平方阶的分而治之算法。     

复杂性测度特征在肺部HRCT图像分析中的应用

研究了分形维和 Lempel- Ziv(LZ)复杂性两类基于视觉复杂性的图像特征在自动区分高分辨率 CT(HRCT)上磨玻璃影 (GGO)与正常区域的表现 .研究样本包括 86个 1 5× 1 5大小的矩形感兴趣区 (ROI) ,其中 44个正常 ,42个 GGO.将从这些 ROI中提取的分形维特征和 LZ复杂性特征作为输入对线性分类器训练并对其分类性能进行评估 .结果表明 ,若将两类特征单独作为分类器的输入 ,相应的 ROC曲线下面积分别为 0 .837和 0 .90 3;当用回代法训练和测试分类器时 ,分别有 75.6%和 79.1 %的 ROI被正确分类 ,而用刀切法时 ,ROI被正确分类的比率相同 .若将两类特征的组合作为分类器输入 ,相应的 ROC曲线下面积提高到 0 .969,而总的分类正确率亦达 91 .9%     

Shell排序及改进算法的算法复杂性估计

本文用参数设计方法进行非线性回归估计。给出shell排序[1][2]和本人改进后的shell算法复杂性估计式。结果表明二者的算法复杂性已接近排序算法的理论下界——O(NLog(N))~*。     

振动外分类算法研究

给出了一种新的外分类算法:振动外分类.它不必预先产生初始归并段,即可得到预期的效果,在特定的数据和硬件配置下,性能上超过了二路平衡归并法和二路多步归并法.详细分析了其系统开销,给出了算法正确性证明,用C语言在PC586及以上机得以实现.     

复杂性研究的新动向--基于主体的建模方法及其启迪

基于主体的建模方法（AMA，Agent-Based Modelling)，具有主动性、层次性、动态性、可操作性等优点，为人们认识和理解一大类复杂系统，即复杂适应系统（CAS，Complex Adaptive System)提供了富有启发性的新思路和新视角，对于社会、经济、生物、环境等由大量具有主动性的主体（Agent)组成的复杂系统来说，具有特别的意义。另一方面，在计算机技术迅速发展的直接推动下，出现了用于实施ABM方法的一系列软件平台，除众所周知的SWARM之外，还有ASCAPE、REPAST、TNG－lab等，这些平台的出现为ABM方法的推广应用提供了方便的条件。从方法论的角度来看，ABM方法也给我们提供了多方面的、有益的启迪。     

The distribution search: An O (n) expected time search

Provided an algorithm for the distribution search and proves the time complexity of the algorithm. This algorithm uses a mathematical formula to searchn elements in the sequence ofn elements in O (n) expected time, and experimental reesult proves that distribution search is superior to binary search. Xu Xusong: born in June 1945, Professor     

试论复杂系统律:整体性原理新探索

一般系统律“整体不等于部分之和”适用于各种系统,复杂性科学的发展揭示复杂系统与简单系统有本质区别。概括复杂性理论提出复杂系统律：“部分之中有整体”,论述其内涵意义、科学表现、理论原因,并作初步应用。     

Efficient algorithms for agglomerative hierarchical clustering methods

Whenevern objects are characterized by a matrix of pairwise dissimilarities, they may be clustered by any of a number of sequential, agglomerative, hierarchical, nonoverlapping (SAHN) clustering methods. These SAHN clustering methods are defined by a paradigmatic algorithm that usually requires 0(n ³) time, in the worst case, to cluster the objects. An improved algorithm (Anderberg 1973), while still requiring 0(n ³) worst-case time, can reasonably be expected to exhibit 0(n ²) expected behavior. By contrast, we describe a SAHN clustering algorithm that requires 0(n ² logn) time in the worst case. When SAHN clustering methods exhibit reasonable space distortion properties, further improvements are possible. We adapt a SAHN clustering algorithm, based on the efficient construction of nearest neighbor chains, to obtain a reasonably general SAHN clustering algorithm that requires in the worst case 0(n ²) time and space.Whenevern objects are characterized byk-tuples of real numbers, they may be clustered by any of a family of centroid SAHN clustering methods. These methods are based on a geometric model in which clusters are represented by points ink-dimensional real space and points being agglomerated are replaced by a single (centroid) point. For this model, we have solved a class of special packing problems involving point-symmetric convex objects and have exploited it to design an efficient centroid clustering algorithm. Specifically, we describe a centroid SAHN clustering algorithm that requires 0(n ²) time, in the worst case, for fixedk and for a family of dissimilarity measures including the Manhattan, Euclidean, Chebychev and all other Minkowski metrics.This work was partially supported by the Natural Sciences and Engineering Research Council of Canada and by the Austrian Fonds zur Förderung der wissenschaftlichen Forschung.