具有2n线性复杂度的2n周期二元序列的3错线性复杂度

线性复杂度和k错线性复杂度是度量密钥流序列的密码强度的重要指标.通过研究周期为2n的二元序列线性复杂度,提出将k错线性复杂度的计算转化为求Hamming重量最小的错误序列.基于Games-Chan算法,讨论了线性复杂度为2n的2n周期二元序列的3错线性复杂度分布情况;给出了对应k错线性复杂度序列的完整计数公式, k=3,4.对于一般的线性复杂度为2n-m的2n周期二元序列,也可以使用该方法给出对应k错线性复杂度序列的计数公式.     

优化算法的复杂度分析

优化算法的收敛性分析是优化中很重要的一个领域,然而收敛性并不足以作为比较不同算法效率的标准,因此需要另外一套衡量优化问题难易程度以及优化算法效率高低的理论,这套理论被称为优化算法的复杂度分析理论.本文共分为5个部分.第1节介绍复杂度分析的背景和理论框架,给出复杂度分析的定义、方法和例子,并总结本文中的复杂度结论.第2节介绍光滑优化问题的复杂度分析,给出不同优化问题的复杂度上界和下界,并给出加速梯度法收敛性分析的框架.第3节介绍非光滑优化问题的复杂度上界,介绍次梯度法、重心法、椭球法和近似点梯度法的复杂度分析.第4节介绍条件梯度法的复杂度分析,介绍条件梯度法的复杂度上界和下界,以及加速条件梯度法的框架.第5节介绍随机优化算法的复杂度分析,比较随机优化算法在凸和非凸问题下收敛的置信水平和复杂度.     

鲁棒控制与系统辨识的复杂度及其关联的综述和探讨

本文利用控制复杂度和辨识复杂度分别来刻画控制和辨识的难度,率先从理论上给出了控制与辨识的复杂度关系.在复杂度框架下,本文还给出了系统增益不确定条件下最小资源分配问题的解.     

基于熵算法的股票指数高频数据复杂度测算与评价

在日内高频环境下检验基于兼容法的柯尔莫哥洛夫熵、样本熵和模糊熵等复杂度测算方法对我国沪深300股票指数的测算效率,并运用筛选后的有效算法分阶段研究和比较了序列复杂度的变化过程与变化幅度.结果表明,模糊熵算法是一种更适用于我国沪深300股票指数的有效复杂度测算方法,其对相似容忍度的敏感性更低,测度值连续性更好.随时间推移,我国沪深300股票指数复杂度整体呈上升趋势,而相较于发达市场甚至周边新兴市场其复杂度偏低.     

混沌振荡系统的空时复杂度

基于相轨迹随时间的变化规律,提出了混沌振荡系统空时复杂度的概念,给出了空时复杂度的定义和计算方法.定义物理意义直观明确,与Lyapunov指数计算相比,方法计算量少,便于实际应用.以Duffing振子为例,通过数值仿真与实验,研究了混沌振荡系统的空时复杂度,实验结果表明空时复杂度可以很好地刻画Duffing振子丰富的动力学特性.     

基于代数曲线上具有高广义联合线性复杂度的多重序列

多重序列的联合线性复杂度是衡量基于字的流密码体系安全的一个重要指标. 由元素取自F_q上的m 重序列和元素取自F_q^m 上的单个序列之间的一一对应, Meidl 和Özbudak 定义多重序列的广义联合线性复杂度为对应的单个序列的线性复杂度. 在本文中, 我们利用代数曲线的常数域扩张, 研究两类多重序列的广义联合线性复杂度. 更进一步, 我们指出这两类多重序列同时具有高联合线性复杂度和高广义联合线性复杂度.     

Chaitin复杂度、事件的Shannon信息量和无穷随机序列(Ⅰ)

基于程序复杂度,Kolmogorov提出了信息论和概率论的逻辑基础。本文的工作旨在进一步加强和完善这一逻辑基础。首先,对一般可计算概率分布的情形,我们从程序复杂度的角度给出了某一序列x∈A^∞是Martin-lf无穷随机序列的充要条件,从而对无穷随机序列这一概念,找到了与Martin-lf定义等价的程序复杂度基础的定义,建立了有穷随机序列和无穷随机序列的统一的复杂度基础的理论。其次,我们给出了Chaitin复杂度与事件的Shannon信息量之间的不等式关系及渐近等价关系。     

基于Kronecker型替换的黑盒多项式稀疏插值

本文基于新的Kronecker型替换,给出两个由黑盒表示的稀疏多项式的新确定性插值算法.令f∈R[x1,……,xn]是一个稀疏黑盒多项式,其次数上界为D.当R是C或者是有限域时,相对于已有算法,新算法具有更好的计算复杂度或者关于D的复杂度更低.特别地,对于一般黑盒模型,D是复杂度中的主要因素,而在所有的确定性算法中,本文的第二个算法的复杂度关于D是最低的.     

达到极大线性复杂度的前馈阵列

讨论了三类达到极大线性复杂度的前馈阵列的输入阵列的结构。一类是达到极大线性复杂度的乘积前馈阵列,完全确定了其输入阵列的结构;给出了两类输入阵列,证明了它们的任意前馈阵列达到极大线性复杂度。     

顶点加权最大团问题的加权分治算法

分支降阶被广泛用来求解NP-Hard问题,该技术的核心思想是将原问题分解成若干个子问题并递归求解这些子问题,但是用来分析算法时间复杂度的常规分析技术不够精确,无法得到较好的时间复杂度.本文设计了一个基于分支降阶的递归算法求解加权最大团问题,对于提出的精确算法,首先运用常规技术对该算法进行时间复杂度分析,得出其时间复杂度为O(1.4656~np(n)),其中n代表图中结点总个数,p(n)代表n的多项式函数;然后运用加权分治技术对原算法进行时间复杂度分析,将该算法的时间复杂性由原来的O(1.4656~np(n))降为O(1.3765~np(n)).研究结果表明运用加权分治技术能够得到较为精确的时间复杂度.     

Conceptualizations of slope in Mexican intended curriculum

Slope is a fundamental mathematics concept in middle and high school that transcends to the university level. An understanding of slope is needed at the university level since slope plays an important role in understanding problems involving variation and change. In this study Mexican curricula documents were examined to determine which conceptualizations of slope are addressed in the intended mathematics curriculum. To explain the results, we use conceptualizations of slope identified in previous research. Our findings reveal that, to a certain extent, the conceptualizations proposed in the Mexican intended mathematics curriculum differ slightly in terms of the emphasis and timing of instruction from what others have identified in the U.S., with slope as a geometric ratio receiving less emphasis in the Mexican curriculum. There was also noted discontinuity within the Mexican curriculum in introducing slope in grade 9 and subsequently introducing of linear functions in grade 10 without explicit mention of slope. Suggestions are made for future studies, both to consider the conceptualizations of slope promoted in the Mexican textbooks and the impact they have in classroom instruction and student learning of slope.     

Integrating design problems in mathematics curriculum: an architecture college case study

This paper reports an attempt to improve results in the mathematics course in one of the architecture colleges in Israel through practise in applications. The effect of integrating structure design problems in the calculus curriculum on students' achievements and attitudes was examined. The applied topics in the curriculum were connected to calculus topics and studied through problembased learning activities. The integrated curriculum was implemented and the learning results in experimental and control groups were assessed by means of achievement tests, attitude questionnaires and student interviews. The learning achievements in the experimental group proved to be significantly higher than in the control group. The positive impact of learning applications on motivation, understanding, creativity and interest in mathematics is indicated.     

角蛋白16和17在部分表皮肿瘤中的表达和意义

目的 研究角蛋白16 和17（K16、K17）在部分表皮肿瘤中的表达和意义。方法 采用免疫组化法检测K16、K17在正常皮肤、脂溢性角化病、日光性角化病、皮角、基底细胞癌、鳞状细胞癌中的表达。结果 K16、K17 在正常皮肤表皮各层呈阴性表达;在脂溢性角化病表皮各层中除了角质层外大多呈阳性表达;在日光性角化病表皮K16 均不表达,K17 除了角质层外在其他各层也不表达;K16 在皮角表皮棘层呈强阳性表达,但在其他各层均呈阴性表达,K17 在皮角表皮各层基本呈阳性或强阳性表达;在基底细胞癌中,K16、K17除了在棘层呈弱阳性表达外,在其他各层均呈阴性表达;在鳞状细胞癌中,K16 在基底层呈阴性表达,但在其他各层及K17 在表皮全层均呈阳性或强阳性表达。K16 除基底层外在肿瘤表皮其他各层表达比较差异均有统计学意义（均P＜0.05）;K17 在表皮各层表达差异均有统计学意义（均P＜0.05）。结论 K16、K17的表达状况可为表皮肿瘤的鉴别诊断提供病理学方面的依据。     

Scientists and mathematicians collaborating to build quantitative skills in undergraduate science

There is general agreement in Australia and beyond that quantitative skills (QS) in science, the ability to use mathematics and statistics in context, are important for science. QS in the life sciences are becoming ever more important as these sciences become more quantitative. Consequently, undergraduates studying the life sciences require better QS than at any time in the past. Ways in which mathematics and science academics are working together to build the QS of their undergraduate science students, together with the mathematics and statistics needed or desired in a science degree, are reported on in this paper. The emphasis is on the life sciences. Forty-eight academics from eleven Australian and two USA universities were interviewed about QS in science. Information is presented on: what QS academics want in their undergraduate science students; who is teaching QS; how mathematics and science departments work together to build QS in science and implications for building the QS of science students. This information leads to suggestions for improvement in QS within a science curriculum.     

Combinatorics of generalized q-Euler numbers

New enumerating functions for the Euler numbers are considered. Several of the relevant generating functions appear in connection to entries in Ramanujan's Lost Notebook. The results presented here are, in part, a response to a conjecture made by M.E.H. Ismail and C. Zhang about the symmetry of polynomials in Ramanujan's expansion for a generalization of the Rogers-Ramanujan series. Related generating functions appear in the work of H. Prodinger and L.L. Cristea in their study of geometrically distributed random variables. An elementary combinatorial interpretation for each of these enumerating functions is given in terms of a related set of statistics.     

Preface

We are presenting in this volume the collection of extended abstracts of 66 talks that were presented at Combinatorics 2012 in Perugia, Italy. Combinatorics 2012 is the 17th in the series of combinatorics conferences held in Italy, first in 1981, next in 1982 and every two years since then.     

A graph theory approach to subcontracting, machine duplication and intercell moves in cellular manufacturing

We address in this paper the problem of finding an optimal strategy for dealing with bottleneck machines and bottleneck parts in the cell formation process in group technology. Three types of economic decisions are considered: subcontracting, machine duplication and intercell moves. The problem is formulated as a minimum weighted node covering problem in a hypergraph, and we show that it can be solved in polynomial time by finding a maximum weighted stable set in a bipartite graph. We extend this result to cellular manufacturing systems in which the sequence of operations of each part is known in advance.     

火灾发生的周期性规律及其在火灾非线性组合预测模型中应用

研究火灾发生规律及发展趋势,具有实用价值.分析历年中国火灾统计数据,发现中国火灾的发生规律同时具有增长趋势性和周期波动性特征:①中国火灾从90年代开始大幅度增加,在2002年达到最大,然后逐年缓慢下降;②每年12个月呈正弦函数波动,周期为12,1、2月发生起数最大,8、9月最小.借助于M ATLAB软件,根据2000-2006年中国火灾统计数据,建立火灾的月发生起数的非线性周期性组合预测模型,预测值与实际值的平均相对误差小于0.07.研究结论为消防研究、消防部门决策提供科学依据.     

Rawlsian altruism with perfect discrimination leads to social efficiency

Recent studies draw attention on the highly specialized capacity of human beings in recognizing altruists versus cheaters in social interactions. These results hint at the existence of specialized abilities that support discriminating behavior in strategic interactions. In this paper, we explore the implications of discriminating behavior in the study of the indirect evolutionary selection of selfish versus altruistic motivations in the context of generic 2×2 base games, and in particular for coordination and cooperation scenarios. We find that inequality averse (Rawlsian) altruism can enforce under rather general conditions socially optimal outcomes, including cases where selfishness cannot, such as in prisoner’s dilemmas. Inequality seeking (Nietzschian) altruism in no case improves upon Rawlsian altruism in terms of social optimality of outcomes, and often does worse. In the cooperation scenario in particular, Nietzschean altruism never manages to implement the cooperative outcome. Under perfect discrimination, moreover, inequality averse (Rawlsian) altruism often evolves at the expense of selfishness. These results suggest that the development of sophisticated discrimination abilities may be strongly adaptive in supporting fairness-oriented forms of pro-sociality in humans in the context of social dilemmas and coordination problems.     

On Potential Theoretic Skeletons of Polyhedra

We prove that any polyhedron in two dimensions admits a type of potential theoretic skeleton called mother body. We also show that the mother bodies of any polyhedron in any number of dimensions are in one-to-one correspondence with certain kinds of decompositions of the polyhedron into convex subpolyhedra. A consequence of this is that there can exist at most finitely many mother bodies of any given polyhedron. The main ingredient in the proof of the first mentioned result consists of showing that any polyhedron in two dimensions contains a convex subpolyhedron which sticks to it in the sense that every face of the subpolyhedron has some part in common with a face of the original polyhedron.