Searching with lies under error cost constraints

The Rényi–Berlekamp–Ulam game is a classical model for the problem of determining the minimum number of queries to find an unknown member in a finite set when up to a finite number of the answers may be erroneous. In the variant considered in this paper, questions with q many possible answers are allowed, further lies are constrained by a bipartite graph with edges weighted by 0,1,2,… (the “channel”). The channel Γ is an arbitrary assignment stipulating the cost of the different possible lies, i.e., of each answer j≠i when the correct answer is i by Γ(i,j). It is also assumed that a maximum cost e (sum of the cost of all wrong answers) can be afforded by the responder during the whole game. We provide tight asymptotic bounds for the number of questions needed to solve this problem. The appropriate searching strategies are actually provided. We also show that adaptiveness can be dramatically reduced when the channel satisfies certain symmetry constraints.     

电磁超表面在微波和太赫兹波段雷达散射截面缩减中的应用研究进展

电磁超表面由于其独特的电磁特性为调控电磁波提供了有力工具,合适地设计成编码、随机、相位不连续、完美吸收器等超表面,就能够控制电磁波的散射以及反射特性,实现雷达散射截面的缩减。本文综述了不同的电磁超表面利用漫反射或者吸收等特性实现在微波和太赫兹波段雷达散射截面缩减中的应用。分析表明,编码超表面由不同的数字单元组成,其反射相位差在很宽的频段范围内满足恒定的关系,设计特殊的单元序列使入射的电磁波产生非定向散射,更高bit编码超表面更容易灵活调控电磁波;随机超表面通过调节阵元的尺寸实现宽带移相从而将金属目标特征性强的反射峰打散成一个无规律、杂乱的波,产生漫反射;不连续超表面由于相位不连续可使电磁波发生漫反射或者异常反射;吸收器通过合理设计结构尺寸实现吸收电磁波能量来减小反射。因此电磁超表面在雷达隐身、宽带通讯、成像等方面具有重要的应用前景。最后对电磁超表面在雷达散射截面缩减中应用的发展趋势进行了初步探讨,未来将向着宽带、柔性、大角度等方面发展。     

阿达玛变换光谱仪狭缝衍射的编码修正

根据阿达玛变换光谱仪的原理与狭缝衍射特性,分析了光谱仪入射狭缝衍射对阿达玛变换光谱仪测量结果造成影响,对衍射情况下的阿达玛变换光谱仪的仪器结构矩阵进行了研究,得出了衍射情况下阿达玛变换光谱仪的编/解码方法,通过对入射光谱的还原分析,验证了编码/解码的正确性。该方法对阿达玛变换光谱仪的高精度光谱测量具有重要意义。     

Hypothesis testing for arbitrarily varying source

Hypothesis testing for arbitrarily varying source (AVS), which is to decide between the two hypotheses for the varying behavior of the distribution of AVS, is considered in this paper. We determine the best asymptotic exponent of the second kind of error probability when the first kind of error probability is fixed. This result generalizes the well-known lemma of Stein in statistics. As a corollary, Strassen's coding theorem for AVS is obtained.Supported by the Young Teacher Foundation of Chinese Educational Ministry and by the National Natural Science Foundation of China.     

The inverse of circulant matrix

A direct method is proposed to get the inverse matrix of circulant matrix that find important application in engineering, the elements of the inverse matrix are functions of zero points of the characteristic polynomial g(z) and g′(z) of circulant matrix, four examples to get the inverse matrix are presented in the paper.     

Silver Cubes

An n × n matrix A is said to be silver if, for i = 1,2,...,n, each symbol in {1,2,...,2n − 1} appears either in the ith row or the ith column of A. The 38th International Mathematical Olympiad asked whether a silver matrix exists with n = 1997. More generally, a silver cube is a triple (K _n ^d , I, c) where I is a maximum independent set in a Cartesian power of the complete graph K _n , and is a vertex colouring where, for v ∈ I, the closed neighbourhood N[v] sees every colour. Silver cubes are related to codes, dominating sets, and those with n a prime power are also related to finite geometry. We present here algebraic constructions, small examples, and a product construction. The nonexistence of silver cubes for d = 2 and some values of n, is proved using bounds from coding theory. Luis A. Goddyn: This research was supported by a Canada NSERC Discovery Grant. Ebadollah S. Mahmoodian: Partially supported by the institutes CECM and IRMACS and the departments of Mathematics and Computing Science at Simon Fraser University. Grateful thanks are extended here and also to the Institute for Advanced Studies in Basic Sciences, Iran for support in the final stages of this paper.     

East Asian mtDNA haplogroup determination in Koreans: haplogroup-level coding region SNP analysis and subhaplogroup-level control region sequence analysis

The present study analyzed 21 coding region SNP markers and one deletion motif for the determination of East Asian mitochondrial DNA (mtDNA) haplogroups by designing three multiplex systems which apply single base extension methods. Using two multiplex systems, all 593 Korean mtDNAs were allocated into 15 haplogroups: M, D, D4, D5, G, M7, M8, M9, M10, M11, R, R9, B, A, and N9. As the D4 haplotypes occurred most frequently in Koreans, the third multiplex system was used to further define D4 subhaplogroups: D4a, D4b, D4e, D4g, D4h, and D4j. This method allowed the complementation of coding region information with control region mutation motifs and the resultant findings also suggest reliable control region mutation motifs for the assignment of East Asian mtDNA haplogroups. These three multiplex systems produce good results in degraded samples as they contain small PCR products (101-154 bp) for single base extension reactions. SNP scoring was performed in 101 old skeletal remains using these three systems to prove their utility in degraded samples. The sequence analysis of mtDNA control region with high incidence of haplogroup-specific mutations and the selective scoring of highly informative coding region SNPs using the three multiplex systems are useful tools for most applications involving East Asian mtDNA haplogroup determination and haplogroup-directed stringent quality control.     

基于一类新的胞腔排除遗传算法求解迭代函数系逆问题

提出求解迭代函数系（IFS）逆问题的一类有效遗传算法,该算法基于新发展的可拼接/可分解编码,并结合使用胞腔排除技巧,对于典型图像的应用表明;该方法可有效应用于基于矩匹配表示的IFS逆向题求解,从而为IFS逆问题的数值方法研究提供了一条新颖途径。     

准绝对式光学编码器的编译码原理

介绍了准绝对式光学编码器的测量原理,根据其码盘特点,设计了实用的编码算法.利用计算机编程辅助实现了最高17位的索引码道编码设计,并提出一种译码的方法,可以实现从循环二进制码到自然二进制码的快速转换,为其进一步工程实现提供理论基础.