Universal cycles of classes of restricted words

It is well known that Universal cycles (U-cycles) of k-letter words on an n-letter alphabet exist for all k and n. In this paper, we prove that Universal cycles exist for several restricted classes of words, including non-bijections, “equitable” words (under suitable restrictions), ranked permutations, and “passwords”. In each case, proving the connectedness of the underlying de Bruijn digraph is a non-trivial step.     

Word maps and spectra of random graph lifts

We study here the spectra of random lifts of graphs. Let G be a finite connected graph, and let the infinite tree T be its universal cover space. If λ₁ and ρ are the spectral radii of G and T respectively, then, as shown by Friedman (Graphs Duke Math J 118 (2003), 19–35), in almost every n‐lift H of G, all “new” eigenvalues of H are ≤ O(λ ρ^1/2). Here we improve this bound to O(λ ρ^2/3). It is conjectured in (Friedman, Graphs Duke Math J 118 (2003) 19–35) that the statement holds with the bound ρ + o(1) which, if true, is tight by (Greenberg, PhD thesis, 1995). For G a bouquet with d/2 loops, our arguments yield a simple proof that almost every d‐regular graph has second eigenvalue O(d^2/3). For the bouquet, Friedman (2008). has famously proved the (nearly?) optimal bound of . Central to our work is a new analysis of formal words. Let w be a formal word in letters g,…,g. The word map associated with w maps the permutations σ₁,…,σ_k ∈ S_n to the permutation obtained by replacing for each i, every occurrence of g_i in w by σ_i. We investigate the random variable X that counts the fixed points in this permutation when the σ_i are selected uniformly at random. The analysis of the expectation ??(X) suggests a categorization of formal words which considerably extends the dichotomy of primitive vs. imprimitive words. A major ingredient of a our work is a second categorization of formal words with the same property. We establish some results and make a few conjectures about the relation between the two categorizations. These conjectures suggest a possible approach to (a slightly weaker version of) Friedman's conjecture. As an aside, we obtain a new conceptual and relatively simple proof of a theorem of A. Nica (Nica, Random Struct Algorithms 5 (1994), 703–730), which determines, for every fixed w, the limit distribution (as n →∞) of X. A surprising aspect of this theorem is that the answer depends only on the largest integer d so that w = u^d for some word u. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 2010     

项链李代数的同构与同构群

研究了一些特殊箭图的同构,这些特殊箭图包括垂直叠加的箭图和水平叠加的箭图. 跟以前的研究方法相比, 文中的研究方法是不同的和新颖的, 即利用指标数组把复杂的李运算转换为多重指标集的运算.     

Modelling of a displacive transformation in two-dimensional system within a single-site approximation of continuous displacement cluster variation method

It is attempted to model a displacive phase transformation by Continuous Displacement Cluster Variation Method. The main focus of the present study is placed on distorted to non-distorted phase transformation in the two-dimensional square lattice. The entropy is formulated within the single-site approximation (point approximation), while the pair-wise atomic interaction energies are combined to stabilize a distorted phase at low temperatures. The distorted to non-distorted phase transformation in the present study is of the second order, and the calculated distribution of atoms suggests that the transformation is of the displacive type in the classification.     

基于贝斯准则和待定词集模糊矩阵的满文识别后处理

将满文单词识别系统的识别信息和满文的词组信息有机地结合起来,建立满文词组和待定词集统计信息库,利用贝叶斯准则,综合满文待定词的后验概率和词组的先验概率信息,建立合理有效便于实现的数据结构,对满文单词识别系统输出存在的拒识词和错识词进行检测和纠正,从而有效地提高满文识别系统的识别率·实验表明:后处理性能除取决于语言模型外,还取决于后概率的精确估计·另外,在单词识别系统识别率高的情况下,后处理的纠错能力会增强·     

基于人工神经网络的汉语数字语音识别系统

利用改进的有序聚类算法得到解决时间规整问题的新算法,在此基础上建立了基于人工神经网络的普通话数字语音识别系统。对基于人工神经网络的算法和基于动态时间伸缩的算法作比较识别实验,结果表明,基于人工神经网络的语音识别算法的识别性能优于传统的动态时间伸缩算法。     

CiLin Expansion and Its Application to Word Sense Disambiguation

40000 new entries are added to CiLin in knowledge engineering. Statistics are presented about the sense ambiguity of Chinese words in CiLin. An automatic solution is proposed for the problem of Chinese sense disambiguation, which utilizes the heuristics of part-of-speech tagging and Naive Bayesy classification based on a partially disambiguated corpus.     

基于散列技术的快速子串归并算法

用统计方法研究东西方语言的多词单元问题和东方语言的未登录词问题时需要删除同频子串(子串归并)．传统的子串归并算法时间复杂度为O(n^2),在大规模语料库的处理中效率低下．提出一种基于散列技术的时间复杂度为O(n^2)的子串归并算法,并用数学方法证明其与O(n^2)复杂度的算法等价,即输入相同时输出也相同．不同规模语料上的实验结果表明新算法能够大大缩短子串归并所需时间,适用于大规模语料库的处理．