On the number of frames in binary words

A frame is a square uu, where u is an unbordered word. Let F(n) denote the maximum number of distinct frames in a binary word of length n. We count this number for small values of n and show that F(n) is at most ⌊n/2⌋+8 for all n and greater than 7n/30−? for any positive ? and infinitely many n. We also show that Fibonacci words, which are known to contain plenty of distinct squares, have only a few frames. Moreover, by modifying the Thue-Morse word, we prove that the minimum number of occurrences of frames in a word of length n is ⌈n/2⌉−2.     

Square-free partial words

We say that a partial word w over an alphabet A is square-free if every factor xx^′ of w such that x and x^′ are compatible is either of the form ?a or a? where ? is a hole and a∈A. We prove that there exist uncountably many square-free partial words over a ternary alphabet with an infinite number of holes.     

Automatic conversion from lexical words to prosodic words for mandarin text-to-speech system

In real speech, not like lexical words (LWs), prosodic words (PWs) are basic rhythmic units. The naturalness of a Text-to-Speech (TTS) system is directly influenced by the segmentation of the PWs. Most of the PWs are the combination of several LWs. In this paper, three Lexical Combination Models are proposed to combine LWs into PWs, including a Directed Acyclic Graph Model, a Segmentation Model and a Markov Model (MM). To cope with the situation where some long LWs should be segmented into two or more PWs, a Lexical Split Model (LSM) is applied to the long LWs. Experimental results prove that relatively constant results with various training data can be obtained from a MM. The Transformation-Based Error Driven Learning (TBED) algorithm, for its high performance of individual property, is applied in combination with the MM to improve the precision of PW segmentation. Experiments show that among the three proposed models, the MM combined with TBED and LSM, leads to the best performance, in which a precision of 93.00% and a recall of 93.23% are achieved. The perception test indicates that by using PWs as the lowest prosodic units a speech sounds more natural and acceptable than by using LWs. This paper is supported by NSFC Project (60503071); 973 Natural Basic Research Program of China (2004CB318102); Postdoctor Science Foundation of P. R. China (20070420275).     

On the arithmetical complexity of Sturmian words

Using the geometric dual technique by Berstel and Pocchiola, we give a uniform O(n³)$O\left(n^3\right)$ upper bound for the arithmetical complexity of a Sturmian word. We also give explicit expressions for the arithmetical complexity of Sturmian words of slope between 1/3 and 2/3 (in particular, of the Fibonacci word). In this case, the difference between the genuine arithmetical complexity function and our upper bound is bounded, and ultimately 2-periodic. In fact, our formula is valid not only for Sturmian words but for rotation words from a wider class.     

Codeterministic automata on infinite words

We prove that any recognizable set of infinite words is the infinite behaviour of some finite codeterministic automaton.     

Moments of conjugacy classes of binary words

For each nonempty binary word w=c₁c₂c_q, where c_i{0,1}, the nonnegative integer ∑_i=1^q (q+1−i)c_i is called the moment of w and is denoted by M(w). Let [w] denote the conjugacy class of w. Define M([w])={M(u): u[w]}, N(w)={M(u)−M(w): u[w]} and δ(w)=max{M(u)−M(v): u,v[w]}. Using these objects, we obtain equivalent conditions for a binary word to be an -word (respectively, a power of an -word). For instance, we prove that the following statements are equivalent for any binary word w with |w|2: (a) w is an -word, (b) δ(w)=|w|−1, (c) w is a cyclic balanced primitive word, (d) M([w]) is a set of |w| consecutive positive integers, (e) N(w) is a set of |w| consecutive integers and 0N(w), (f) w is primitive and [w]St.     

基于论坛语料识别中文未登录词的方法

为解决中文分词中未登录词识别效率低的问题,提出了基于论坛语料识别中文未登录词的新方法.利用网络蜘蛛下载论坛网页构建一个语料库,并对该语料库进行周期性的更新以获取具备较强时效性的语料;利用构造出的新统计量MD(由Mutual Information函数和Duplicated Combination Frequency函数构造)对语料库进行分词产生候选词表;最后通过对比候选词表与原始词表发现未登录词,并将识别出的未登陆词扩充到词库中.实验结果表明,该方法可以有效提高未登录词的识别效率.     

Syntactic systematicity in sentence processing with a recurrent self-organizing network

As potential candidates for explaining human cognition, connectionist models of sentence processing must demonstrate their ability to behave systematically, generalizing from a small training set. It has recently been shown that simple recurrent networks and, to a greater extent, echo-state networks possess some ability to generalize in artificial language learning tasks. We investigate this capacity for a recently introduced model that consists of separately trained modules: a recursive self-organizing module for learning temporal context representations and a feedforward two-layer perceptron module for next-word prediction. We show that the performance of this architecture is comparable with echo-state networks. Taken together, these results weaken the criticism of connectionist approaches, showing that various general recursive connectionist architectures share the potential of behaving systematically.     

Semiparametric and nonparametric analysis of recurrent events with observation gaps

This paper considers statistical analysis of recurrent event data when there exist observation gaps. By observation gaps, we mean that some study subjects are out of the study for a period of time for various reasons and then are back in the study again and this may happen more than once. Most of existing studies of recurrent events discuss situations where study subjects are under observation over continuous time periods. For recurrent event data with observation gaps, a naive analysis method is to treat them as usual recurrent events without gaps by either censoring observations at times when subjects first leave the study or ignoring the gaps. As expected and shown below, this could yield biased and misleading results. In this paper, we present some appropriate methods for the problem. In particular, we consider estimation of the underlying mean function and regression analysis of recurrent event data in the presence of observation gaps. The presented analysis methods are evaluated and compared to the naive approach that ignores observation gaps using extensive simulation studies and an example.     

Exponential synchronization of memristor-based recurrent neural networks with time delays

In this paper, the synchronization control of a general class of memristor-based recurrent neural networks with time delays is investigated. A delay-dependent feedback controller is derived to achieve the exponential synchronization based on the drive-response concept, linear matrix inequalities (LMIs) and Lyapunov functional method. Finally, a numerical example is given to illustrate the derived theoretical results.     

应用特征词分类贡献的垃圾邮件过滤研究

在垃圾邮件过滤中,考虑到特征词对合法邮件和垃圾邮件分类贡献的不同,通过定义分类贡献比系数,将特征词分类贡献的思想应用到特征选择和朴素贝叶斯过滤器的设计中,在英文语料库上进行实验,实验结果表明,应用特征词分类贡献的垃圾邮件过滤方法可以有效提高过滤器对合法邮件和垃圾邮件的识别能力,降低过滤器对合法邮件和垃圾邮件的误判率。     

Modeling and recognition of cursive words with hidden Markov models

In this paper, a new method for modeling and recognizing cursive words with hidden Markov models (HMM) is presented. In the proposed method, a sequence of thin fixed-width vertical frames are extracted from the image, capturing the local features of the handwriting. By quantizing the feature vectors of each frame, the input word image is represented as a Markov chain of discrete symbols. A handwritten word is regarded as a sequence of characters and optional ligatures. Hence, the ligatures are also explicitly modeled. With this view, an interconnection network of character and ligature HMMs is constructed to model words of indefinite length. This model can ideally describe any form of handwritten words, including discretely spaced words, pure cursive words and unconstrained words of mixed styles. Experiments have been conducted with a standard database to evaluate the performance of the overall scheme. The performance of various search strategies based on the forward and backward score has been compared. Experiments on the use of a preclassifier based on global features show that this approach may be useful for even large-vocabulary recognition tasks.     

Formulation of linguistic regression model based on natural words

When human experts express their ideas and thoughts, human words are basically employed in these expressions. That is, the experts with much professional experiences are capable of making assessment using their intuition and experiences. The measurements and interpretation of characteristics are taken with uncertainty, because most measured characteristics, analytical result, and field data can be interpreted only intuitively by experts. In such cases, judgments may be expressed using linguistic terms by experts. The difficulty in the direct measurement of certain characteristics makes the estimation of these characteristics imprecise. Such measurements may be dealt with the use of fuzzy set theory. As Professor L. A. Zadeh has placed the stress on the importance of the computation with words, fuzzy sets can take a central role in handling words [12, 13]. In this perspective fuzzy logic approach is offten thought as the main and only useful tool to deal with human words. In this paper we intend to present another approach to handle human words instead of fuzzy reasoning. That is, fuzzy regression analysis enables us treat the computation with words. In order to process linguistic variables, we define the vocabulary translation and vocabulary matching which convert linguistic expressions into membership functions on the interval [0–1] on the basis of a linguistic dictionary, and vice versa. We employ fuzzy regression analysis in order to deal with the assessment process of experts from linguistic variables of features and characteristics of an objective into the linguistic expression of the total assessment. The presented process consists of four portions: (1) vocabulary translation, (2) estimation, (3) vocabulary matching and (4) dictionary. We employed fuzzy quantification theory type 2 for estimating the total assessment in terms of linguistic structural attributes which are obtained from an expert.This research was supported in part by Grant-in Aid for Scientific Research(C-2); Grant No.11680459 of Ministry of Education of Science, Sports and Culture.     

On quasi orders of words and the confluence property

We investigate the confluence property, that is, the property of a language to contain, for any two words of it, one which is bigger, with respect to a given quasi order on the respective free monoid, than each of the former two. This property is investigated mainly for regular and context-free languages. As a consequence of our study, we give an answer to an old open problem raised by Haines concerning the effective regularity of the sets of subwords. Namely, we prove that there are families with a decidable emptiness problem for which the regularity of the sets of subwords is not effective.     

Periodic musical sequences and Lyndon words

When one enumerates periodic musical structures, the computation is done up to a cyclic shift. This means that two solutions which are cyclic shifts of one another are considered the same. Lyndon words provide a powerful way to do so. We illustrate this by two examples taken from African traditional music.     

Algorithms for testing that sets of DNA words concatenate without secondary structure

We present an efficient algorithm for determining whether all moleculesin a combinatorial set of DNA or RNA strandsare structure free, and thus availablefor bonding to their Watson-Crick complements.This work is motivated by the goalof testing whether strands used in DNAcomputations or as molecular bar-codesare structure free, where the strands areconcatenations of short words. We alsopresent an algorithm for determining whetherall words in S*, for some finite setS of equi-length words, are structure free. This revised version was published online in June 2006 with corrections to the Cover Date.     

SOM time series clustering and prediction with recurrent neural networks

Local models for regression have been the focus of a great deal of attention in the recent years. They have been proven to be more efficient than global models especially when dealing with chaotic time series. Many models have been proposed to cluster time series and they have been combined with several predictors. This paper presents an extension for recurrent neural networks applied to local models and a discussion about the obtained results.     

A learning result for continuous-time recurrent neural networks

The following learning problem is considered, for continuous-time recurrent neural networks having sigmoidal activation functions. Given a “black box” representing an unknown system, measurements of output derivatives are collected, for a set of randomly generated inputs, and a network is used to approximate the observed behavior. It is shown that the number of inputs needed for reliable generalization (the sample complexity of the learning problem) is upper bounded by an expression that grows polynomially with the dimension of the network and logarithmically with the number of output derivatives being matched.     

The almost periodic solution of Lotka-Volterra recurrent neural networks with delays

By the fixed-point theorem subject to different polyhedrons and some inequalities (e.g., the inequality resulted from quadratic programming), we obtain three theorems for the Lotka-Volterra recurrent neural networks having almost periodic coefficients and delays. One of the three theorems can only ensure the existence of an almost periodic solution, whose existence and uniqueness the other two theorems are about. By using Lyapunov function, the sufficient condition guaranteeing the global stability of the solution is presented. Furthermore, two numerical examples are employed to illustrate the feasibility and validity of the obtained criteria. Compared with known results, the networks model is novel, and the results are extended and improved.