Range mode and range median queries in constant time and sub-quadratic space

Given a list of n items and a function defined over sub-lists, we study the space required for computing the function for arbitrary sub-lists in constant time.For the function mode we improve the previously known space bound O(n²/logn) to O(n²loglogn/log²n) words.For median the space bound is improved to O(n²loglog²n/log²n) words from O(n²⋅log(k)n/logn), where k is an arbitrary constant and log(k) is the iterated logarithm.     

On the distribution function of the complexity of finite sequences

Investigations of complexity of sequences lead to important applications such as effective data compression, testing of randomness, discriminating between information sources and many others. In this paper we establish formulae describing the distribution functions of random variables representing the complexity of finite sequences introduced by Lempel and Ziv in 1976. It is known that this quantity can be used as an estimator of entropy. We show that the distribution functions depend affinely on the probabilities of the so-called “exact” sequences.     

The quantum query complexity of the determinant

In this paper we give tight quantum query complexity bounds of some important linear algebra problems. We prove Θ(n²) quantum query bounds for verify the determinant, rank, matrix inverse and the matrix power problem.     

The subsequence composition of a string

Words that appear as constrained subsequences in a text-string are considered as possible indicators of the host string structure, hence also as a possible means of sequence comparison and classification. The constraint consists of imposing a bound on the number ω$\omega$ of positions in the text that may intervene between any two consecutive characters of a subsequence. A subset of such ω$\omega$-sequences is then characterized that consists, in intuitive terms, of sequences that could not be enriched with more characters without losing some occurrence in the text. A compact spatial representation is then proposed for these representative sequences, within which a number of parameters can be defined and measured. In the final part of the paper, such parameters are empirically analyzed on a small collection of text-strings endowed with various degrees of structure.     

Limiting negations in non-deterministic circuits

The minimum number of NOT gates in a Boolean circuit computing a Boolean function f is called the inversion complexity of f. In 1958, Markov determined the inversion complexity of every Boolean function and, in particular, proved that log₂(n+1) NOT gates are sufficient to compute any Boolean function on n variables. In this paper, we consider circuits computing non-deterministically and determine the inversion complexity of every Boolean function. In particular, we prove that one NOT gate is sufficient to compute any Boolean function in non-deterministic circuits if we can use an arbitrary number of guess inputs.     

Parametric polynomial spectral factorization using the sum of roots and its application to a control design problem

This paper presents an algebraic approach to polynomial spectral factorization, an important mathematical tool in signal processing and control. The approach exploits an intriguing relationship between the theory of Gröbner bases and polynomial spectral factorization which can be observed through the sum of roots, and allows us to perform polynomial spectral factorization in the presence of real parameters. It is discussed that parametric polynomial spectral factorization enables us to express quantities such as the optimal cost in terms of parameters and the sum of roots. Furthermore an optimization method over parameters is suggested that makes use of the results from parametric polynomial spectral factorization and also employs two quantifier elimination techniques. This proposed approach is demonstrated in a numerical example of a particular control problem.     

Adaptive binary tree for fast SVM multiclass classification

This paper presents an adaptive binary tree (ABT) to reduce the test computational complexity of multiclass support vector machine (SVM). It achieves a fast classification by: (1) reducing the number of binary SVMs for one classification by using separating planes of some binary SVMs to discriminate other binary problems; (2) selecting the binary SVMs with the fewest average number of support vectors (SVs). The average number of SVs is proposed to denote the computational complexity to exclude one class. Compared with five well-known methods, experiments on many benchmark data sets demonstrate our method can speed up the test phase while remain the high accuracy of SVMs.     

一类混沌序列线性复杂度的分析

针对传统密码学中由线性移位寄存器生成的序列在统计特性上的不足,提出一种基于混沌的序列密码生成方法,并在有限精度实现时引入Legendre扰动序列使得输出具有良好的统计特性。用B-M算法对其进行线性复杂度分析,并与等效的线性反馈移位寄存器的复杂度进行比较,结果显示该混沌序列具有良好的非线性特性,保密性好且软件实现简单。     

改进的Sunday模式匹配算法

在基于模式匹配的检测方法中,匹配效率是检测技术的瓶颈,间接影响入侵检测系统的实时性能。该文对4种模式匹配算法进行分析后,选择最优的Sunday算法进行改进。该算法进行匹配前先找到模式串中的特征字符（出现概率最小的字符）,进行特征字符与尾字符双重匹配,失败则移动尽可能远的距离。实验结果证明匹配效率比Sunday算法有一定的提高。     

基于改进基因表达式程序设计的股票指数预测

介绍基因表达式程序设计方法的基本原理,针对股票指数分析与预测问题,在经典的GEP算法基础上,提出一种基于动态变异算子的改进的GEP算法——IGEP算法,动态变异算子随着进化代数和染色体所含基因数目不同而变化,从而加快了GEP的收敛速度和精确度,对算法进行了复杂度和收敛性分析。设计一种基于IGEP的股票指数分析与预测算法,数值实验结果表明,该算法优于经典GEP算法,具有较广泛的通用性。