Infinite games on finitely coloured graphs with applications to automata on infinite trees

We examine a class of infinite two-person games on finitely coloured graphs. The main aim is to construct finite memory winning strategies for both players. This problem is motivated by applications to finite automata on infinite trees. A special attention is given to the exact amount of memory needed by the players for their winning strategies. Based on a previous work of Gurevich and Harrington and on subsequent improvements of McNaughton we propose a unique framework that allows to reestablish and to improve various results concerning memoryless strategies due to Emerson and Jutla, Mostowski, Klarlund.     

Railway Computation for Infinite Linear Systems

The problem of solving an infinite system of linear equations finitely expressed is addressed. Modifications of the Gauss–Seidel method are presented, especially suitable for the implementation on SMP machines with a small number of processors. One of the proposed parallel algorithms, which concentrates the computational efforts where they are most needed, results to be more efficient than the sequential algorithm, even from the point of view of the total number of operations.     

无穷时域的连续时间广义预测控制

将无穷时域的性能指标引入连续时间的广义预测控制,通过施加新的终端等式约束,把包含无穷时域性能指标的优化问题转化成可解的二次规划问题.利用后退时域性能指标的单调性,给出了保证连续时间广义预测控制闭环稳定性的条件.仿真例子验证了该算法的有效性.     

On stabilizers of infinite words

The stabilizer of an infinite word over a finite alphabet Σ is the monoid of morphisms over Σ that fix . In this paper we study various problems related to stabilizers and their generators. We show that over a binary alphabet, there exist stabilizers with at least n generators for all n. Over a ternary alphabet, the monoid of morphisms generating a given infinite word by iteration can be infinitely generated, even when the word is generated by iterating an invertible primitive morphism. Stabilizers of strict epistandard words are cyclic when non-trivial, while stabilizers of ultimately strict epistandard words are always non-trivial. For this latter family of words, we give a characterization of stabilizer elements.     

Infinite reflection models for the visual arts

Artists do not always pursue photographic realism. The image abstraction and deformation of three-dimensional scenes are methods to communicate ideas. Images are the visual interpretation of real life or imaginary scenes. This paper describes the idea of an infinite reflection model in which synthetic objects to be rendered are surrounded by closed reflective surfaces. The closed mirror surfaces create the ‘feedback’ effect which deforms objects inside the reflective space. Lens distortion effects are achieved by surrounding infinitely reflective curved surfaces. This technique provides a new visual tool for artists and graphic designers.     

On two-sided infinite fixed points of morphisms

Let Σ be a finite alphabet, and let h:Σ^* → Σ^* be a morphism. Finite and infinite fixed points of morphisms—i.e., those words w such that h(w)=w—play an important role in formal language theory. Head characterized the finite fixed points of h, and later, Head and Lando characterized the one-sided infinite fixed points of h. Our paper has two main results. First, we complete the characterization of fixed points of morphisms by describing all two-sided infinite fixed points of h, for both the “pointed” and “unpointed” cases. Second, we completely characterize the solutions to the equation h(xy)=yx in finite words.     

基于跨地域分布式架构的无限加盟电子商务新模式

在给出了一种全新的跨地域分布式电子商务系统架构的基础上,提出了全球化跨地域无限加盟的电子商务新模式.这种分散式架构可以充分利用计算机新技术的优势,将商务事件逻辑合理地分布在地域各异的多个服务器阵列上,充分利用松散耦合的服务构件集成多种业务活动,提高了系统的可扩展性、可成长性、可复用性以及互操作性和可维护性,为构建大型地域分布式电子商务系统提供了崭新的思路.基于该架构的无限加盟电子商务新模式,使得商家和企业可以方便地在其当地通过发布服务低成本加入到全球卖场,并可涵盖传统的B2B,C2C和B2C 3种交易模式,其意义不言而喻.     

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.     

Infinite fuzzy relation equations with continuous t-norms

This study develops a concept of infinite fuzzy relation equations with a continuous t-norm. It extends the work by Xiong and Wang [Q.Q. Xiong, X.P. Wang, Some properties of sup-min fuzzy relational equations on infinite domains, Fuzzy Sets and Systems 151 (2005) 393-402]. We describe attainable (respectively, unattainable) solutions, which are closely related to minimal solutions to the equations. It is shown that a solution set comprises both attainable and unattainable solutions. The study offers a characterization of these solutions. Under some assumptions, the solution set is presented and discussed. Two applications are also given.     

Weak associativity and restricted rotation

A restricted rotation induced by a weak associative law is introduced. The corresponding equivalence relation is identical to the Glivenko congruence on Tamari lattices, i.e. lattices of binary trees endowed by the well-known rotation operation.     

融合正弦余弦和无限折叠迭代混沌映射的蝴蝶优化算法

针对蝴蝶优化算法求解精度不高、收敛速度较慢等问题,提出融合正弦余弦和无限折叠迭代混沌映射(ICMIC)的蝴蝶优化算法.首先,采用ICMIC映射对蝴蝶个体状态进行初始化,避免算法陷入局部最优.然后,在自身认知飞行部分引入正弦余弦算子,平衡算法的局部搜索能力与全局搜索能力.最后,通过改进依赖香味大小的幂指数调整吸收程度,获取更好的最优解.在8个基准函数上的实验表明,文中算法具有较优的全局搜索能力和求解鲁棒性,寻优精度较高,收敛速度较快.     

Infinite Liouville mixture models with application to text and texture categorization

This paper addresses the problem of proportional data modeling and clustering using mixture models, a problem of great interest and of importance for many practical pattern recognition, image processing, data mining and computer vision applications. Finite mixture models are broadly applicable to clustering problems. But, they involve the challenging problem of the selection of the number of clusters which requires a certain trade-off. The number of clusters must be sufficient to provide the discriminating capability between clusters required for a given application. Indeed, if too many clusters are employed overfitting problems may occur and if few are used we have a problem of underfitting. Here we approach the problem of modeling and clustering proportional data using infinite mixtures which have been shown to be an efficient alternative to finite mixtures by overcoming the concern regarding the selection of the optimal number of mixture components. In particular, we propose and discuss the consideration of infinite Liouville mixture model whose parameter values are fitted to the data through a principled Bayesian algorithm that we have developed and which allows uncertainty in the number of mixture components. Our experimental evaluation involves two challenging applications namely text classification and texture discrimination, and suggests that the proposed approach can be an excellent choice for proportional data modeling.     

Periodic and Sturmian languages

Counting the number of distinct factors in the words of a language gives a measure of complexity for that language similar to the factor-complexity of infinite words. Similarly as for infinite words, we prove that this complexity function f(n) is either bounded or f(n)?n+1. We call languages with bounded complexity periodic and languages with complexity f(n)=n+1Sturmian. We describe the structure of periodic languages and characterize the Sturmian languages as the sets of factors of (one- or two-way) infinite Sturmian words.     

On the Approximation of Infinite Dimensional Optimal Stopping Problems with Application to Mathematical Finance

We consider the approximation of the optimal stopping problem for infinite dimensional processes by variational methods. To this end, we employ a Fourier-Legendre representation for the state space and exhaust an indexed family of regularized Hamilton-Jacobi characterizations. We implement our results utilizing penalization and a method-of-lines semi-implicit finite element method; application to term-structure valuation problems from mathematical finance demonstrate the applicability of the approach. This research was supported by the U.S. National Science Foundation, award number DMI-0422985.     

Infinite horizon cancer treatment model with isoperimetrical constraint: existence of optimal solutions and numerical analysis

In this paper, a class of infinite horizon optimal control problems with a mixed control-state isoperimetrical constraint, also interpreted as a budget constraint, is considered. The underlying dynamics is assumed to be affine-linear in control. The crucial idea which is followed in this paper is the choice of a weighted Sobolev space as the state space. For this class of problems, we establish an existence result and apply it to a bilinear model of optimal cancer treatment with an isoperimetrical constraint including the overall amount of drugs used during the whole therapy horizon. A numerical analysis of this model is provided by means of open source software package OCMat, which implements a continuation method for solving discounted infinite horizon optimal control problems.     

Skew and infinitary formal power series

We investigate finite-state systems with weights. Departing from the classical theory, in this paper the weight of an action does not only depend on the state of the system, but also on the time when it is executed; this reflects the usual human evaluation practices in which later events are considered less urgent and carry less weight than close events. We first characterize the terminating behaviors of such systems in terms of rational formal power series. This generalizes a classical result of Schützenberger.     

基于分块DCT变换和Arnold置乱的自适应图像水印算法

提出了一种基于分块DCT变换和Arnold置乱变换的自适应图像水印算法,该算法在水印嵌入过程中充分考虑了人类视觉系统(HVS)的特点,在不同的DCT块中嵌入不同的水印能量,从而使算法具有自适应能力。实验结果表明：该算法对于常见的图像处理具有较强的鲁棒性,特别是具有十分有效的抗击剪切的能力。