A representation and the norm of Toeplitz operators

The Toeplitz operator has been used in system and control theory for quite a long time. Recently, it played a conspoicuous in H_∞-control theory. One of the important properties of the Toeplitz operator is that its norm is identical to the norm of the Laurent operator with the same symbol. The original proof of this property relies on some advanced tools in operator theory. In this paper, for Toeplitz operators with symbols consisting of an infinite-dimensional stable part and a finite-dimensional unstable part, an elementary and self-contained proof of this property is given. Our proof is based on a representation of the Toeplitz operator presented in this paper and the well known fact that an inner matrix defines an isometry. The representation presented in this paper gives insight into the structure of the Toeplitz operator. A further application of this representation is also presented.     

Model reduction via time-interval balanced stochastic truncation for linear time invariant systems

In this article, a new method for model reduction of linear dynamical systems is presented. The proposed technique is from the family of gramian-based relative error model reduction methods. The method uses time-interval gramians in the reduction procedure rather than ordinary gramians and in such a way it improves the accuracy of the approximation within the time interval which is applied. It is proven that the reduced order model is stable when the proposed method applies to a stable system. The method uses a recently proposed inner–outer factorisation algorithm which enhances the numerical accuracy and efficiency. In order to avoid numerical instability and also to further increase the numerical efficiency, projector matrices are constructed instead of the similarity transform approach for reduction. The method is illustrated by a numerical example and finally it is applied to a practical CD player example. The numerical results show that the method is more accurate than ordinary balanced stochastic truncation.     

Research on the expanding deformation of ring radius in cold profiled ring rolling process

Cold profiled ring rolling is an advanced local plastic deformation technology widely used to precisely manufacture various complex seamless ring parts.It plays an important role in many industrial fields such as aeronautics,astronautics,automobile,bearings,etc.In the cold ring rolling process,the ring radius expands gradually with the increase of the feeding amount(i.e.rolling reduction),and the expanding deformation of the ring radius is closely related to the rolling reduction.It is very important to inv...     

基于向量内积不等式的分布式k均值聚类算法

聚类分析是数据挖掘领域的一项重要研究课题．随着数据量的急剧增加,针对大数据集的聚类分析成为一个难点．虽然k均值算法具有易实现、复杂度与数据集大小成线性关系的优点,将其应用于大数据集时仍然存在效率低的问题．分布式聚类是解决这一问题的有效方法．在已有分布式聚类算法k—DMeans基础上,结合向量内积不等式关系对算法加以优化,提出分布式聚类算法k—DCBIP．理论分析和实验结果表明,算法k—DCBIP优于k-DMeans,可以有效地解决大数据集聚类问题,算法是有效可行的．     

From algebraic semantics to denotational semantics for Verilog

This paper considers how the algebraic semantics for Verilog relates with its denotational semantics. Our approach is to derive the denotational semantics from the algebraic semantics. We first present the algebraic laws for Verilog. Every program can be expressed as a guarded choice that can model the execution of a program. In order to investigate the parallel expansion laws, a sequence is introduced, indicating which instantaneous action is due to which exact parallel component. A head normal form is defined for each program by using a locality sequence. We provide a strategy for deriving the denotational semantics based on head normal form. Using this strategy, the denotational semantics for every program can be calculated. Program equivalence can also be explored by using the derived denotational semantics. A short version of this paper appeared in Proc. ICECCS 2006: 11th IEEE International Conference on Engineering of Complex Computer Systems [48]. This work is partially supported by the National Basic Research Program of China (No. 2005CB321904), the National High Technology Research and Development Program of China (No. 2007AA010302) and the National Natural Science Foundation of China (No. 90718004). Jonathan Bowen is a visiting professor at King’s College London and an emeritus professor at London South Bank University.     

A unified neurofuzzy model for classification

This work proposes a unified neurofuzzy modelling scheme. To begin with, the initial fuzzy base construction method is based on fuzzy clustering utilising a Gaussian mixture model (GMM) combined with the analysis of covariance (ANOVA) decomposition in order to obtain more compact univariate and bivariate membership functions over the subspaces of the input features. The mean and covariance of the Gaussian membership functions are found by the expectation maximisation (EM) algorithm with the merit of revealing the underlying density distribution of system inputs. The resultant set of membership functions forms the basis of the generalised fuzzy model (GFM) inference engine. The model structure and parameters of this neurofuzzy model are identified via the supervised subspace orthogonal least square (OLS) learning. Finally, instead of providing deterministic class label as model output by convention, a logistic regression model is applied to present the classifier’s output, in which the sigmoid type of logistic transfer function scales the outputs of the neurofuzzy model to the class probability. Experimental validation results are presented to demonstrate the effectiveness of the proposed neurofuzzy modelling scheme.     

基于投影的快速模板匹配算法

针对传统模板匹配算法效率不高,计算时间长等缺点,本文提出一种基于投影的快速匹配算法,利用对图像色度的投影到一水平轴,使图像数据空间的维度降到一维,并用内积计算相关度,根据已计算的相关度,决定下一次匹配的步长,过滤一些可忽略的子图投影;在计算水平域投影时,不需要从新计算,只需在上一次的结果中,增减一行色度,而且,一次投影...     

A cognitive semantics for the association construct

The unified modelling language (UML), besides its traditional use in describing software artifacts, is increasingly being used for conceptual modelling, the activity of describing an application domain. For models to be clear and unambiguous, every construct of the modelling language must have well-defined semantics, which is its mapping to elements of the semantic domain. When used for conceptual modelling, the semantic domain of UML is the application domain, as perceived by the modeller. Modellers perceive and structure their perceptions using cognitive concepts. This paper proposes a mapping of the UML association construct to those concepts. Implications for the use of the association construct for conceptual modelling are derived, a UML profile for conceptual modelling is presented, along with the results of a case study using the semantics and profile.

A semantics for Fuzzy Logic

 We present a semantics for certain Fuzzy Logics of vagueness by identifying the fuzzy truth value an agent gives to a proposition with the number of independent arguments that the agent can muster in favour of that proposition. Received: 25 February 1997 / Accepted: 12 March 1997     

模糊支持向量机在人脸识别中的应用

针对人脸图像特征提取领域应用主成分分析和二维主成分分析方法,使用二维特征值求解相关样本隶属度,并利用相关特征值方法进行分类。该方法结合二维特征值,在特征提取时进行人脸图像重构,具有快速稳定和局部特征清晰的优点。通过引入矩阵内积与二维主成分分析特征分类结果进行比较,实验结果表明,在ORL和Yale数据库中利用该方法进行识别分类取得了很好的效果。     

A structured operational semantics for UML-statecharts

The Unified Modeling Language (UML) has gained wide acceptance in very short time because of its variety of well-known and intuitive graphical notations. However, this comes at the price of an unprecise and incomplete semantics definition. This insufficiency concerns single UML diagram notations on their own as well as their integration. In this paper, we focus on the notation of UML-statecharts. Starting with a precise textual syntax definition, we develop a precise structured operational semantics (SOS) for UML-statecharts. Besides the support of interlevel transitions and in contrast to related work, our semantics definition supports characteristic UML-statechart features like the history mechanism as well as entry and exit actions. Initial submission: 19 February 2002 / Revised submission: 28 October 2002 Published online: 2 December 2002     

A differential semantics for jointree algorithms

A new approach to inference in belief networks has been recently proposed, which is based on an algebraic representation of belief networks using multi-linear functions. According to this approach, belief network inference reduces to a simple process of evaluating and differentiating multi-linear functions. We show here that mainstream inference algorithms based on jointrees are a special case of the approach based on multi-linear functions, in a very precise sense. We use this result to prove new properties of jointree algorithms. We also discuss some practical and theoretical implications of this new finding.     

A compositional natural semantics and Hoare logic for low-level languages

The advent of proof-carrying code has generated significant interest in reasoning about low-level languages. It is widely believed that low-level languages with jumps must be difficult to reason about because of being inherently non-modular. We argue that this is untrue. We take it seriously that, unlike statements of a high-level language, pieces of low-level code are multiple-entry and multiple-exit. And we define a piece of code as consisting of either a single labelled instruction or a finite union of pieces of code. Thus we obtain a compositional natural semantics and a matching Hoare logic for a basic low-level language with jumps. By their simplicity and intuitiveness, these are comparable to the standard natural semantics and Hoare logic of While. The Hoare logic is sound and complete wrt the semantics and allows for compilation of proofs of the Hoare logic of While.     

A new fixpoint semantics for general logic programs compared with the well-founded and the stable model semantics

We study a new fixpoint semantics for logic programs with negation. Our construction is intermediate between Van Gelder’s well-founded model and Gelfond and Lifschitz’s stable model semantics. We show first that the stable models of a logic programP are exactly the well-supported models ofP, i.e. the supported models with loop-free finite justifications. Then we associate to any logic programP a non-monotonic operator over the semilattice of justified interpretations, and we define in an abstract form its ordinal powers. We show that the fixpoints of this operator are the stable models ofP, and that its ordinal powers after some ordinala are extensions of the well-founded partial model ofP. In particular ifP has a well-founded model then that canonical model is also an ordinal power and the unique fixpoint of our operator. We show with examples of logic programs which have a unique stable model but no well-founded model that the converse is false. We relate also our work to Doyle’s truth maintenance system and some implementations of rule-based expert systems.     

Fibred semantics for feature-based grammar logic

This paper gives a simple method for providing categorial brands of feature-based unification grammars with a model-theoretic semantics. The key idea is to apply the paradigm of fibred semantics (or layered logics, see Gabbay (1990)) in order to combine the two components of a feature-based grammar logic. We demonstrate the method for the augmentation of Lambek categorial grammar with Kasper/Rounds-style feature logic. These are combined by replacing (or annotating) atomic formulas of the first logic, i.e. the basic syntactic types, by formulas of the second. Modelling such a combined logic is less trivial than one might expect. The direct application of the fibred semantics method where a combined atomic formula like np (num: sg & pers: 3rd) denotes those strings which have the indicated property and the categorial operators denote the usual left- and right-residuals of these string sets, does not match the intuitive, unification-based proof theory. Unification implements a global bookkeeping with respect to a proof whereas the direct fibring method restricts its view to the atoms of the grammar logic. The solution is to interpret the (embedded) feature terms as global feature constraints while maintaining the same kind of fibred structures. For this adjusted semantics, the anticipated proof system is sound and complete.     

A weakest precondition semantics for communicating processes

A weakest precondition semantics for communicating processes is presented, based on a centralized, one-level approach. Semantic equations are given for the CSP constructs and their continuity is proved. The equivalence of two weakest precondition definitions, one with certain order preferences, and another one, preference-free, is shown. The representation of various operational concepts, including delay, is discussed. Several examples of applying the rules are given.     

Transformation for Refining Unraveled Conditional Term Rewriting Systems

Unravelings, transformations from conditional term rewriting systems (CTRSs, for short) into unconditional term rewriting systems, are valuable for analyzing properties of CTRSs. In order to completely simulate rewrite sequences of CTRSs, the restriction by a particular context-sensitive and membership condition that is determined by extra function symbols introduced due to the unravelings, must be imposed on the rewrite relations of the unraveled CTRSs. In this paper, in order to weaken the context-sensitive and membership condition, we propose a transformation applied to the unraveled CTRSs, that reduces the number of the extra symbols. In the transformation, updating the context-sensitive condition properly, we remove the extra symbols that satisfy a certain condition. If the transformation succeeds in removing all of the extra symbols, we obtain the TRSs that are computationally equivalent with the original CTRSs.