Extracting a polyhedron from a single-view sketch: Topological construction of a wireframe sketch with minimal hidden elements

An essential prerequisite to construct a manifold trihedral polyhedron from a given natural (or partial-view) sketch is solution of the “wireframe sketch from a single natural sketch (WSS)” problem, which is the subject of this paper. Published solutions view WSS as an “image-processing”/“computer vision” problem where emphasis is placed on analyzing the given input (natural sketch) using various heuristics. This paper proposes a new WSS method based on robust tools from graph theory, solid modeling and Euclidean geometry. Focus is placed on producing a minimal wireframe sketch that corresponds to a topologically correct polyhedron.     

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.     

An algebraic criterion for robust stability of linear controlsystems

A new robust stability test for linear control systems is described. The condition at which robust stability is violated is transformed into an equivalent problem in which the existence of a real root of a multivariable polynomial is investigated. This multivariable problem is reduced to that of the solvability of a set of univariable polynomial equations in real numbers, for which a number of efficient numerical methods are available. The use of the method is illustrated in the design of feedback control for an open-loop unstable batch chemical reactor     

Quantitative criterion of conditioning for systems of linear algebraic equations

Conventional conditioning criteria are shown to be invalid for estimating the accuracy of a numerical calculation for systems of linear algebraic equations. A new conditioning criterion is proposed, quantitatively describing the actual loss of decimal digits in calculations. The adequacy of this criterion is confirmed by examples of numerical calculations. Conditioning criteria have been obtained for some types of linear systems arising in important applied problems, in particular, in the difference solution of differential or integral equations.     

Multidimensional behaviours: an algebraic approach to control theory for PDE

This paper gives an overview of the algebraic theory of multidimensional behaviours, and it contains some new aspects as well. Some known results are restated with a new proof. After a short introduction to behavioural systems theory, we briefly describe the mathematical background of the algebraic approach. Then we study structural properties such as autonomy and over-determined systems on the one hand, and controllability and flat systems on the other.     

FID-sketch: an accurate sketch to store frequencies in data streams

World Wide Web - Sketches are being extensively used in a large number of real world applications to estimate frequencies of data items. Due to the unprecedented increase in the amount of Internet...     

关于线性中立型时滞系统稳定性代数准则的一个注记

研究了线性时滞中立型微分系统的渐近稳定性, 基于系统的特征方程, 利用恰当的模矩阵、谱半径和矩阵乘法公式导出了新的时滞无关的稳定性准则, 例子表明所给准则的有效性和较低的保守性.     

An algebraic criterion for detecting the fact and time a fault occurs in control systems of dynamic plants

This paper proposes a new algebraic criterion for fault detection in control systems of dynamic plants; this criterion uses only the measurements of input and output signals and is based on the solvability condition for the problem of identifying the mathematical model of a dynamic plant. To estimate the proposed criterion, it is compared with a criterion based on analyzing prediction errors in solving a fault detection problem for a stabilizer actuator.     

Ready to preorder: an algebraic and general proof

There have been quite a few proposals for behavioural equivalences for concurrent processes, and many of them are presented in Van Glabbeek’s linear time-branching time spectrum. Since their original definitions are based on rather different ideas, proving general properties of them all would seem to require a case-by-case study. However, the use of their axiomatizations allows a uniform treatment that might produce general proofs of those properties. Recently Aceto, Fokkink and Ingólfsdóttir have presented a very interesting result: for any process preorder coarser than the ready simulation in the linear time-branching time spectrum they show how to get an axiomatization of the induced equivalence. Unfortunately, their proof is not uniform and requires a case-by-case analysis. Following the algebraic approach suggested above, in this paper we present a much simpler proof of that result which, in addition, is more general and totally uniform, so that it does not need to consider one by one the different semantics in the spectrum.     

An application of algebraic topology to solid modeling in molecular biology

A recurring problem in solid modeling, computer graphics, and molecular modeling is the computation of the intersection of two objects. A general solution to this problem is obtained by applying two ideas of algebraic topology: (1) a chain complex, and (2) a boundary formula for the intersection of two objects. A general data structure for a chain complex made up of piecewise polynomial cells is described, as are algorithms for connectivity, containment and intersection. The basic ideas of this work are abstract, topological, and for the most part, independent of the shape and dimensionality of the objects. An application to structural molecular biology is presented. The application identifies convex and concave features of protein surfaces.