Running time experiments on some algorithms for solving propositional satisfiability problems

Satisfiability problems are of importance for many practical problems. They are NP-complete problems. However, some instances of the SAT problem can be solved efficiently. This paper reports on a study concerning the behaviour of a variety of algorithmic approaches to this problem tested on a set of problems collected at FAW. The results obtained give a lot of insight into the algorithms and problems, yet also show some general technical and methodological problems associated with such comparisons.     

George B. Dantzig and systems optimization

We pay homage to George B. Dantzig by describing a less well-known part of his legacy–his early and dedicated championship of the importance of systems optimization in solving complex real-world problems.     

Fuzzy信息系统的Rough集理论

提出 Fuzzy信息系统的概念 ,建立 fuzzy信息系统上的 Rough集理论 ,给出 Fuzzy信息系统与经典信息系统的关系 ,讨论 Fuzzy信息系统的知识约简问题     

Theo’s reinvention of the logic of conditional statements’ proofs rooted in set-based reasoning

This report documents how one undergraduate student used set-based reasoning to reinvent logical principles related to conditional statements and their proofs. This learning occurred in a teaching experiment intended to foster abstraction of these logical relationships by comparing the relationships between predicates within the conditional statements and inference structures among various proofs (in number theory and geometry). We document the progression of Theo’s set-based emergent model (Gravemeijer, 1999) from a model-of the truth of statements to a model-for logical relationships. This constitutes some of the first evidence for how students can abstract such logical concepts in this way and provides evidence for the viability of the learning progression that guided the instructional design.     

Enzyme-regulated the changes of pH values for assembling a colorimetric and multistage interconnection logic network with multiple readouts

Based on enzymatic reactions-triggered changes of pH values and biocomputing, a novel and multistage interconnection biological network with multiple easy-detectable signal outputs has been developed. Compared with traditional chemical computing, the enzyme-based biological system could overcome the interference between reactions or the incompatibility of individual computing gates and offer a unique opportunity to assemble multicomponent/multifunctional logic circuitries. Our system included four enzyme inputs: β-galactosidase (β-gal), glucose oxidase (GOx), esterase (Est) and urease (Ur). With the assistance of two signal transducers (gold nanoparticles and acid–base indicators) or pH meter, the outputs of the biological network could be conveniently read by the naked eyes. In contrast to current methods, the approach present here could realize cost-effective, label-free and colorimetric logic operations without complicated instrument. By designing a series of Boolean logic operations, we could logically make judgment of the compositions of the samples on the basis of visual output signals. Our work offered a promising paradigm for future biological computing technology and might be highly useful in future intelligent diagnostics, prodrug activation, smart drug delivery, process control, and electronic applications.     

ON UNILATERALLY CONSTRAINED MOTIONS OF RIGID BODIES SYSTEMS

ＯＮＵＮＩＬＡＴＥＲＡＬＬＹＣＯＮＳＴＲＡＩＮＥＤＭＯＴＩＯＮＳＯＦＲＩＧＩＤＢＯＤＩＥＳＳＹＳＴＥＭＳＬｉＨｏｎｇｂｏ（李洪波）（ＭＭＲＣ，ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ１０００８０...     

命题逻辑公式的压缩表示及其相应的形式系统

提出一种将命题逻辑公式压缩表示的方法--公式的压缩图,给出相应的形式系统,并证明该系统的证明效率比传统相继式演算系统Gentzen\{cut}有指数级的提高,从而为命题逻辑提供了一种新的有效的推理系统.     

Residue integrals and Waring’s formulas for algebraic or even transcendental systems

The present article is focused on the study of a special class of systems of non-linear transcendental equations for which classical algebraic and symbolic methods are inapplicable. For the purpose of study of such systems we develop a method for computing residue integrals with integration over certain cycles. We describe conditions under which the mentioned residue integrals coincide with power sums of the inverses to the roots of a system of equations (i.e. multidimensional Waring’s formulas). Based on this, we develop an algorithm that computes such power sums without computing the roots. As an application of the suggested method, we consider a problem of finding sums of multi-variable number series.     

Dynamical linked cluster expansions with applications to disordered systems

Dynamical linked cluster expansions are linked cluster expansions with hopping parameter terms endowed with their own dynamics. We discuss physical applications to systems with annealed and quenched disorder. Examples are the bond-diluted Ising model and the Sherrington-Kirkpatrick spin glass. We derive the rules and identify the full set of graphs that contribute to the series in the quenched case. This way it becomes possible to avoid the vague extrapolation from positive integer n to n = 0, that usually goes along with an application of the replica trick. Received 13 December 2001 Published online 25 June 2002