The number of spanning trees in a new lexicographic product of graphs

The problem of counting the number of spanning trees is an old topic in graph theory with important applications to reliable network design. Usually, it is desirable to put forward a formula of the number of spanning trees for various graphs, which is not only interesting in its own right but also in practice. Since some large graphs can be composed of some existing smaller graphs by using the product of graphs, the number of spanning trees of such large graph is also closely related to that of the corresponding smaller ones. In this article, we establish a formula for the number of spanning trees in the lexicographic product of two graphs, in which one graph is an arbitrary graph G and the other is a complete multipartite graph. The results extend some of the previous work, which is closely related to the number of vertices and Lapalacian eigenvalues of smaller graphs only.     

Synchronization of second-order Kuramoto networks from the perspective of edge dynamics

This paper presents new synchronization conditions for second-order phase-coupled Kuramoto oscillators in terms of edge dynamics. Two types of network-underlying graphs are studied, the positively weighted and signed graphs, respectively. We apply an edge Laplacian matrix for a positively weighted network to represent the edge connections. The properties of the edge Laplacian matrix are analyzed and incorporated into the proposed conditions. These conditions take account of the dynamics of edge-connected oscillators instead of all oscillator pairs in conventional studies. For a network with positive and negative weights, we represent the network by its spanning tree dynamics, and derive conditions to evaluate the synchronization state of this network. These conditions show that if all edge weights in the spanning tree are positive, and the tree-induced dynamics are in a dominant position over the negative edge dynamics, then this network achieves synchronization. The theoretical findings are validated by numerical examples.     

Laplacian spectrum analysis and spanning tree algorithm for circuit partitioning problems

The spectrum of a graph is the set of all eigenvalues of the Laplacian matrix of the graph. There is a closed relationship between the Laplacian spectrum of graphs and some properties of graphs such as connectivity. In the recent years Laplacian spectrum of graphs has been widely applied in many fields. The application of Laplacian spectrum of graphs to circuit partitioning problems is reviewed in this paper. A new criterion of circuit partitioning is proposed and the bounds of the partition ratio for weighted graphs are also presented. Moreover, the deficiency of graph-partitioning algorithms by Laplacian eigenvectors is addressed and an algorithm by means of the minimal spanning tree of a graph is proposed. By virtue of taking the graph structure into consideration this algorithm can fulfill general requirements of circuit partitioning.     

Property analysis of logic Petri nets by marking reachability graphs

Logic Petri nets （LPNs） are suitable to describe and analyze batch processing functions and passing value indeterminacy in cooperative systems. To investigate the dynamic properties of LPNs directly, a new method for analyzing LPNs is proposed based on marking reachability graphs in this paper. Enabled conditions of transitions are obtained and a marking reachability graph is constructed. All reach- able markings can be obtained based on the graph; the fairness and reversibility of LPNs are analyzed. Moreover, the computing complexity of the enabled conditions and reachable markings can be reduced by this method. The advantages of the proposed method are illustrated by examples and analysis.     

Belief Revision by Sets of Sentences

The aim of this paper is to extend the system of belief revision developed by Alchourron,Gaerdenfors and Makinson(AGM)to a more general framework.This extension enables a treatment of revision not only by single sentences but also by any sets of entences,especially by infinite sets.The extended revision and contraction operators will be called general ones,respectively.A group of postulates for each operator is provided in such a way that it coincides with AGM‘s in the limit case.A notion of the nice-ordering partition is introduced to characterize the general contraction opeation.A computation-oriented approach is provided for belief revision operations.     

Reaction Graph

The paper proposes reaction graphs as graphical representations of computational objects.A reaction graph is a directed graph with all its arrows and some of its nodes labeled.Computations are modled by graph rewriting of a simple nature.The basic rewriting rules embody the essence of both the communications among processes and cut-eliminations in proofs.Calculi of graphs are ideentified to give a formal and algebraic account of reaction graphs in the spirit of process algebra.With the help of the calculi,it is demonstrated that reaction graphs capture many interesting aspects of computations.     

Effect of properties of zirconia powder on performance of planar oxygen sensor chip北大核心CSCD

Three kinds of powders were used in the experiment. Chemical composition, phase composition, particle morphology, surface area, and sintering properties, Suitability for cast taping, performance of prepared planar oxygen sensor chip were studied comprehensively. The results showed that POWDER A was suitable for tape casting, but the sintering temperature (1500 ℃) is highest among those three powder, and there exist a lot of small-sized pores in sintered ceramics. The reason for this phenomenon is the presence of two-phase composition in POWDER A. But this powder can be prepared to planar oxygen sensor which has good response for oxygen. The substrate prepared by tape casting using POWDER C is very soft, which resulting in the follow-up process is difficult, and there is no measured signal for the preparaed planar oxygen sensor chip samples. Substrate prepared by POWDER B is brittle, and the impurity content also is high, sample signal is not detected for the prepared sensor chip. The requirement of planar oxygen sensor by tape-casting for YSZ powder is: Si and Fe content should be as low as possible; particles have a small particle diameter, monodisperse size distribution; specific surface area should be controlled at 12 m2/g~15 m2/g. ©, 2014, The Editorial Office of Chinese Journal of Sensors and Actuators. All right reserved.     

Studies on algorithms for self-stabilizing communication protocols

In this paper the algorithms for self-stabilizing communication protocols are studied.First some concepts and a formal method for describing the proposed algorithms are described,then an improved algorithm for achieving global states is presented.The study shows that the improved algorithm can be applied to obtain the global states in the case of a loss of cooperation of the different processes in th protocol,which can be used as a recovery point that will be used by the following recovery procdure.Thus,the improved algorithm can be used to self-stabilize a communication protocol.Meanwhile,a recovery algorithm for selastabilizing communication protocols is presented.After a failure is detected,all processes can eventually know the error.The recovery algorithm uses the contextual information exchanged during the progress of the protocol and recorded on the stable memory.The proof of correctness and analysis of complexity for these algorithms have been made.The availability and efficiency of the algorithms have been verified by illustrating the example protocols.Finally,some conclusions and remarks are given.     

A Shape Graph Logic and A Shape System

Analysis and verification of pointer programs are still difficult problems so far. This paper uses a shape graph logic and a shape system to solve these problems in two stages. First, shape graphs at every program point are constructed using an analysis tool. Then, they are used to support the verification of other properties （e.g., orderedness）. Our prototype supports automatic verification of programs manipulating complex data structures such as splay trees, treaps, AVL trees and AA trees, etc. The proposed shape graph logic, as an extension to Hoare logic, uses shape graphs directly as assertions. It can be used in the analysis and verification of programs manipulating mutable data structures. The benefit using shape graphs as assertions is that it is convenient for acquiring the relations between pointers in the verification stage. The proposed shape system requires programmers to provide lightweight shape declarations in recursive structure type declarations. It can help rule out programs that construct shapes deviating from what programmers expect （reflected in shape declarations） in the analysis stage. As a benefit, programmers need not provide specifications （e.g., pre-/post-conditions, loop invariants） about pointers. Moreover, we present a method doing verification in the second stage using traditional Hoare logic rules directly by eliminating aliasing with the aid of shape graphs. Thus, verification conditions could be discharged by general theorem provers.     

A General Approach to L（h,k）-Label Interconnection Networks

Given two non-negative integers h and k, an L（h, k）-labeling of a graph G = （V, E） is a function from the set V to a set of colors, such that adjacent nodes take colors at distance at least h, and nodes at distance 2 take colors at distance at least k. The aim of the L（h, k）-labeling problem is to minimize the greatest used color. Since the decisional version of this problem is NP-complete, it is important to investigate particular classes of graphs for which the problem can be efficiently solved. It is well known that the most common interconnection topologies, such as Butterfly-like, Beneg, CCC, Trivalent Cayley networks, are all characterized by a similar structure： they have nodes organized as a matrix and connections are divided into layers. So we naturally introduce a new class of graphs, called （l × n）-multistage graphs, containing the most common interconnection topologies, on which we study the L（h, k）-labeling. A general algorithm for L（h, k）-labeling these graphs is presented, and from this method an efficient L（2, 1）-labeling for Butterfly and CCC networks is derived. Finally we describe a possible generalization of our approach.     

一种基于神经网络的分形几何图的产生与编码

本文提出用概率逻辑神经网产生一类自（互）相似（分形）图的方法，指出这类图能用一组压缩编码表示，给出快速寻找该编码的算法，既识别该分形几何图的算法，证明该编码是最优的，即码的长度最短，这些成果有希望在图象压缩和模式识别中得到应用。     

Undecidability of the trace coding problem and some decidable cases

We introduce and investigate the notion of weak morphisms of trace monoids with the aim of dealing with the problem of deciding the existence of codings between trace monoids. We prove that this problem is not recursively enumerable, which answers the question raised by Ochma ski in 1988. On the other hand, we show its decidability when restricted to instances with domain monoids defined by acyclic dependence graphs. We also partially answer the question of Diekert from 1990 about the number of free monoids needed for encoding a given trace monoid into their direct product.     

Nonterminals,homomorphisms and codings in different variations of OL-systems

Summary Continuing the work begun in Part I of this paper, we consider now variations of nondeterministic OL-systems. The present Part II of the paper contains a systematic classification of the effect of nonterminals, codings, weak codings, nonerasing homomorphisms and homomorphisms for all basic variations of non-deterministic OL-languages, including table languages.Part I of this paper appeared in Acta Informatica 4/1 (1974).     

Visual coding by optimal graph-coloring

A formal study of visual codings in user interface design is presented. Visual codings for maximum distinction of different objects in displayed images are formulated as a discrete optimization problem of maximum-distance graph-coloring. The formulation is a generalization of the classical coloring problem in graph theory. Having pointed out that maximum-distance graph-coloring is NP-complete, we develop new, fast approximation algorithms for optimal visual codings. The proposed algorthms run inO (M N) time, whereM is the number of visual codes used andN is the number of objects to be encoded. Besides being efficient, the algorithms are simple and easy to implement. Our experiments showed that geographic maps automatically colored by the new algorithms were preferred to those colored by the previous graph-theoretical approach and they are competitive, if not better, in terms of the visual distinction of different regions than those drawn by hand.Supported by grans from Natural Science and Enginneering Research Council of Canada     

Nonterminals,homomorphisms and codings in different variations of OL-systems

Summary The use of nonterminals versus the use of homomorphisms of different kinds in the basic types of deterministic OL-systems is studied. A rather surprising result is that in some cases the use of nonterminals produces a comparatively low generative capacity, whereas in some other cases the use of nonterminals gives a very high generative capacity. General results are obtained concerning the use of erasing productions versus the use of erasing homomorphisms. The paper contains a systematic classification of the effect of nonterminals, codings, weak codings, nonerasing homomorphisms and homomorphisms for all basic types of deterministic OL-languages, including table languages.     

Homomorphic images of sentential form languages defined by semi-Thue systems

We investigate various language families which can be obtained from sentential form languages of semi-Thue systems by applying codings, weak codings, non-erasing homomorphisms, and arbitrary homomorphisms. We also distinguish between monotone, context-independent, and context-dependent semi-Thue systems with at most one or finitely many starting words. Finally, we study the effect of erasing productions u → λ.We obtain complete diagrams which show inclusions and incomparabilities of all the language families so defined.     

Online error correcting output codes

This article proposes a general extension of the error correcting output codes framework to the online learning scenario. As a result, the final classifier handles the addition of new classes independently of the base classifier used. In particular, this extension supports the use of both online example incremental and batch classifiers as base learners. The extension of the traditional problem independent codings one-versus-all and one-versus-one is introduced. Furthermore, two new codings are proposed, unbalanced online ECOC and a problem dependent online ECOC. This last online coding technique takes advantage of the problem data for minimizing the number of dichotomizers used in the ECOC framework while preserving a high accuracy. These techniques are validated on an online setting of 11 data sets from UCI database and applied to two real machine vision applications: traffic sign recognition and face recognition. As a result, the online ECOC techniques proposed provide a feasible and robust way for handling new classes using any base classifier.     

MPEG-2 Coded Video Traces Transmitted Over a Satellite Link: Scalable and Non-Scalable Solutions in Rain Fading Conditions

The literature is poor in the analyses of the effects produced by corrupted bits in compressed video bitstreams. This paper presents the results of a transmission experiment of MPEG-2 coded video data over a satellite link affected by noise, in order to investigate under which conditions this type of transmission is economically feasible. The signal-to-noise ratio scalability feature of the MPEG-2 encoder was used to produce different bitstreams of the same movie sequence. The scope of the study was to verify which are the best combinations of video and channel codings in the presence of attenuation on the satellite link, in order to optimize the bandwidth utilisation for a requested image quality. The results obtained give indications about the data channel codings to be used to counter the rain fade on the transmission link, which is a non negligible problem especially when satellite transmissions are in the Ka band. Moreover, the results highlight the flexibility of the scalable video coding in the examined scenario.     

Semantics of trees

We introduce F-structures and investigate interpretations of trees in F-structures. Thus trees are viewed as schemes of computations in F-structures. Every tree is shown to be strongly equivalent to some chain-free tree. This enables us to use the grammatical codings of [2] to define formulas for arbitrary interpreted trees. We also introduce a syntactic way to compute the values of interpreted trees.     

具有可自适应性的问卷设计器的设计

文章首先分析了目前问卷调查系统所存在的问题,提出了改进的意见。然后从便于问卷的界面实现和结果保存关键问题出发,探讨问卷组成成分、答题顺序控制和答题结果编码等环节的解决方案,为问卷的存储、答卷界面动态生成和答卷结果实时保存的实现提供技术支持。根据设计器的技术要求,采用动态界面生成技术和编码技术,对问卷的表现形式、问卷对象的属性和问卷对象的方法进行详尽的描述,设计了问卷设计器的数据结构和处理流程,完成了可自适应性的问卷设计器的设计。