Extending the theory of conflict equilibria

New symmetric coalition conflict equilibria are proposed. Together with already known equilibria, they allow one to find the strongest equilibrium in the majority of static and dynamic conflict problems. The study is carried out according to the OITVS RAN program, Project No. 1.3. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 80–89, March–April 2007.     

Extending abstract argumentation systems theory

In this paper, we extend the theory of abstract argumentation systems proposed by Vreeswijk (1997). This framework stands at a high abstraction level and provides a general model for argumentation activity. However, the theory reveals an inherent limitation in that the premises of the argumentation process are assumed to be indefeasible, and this introduces the need of an implicit constraint on the strength of the arguments, in order to preserve correctness. In many application contexts the information available to start reasoning is not guaranteed to be completely reliable, therefore it is natural to assume that premises can be discarded during the argumentation process. We extend the theory by admitting that premises can be defeated and relaxing the implicit assumption about their strength.Besides fixing the technical problems related to this hidden assumption (e.g., ensuring that warranted arguments are compatible), our proposal provides an integrated model for belief revision and defeasible reasoning, confirming the suitability of argumentation as a general model for the activity of intelligent reasoning in presence of various kinds of uncertainty.     

Extending cable theory to heterogeneous dendrites

Dendrites may exhibit many types of electrical and morphological heterogeneities at the scale of a few micrometers. Models of neurons, even so-called detailed models, rarely consider such heterogeneities. Small-scale fluctuations in the membrane conductances and the diameter of dendrites are generally disregarded and spines merely incorporated into the dendritic shaft. Using the two-scales method known as homogenization, we establish explicit expressions for the small-scale fluctuations of the membrane voltage, and we derive the cable equation satisfied by the voltage when these fluctuations are averaged out. This allows us to rigorously establish under what conditions a heterogeneous dendrite can be approximated by a homogeneous cable. We consider different distributions of synapses, orderly or random, on a passive dendrite, and we investigate when replacing excitatory and inhibitory synaptic conductances by their local averages leads to a small error in the voltage. This indicates in which regimes the approximations made in compartmental models are justified. We extend these results to active membranes endowed with voltage-dependent conductances or NMDA receptors. Then we examine under which conditions a spiny dendrite behaves as a smooth dendrite. We discover a new regime where this holds true, namely, when the conductance of the spine neck is small compared to the conductance of the synapses impinging on the spine head. Spines can then be taken into account by an effective excitatory current, the capacitance of the dendrite remaining unchanged. In this regime, the synaptic current transmitted from a spine to the dendritic shaft is strongly attenuated by the weak coupling conductance, but the total current they deliver can be quite substantial. These results suggest that pedunculated spines and stubby spines might play complementary roles in synaptic integration. Finally, we analyze how varicosities affect voltage diffusion in dendrites and discuss their impact on the spatiotemporal integration of synaptic input.     

Extending statecharts with process algebra operators

This paper describes an adaptation of statecharts to take advantage of process algebra operators like those found in CSP and EB³. The resulting notation is called algebraic state transition diagrams (ASTDs). The process algebra operators considered include sequence, iteration, parallel composition, and quantified synchronization. Quantification is one of the salient features of ASTDs, because it provides a powerful mechanism to precisely and explicitly define cardinalities in a dynamic model. The formal semantics of ASTDs is expressed using the operational style typically used in process algebras. The target application domain is the specification and implementation of information systems.     

Extending existing dependency theory to temporal databases

Normal forms play a central role in the design of relational databases. Several normal forms for temporal relational databases have been proposed. These definitions are particular to specific temporal data models, which are numerous and incompatible. The paper attempts to rectify this situation. We define a consistent framework of temporal equivalents of the important conventional database design concepts: functional dependencies, primary keys, and third and Boyce-Codd normal forms. This framework is enabled by making a clear distinction between the logical concept of a temporal relation and its physical representation. As a result, the role played by temporal normal forms during temporal database design closely parallels that of normal forms during conventional database design. These new normal forms apply equally well to all temporal data models that have timeslice operators, including those employing tuple timestamping, backlogs, and attribute value timestamping. As a basis for our research, we conduct a thorough examination of existing proposals for temporal dependencies, keys, and normal forms. To demonstrate the generality of our approach, we outline how normal forms and dependency theory can also be applied to spatial and spatiotemporal databases     

Extending process automation systems with multi-agent techniques

This paper presents a design of a process automation system extended with multi-agent systems (MAS) and experiments with its implementation. According to this design, MAS can be used to extend the functionality of ordinary process automation systems at higher levels of control. Anticipated benefits of this include enhanced reconfigurability, responsiveness and flexibility of the resulting automation system. The design also takes into account particular characteristics of process automation. An agent platform for process automation is presented as a basis for applying MAS. A FIPA-compliant agent platform is extended with process automation specific functionality. The platform utilizes a hierarchical agent organization and a BDI-agent model. Two applications are implemented using the platform. One of these shows how the techniques of distributed planning can be applied in discrete control. The other provides a model for supervisory continuous control using the techniques of distributed search. Experiments performed with a laboratory test environment using the applications are presented. They are able to demonstrate the feasibility of the approach in test scenarios.     

Number theory in mathematics education: Perspectives and prospects

Zazkis, R., & Campbell, S.R. (Eds.). (2006). Number Theory in Mathematics Education: Perspectives and Prospects. Mahwah, NJ: Lawrence Erlbaum. ISBN 0–8058–5407‐X (cloth); 0–8058–5408–8 (paper)     

Amorphous computing: examples, mathematics and theory

The cellular automata model was described by John von Neumann and his friends in the 1950s as a representation of information processing in multicellular tissue. With crystalline arrays of cells and synchronous activity, it missed the mark (Stark and Hughes, BioSystems 55:107–117, 2000). Recently, amorphous computing, a valid model for morphogenesis in multicellular information processing, has begun to fill the void. Through simple examples and elementary mathematics, this paper begins a computation theory for this important new direction.     

Extending extension theory for classifying data with numerical values

The extension theory (ET) is one of the simplest and most attractive pattern classification methods. However, it has difficulty determining the classical domain. In addition, the traditional extended relational function used in extension theory does not provide very useful summaries of asymmetrical data. This study proposes a modified extension theory (MET) to overcome these shortcomings. The MET applies the largest sphere concept to determine the range of the classical domains and incorporates the information about the data distribution when calculating the relevance of an element belonging to a set. Experimental results indicate that the MET consistently achieved better or comparable results than the traditional ET. The MET also produces a classifier with satisfactory classification accuracy compared with well-known classifiers (e.g., decision trees and k-nearest neighbor).     

论函数编程技术在计算机数学教学中的应用

计算机数学作为计算机学科一门重要专业基础课程在计算机的教授与学习中起到承上启下的作用.随着网络时代的到来,企业、政府、个人都看到了计算机在生产生活中必不可少的作用,计算机成为生活中必不可少的东西.网络时代的发展也带动了计算机学科的发展,成为热门学科.计算机学科和数学是分不开的,因此也称为最有难度的一个学科.虽然很多学生选择计算机学科,但是在实际课堂教育中,学生的听课效率却不如预期,主要因为计算机数学内容理论性很强,而且一些概念知识很抽象,让学生很难理解,从而对学科内容不感兴趣.函数编程技术在教学中应用,对计算机数学的学习起到了辅助作用,让学生可以利用这种编程语言了解计算机数学的一些抽象性概念,更好的在实践中运用计算机数学.函数编程技术在计算机数学中应用,使得死板的理论学科变得稍显活泼,这回让学生对该学科更感兴趣,带动学生积极主动地学习.     

Receptive process theory

An algebraic theory of receptive processes is presented. A receptive process models the interaction by input events and output events between a system and its environment. Input from the environment and output to the environment are never blocked; but if a system is not ready to receive a particular input, its subsequent behaviour is undefined.In essence, this paper reworks Hoare's theory of Communicating Sequential Processes under the above assumption about communication. The resulting model is more attractive than the failures-divergences model of CSP because the refusal sets of the latter are simplified out of existence. Like CSP, receptive process theory is equipped with a sound and complete set of algebraic laws.Applications of the theory include the design of asynchronous circuits and the study of data flow networks. As an example, this paper verifies algebraically the design of a Muller C-element from a majority-element.     

基于建构主义的离散数学教学探讨

将建构主义理论应用于离散数学的教学实践中,在教师课前准备、课堂授课和学生课后复习等环节作了有益的尝试。教学实践表明,在建构主义理论指导下的教学方法能够有效地提高学生的学习兴趣,加深他们对课程内容的理解。     

Parallel process diagnosis based on qualitative models

This paper presents a method for process diagnosis based on a relational process model. To overcome the exponential complexity of the modelling and diagnostic tasks, three main results are described. First, the modelling complexity is reduced by building the overall system model from subsystem models in a component-oriented way. Second, a solution of the diagnostic problem based on relational algebra is presented and successively improved by exploiting the inherent structure of the diagnostic problem. The third idea is to decompose the diagnostic problem and to solve the resulting subproblems in parallel on a multicomputer system. A communication scheme which ensures the correct solution of the diagnostic problem is given. The theoretical results are illustrated by a diagnostic problem occurring in a power station.     

Extending the decision field theory to model operators' reliance on automation in supervisory control situations

Appropriate trust in and reliance on automation are critical for safe and efficient system operation. This paper fills an important research gap by describing a quantitative model of trust in automation. We extend decision field theory (DFT) to describe the multiple sequential decisions that characterize reliance on automation in supervisory control situations. Extended DFT (EDFT) represents an iterated decision process and the evolution of operator preference for automatic and manual control. The EDFT model predicts trust and reliance, and describes the dynamic interaction between operator and automation in a closed-loop fashion: the products of earlier decisions can transform the nature of later events and decisions. The simulation results show that the EDFT model captures several consistent empirical findings, such as the inertia of trust and the nonlinear characteristics of trust and reliance. The model also demonstrates the effects of different types of automation on ttrust and reliance. It is possible to expand the EDFT model for multioperator multiautomation situations.     

Idempotent conjunctive combination of belief functions: Extending the minimum rule of possibility theory

When conjunctively merging two belief functions concerning a single variable but coming from different sources, Dempster rule of combination is justified only when information sources can be considered as independent. When dependencies between sources are ill-known, it is usual to require the property of idempotence for the merging of belief functions, as this property captures the possible redundancy of dependent sources. To study idempotent merging, different strategies can be followed. One strategy is to rely on idempotent rules used in either more general or more specific frameworks and to study, respectively, their particularization or extension to belief functions. In this paper, we study the feasibility of extending the idempotent fusion rule of possibility theory (the minimum) to belief functions. We first investigate how comparisons of information content, in the form of inclusion and least-commitment, can be exploited to relate idempotent merging in possibility theory to evidence theory. We reach the conclusion that unless we accept the idea that the result of the fusion process can be a family of belief functions, such an extension is not always possible. As handling such families seems impractical, we then turn our attention to a more quantitative criterion and consider those combinations that maximize the expected cardinality of the joint belief functions, among the least committed ones, taking advantage of the fact that the expected cardinality of a belief function only depends on its contour function.     

A qualitative temporal information system for process control

A general system is presented in this paper which supports the expression of relative temporal knowledge in process control and management. This system allows knowledge of Allen's temporal relations over time elements, which may be both intervals and points. The objectives and characteristics of two major temporal attributes, i.e. ‘transaction time’ and ‘valid time’, are described. A graphical representation for the temporal network is presented, and inference over the network may be made by means of a consistency checker in terms of the graphical representation. An illustrative example of the system as applied to process control and management is provided.     

Extending social responsibility to small and medium-sized suppliers in supply chains: A fuzzy-set qualitative comparative analysis

Buying firms’ sales and reputation will be greatly damaged by any non-responsible behaviors on the part of suppliers, especially when those suppliers, like small and medium-sized enterprises (SMEs), have restricted resources and capabilities. To eradicate these risks, a growing number of buying firms have introduced socially responsible supplier development (SRSD). SRSD, including monitoring and evaluating suppliers, can provide them with incentives and assistance. Based on configuration theory and contingency theory, fuzzy-set qualitative comparative analysis (fsQCA) is adopted in this study to examine how SRSD practices adopted by buying firms, supply chain partnership, and market turbulence affect the corporate social responsibility (CSR) performance of their SME suppliers. We find that, as core factors, supplier monitoring, supplier assistance, and supply chain partnership can work together with peripheral conditions to achieve superior CSR performance. In addition, even at different levels of market turbulence, superior CSR performance can be realized through different causal configurations.     

Application of the catastrophe theory in studying the magnetic reconnection process

A mathematical model of the magnetic reconnection process in the vicinity of critical points is discussed. The diagram method of the catastrophe theory for studying the process of the transformation of structurally unstable magnetic configurations into structurally stable ones is presented. The results of analytical research are confirmed by numerical calculations.     

关于过程神经元网络的理论探讨

过程神经元网络是一种适合于处理过程式信号输入的网络，其基本单元是过程神经元——新近出现的神经元模型．过程神经元和传统神经元有着本质的区别，但二者之间也存在着紧密的联系，前者可用后者以任意精度无限逼近．文中给出2个定理及其详细证明，分别论述了过程神经元的2种传统神经元逼近模型：时域特征扩展模型和正交分解特征扩展模型．基于第2个定理，给出了过程神经元网络相关的2个推论．最后，针对过程神经元网络面临的主要问题进行讨论，指出了一些具有前景的研究方向．文中得到的结果对过程神经元模型及其网络的研究具有一定的理论意义．     

泛在学习理论下高等数学网络学习资源优化探讨

基于泛在学习的理论和特点,提出以学习元为基础的网络学习资源建设,避免内容重复构建,提升知识点间的动态关联,构建层次化结构,拓展知识的外延性和内涵性,设定多个模块引导学习.该方法的运用能促进高等数学课程网路学习资源优化,满足学习者无时无刻无处不在的无缝学习,有效提高教学活动的开展,解决现行教学活动中遇到的实际问题.