Guiding functions and periodic solutions for inclusions with causal multioperators

In the present paper, the method of guiding functions is applied to study the periodic problem for a differential inclusion with a causal multioperator. At first we consider the case when the multioperator is closed and convex-valued. Then the case of a non-convex-valued and lower semicontinuous right-hand part is considered. Thereafter, the theory is extended to the case of non-smooth guiding functions.     

Cybernetic causality: A unitary theory of causal recursion in natural and social systems

The phenomena connected with non-linear difference and differential equations are approached from a unifying point of view, offered by the general concept of causal recursion (Sections 1 and 2). After a short discussion of nilpotent causal recursions (Section 3), the properties of full causal recursions near or steadily developing states are considered in detail (Section 4). In the general case of causal recursion, a theorem based on a differential-geometric argument is proved concerning the convergence of trajectories, and an exhaustive classification of systems having causal recursion is obtained (Section 5). It gives, among some other things, a mathematical foundation to the concept of a self-steering system (as distinguished from that of a self-regulating system), applied in recent sociocybernetic analyses.     

CoLab: A hybrid knowledge representation and compilation laboratory

Knowledge bases for real-world domains such as mechanical engineering require expressive and efficient representation and processing tools. We pursue a declarative-compilative approach to knowledge engineering.While Horn logic (as implemented in PROLOG) is well-suited for representing relational clauses, other kinds of declarative knowledge call for hybrid extensions: functional dependencies and higher-order knowledge should be modeled directly. Forward (bottom-up) reasoning should be integrated with backward (top-down) reasoning. Constraint propagation should be used wherever possible instead of search-intensive resolution. Taxonomic knowledge should be classified into an intuitive subsumption hierarchy.Our LISP-based tools provide directtranslators of these declarative representations into abstract machines such as an extended Warren Abstract Machine (WAM) and specialized inference engines that are interfaced to each other. More importantly, we provide source-to-sourcetransformers between various knowledge types, both for user convenience and machine efficiency.These formalisms with their translators and transformers have been developed as part of CoLab, acompilationlaboratory for studying what we call, respectively, vertical and horizontal compilation of knowledge, as well as for exploring the synergeticcolaboration of the knowledge representation formalisms.A case study in the realm of mechanical engineering has been an important driving force behind the development of CoLab. It will be used as the source of examples throughout the paper when discussing the enhanced formalisms, the hybrid representation architecture, and the compilers.Supported by BMFT Research Project ARC-TEC (grant ITW 8902 C4)     

Probabilistic temporal networks: A unified framework for reasoning with time and uncertainty

Complex real-world systems consist of collections of interacting processes/events. These processes change over time in response to both internal and external stimuli as well as to the passage of time itself. Many domains such as real-time systems diagnosis, story understanding, and financial forecasting require the capability to model complex systems under a unified framework to deal with both time and uncertainty. Current models for uncertainty and current models for time already provide rich languages to capture uncertainty and temporal information, respectively. Unfortunately, these semantics have made it extremely difficult to unify time and uncertainty in a way which cleanly and adequately models the problem domains at hand. Existing approaches suffer from significant trade offs between strong semantics for uncertainty and strong semantics for time. In this paper, we explore a new model, the Probabilistic Temporal Network (PTN), for representing temporal and atemporal information while fully embracing probabilistic semantics. The model allows representation of time constrained causality, of when and if events occur, and of the periodic and recurrent nature of processes.     

A composition theorem for weighted pseudo-almost automorphic functions and applications

In this paper, we establish a composition theorem for weighted pseudo-almost automorphic functions under a weaker Lipschitz condition. Our composition theorem generalizes some known results. Moreover, the existence and uniqueness of pseudo-almost automorphic solutions for abstract semilinear evolution equations are studied.     

A task and resource scheduling system for automated planning

Planning is done at both the strategic and tactical levels. This paper classifies some previous planning techniques into these different levels, and details of some of their problems. A planning technique known as heuristic task scheduling is then presented along with a planner architecture that integrates task-scheduling with more traditional techniques to form a system that bridges the strategic/tactical division     

New approach for weighted pseudo-almost periodic functions under the light of measure theory,basic results and applications

The aim of this work is to present new approach to study weighted pseudo almost periodic functions using the measure theory. We present a new concept of weighted ergodic functions which is more general than the classical one. Then we establish many interesting results on the functional space of such functions like completeness and composition theorems. The theory of this work generalizes the classical results on weighted pseudo almost periodic functions. For illustration, we provide some applications for evolution equations which include reaction diffusion systems and partial functional differential equations.     

A preconditioner for constrained and weighted least squares problems with Toeplitz structure

We study methods for solving the constrained and weighted least squares problem min _x by the preconditioned conjugate gradient (PCG) method. HereW = diag (₁, , _m ) with _{1 m} 0, andA ^T = [T ₁ ^T , ,T _k ^T ] with Toeplitz blocksT _l R ^{n × n} ,l = 1, ,k. It is well-known that this problem can be solved by solving anaugmented linear 2 × 2 block linear systemM +Ax =b, A ^T = 0, whereM =W ^–1. We will use the PCG method with circulant-like preconditioner for solving the system. We show that the spectrum of the preconditioned matrix is clustered around one. When the PCG method is applied to solve the system, we can expect a fast convergence rate.Research supported by HKRGC grants no. CUHK 178/93E and CUHK 316/94E.     

A novel group ranking model for revealing sequence and quantity knowledge

The aggregation of individuals’ preferences into a consensus ranking is a group ranking problem which has been widely utilized in various applications, such as decision support systems, recommendation systems, and voting systems. Gathering the comparison of preferences and aggregate them to gain consensuses is a conventional issue. For example, b > c ? d ? a indicates that b is favorable to c, and c (d) is somewhat favorable but not fully favorable to d (a), where > and ? are comparators, and a, b, c, and d are items. Recently, a new type of ranking model was proposed to provide temporal orders of items. The order, b&c → a, means that b and c can occur simultaneously and are also before a. Although this model can derive the order ranking of items, the knowledge about quantity-related items is also of importance to approach more real-life circumstances. For example, when enterprises or individuals handle their portfolios in financial management, two considerations, the sequences and the amount of money for investment objects, should be raised initially. In this study, we propose a model for discovering consensus sequential patterns with quantitative linguistic terms. Experiments using synthetic and real datasets showed the model’s computational efficiency, scalability, and effectiveness.     

A wavelet theory for local fields and related groups

Let G be a locally compact abelian group with compact open subgroup H. The best known example of such a group is G = ℚ_p, the field of padic rational numbers (as a group under addition), which has compact open subgroup H = ℤ_p, the ring of padic integers. Classical wavelet theories, which require a non trivial discrete subgroup for translations, do not apply to G, which may not have such a subgroup. A wavelet theory is developed on G using coset representatives of the discrete quotient Ĝ/H^⊥ to circumvent this limitation. Wavelet bases are constructed by means of an iterative method giving rise to socalled wavelet sets in the dual group Ĝ. Although the Haar and Shannon wavelets are naturally antipodal in the Euclidean setting, it is observed that their analogues for G are equivalent.     

A model for maintenance service contract design,negotiation and optimization

A model is presented in this paper for maintenance service contract design, negotiation and optimization. The model was developed under the assumption that there are one customer and one unique service provider who is the Original Equipment Manufacturer (OEM) and is called the agent in this paper. This is typically applied to the situation where the OEM is the only possible service supplier such as in the case of major military equipment in the defense sector. Three contract options were considered, depending on the extent of outsourced maintenance activities. From an agent point of view, they are, (1), the agent carries out all repairs and inspections; (2), the agent carries out failure based repairs, and (3), the agent does inspections and repairs to the defects identified at inspections. For options two and three, the customer does the rest of maintenance. The relationship between inspections and failures was modeled using the delay time concept and a numerical example was illustrated. The cases of perfect information to both parties and information asymmetry were also discussed in the example. The model developed can be used for contract design, negotiation and optimization.     

A sequent calculus for logic of knowledge and past time: Completeness and decidability

We consider logic of knowledge and past time. This logic involves the discrete-time linear temporal operators next, until, weak yesterday, and since. In addition, it contains an indexed set of unary modal operators agent i knows.We consider the semantic constraint of the unique initial states for this logic. For the logic, we present a sequent calculus with a restricted cut rule. We prove the soundness and completeness of the sequent calculus presented. We prove the decidability of provability in the considered calculus as well. So, this calculus can be used as a basis for automated theorem proving. The proof method for the completeness can be used to construct complete sequent calculi with a restricted cut rule for this logic with other semantical constraints as well. Published in Lietuvos Matematikos Rinkinys, Vol. 46, No. 3, pp. 427–437, July–September, 2006.     

A simple “market value” bargaining model for weighted voting games: characterization and limit theorems

We offer a bargaining model for weighted voting games that is a close relative of the nucleolus and the kernel. We look for a set of weights that preserves winning coalitions that has the property of minimizing the difference between the weight of the smallest and the weight of the largest Minimum Winning Coalition. We claim that such a set of weights provides an a priori measure of a weighted voter’s bribeworthiness or market value. After introducing our model, we provide a characterization result for this model and show its links to other bargaining model approaches in the literature. Then we offer some limit results showing that, with certain reasonable conditions on the distributions of weights, as the size of the voting body increases, the values of bribeworthiness we calculate will approach both the weights themselves and the Banzhaf scores for the weighted voting game. We also show that, even for relatively small groups using weighted voting, such as the membership of the European Council of Ministers (and its predecessors) 1958–2003, similarities among the usual a priori power scores, bribeworthiness/market value, and the weights themselves, will be quite strong.     

NSD序列加权和的中心极限定理及其在EV回归模型中的应用

基于负超可加相依(简称为NSD)随机序列的性质及其一些不等式,利用随机变量的截断方法建立了NSD随机序列加权和的中心极限定理,从而推广了负相协NA随机序列的相应结论.并将其应用到变系数EV回归模型,得到了未知参数LS估计的渐近正态性.     

QML-Morven: A novel framework for learning qualitative differential equation models using both symbolic and evolutionary approaches

In this paper, a novel qualitative differential equation model learning (QML) framework named QML-Morven is presented. QML-Morven employs both symbolic and evolutionary approaches as its learning strategies to deal with models of different complexity. Based on this framework, a series of experiments were designed and carried out to: (1) investigate factors that influence the learning precision and minimum data requirement for successful learning; (2) address the scalability issue of QML systems.