A framework for ex ante project risk assessment based on absorptive capacity

This paper explores the applicability of the concepts of absorptive capacity and “ba” to ex ante project risk. We develop a hybrid framework to explain knowledge transfer based on these concepts—one that proposes a hybrid transference process. We then apply this framework to develop a methodology and metric for assessing ex ante software project risk, the risk that a new technology introduced into an organization may not be used as designed or may not achieve the anticipated benefits. As a preliminary validation of these concepts, we describe three case studies, employing the framework and metric to show how examining absorptive capacity can help to assess the risk level of software projects.     

Developing a theory of mathematical growth

In this paper I formulate a basic theoretical framework for the ways in which mathematical thinking grows as the child develops and matures into an adult. There is an essential need to focus on important phenomena, to name them and reflect on them to build rich concepts that are both powerful in use and yet simple to connect to other concepts. The child begins with human perception and action, linking them together in a coherent way. Symbols are introduced to denote mathematical processes (such as addition) that can be compressed as mathematical concepts (such as sum) to give symbols that operate flexibly as process and concept (procept). Knowledge becomes more sophisticated through building on experiences met before, focussing on relationships between properties, leading eventually to the advanced mathematics of concept definition and deduction. This gives a theoretical framework in which three modes of operation develop and grow in sophistication from conceptual-embodiment using thought experiments, to proceptual-symbolism using computation and symbol manipulation, then on to axiomatic-formalism based on concept definitions and formal proof.     

Dynamic consistency in incomplete information games under ambiguity

We develop a general framework of incomplete information games under ambiguity which extends the traditional framework of Bayesian games to the context of Ellsberg-type ambiguity. We then propose new solution concepts called ex ante and interim Γ-maximin equilibrium for solving such games. We show that, unlike the standard notion of Bayesian Nash equilibrium, these concepts may lead to rather different recommendations for the same game under ambiguity. This phenomenon is often referred to as dynamic inconsistency. Moreover, we characterize the sufficient condition under which dynamic consistency is assured in this generalized framework.     

Transaction independence: The road to cooperative systems

The cooperation and consistency among transactions in cooperative systems suggest that traditional transaction processing paradigms need to be modified for target applications. We propose a new framework that borrows its concepts from the evolution of database management systems. Transaction Independence and Incorporation of Workflow ideas within applications are the foundations of this framework. Cooperation is gained by TCMS, an external, domain-independent framework. This paper outlines the requirements, approach, architecture, and the implementation of TCMS.     

Chords in a circle and linear algebra over GF(2)

A common framework for the two concepts of the title is developed to yield an alternative proof to a theorem of Cohn and Lempel relating the number of orbits of a product of a full cycle by disjoint transpositions to the rank over GF(2) of the associated chord-intersection-matrix.     

Developing a platform for comparison of hospital admission systems: An illustration

There is an increasing need to develop a platform for comparing hospital admission planning systems due to a shift in the service paradigm in the health sector. The current service concept of hospital admission planning aims at optimising the use of scarce hospital resources without paying much attention to the level of service offered to patients. As patients nowadays do not accept long waiting times for hospital admission, it becomes necessary to consider alternative admission service concepts. Waiting lists have also become a political issue, and alternative concepts have been advocated such as giving all patients an appointment for admission. A simulation model was built to examine the impacts of extreme admission service concepts in a simplified hospital setting. The alternative concepts considered are based on the ‘zero waiting time’ principle (immediate treatment), and the ‘booked admissions’ principle (using an appointment for admission). The results of these admission service concepts are compared with the results of the current concept, based on the ‘maximising resource use’ principle. The paper deals with the development of a framework and tool that allows evaluating different, somehow conflicting, hospital admission planning concepts and the usefulness of such framework and tool for more refined/real-life approaches to hospital admission planning.     

Critical heuristics of social systems design

Health care planning, city and regional planning, energy and transportation planning, environmental design and other areas of social systems design are becoming issues of increasing concern to policy makers. Faced with complex steering problems that may have far-reaching societal implications, they except help from applied disciplines such as Operational Research, systems science, technology assessment, program evaluation, cost-effectiveness analysis, and similar approaches to scientifically informed planning. But these approaches offer little help in critically reflecting on the normative implications of the problem definitions and solution proposals they inspire.Critical Heuristics seeks to provide both the involved planners and affected citizens with a conceptual framework for identifying and discussing the normative implications of problem definitions, systems designs, program evaluations, etc. The paper introduces some key concepts of Critical Heuristics and briefly discusses their significance to ‘rational’ planning.     

A DSS design framework for competitive strategy formulation

This paper discusses the design framework that is actually being used in a large corporation for building a special purpose decision support system for competitive strategy formulation. The main features of the design framework employed are its ability to provide (i) support for decision-making through management science/operations research, (ii) decision-making support to managers of different levels and functions, (iii) methods to evaluate the performances of managers of different levels as well as that of the firm, (iv) to integrate a variety of decision-making models into a competitive strategy formulation model, and (v) to increase the effectiveness through an evolutionary and participatory development process.     

A DNR perspective on mathematics curriculum and instruction. Part II: with reference to teacher’s knowledge base

Two questions are on the mind of many mathematics educators; namely: What is the mathematics that we should teach in school? and how should we teach it? This is the second in a series of two papers addressing these fundamental questions. The first paper (Harel, 2008a) focuses on the first question and this paper on the second. Collectively, the two papers articulate a pedagogical stance oriented within a theoretical framework called DNR-based instruction in mathematics. The relation of this paper to the topic of this Special Issue is that it defines the concept of teacher’s knowledge base and illustrates with authentic teaching episodes an approach to its development with mathematics teachers. This approach is entailed from DNR’s premises, concepts, and instructional principles, which are also discussed in this paper.     

The interactive constitution of mathematical meaning in one second grade classroom: an illustrative example

The manner in which a horizontal addition and subtraction number sentence activity was constituted in one second grade classroom is analyzed for the purpose of discussing and illustrating how mathematical meaning is interactively constituted in the classroom. In particular, the teacher's emphasis on different solutions contributed to students' development of increasingly sophisticated concepts of ten. In turn, students' solutions contributed to the teacher's development of an increasingly sophisticated understanding of the children's mathematical activity and their concepts of ten.     

Taking a strategic view of BPR to develop a multidisciplinary framework

Despite undoubtedly being one of the latest fads, Business Process Reengineering (BPR) has provoked much debate about how organisations should be managed if dramatic improvements in performance are to be achieved. This paper takes a multidisciplinary view of BPR and focuses upon a number of the emergent issues. These include the role of strategy making, the promotion of communication and creativity, the role of statistics, and the effective use of performance measurement systems within a learning environment. The paper develops a framework that capitalises on the role of modelling in MS/OR as well as the various disciplines of the authors. As such, the framework draws on recent advances, as well as established thinking, in the areas of strategy development, information systems, quality management and statistical science. More importantly, the framework also provides an iterative approach to BPR enabling organisations to design, implement and monitor progress on an ongoing basis. Emphasis is placed on building effective communications, developing an organisational memory and supporting organisational learning.     

A reconsideration of Legendre-Jacobi symbols

The classical definition of the Jacobi symbol (a:b) was badly conceived for negative values of b. Alternative useful definitions of (a:?1) are proposed here. This is an elaboration of a point in the article “Spinor genera of binary quadratic forms” in this issue.     

Statistical inference in non-nested econometric models

The purpose of this paper is to discuss some procedures that are available for testing non-nested (or separate) hypotheses in the statistics and econometrics literature. Since many of these techniques may also be exploited in other disciplines, it is hoped that an elaboration of the principal theoretical findings may make them more readily accessible to researchers in other disciplines. Several simple examples are used to illustrate the concepts of nested and non-nested hypotheses and, within the latter category, “global” and “partial” non-nested hypotheses. Two alternative methods of testing non-nested hypotheses are discussed and contrasted: the first of these is Cox's modification of the likelihood-ratio statistic, and the second is Atkinson's comprehensive model approach. A major emphasis is placed on the role of the Cox principle of hypothesis testing, which enables a broad range of hypotheses to be tested within the same framework. The problem associated with the application of the comprehensive model approach to composite non-nested hypotheses is also highlighted; Roy's union-intersection principle is presented as a viable method of dealing with this problem. Simulation results concerning the finite-sample properties of various tests are discussed, together with an analysis of some attempts to correct the poor size of the Cox and related tests.     

A definition of spectrum for differential equations on finite time

Hyperbolicity of an autonomous rest point is characterised by its linearization not having eigenvalues on the imaginary axis. More generally, hyperbolicity of any solution which exists for all times can be defined by means of Lyapunov exponents or exponential dichotomies. We go one step further and introduce a meaningful notion of hyperbolicity for linear systems which are defined for finite time only, i.e. on a compact time interval. Hyperbolicity now describes the transient dynamics on that interval. In this framework, we provide a definition of finite-time spectrum, study its relations with classical concepts, and prove an analogue of the Sacker-Sell spectral theorem: For a d-dimensional system the spectrum is non-empty and consists of at most d disjoint (and often compact) intervals. An example illustrates that the corresponding spectral manifolds may not be unique, which in turn leads to several challenging questions.     

Density Based Problem Space Search for the Capacitated Clustering p-Median Problem

In the Capacitated Clustering Problem (CCP), a given set of n weighted points is to be partitioned into p clusters such that, the total weight of the points in each cluster does not exceed a given cluster capacity. The objective is to find a set of p centers that minimises total scatter of points allocated to them. In this paper a new constructive method, a general framework to improve the performance of greedy constructive heuristics, and a problem space search procedure for the CCP are proposed. The constructive heuristic finds patterns of natural subgrouping in the input data using concept of density of points. Elements of adaptive computation and periodic construction–deconstruction concepts are implemented within the constructive heuristic to develop a general framework for building efficient heuristics. The problem-space search procedure is based on perturbations of input data for which a controlled perturbation strategy, intensification and diversification strategies are developed. The implemented algorithms are compared with existing methods on a standard set of bench-marks and on new sets of large-sized instances. The results illustrate the strengths of our algorithms in terms of solution quality and computational efficiency.     

Markov Chains on Graded Posets

We consider two types of discrete-time Markov chains where the state space is a graded poset and the transitions are taken along the covering relations in the poset. The first type of Markov chain goes only in one direction, either up or down in the poset (an up chain or down chain). The second type toggles between two adjacent rank levels (an up-and-down chain). We introduce two compatibility concepts between the up-directed transition probabilities (an up rule) and the down-directed (a down rule), and we relate these to compatibility between up-and-down chains. This framework is used to prove a conjecture about a limit shape for a process on Young’s lattice. Finally, we settle the questions whether the reverse of an up chain is a down chain for some down rule and whether there exists an up or down chain at all if the rank function is not bounded.