The Mathematics of Control Theory

This text contains papers presented at the Institute of Mathematics and its Applications Conference on Control Theory, held at the University of Strathclyde in Glasgow. The contributions cover a wide range of topics of current interest to theoreticians and practitioners including algebraic systems theory, nonlinear control systems, adaptive control, robustness issues, infinite dimensional systems, applications studies and connections to mathematical aspects of information theory and data-fusion.

Complexity theory and planning: examining 'fractals' for organising policy domains in planning practice

This article examines selected methodological insights that complexity theory might provide for planning. In particular, it focuses on the concept of fractals and, through this concept, how ways of organising policy domains across scales might have particular causal impacts. The aim of this article is therefore twofold: (a) to position complexity theory within social science through a ‘generalised discourse’, thereby orienting it to particular ontological and epistemological biases and (b) to reintroduce a comparatively new concept – fractals – from complexity theory in a way that is consistent with the ontological and epistemological biases argued for, and expand on the contribution that this might make to planning. Complexity theory is theoretically positioned as a neo-systems theory with reasons elaborated. Fractal systems from complexity theory are systems that exhibit self-similarity across scales. This concept (as previously introduced by the author in ‘Fractal spaces in planning and governance’) is further developed in this article to (a) illustrate the ontological and epistemological claims for complexity theory, and to (b) draw attention to ways of organising policy systems across scales to emphasise certain characteristics of the systems – certain distinctions. These distinctions when repeated across scales reinforce associated processes/values/end goals resulting in particular policy outcomes. Finally, empirical insights from two case studies in two different policy domains are presented and compared to illustrate the workings of fractals in planning practice.

Metaphors in complexity theory and planning

This article reviews the use of complexity theory in planning theory using the theory of metaphors for theory transfer and theory construction. The introduction to the article presents the author's positioning of planning theory. The first section thereafter provides a general background of the trajectory of development of complexity theory and discusses the rationale of using the theory of metaphors for evaluating the use of complexity theory in planning. The second section introduces the workings of metaphors in general and theory-constructing metaphors in particular, drawing out an understanding of how to proceed with an evaluative approach towards an analysis of the use of complexity theory in planning. The third section presents two case studies – reviews of two articles – to illustrate how the framework might be employed. It then discusses the implications of the evaluation for the question ‘can complexity theory contribute to planning?’ The concluding section discusses the employment of the ‘theory of metaphors’ for evaluating theory transfer and draws out normative suggestions for engaging in theory transfer using the metaphorical route.

Another Waltz? Methodological rhetoric and practice in theory of international politics

Although Theory of International Politics is a standard-bearer for explanatory theory in international relations (IR), Waltz’s methodology has been subject to numerous quite disparate analyses. One reason why it has proved hard to pin down is that too little attention has been paid to how, in practice, Waltz approaches real-world problems. Despite his neopositivist rhetoric, Waltz applies neorealism in a notably loose, even indeterminate, fashion. There is therefore a disjunction between what he says and what he does. This is partly explained by his unsatisfactory attempt to reconcile his avowed neopositivism with his belief that international politics is characterized by organized complexity. The inconsistencies thus created also help to make sense of why competing interpretations of his methodology have emerged. Some aspects of his work do point beyond these particular methodological travails in ways that will continue to be of interest to IR theorists, but its most enduring methodological lesson may be that rhetoric and practice do not necessarily fit harmoniously together.

Testing the expectations theory of the term structure in threshold models

We test the expectations theory of the term structure of U.S. interest rates in nonlinear systems. These models allow the response of the change in short rates to past values of the spread to depend upon the level of the spread. The nonlinear system is tested against a linear system, and the results of testing the expectations theory in both models are contrasted. We find that the results of tests of the implications of the expectations theory depend on the size and sign of the spread. The long maturity spread predicts future changes of the short rate only when it is high.

Service oriented approach to facility management using extended building information modelling

Facility management (FM), from a service oriented approach, addresses the functions and requirements of different services such as energy management, space planning and security service. Different service requires different information to meet the needs arising from the service. Object-based Building Information Modelling (BIM) is limited to support FM services; though this technology is able to generate 3D models that semantically represent facility’s information dynamically over the lifecycle of a building. This paper presents a semiotics-inspired framework to extend BIM from a service-oriented perspective. The extended BIM, which specifies FM services and required information, will be able to express building service information in the right format for the right purposes. The service oriented approach concerns pragmatic aspect of building’s information beyond semantic level. The pragmatics defines and provides context for utilisation of building’s information. Semiotics theory adopted in this paper is to address pragmatic issues of utilisation of BIM for FM services.

Culture-area relation in Axelrod`s model for culture dissemination

Axelrod`s model for culture dissemination offers a nontrivial answer to the question of why there is cultural diversity given that people`s beliefs have a tendency to become more similar to each other`s as they interact repeatedly. The answer depends on the two control parameters of the model, namely, the number F of cultural features that characterize each agent, and the number q of traits that each feature can take on, as well as on the size A of the territory or, equivalently, on the number of interacting agents. Here, we investigate the dependence of the number C of distinct coexisting cultures on the area A in Axelrod`s model, the culture-area relationship, through extensive Monte Carlo simulations. We find a non-monotonous culture-area relation, for which the number of cultures decreases when the area grows beyond a certain size, provided that q is smaller than a threshold value q (c) = q (c) (F) and F a parts per thousand yen 3. In the limit of infinite area, this threshold value signals the onset of a discontinuous transition between a globalized regime marked by a uniform culture (C = 1), and a completely polarized regime where all C = q (F) possible cultures coexist. Otherwise, the culture-area relation exhibits the typical behavior of the species-area relation, i.e., a monotonically increasing curve the slope of which is steep at first and steadily levels off at some maximum diversity value.

Package models and the information crisis of prebiotic evolution

The coexistence between different types of templates has been the choice solution to the information crisis of prebiotic evolution, triggered by the finding that a single RNA-like template cannot carry enough information to code for any useful replicase. In principle, confining d distinct templates of length L in a package or protocell, whose Survival depends on the coexistence of the templates it holds in, could resolve this crisis provided that d is made sufficiently large. Here we review the prototypical package model of Niesert et al. [1981. Origin of life between Scylla and Charybdis. J. Mol. Evol. 17, 348-353] which guarantees the greatest possible region of viability of the protocell population, and show that this model, and hence the entire package approach, does not resolve the information crisis. In particular, we show that the total information stored in a viable protocell (Ld) tends to a constant value that depends only on the spontaneous error rate per nucleotide of the template replication mechanism. As a result, an increase of d must be followed by a decrease of L, so that the net information gain is null. (C) 2008 Elsevier Ltd. All rights reserved.

A quasispecies approach to the evolution of sexual replication in unicellular organisms

This study develops a simplified model describing the evolutionary dynamics of a population composed of obligate sexually and asexually reproducing, unicellular organisms. The model assumes that the organisms have diploid genomes consisting of two chromosomes, and that the sexual organisms replicate by first dividing into haploid intermediates, which then combine with other haploids, followed by the normal mitotic division of the resulting diploid into two new daughter cells. We assume that the fitness landscape of the diploids is analogous to the single-fitness-peak approach often used in single-chromosome studies. That is, we assume a master chromosome that becomes defective with just one point mutation. The diploid fitness then depends on whether the genome has zero, one, or two copies of the master chromosome. We also assume that only pairs of haploids with a master chromosome are capable of combining so as to produce sexual diploid cells, and that this process is described by second-order kinetics. We find that, in a range of intermediate values of the replication fidelity, sexually reproducing cells can outcompete asexual ones, provided the initial abundance of sexual cells is above some threshold value. The range of values where sexual reproduction outcompetes asexual reproduction increases with decreasing replication rate and increasing population density. We critically evaluate a common approach, based on a group selection perspective, used to study the competition between populations and show its flaws in addressing the evolution of sex problem.

Analysis of cultural conflict in the development of web-enabled information systems

The advent of the World Wide Web (WWW) and the emergence of Internet commerce have given rise to the web as a medium of information exchange. In recent years, the phenomenon has affected the realm of transaction processing systems, as organizations are moving from designing web pages for marketing purposes, to web-based applications that support business-to-business (WEB) and business-to-consumer (B2C) interactions, integrated with databases and other back-end systems (Isakowitz, Bieber et al., 1998). Furthermore, web-enabled applications are increasingly being used to facilitate transactions even between various business units within a single enterprise. Examples of some of the more popular web-enabled applications in use today include airline reservation systems, internet banking, student enrollment systems in universities, and Human Resource (HR) and payroll systems. The prime motive behind the adoption of web-enabled applications are productivity gains due to reduced processing time, decrease in the usage of paper-based documentation and conventional modes of communication (such as letters, fax, or telephone), and improved quality of services to clients. Indeed, web-based solutions are commonly referred to as customer-centric (Li, 2000), which means that they provide user interfaces that do not necessitate high level of computer proficiency. Thus, organizations implement such systems to streamline routine transactions and gain strategic benefits in the process (Nambisan & Wang, 1999), though the latter are to be expected in the long-term. Notwithstanding the benefits of web technology adoption, the web has ample share of challenges for initiators and developers. Many of these challenges are associated with the unique nature of web-enabled applications. Research in the area of web-enabled information systems has revealed several differences with traditional applications. These differences exist with regards to system development methodology, stakeholder involvement, tasks, and technology (Nazareth, 1998). According to Fraternali (1999), web applications are commonly developed using an evolutionary prototyping approach, whereby the simplified version of the application is deployed as a pilot first, in order to gather user feedback. Thus, web-enabled applications typically undergo continuous refinement and evolution (Ginige, 1998; Nazareth, 1998; Siau, 1998; Standing, 2001). Prototype-based development also leads web-enabled information systems to have much shorter development life cycles, but which, unlike traditional applications, are regrettably developed in a rather adhoc fashion (Carstensen & Vogelsang, 2001). However, the principal difference between the two kinds of applications lies in the broad and diverse group of stakeholders associated with web-based information systems (Gordijn, Akkermans, et al., 2000; Russo, 2000; Earl & Khan, 2001; Carter, 2002; Hasselbring, 2002; Standing, 2002; Stevens & Timbrell, 2002). Stakeholders, or organizational members participating in a common business process (Freeman, 1984), vary in their computer competency, business knowledge, language and culture. This diversity is capable of causing conflict between different stakeholder groups with regards to the establishment of system requirements (Pouloudi & Whitley, 1997; Stevens & Timbrell, 2002). Since, web-based systems transcend organizational, departmental, and even national boundaries, the issue of culture poses a significant challenge to the web systems’ initiators and developers (Miles & Snow, 1992; Kumar & van Dissel, 1996; Pouloudi & Whitley, 1996; Li & Williams, 1999).