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.

Quantitative Information Flow, Relations and Polymorphic Types

This paper uses Shannon's information theory to give a quantitative definition of information flow in systems that transform inputs to outputs. For deterministic systems, the definition is shown to specialise to a simpler form when the information source and the known inputs jointly determine the inputs. For this special case, the definition is related to the classical security condition of non-interference and an equivalence is established between non-interference and independence of random variables. Quantitative information flow for deterministic systems is then presented in relational form. With this presentation, it is shown how relational parametricity can be used to derive upper and lower bounds on information flows through families of functions defined in the second order lambda calculus.

Flexible information acquisition and optimal Tobin tax in tractable dynamic global games

My dissertation focuses on dynamic aspects of coordination processes such as reversibility of early actions, option to delay decisions, and learning of the environment from the observation of other people’s actions. This study proposes the use of tractable dynamic global games where players privately and passively learn about their actions’ true payoffs and are able to adjust early investment decisions to the arrival of new information to investigate the consequences of the presence of liquidity shocks to the performance of a Tobin tax as a policy intended to foster coordination success (chapter 1), and the adequacy of the use of a Tobin tax in order to reduce an economy’s vulnerability to sudden stops (chapter 2). Then, it analyzes players’ incentive to acquire costly information in a sequential decision setting (chapter 3). In chapter 1, a continuum of foreign agents decide whether to enter or not in an investment project. A fraction λ of them are hit by liquidity restrictions in a second period and are forced to withdraw early investment or precluded from investing in the interim period, depending on the actions they chose in the first period. Players not affected by the liquidity shock are able to revise early decisions. Coordination success is increasing in the aggregate investment and decreasing in the aggregate volume of capital exit. Without liquidity shocks, aggregate investment is (in a pivotal contingency) invariant to frictions like a tax on short term capitals. In this case, a Tobin tax always increases success incidence. In the presence of liquidity shocks, this invariance result no longer holds in equilibrium. A Tobin tax becomes harmful to aggregate investment, which may reduces success incidence if the economy does not benefit enough from avoiding capital reversals. It is shown that the Tobin tax that maximizes the ex-ante probability of successfully coordinated investment is decreasing in the liquidity shock. Chapter 2 studies the effects of a Tobin tax in the same setting of the global game model proposed in chapter 1, with the exception that the liquidity shock is considered stochastic, i.e, there is also aggregate uncertainty about the extension of the liquidity restrictions. It identifies conditions under which, in the unique equilibrium of the model with low probability of liquidity shocks but large dry-ups, a Tobin tax is welfare improving, helping agents to coordinate on the good outcome. The model provides a rationale for a Tobin tax on economies that are prone to sudden stops. The optimal Tobin tax tends to be larger when capital reversals are more harmful and when the fraction of agents hit by liquidity shocks is smaller. Chapter 3 focuses on information acquisition in a sequential decision game with payoff complementar- ity and information externality. When information is cheap relatively to players’ incentive to coordinate actions, only the first player chooses to process information; the second player learns about the true payoff distribution from the observation of the first player’s decision and follows her action. Miscoordination requires that both players privately precess information, which tends to happen when it is expensive and the prior knowledge about the distribution of the payoffs has a large variance.

SysPRE: systematized process for requirements engineering in knowledge discovery projects

The domain of Knowledge Discovery (KD) and Data Mining (DM) is of growing importance in a time where more and more data is produced and knowledge is one of the most precious assets. Having explored both the existing underlying theory, the results of the ongoing research in academia and the industry practices in the domain of KD and DM, we have found that this is a domain that still lacks some systematization. We also found that this systematization exists to a greater degree in the Software Engineering and Requirements Engineering domains, probably due to being more mature areas. We believe that it is possible to improve and facilitate the participation of enterprise stakeholders in the requirements engineering for KD projects by systematizing requirements engineering process for such projects. This will, in turn, result in more projects that end successfully, that is, with satisfied stakeholders, including in terms of time and budget constraints. With this in mind and based on all information found in the state-of-the art, we propose SysPRE - Systematized Process for Requirements Engineering in KD projects. We begin by proposing an encompassing generic description of the KD process, where the main focus is on the Requirements Engineering activities. This description is then used as a base for the application of the Design and Engineering Methodology for Organizations (DEMO) so that we can specify a formal ontology for this process. The resulting SysPRE ontology can serve as a base that can be used not only to make enterprises become aware of their own KD process and requirements engineering process in the KD projects, but also to improve such processes in reality, namely in terms of success rate.

Local Field Potentials in the Gustatory Cortex Carry Taste Information

It has been recently shownthat localfield potentials (LFPs)fromthe auditory and visual cortices carry information about sensory stimuli, but whether this is a universal property of sensory cortices remains to be determined. Moreover, little is known about the temporal dynamics of sensory information contained in LFPs following stimulus onset. Here we investigated the time course of the amount of stimulus information in LFPs and spikes from the gustatory cortex of awake rats subjected to tastants and water delivery on the tongue. We found that the phase and amplitude of multiple LFP frequencies carry information about stimuli, which have specific time courses after stimulus delivery. The information carried by LFP phase and amplitude was independent within frequency bands, since the joint information exhibited neither synergy nor redundancy. Tastant information in LFPs was also independent and had a different time course from the information carried by spikes. These findings support the hypothesis that the brain uses different frequency channels to dynamically code for multiple features of a stimulus.

Using network connectance and autonomy analyses to uncover patterns of photosynthetic responses in tropical woody species

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)