We consider Benjamini-Schramm limits of Rauzy Graphs of low-complexity words. Low-complexity words are infinite words (over a finite alphabet), for which the number of subwords of length n is bounded by some Kn --- examples of such a word include the Thue-Morse word 01101001... and the Fibonacci word. Rauzy graphs Rn (omega) have the length n subwords of omega as vertices, and the oriented edges between vertices indicate that two words appear immediately adjacent to each other in omega (with overlap); the edges are also equipped with labels, which indicate what "new letter" was appended to the end of the terminal vertex of an edge. In a natural way, the labels of consecutive edges in a Rauzy graph encode subwords of omega. The Benjamini-Schramm limit of a sequence of graphs is a distribution on (possibly infinite) rooted graphs governed by the convergence in distribution of random neighborhoods of the sequence of finite graphs. In the case of Rauzy graphs without edge-labelings, we establish that the Rauzy graphs of aperiodic low-complexity words converge to the line graph in the Benjamini-Schramm sense. In the same case, but for edge-labelled Rauzy graphs, we also prove that that the limit exists when the frequencies of all subwords in the infinite word, omega, are well defined (when the subshift of omega is uniquely ergodic), and we show that the limit can be identified with the unique ergodic measure associated to the subshift generated by the word. The eventually periodic (i.e. finite) cases are also shown. Finally, we show that for non-uniquely ergodic systems, the Benjamini-Schramm limit need not exist ---though it can in some instances--- and we provide examples to demonstrate the variety of possible behaviors.

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This study explores how governments use knowledge to inform telecommunications policy-making and policy-implementation in regional development. It focuses on epistemological aspects and assumptions made within the parameters of Enlightenment thinking or the Newtonian paradigm, also known as the classical scientit1c paradigm. It argues that lmowledge formed within this paradigm, usually generated at a distance, has been individ,uated, detached, segmented and abstracted. 'Individuation' focuses on individuals and things rather than communities and processes. 'Detachment' separates the subjective mind from the objective environment to produce reliable information. 'Segmentation' produces validity of information by parsing the objective environment from its social and historical context. 'Abstraction' allows objectivity and systematisation of information. When used to inform policy, such knowledge creates a narrow 'standardising gaze' that 'disciplines' communities to conform to dominant social behaviour and beliefs. Case studies are used to demonstrate that the two major models of development, as products ofthis paradigm, employ this gaze rendering replicability difficult ifnot impossible. These models are the top-down and bottom-up approach that are epitomised by the Silicon Valley model and telecentre moveluent respectively. How this gaze inhibits/facilitates development in policy implementation is then examined in the Goldfields Esperance region in Western Australia. An holistic approach using cotnplex adaptive systems is used to understand the multidisciplinary aspects involved in development. This is combined with action research, a reflexive methodology. Action research has the ability to access local knowledge to provide data and evaluation in situ rather than on a post hoc basis. The findings demonstrate that complex systems analysis and action research provide a modus operandi that: a) recognises the interplay of various factors (such as power relations, economic cycle, social and political institutions) at different levels of the system; b) recognises time, context and path-dependence of regional development; c) provides a filter that minimises the 'standardising gaze' and d) gives an access to knowledge and insight to local issues, which can facilitate policy implementation of development that is sympathetic to regional communities.

During the 1990s a large-scale study of Port Phillip Bay, Australia, was undertaken by the CSIRO (the Commonwealth Scientific and Industrial Research Organisation, Australia's national research body). A major outcome of the study was a complex ecosystem model intended to provide scientific input into management decisions concerning the nutrient load to the bay. However, its development was costly and time-consuming. Given this effort, it is natural to seek smaller models (reduced models) that reproduce the performance measures of the large model (the full model) that are of interest to decision makers. This thesis is concerned with identifying such models. More generally, this thesis is concerned with developing methods for identifying these smaller models. Several methods are developed for this purpose, each simplifying the full model in different ways. In particular, methods are proposed for aggregating state variables, setting state variables to constants, simplifying links in the ecological network, and eliminating rates from the full model. Moreover, the methods can be implemented automatically, so that they are transferable to other ecological modelling situations, and so that the reduced models are obtained objectively. In the case of the Port Phillip Bay model, significant reduction in model complexity is possible even when estimates of all the performance measures are of interest. Thus, this model is unnecessarily complex. Furthermore, the most significant reductions in complexity occur when the methods are combined. With this in mind, a procedure for combining the methods is proposed that can be implemented for any ecological model with a large number of components. Aside from generating reduced models, the process of applying the methods reveals insights into the mechanisms built into the system. Such insights highlight the extent to which the model simplification process can be applied. Given the effectiveness of the model simplification process developed here, it is concluded that this process should be more routinely applied to large ecosystem models. In some cases, the full sequence of methods might prove too computationally expensive to justify its purpose. However, it is shown that even the application of a subset of the methods can yield both simpler models and insight into the structure and behaviour of the system being modelled.

In recent years, new and powerful research into "condition numbers" for convex optimization has been developed, aimed at capturing the intuitive notion of problem behavior. This research has been shown to be important in studying the efficiency of algorithms, including interior-point algorithms, for convex optimization as well as other behavioral characteristics of these problems such as problem geometry, deformation under data perturbation, etc. This paper studies measures of conditioning for a conic linear system of the form (FPd): Ax = b, x E Cx, whose data is d = (A, b). We present a new measure of conditioning, denoted pd, and we show implications of lid for problem geometry and algorithm complexity, and demonstrate that the value of = id is independent of the specific data representation of (FPd). We then prove certain relations among a variety of condition measures for (FPd), including ld, pad, Xd, and C(d). We discuss some drawbacks of using the condition number C(d) as the sole measure of conditioning of a conic linear system, and we then introduce the notion of a "pre-conditioner" for (FPd) which results in an equivalent formulation (FPj) of (FPd) with a better condition number C(d). We characterize the best such pre-conditioner and provide an algorithm for constructing an equivalent data instance d whose condition number C(d) is within a known factor of the best possible.

We consider the optimization problem of safety stock placement in a supply chain, as formulated in [1]. We prove that this problem is NP-Hard for supply chains modeled as general acyclic networks. Thus, we do not expect to find a polynomial-time algorithm for safety stock placement for a general-network supply chain. / Singapore-MIT Alliance (SMA)

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Given a limited number of samples for classification, several issues arise with respect to design, performance and analysis of classifiers. This is especially so in the case of microarray-based classification. In this paper, we use a complexity measure based mixture model to study classifier performance for small sample problems. The motivation behind such a study is to determine the conditions under which a certain class of classifiers is suitable for classification, subject to the constraint of a limited number of samples being available. Classifier study in terms of the VC dimension of a learning machine is also discussed.

Major Depressive Disorder (MDD) is exceedingly prevalent and considered to be one of the leading cause of disability worldwide. Depression is also a heterogeneous disorder characterized by complex diagnotic approaches with a lack of diagnostic biomarker, an inconsistent response to treatment, no established mechanism, and affecting multiple physiological systems such as endocrine, immunological and cardiovasular as well. The growing impact of the analysis of complex signals on biology and medicine is fundamentally changing our view of living organisms, physiological systems, and disease processes. In this endeavour, the basic challenge is to reveal how the coordinated, dynamical behavior of cells and tissues at the macroscopic level, emerges from the vast number of random molecular interactions at the microscopic level. In this way, the fundamental questions could be: (i) how physiological systems function as a whole, (ii) how they transduce and process dynamical information, (iii) how they respond to external stimuli, and mostly (iv), how they change during a pathological processus. These challenges are of interest from a number of perspectives including basic modeling of physiology and practical bedside approaches to medical and risk stratification. The general purpose of this thesis, therefore, is to study physiological time series to provide a new understanding of sleep dynamics in health, specifically as they apply to the pathological condition of MDD. More precisely: (1) to quantitatively characterize the complex, nonlinear behaviour of cardiovascular (ECG) and electroencephalographic (EEG) time series during sleep, in health and in MDD. This project will test the hypotheses that both the sleep EEG and ECG detects reorganization in the system dynamics in patient suffering from depression. (2) To develop new diagnostic and prognostic tests for MDD, by detecting and extracting “hidden information” in the ECG and EEG datasets. Three different methods are introduced in this thesis for the analysis of dynamical systems. The first one, detrended fluctuation analysis, can reveal the presence of long-term correlations ("memory" in the physiological system) even when embedded in non-stationary time series. Graph theoretical measures were then applied to test whether disrupting an optimal pattern ["small-world network"] of functional brain connectivity underlies depression. Finally, multiscale entropy method, which is aimed at quantifying the complexity of the systems' output resulting from the presence of irregular structures on multiple scales, was applied on the ECG signal. The results indicate that healthy physiologic systems, measured through the EEG and the ECG signals, are the most complex. According to the decomplexification theory, the depressive disease model exhibits a loss of system complexity, with potential important applications in the development and testing of basic physiologic models, of new diagnostic and prognostic tools in psychiatry, and of clinical risk stratification.

Since the 1950s, inquiry has been considered an effective strategy to promote students’ science learning. However, the use of inquiry in contemporary science classrooms is minimal, despite its long history and wide recognition elsewhere. Besides, inquiry is commonly confused with discovery learning, which needs minimal level of teacher supervision. The lack of thorough description of how inquiry works in diverse classroom settings is known to be a critical problem. To analyze the complex and dynamic nature of inquiry practices, a comprehensive tool is needed to capture its essence. In this dissertation, I studied inquiry lessons conducted by one high school science teacher of 9th grade students. The inquiry sequence lasted for 10 weeks. Using the Scientific Practices Analysis (SPA)-map and the Mathematics and Science Classroom Observation Profile System (M-SCOPS), elements of inquiry were analyzed from multiple perspectives. The SPA-map analysis, developed as a part of this dissertation, revealed the types of scientific practices in which students were involved. The results from the M-SCOPS provide thorough descriptions of complex inquiry lessons in terms of their content, flow, instructional scaffolding and representational scaffolding. In addition to the detailed descriptions of daily inquiry practices occurring in a dynamic classroom environment, the flow of the lessons in a sequence was analyzed with particular focus on students’ participation in scientific practices. The findings revealed the overall increase of student-directed instructional scaffolding within the inquiry sequence, while no particular pattern was found in representational scaffolding. Depending on the level of cognitive complexity imposed on students, the lessons showed different association patterns between the level of scaffolding and scientific practices. The findings imply that teachers need to provide scaffolding in alignment with learning goals to achieve students’ scientific proficiency.