<p> Three existing techniques are selected as the most promising methods of system reduction. These methods are analysed and then applied to a realistic high order system. A second order model of the actual system is derived using each of the reduction techniques. The step response of the actual system and each of the models is obtained for comparison purposes. The reduction methods are compared with a view to application, limitations and accuracy. A new method for system reduction is also proposed which fashions a low order model after the response characteristics of the actual system. </p> / Thesis / Master of Engineering (MEngr)

In Stockholm, an empty station echoes the sounds of passing trains. Built in 1977 but unused since. Imagine this station transformed into a wonderland, where the absence of a surrounding locality becomes an asset. Envision a performance center where the daily rhythm of train arrivals and departures is integrated into performance art. Stepping off the train, visitors enter an interactive realm, breaking the barriers between audience and performer, observer and participant. This transformation aims to challenge the status quo, encouraging visitors to shape their own narratives rather than passively consuming culture. The design consists of three interwoven levels. The platform where one arrives where a curtain system has been designed. Allowing fordifferent temporary rooms to be coordinated following an overall geometry. The upper ground consists of a landscape design where topography curves have been used tocreate different types of scenes. Allowing for multiple interpretations, movements andhappenings in the inbetween. The third level are studios where either the artists can seek refuge, use it as backstage ordevelop their art, or as a room for performances to happen as well where the public is invited.

<p>Infectious diseases spreading in a human population can occasionally exhibit sudden transitions in their qualitative dynamics. Previous work has been very successful in predicting such transitions in New York City's measles incidence rates using the standard SIR model (susceptible, infected, recovered). This work relied on a dataset spanning 45 years, which we have extended to 93 years (1891-1984). We continue previous research in transition analysis on this larger dataset, and compare resonant and transient periods predicted to exist in NYC's measles incidence rates with those observed through a continuous wavelet transform of the data. We find good agreement between SIR predictions and observation, and in particular note the likely existence of previously unobserved hysteresis early in our new time-series.</p> / Master of Science (MSc)

<p>The aim of this thesis is to provide mathematical tools for an alternative to the mainstream study of macroeconomics with a focus on debt-driven dynamics.</p> <p>We start with a survey of the literature on formalizations of Minsky's Financial Instability Hypothesis in the context of stock-flow consistent models.</p> <p>We then study a family of macro-economical models that date back to the Goodwin model. In particular, we propose a stochastic extension where noise is introduced in the productivity. Besides proving existence and uniqueness of solutions, we show that orbits must loop around a specific point indefinitely.</p> <p>Subsequently, we analyze the Keen model, where private debt is introduced. We demonstrate that there are two key equilibrium points, intuitively denoted good and bad equilibria. Analytical stability analysis is followed by numerical study of the basin of attraction of the good equilibrium.</p> <p>Assuming low interest rate levels, we derive an approximate solution through perturbation techniques, which can be solved analytically. The zero order solution, in particular, is shown to converge to a limit cycle. The first order solution, on the other hand, is shown to explode, rendering its use dubious for long term assessments.</p> <p>Alternatively, we propose an extension of the Keen model that addresses the immediate completion time of investment projects. Using distributed time delays, we verify the existence of the key equilibrium points, good and bad, followed by their stability analysis. Through bifurcation theory, we verify the existence of limit cycles for certain mean completion times, which are absent in the original Keen model.</p> <p>Finally, we examine the Keen model under government intervention, where we introduce a general form for the government policy. Besides performing stability analysis, we prove several results concerning the persistence of both profits and employment. In economical terms, we demonstrate that when the government is responsive enough, total economic meltdowns are avoidable.</p> / Doctor of Philosophy (PhD)

The impetus for this study grew from observations in clinical practice that many individuals survived all sorts of hardships with minimal distress, or with the ability to tolerate their distress, and move on with their lives in a positive manner. A review of the literature led to the conclusions that the research investigating resilience was making minimal inroads into understanding what made these people different, and that the richness of who they were was being lost in the scientific process. This dissatisfaction led to the decision to explore the construct from a phenomenological framework, and to try and discover the essential elements of resilience through analysis of the subjective experience of resilience. A qualitative study involving thirteen participants identified by their peers as resilient was undertaken and the underlying themes of their stories were analysed. This led to the development of a model of resilience that attempted to balance the need for parsimony with that of explanatory breadth, and which had the potential to tolerate the complexity and instability of the construct itself. The model developed identified three core elements that embraced the construct of resilience. These included the physiological capacity to be resilient, and from this basis the ability to be adaptive and the ability to maintain well-being emerge. Factors identified with these elements include individual reactivity to and recovery from adverse events, the ability to be effective and efficient in the management of adverse events, and the beliefs about the world and the self that promote well-being when exposed to adverse events. The model has a basis within neurobiology and is framed within the context of Dynamic Systems Theory. The theory itself is a culmination of clinical observations with what is known from within the current literature and the results of this study.

A introdução de uma nova expressão matemática para a entropia permite construir novos ensembles na Teoria das Matrizes Aleatórias. Neste trabalho, apresenta-se uma estrutura geral para construção de todos os possíveis ensemble. Portanto, os elementos das matrizes podem ser números reais, complexos ou mesmo quaternions. O principio da entropia (não-extensiva) máxima e o Cálculo Variacional são usados para realizar essa façanha. Esta tese está comprometida com a construção do Ensemble Ortogonal Generalizado, cujas matrizes aleatórias são simétricas e seus elementos são os números reais, especificamente. As distribuições das matrizes, as distribuições de um elemento da matriz e as estatísticas espectrais são obtidas, estudadas e os resultados apresentados. / The introduction of a new mathematical expression for the entropy allows the construction of new ensembles in Random Matrices Theory. A general structure is presented to the construction of all possible ensembles. Therefore the matrix\'s elements can be real numbers, complex numbers or even quaternions. The generalized of the maximum entropy (nonextensive) principle and the variational calculus are to use to realize this achievement. This thesis concerned with the construction of the Generalized Orthogonal Ensemble, whose random matrices are symetric and its elements are real numbers. The matrix distribuit ion, the distribuition of an element of the matrix and the spectrum statistical were to obtained, studied and the results presented.

Executive function (EF) is a central aspect of cognition that undergoes significant changes in early childhood. Changes in EF in early childhood are robustly predictive of academic achievement and general quality of life measures later in adulthood. I develop a dynamic neural field (DNF) model which provides a process-based account of behavior and developmental change in a key task used to probe the early development of executive function--the Dimensional Change Card Sort (DCCS) task. In the DCCS, children must flexibly switch from sorting cards either by shape or color to sorting by the other dimension. Typically, 3-year-olds, but not 5-year-olds, lack the flexibility to do so and perseverate on the first set of rules when instructed to switch. In Study 1, I use the DNF model to integrate behavioral and neural processes by simulating hemodynamics associated with the early emergence of flexible rule-use. I then test predictions of the model using near-infrared spectroscopy. In Study 2, I develop a DCCS that can be used with adults that sheds light on key aspects of the task as they have been revealed with children. Using fMRI, a pattern of behavioral and neural effects shed light on the central processes involved in flexible rule-use. These two studies demonstrate that performance emerges as a property of system-wide interactions and that common neurocognitive effects .can be found between childhood and adulthood.

<p>Theories predicting performance of human control of complex dynamic systems must assess how decision makers capture and utilise knowledge for achieving and maintaining control. Traditional problem solving theories and corresponding measures such as Ravens matrices have been applied to predict performance in complex dynamic systems. While they assume stable properties of decision makers to predict control performance in decision-making tasks these tests have shown to provide only a limited degree of prediction in human control of complex dynamic systems. This paper reviews theoretical developments from recent empirical studies and tests the theoretical predictions of a model of dynamic decision-making using a complex dynamic microworld – Moro. The requirements for control of the microworld is analysed in study one. Theoretical predictions from the reviewed theory and results from study one are tested in study two. In study three additional hypotheses are derived by including meta cognitive dynamics to explain anomalies found in study two. A total of 21 Hypotheses are tested. Results indicate that for predicting human control of complex dynamic opaque systems a number of meta cognitive processes play an important role in determining outcome. Specifically, results show that we cannot expect a lower risk of failure in complex dynamic opaque systems from people with high problem solving capabilities when these also express higher goals. Further research should seek to explore the relative contribution of task characteristics to determine conditions under which these meta cognitive processes of decision makers take a dominant role over problem-solving capabilities – enabling improved decision-maker selection and support.</p> / Rapportkod: LiU-Tek-Lic-2002:4. I den tryckta versionen är bilagorna bifogade som CD-skiva. Den elektroniska versionen innehåller den kompletta avhandlingen.

This paper explores automating the qualitative analysis of physical systems. It describes a program, called PLR, that takes parameterized ordinary differential equations as input and produces a qualitative description of the solutions for all initial values. PLR approximates intractable nonlinear systems with piecewise linear ones, analyzes the approximations, and draws conclusions about the original systems. It chooses approximations that are accurate enough to reproduce the essential properties of their nonlinear prototypes, yet simple enough to be analyzed completely and efficiently. It derives additional properties, such as boundedness or periodicity, by theoretical methods. I demonstrate PLR on several common nonlinear systems and on published examples from mechanical engineering.

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