Cybernetics is the science of effective organization, i.e. the science that describes the general principles of growth, learning and adaptation in complex, dynamical systems. Stafford Beer regards his viable system model as a design for effective formal organization. He also declares that since his model is explicitly based upon the principles of cybernetics, it facilitates consideration of what is and is not possible within formal organizations and provides guidance in creating efficient structures. The purpose of this research is to demonstrate and test Stafford Beer's ideas on the viable system model via the simulation of certain business activities. A methodology for getting access to the cybernetic body of knowledge is given as well as examples of cybernetic laws relevant to managerial and business practice. An important part of the work is devoted to the explanation and discussion of Stafford Beer's viable system model, and the importance it represents as a cybernetic method for the design of organizational structures. Simulation models incorporating the major activities of a business firm are represented and used as case studies to investigate how basic industrial organizations based on Beer's viable system model work under operational conditions.

The aim of this thesis is to seek a low-dimensional description of baroclinic instability in general, and of the Martian atmosphere in particular, where both forcing and spatial resonance are relevant to the dynamics of the system being analysed. The Proper Orthogonal Decomposition (POD) is used to determine a basis for the modal decomposition of climatic simulations of Mars, obtained by using two General Circulation Models (GCMs): (a) a simple GCM, which is an idealised model in which the meteorological primitive equations are solved on a sphere with simplified physical parameters and (b) the Martian GCM, a more realistic model in which a comprehensive range of the relevant Martian physical parameters and topography are represented. Results of these analyses are presented for a range of Martian seasons and climatic conditions. The effects of using different forms of energy norm in performing the analysis is considered, with the objective of providing analyses which represents the physically most significant components of the circulation, with optimal efficiency. Reduced low-dimensional models that replicated the full simple GCM streamfunction simulations are formulated by projecting the spherical quasi-geostrophic equations onto the PODs of the large-scale calculations. The resulting models are analysed by using a combination of solution continuation and numerical integration methods. A thorough analysis of the models reveals that a 6-D POD model is capable of reproducing the amplitude, frequency and behaviour of the leading oscillatory structures of the simple GCM, to within a 1% error. Such an excellent reproduction of the original system is shown to be due to (1) an accurate vertical formulation scheme, (2) the use of the correct norm, (3) a sufficiently high level of truncation and (4) the fact that the original system is a steady wave flow. The behaviour of the various regimes observed in the low-order models are comparable with observations from studies of large-scale waves and instabilities in planetary atmospheres, including a range of hydrodynamical experiments on baroclinic wave interactions of a stratified fluid in cylindrical containers.

We report progress made on an analytic investigation of low-frequency cardiorespiratory variability in humans. The work is based on an existing physiological model of chemically-mediated blood-gas control via the central and peripheral chemoreceptors, that of Grodins, Buell & Bart (1967). Scaling and simplification of the Grodins model yields a rich variety of dynamical subsets; the thesis focusses on the dynamics obtained under the normoxic assumption (i.e., when oxygen is decoupled from the system). In general, the method of asymptotic reduction yields submodels that validate or invalidate numerous (and more heuristic) extant efforts in the literature. Some of the physiologically-relevant behaviour obtained here has therefore been reported before, but a large number of features are reported for the first time. A particular novelty is the explicit demonstration of cardiorespiratory coupling via chemosensory control. The physiology and literature reviewed in Chapters 1 and 2 set the stage for the investigation. Chapter 3 scales and simplifies the Grodins model; Chapters 4, 5, 6 consider carbon dioxide dynamics at the central chemoreceptor. Chapter 7 begins analysis of the dynamics mediated by the peripheral receptor. Essentially all of the dynamical behaviour is due to the effect of time delays occurring within the conservation relations (which are ordinary differential equations). The pathophysiology highlighted by the analysis is considerable, and includes central nervous system disorders, heart failure, metabolic diseases, lung disorders, vascular pathologies, physiological changes during sleep, and ascent to high altitude. Chapter 8 concludes the thesis with a summary of achievements and directions for further work.

This thesis mainly concerns modeling, approximation and inference of gene regulatory dynamics on the basis of gene expression patterns. The dynamical behavior of gene expressions is represented by a system of ordinary dierential equations. We introduce a gene-interaction matrix with some nonlinear entries, in particular, quadratic polynomials of the expression levels to keep the system solvable. The model parameters are determined by using optimization. Then, we provide the time-discrete approximation of our time-continuous model. We analyze the approximating model under the aspect of stability. Finally, from the considered models we derive gene regulatory networks, discuss their qualitative features of the networks and provide a basis for analyzing networks with nonlinear connections.

The notion of a normal number and the Normal Number Theorem date back over 100 years. Émile Borel first stated his Normal Number Theorem in 1909. Despite their seemingly basic nature, normal numbers are still engaging many mathematicians to this day. In this paper, we provide a reinterpretation of the concept of a normal number. This leads to a new proof of Borel's classic Normal Number Theorem, and also a construction of a set that contains all absolutely normal numbers. We are also able to use the reinterpretation to apply the same definition for a normal number to any point in a symbolic dynamical system. We then provide a proof that the Fibonacci system has all of its points being normal, with respect to our new definition. / Graduation date: 2012

This thesis describes the comparison of time-lapse field observations of suncups on alpine snow with numerical simulations. The simulations consist of solutions to a nonlinear partial differential equation which exhibits spontaneous pattern formation from a low amplitude, random initial surface. Both the field observations and the numerical solutions are found to saturate at a characteristic height and fluctuate chaotically with time. The timescale of these fluctuations is found to be instrumental in determining the full set of parameters for the numerical model such that it mimics the nonlinear dynamics of suncups. These parameters in turn are related to the change in albedo of the snow surface caused by the presence of suncups. This suggests the more general importance of dynamical behaviour in gaining an understanding of pattern formation phenomena.

An important part of the study of dynamical systems is the fitting of models to time-series data. That is, given the data, a series of observations taken from a (not fully understood) system of interest, we would like to specify a model, a mathematical system which generates a sequence of “simulated” observations. Our aim is to obtain a “good” model — one that is in agreement with the data. We would like this agreement to be quantitative — not merely qualitative. The major subject of this thesis is the question of what good quantitative agreement means. Most approaches to this question could be described as “predictionist”. In the predictionist approach one builds models by attempting to answer the question, “given that the system is now here, where will it be next?” The quality of the model is judged by the degree to which the states of the model and the original system agree in the near future, conditioned on the present state of the model agreeing with that of the original system. Equivalently, the model is judged on its ability to make good short-term predictions on the original system. The main claim of this thesis is that prediction is often not the most appropriate criterion to apply when fitting models. We show, for example, that one can have models that, while able to make good predictions, have long term (or free-running) behaviour bearing little resemblance to that exhibited in the original time-series. We would hope to be able to use our models for a wide range of purposes other than just prediction — certainly we would like our models to exhibit good free-running behaviour. This thesis advocates a “behaviourist” approach, in which the criterion for a good model is that its long-term behaviour matches that exhibited by the data. We suggest that the behaviourist approach enjoys a certain robustness over the predictionist approaches. We show that good predictors can often be very poorly behaved, and suggest that well behaved models cannot perform too badly at the task of prediction. The thesis begins by comparing the predictionist and behaviourist approaches in the context of a number of simplified model-building problems. It then presents a simple theory for the understanding of the differences between the two approaches. Effective methods for the construction of well-behaved models are presented. Finally, these methods are applied to two real-world problems — modelling of the response of a voltage-clamped squid “giant” axon, and modelling of the “yearly sunspot number”.

Techn. Univ., Diss.--Hamburg-Harburg, 2002.

Thesis (Ph. D.)--Physics, Georgia Institute of Technology, 2005. / Jean Bellissard, Committee Member ; Turgay Uzer, Committee Member ; Roman Grigoriev, Committee Member ; Konstantin Mischaikow, Committee Member ; Predrag Cvitanovic, Committee Chair. Vita. Includes bibliographical references.

Thesis (Honors)--College of William and Mary, 2009. / Includes bibliographical references (leaves 56-57). Also available via the World Wide Web.