From the Introduction, p. 1. During the past decade, the theory of twistors has been introduced and developed, primarily by Professor Roger Penrose, as part of a long-term program aimed at resolving certain difficulties in present-day physical theory. These difficulties include, firstly, the problem of combining quantum mechanics and general relativity, and, secondly, the question of whether the concept of a continuum is at all relevant to physics. Most models of space-time used in general relativity employ the idea of a manifold consisting of a continuum of points. This feature of the models has often been criticised, on the grounds that physical observations are essentially discrete in nature; for reasons that are mathematical, rather than physical, the gaps between these observations are filled in a continuous fashion (see, for example, Schrodinger (I), pp.26-31). Although analysis (in its generally accepted form) demands that quantities should take on a continuous range of values, physics, as such,does not make such a demand. The situation in quantum mechanics is not all that much better since, although some quantities such as angular momentum can only take on certain discrete values, one still has to deal with the complex continuum of probability amplitudes. From this point of view it would be desirable to have all physical laws expressed in terms of combinatorial mathematics, rather than in terms of (standard) analysis.

The purpose of this thesis is to compare a different conception of time in Kant's and Bergson's work and demonstrate the role of their conceptions within their philosophical projects. Time in Kant's work is both a pure a priori intuition represented as an infinite multitude of a priori successive moments and a form in which an empirical manifold appears. Manifold of pure intuition of time is united by an act of understanding and its objective unity makes synthetic a priori knowledge possible. Bergson, on the other hand, stood up against the idea of infinite divisibility of a time line. Homogenous time of mathematics considers only atemporal moments and it cannot conceive a temporal interval having time duration between two points. A pure duration therefore has to be a heterogeneous development of specific time matter, not a homogenous form in which empirical matter is quantitatively ordered as if it were without change and as an external part of change. Unity of time is therefore not quantitative but qualitative. Heterogeneous development is also on many levels permeated with homogeneity. This idea, at first sight contradictory, has to be explained by Bergson without retreating to the concept of homogenous time. Powered by TCPDF (www.tcpdf.org)

The aim of this thesis is to investigate of bootstrap methods (Efron, 1979), in the the performance estimation of parameter estimates in non-linear time series models, in particular SETAR models (Tong, 1993). First and higher order SETAR models in known and unknown thresholds cases are considered. To assess the performance of bootstrap methods, we first give an extensive simulation study (by using simulated normal errors), in chapters 3 and 4, to investigate large and small sample behaviours of the true sampling distributions of parameter estimates of SETAR models and how they are affected by sample size. First and higher order SETAR models in the known and unknown threshold cases are considered. An introduction to the bootstrap methods (Efron, 1979 ) is given in chapter 5. The effect of sample size on the bootstrap distributions of parameter estimates of first and higher order SETAR models in the known and unknown threshold cases ( for given order, delay and number of thresholds ) are also investigated in this chapter, via simulation and by using the same models used in the simulated normal errors 'true distribution' case ( chapters 3 & 4). The results are compared with simulated normal case in order to assess the bootstrap results. Tong and Lim (1980) method is used for fitting SETAR models to bootstrap samples, which is also used in the initial fit. Moreover, applications of bootstrap to celebrated data sets, namely, the logarithmically transformed lynx data covering the period (182-1934); and the sunspot numbers covering the period (1700- 1920), are attempted. The cyclical behaviours of bootstrap models are also examined. Finally, in chapter 5, an attempt is also made to study the problem of non-linear properties of the skeleton of a non-linear autoregressive process (Jones, 1976) via simulation and we study in particular a limit cycle behaviour.

M.Com. (Industrial Psychology) / The twentieth century is marked by fast developing communities which are currently moving into a new era of social, political, economic and cultural change. These developments include, among other, increased economic activities, over-population and an international tendency towards political conflict. In the South African environment these factors, together with the socio-economic structure and heterogeneous racial composition place an ever increasing demand on the occupational and organisational environment...

No abstract available. / Dissertation (MSc (Mathematical Statistics))--University of Pretoria, 2007. / Mathematics and Applied Mathematics / unrestricted

The purpose of the study was to establish a new place order in the transport grain for taxis through a design that will suit the urban context. It attempts to render taxis and their associated facilities preferable and acceptable for the city user and bystander. The relationship between time and movement was studied to generate a design concept that depicts the path of the user as an experience of comfort and convenience. A quantitative and qualitative method was applied. The study examined current taxi ranks through case studies, site visits, interviews and discussions. This information was interpreted within an urban scope. The process of elimination defined the urban taxi facility. Certain requirements gained prominence to achieve the aim of a sustainable multi-functional facility with the user as primary focus. The main conclusion was that architects have a responsibility towards the environment, and should design spaces that display a relationship between human and nature thereby creating a new typology for taxi facilities. / Dissertation (MArch(Prof))--University of Pretoria, 2010. / Architecture / unrestricted

A performance evaluation of CSTC (Cooperative Space Time Coding) with spatially cor-related fading and imperfect channel estimation in Gaussian as well as impulsive noise is presented. Closed form expressions for the pairwise error probability conditioned on the estimated channel gains are derived by assuming the components of the received vector are independent given the estimated channel gains. An expurgated union bound using the limiting before averaging technique given the estimated channel gains is then obtained. Although this assumption is not strictly valid, simulation results show that the bound is accurate in estimating the diversity order as long the channel estimation is not very poor. It is found that CSTC with block fading channels can reduce the frame error rate (FER) relative to SUSTC (Single User Space Time Coding) with quasi-static fading channels, even when the channel gains for each user are strongly correlated and when the channel estimations are very poor. A decision metric for CSTC with spatially correlated fading, imperfect channel estimation, and impulsive mixture Gaussian noise is derived which yields lower FERs than the Gaussian noise decision metric. Simulation results show that the FER performance of CSTC with mixture Gaussian noise outperforms CSTC with Gaussian noise at low SNR. At high SNR, the FER performance of CSTC with Gaussian noise is better than the FER performance of CSTC with mixture Gaussian noise due to the heavy tail of the mixture Gaussian noise. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

Causal analysis is a significant role-playing field in the applied sciences such as statistics, econometrics, and technometrics. Particularly, probability-raising models have warranted significant research interest. Most of the discussions in this area are philosophical in nature. Contemporarily, the econometric causality theory, developed by C.J.W. Granger, is popular in practical, time series causal applications. While this type of causality technique has many strong features, it has serious limitations. The processes studied, in particular, should be stationary and causal relationships are restricted to be linear. However, we cannot classify regime-switching processes as linear and stationary. I.J. Good proposed a probabilistic, event-type explication of causality that circumvents some of the limitations of Granger’s methodology. This work uses the probability raising causality ideology, as postulated by Good, to propose some causal analysis methodology applicable in a stochastic, non-stationary domain. There is a proposal made for a Good’s causality test, by transforming the originally specified probabilistic causality theory from random events to a stochastic, regime-switching framework. The researcher performed methodological validation via causality simulations for a Markov, regime-switching model. The proposed test can be used to detect whether none stochastic process is causal to the observed behaviour of another, probabilistically. In particular, the regime-switch causality explication proposed herein is pivotal to the results articulated. This research also examines the power of the proposed test by using simulations, and outlines some steps that one may take in using the test in a practical setting.

Opinion dynamics is extensively used in studying large-scale social, economical, political and natural phenomena that involve many interacting agents. It also can be used to model the evolution of teams of autonomous vehicles operating in a coordinated fashion with civilian and military applications, when arbitration among individual goals needs to be negotiated. Recently, research was conducted on how opinion dynamics can be the core of collective decision-making mechanisms for swarm robotics. Opinion dynamics with a time varying opinion space, which is the set of all possible opinions an agent may have, is a relatively recent research topic. In this work, the Deffuant-Weisbuch model (DW model), which allows to model opinion dynamics in shrinking opinion spaces, was applied. In simulating this class of systems and in extracting information from them it is crucial to establish reliable algorithms and criteria for counting the numbers of clusters, as this ultimately affects the determination of the steady state of the system. A method was applied to combine Fuzzy c-means clustering and subtractive clustering to check convergence of the system and avoid negative influence of outliers. Different scenarios are simulated to study the influence of characteristic parameters on the formation of opinions, which is quantified by the formation of clusters in the opinion space. Additionally, we simulate the scenario of a two dimensional opinion space in which one side shrinks, and evaluate how the rate of shrinking influences the steady state opinion space. This is a simplified model to gain some insight on the effect of extreme changes of opinions in multi-dimensional opinion space.

In this thesis I seek to explain a simple and yet quite difficult point about the nature of time: time is not motion, despite the fact that time and motion seem to be intertwined and interdependent. Aristotle calls time “something of motion (ti tēs kinēseōs).” His most concentrated account of time is presented within his treatise on physics, which is devoted to the study of motion and its principles and causes. The challenge of interpreting Aristotle’s account of time is to understand how it is fitting both that 1) a discussion about the nature of time emerges within the Physics, and that 2) a full and adequate account of time must exceed the scope of physics. Such a challenge obliges our attention not only as readers of Aristotle, but is furthermore relevant to anyone who seeks to give a coherent account of time, as one must in any case confront the ways in which time differs from motion while being an indispensable condition of it. Near the end of his account of time in the Physics, Aristotle presents us with an aporia that speaks directly to this challenge when he asks whether or not there can be time without soul. I suggest that a negative answer to this question – if time cannot exist without soul – means that the nature of time properly extends beyond physics. Aristotle has left it up to us to explore this possibility, since he does not pursue it explicitly himself. He merely formulates it in the Physics as a question. However, I argue that the absence of a definitive answer to this question there is not a sign that the nature of time is somehow beyond the capacity of Aristotle’s thought. After examining Aristotle’s account of time in the Physics, I look at his corpus more broadly, paying close attention to the way that Aristotle distinguishes the soul from the rest of nature at the beginning of the De Anima. The distinction between the living and the non-living is not made in the Physics, because it is not required for that study. In the Physics Aristotle studies what is shared by living things and the elements that sustain life within the ordered cosmos. As such, the focus of the Physics is on the causes of motion and change as what connects and distinguishes embodied individuals within this whole. But what it would mean to say that time depends on soul, and not simply on motion, cannot be addressed adequately in the Physics, since what distinguishes the activities of living from the incomplete activity of moving does not pertain to the main concerns of this treatise. By paying respectful attention to the structure of distinctions that organize Aristotle’s works as such, I make the case for time’s dependence on soul. I examine Aristotle’s accounts of animal and human awareness of time in the De Anima and Parva Naturalia and find that certain activities of the soul – sensation, memory, and deliberative reasoning - provide resources that can help us come to understand the most perplexing features of his account of time in the Physics, precisely those features that the analogies between time and motion or magnitude fail to explain: the simultaneity of diverse motion, the sameness and difference of the now, the differentiation of time into parts, and the way that time contains and exceeds (“numbers”) all possible motions. Thus I conclude that there cannot be time without soul, because the soul’s active nature must come into view in order to explain the features of time that distinguish it from motion.