Chaos Theory and Socio-Economic Renewal in Hungary

We utilised methods of chaos theory that were originally used in a 1990’s study to analyse the behaviour of various Hungarian socio-economic macro indicators, both historically and their expected behaviour in the future. In this study, we present the method adapted to PC and the behaviour of the selected macro indicators. We characterize the pathways our society and economy has experienced and where they are heading to into the future by the means of these indicators. Comparing the present results of analysis with the results twenty years ago (when today’s present was the future) we came to the conclusion that most of the indicators became less chaotic, thus the socio-economic courses were getting more stable over the past two decades. We conclude that the opportunity to change them is slowly diminishing, it will be more and more difficult to renew the Hungarian socio-economic indicators, and to turn the processes to more desirable courses. Recommendations for change interventions are then provided.

On Chaos and Fractals in General Topological Spaces

The present study on chaos and fractals in general topological spaces. Chaos theory originated with the work of Edward Lorenz. The phenomenon which changes order into disorder is known as chaos. Theory of fractals has its origin with the frame work of Benoit Mandelbrot in 1977. Fractals are irregular objects. In this study different properties of topological entropy in chaos spaces are studied, which also include hyper spaces. Topological entropy is a measures to determine the complexity of the space, and compare different chaos spaces. The concept of fractals can’t be extended to general topological space fast it involves Hausdorff dimensions. The relations between hausdorff dimension and packing dimension. Regular sets in Metric spaces using packing measures, regular sets were defined in IR” using Hausdorff measures. In this study some properties of self similar sets and partial self similar sets. We can associate a directed graph to each partial selfsimilar set. Dimension properties of partial self similar sets are studied using this graph. Introduce superself similar sets as a generalization of self similar sets and also prove that chaotic self similar self are dense in hyper space. The study concludes some relationships between different kinds of dimension and fractals. By defining regular sets through packing dimension in the same way as regular sets defined by K. Falconer through Hausdorff dimension, and different properties of regular sets also.

The chaos machine: analogue computing rediscovered (1)

Analogue computers provide actual rather than virtual representations of model systems. They are powerful and engaging computing machines that are cheap and simple to build. This two-part Retronics article helps you build (and understand!) your own analogue computer to simulate the Lorenz butterfly that's become iconic for Chaos theory.

Financial time series analysis : Chaos and neurodynamics approach

This work aims at combining the Chaos theory postulates and Artificial Neural Networks classification and predictive capability, in the field of financial time series prediction. Chaos theory, provides valuable qualitative and quantitative tools to decide on the predictability of a chaotic system. Quantitative measurements based on Chaos theory, are used, to decide a-priori whether a time series, or a portion of a time series is predictable, while Chaos theory based qualitative tools are used to provide further observations and analysis on the predictability, in cases where measurements provide negative answers. Phase space reconstruction is achieved by time delay embedding resulting in multiple embedded vectors. The cognitive approach suggested, is inspired by the capability of some chartists to predict the direction of an index by looking at the price time series. Thus, in this work, the calculation of the embedding dimension and the separation, in Takens‘ embedding theorem for phase space reconstruction, is not limited to False Nearest Neighbor, Differential Entropy or other specific method, rather, this work is interested in all embedding dimensions and separations that are regarded as different ways of looking at a time series by different chartists, based on their expectations. Prior to the prediction, the embedded vectors of the phase space are classified with Fuzzy-ART, then, for each class a back propagation Neural Network is trained to predict the last element of each vector, whereas all previous elements of a vector are used as features.

Complexity theory and organizing form dualities

Purpose – The purpose of this paper is to describe how order-generated rules applied to organizing form dualities can assist in creating the conditions for emergent, self-organized behavior in organizations, thereby offering an operational deployment of complexity theory.

Design/methodology/approach – The paper begins by showing that the concept of dualities is consistent with complexity-thinking. In addition, when applied to organizing forms, dualities represent a practical way of affecting an organization's balance between chaos and order. Thus, when augmented with order-generating rules, organizing form dualities provide an access point for the practical instigation of edge of chaos conditions and the potential for emergence.

Findings – The paper maintains that many attempts to “manage” complexity have been associated with changes to organizing forms, specifically toward new forms of organizing. It is suggested that organizing form dualities provide some management guidance for encouraging the “edge of chaos” conditions advocated in complexity theory, although the details of self-organization cannot be prescribed given the assumptions of non-linearity associated with complexity theory perspectives. Finally, it is proposed that organizing dualities can elucidate the nature and application of order-generating rules in non-linear complex systems.

Practical implications – Dualities offer some guidance toward the practical implementation of complexity theory as they represent an accessible sub-system where the forces for order and chaos – traditional and new forms of organizing respectively – are accessible and subject to manipulation.

Originality/value – The commonalities between dualities and complexity theory are intuitive, but little conceptual work has shown how the former can be employed as a guide to managing organizing forms. Moreover, this approach demonstrates that managers may be able to stimulate “edge of chaos” conditions in a practical way, without making positivistic assumptions about the causality associated with their efforts.

Chaos rules : an exploration of the work of instructional designers in distance education

This thesis provides an examination of the work of instructional designers in distance education, through the conceptual lens of chaos theory. Chaos theory was chosen as an analytical tool because of its ability to reveal the patterns and processes of complex systems as they move between order and turbulence. Recent work in the social sciences, specifically literary theory, has provided impetus for applications of chaos theory to educational settings. Specifically, chaos theory is used to analyse eight case studies of projects volunteered by instructional designers working in five institutions in Hong Kong and Australia. Data were gathered over a period of months with each participant, chiefly through interviews, but also involving diary accounts, electronic mail and letters. The methodology was thus qualitative, specifically informed by Eisner's vision of the ‘critical connoisseur’. Eisner equates an ‘enlightened eye’ with attainment of the skills of a critical connoisseur. First, an effective qualitative researcher must develop connoisseurship, the art of appreciation. On its own, though, connoisseurship is not enough; it is a private act, and thus needs a public face or presence. Criticism is this link, criticism being the art of disclosure. The critical connoisseur aims to help others to increase perception and deepen understanding of an educational situation or event. In addition to the empirical work, a parallel strand of this thesis investigates the theory and reported practice of instructional design. A brief history of instructional design is presented, along with discussion of acknowledged deficiencies of current theory and approaches. Recent reported investigations of both theory and practice are analysed from the viewpoint of chaos theory. Examination of key contributions in the literature of instructional design and distance education reveals considerable resonance between these contributions and the fundamental properties of chaotic systems. Links are made, in both the theoretical and empirical strands, between instructional design and the behaviour of dissipative structures, attractors and the process of bifurcation. Use is also made of the time-dependent nature of chaos theory as a theory of becoming, rather than one of being. The thesis comprises eight chapters, two appendices and a references section. The introductory chapter explains the research problem, and outlines the structure of the thesis. Methodological considerations are left until after an assessment of instructional design literature and (reported) practice. This deliberately theoretical investigation (Chapters 2 and 3) comprises the first of the parallel strands that are presented. The basic conclusions are that instructional design theory has not been particularly helpful to or used by instructional designers, and that chaos theory might provide an alternative way of viewing instructional design practice. The other parallel strand is the empirical work, which for four chapters outlines the methodology and my findings concerning the role of instructional designers in distance education. The methodology is detailed in Chapter 4. Chapter 5 establishes the contexts of the participants, by examining their backgrounds and introductions to their roles. It also investigates their views on their role and status within their institutions and with working colleagues. Chapter 6 is an exploration of the major issues that influenced the work of the instructional designers. These are the issues that arose naturally in the interviews as the participants outlined the development and interactions that took place on a day to day basis. Time emerges as a key influence in their work, and its effects on the projects are outlined and analysed. The ways that instructional designers give advice to those with whom they work is also investigated. The next chapter continues consideration of their work, but this time as they reflect on their role and its demands. This includes their reactions to the various metaphors that have appeared in the literature, along with those that they introduced into our discussions. The links that are established between the two parallel strands are drawn more explicitly in the final chapter, Chapter 8, which is a notion of what a model of instructional design based on my conclusions might resemble. It summarises the evidence that it is not necessarily by striving for order—in fact quite the opposite — during key periods of course development, that leads to creative outcomes. The introduction of uncertainty and turbulence does, in some cases and under some conditions, move the system to a higher level. The image that is offered from chaos theory is that of time-bound dissipative structures, interacting with their open environment at far-from-equilibrium conditions, and transforming themselves from disorder to order through bifurcation. The role of strange or chaotic attractors is highlighted in the process. The first appendix gives background information in terms of the methodology. The second is the heart of the data upon which the thesis draws. That is, the second appendix outlines the case studies of the participants. Most are short summaries, but the final one is a detailed study, tracing the progress of the design and development of a subject in distance education.

Stick-slip chaos in a non-ideal self-excited system

In engineering practical systems the excitation source is generally dependent on the system dynamic structure. In this paper we analyze a self-excited oscillating system due to dry friction which interacts with an energy source of limited power supply (non ideal problem). The mechanical system consists of an oscillating system sliding on a moving belt driven by a limited power supply. In the oscillating system considered here, dry friction acts as an excitation mechanism for stick-slip oscillations. The stick-slip chaotic oscillations are investigated because the knowledge of their dynamic characteristics is an important step in system design and control. Many engineering systems present stick-slip chaotic oscillations such as machine tools, oil well drillstrings, car brakes and others.

Chaos induced by turbulent and erratic functions

Let (X, d) be a compact metric space and f: X → X a continuous function and consider the hyperspace (K(X), H) of all nonempty compact subsets of X endowed with the Hausdorff metric induced by d. Let f̄: K(X) → K (X) be defined by f̄(A) = {f(a)/a ∈ A} the natural extension of f to K(X), then the aim of this work is to study the dynamics of f when f is turbulent (erratic, respectively) and its relationships.

Tom Stoppard: Humanizing chaos

The purpose of this study was to critically evaluate Tom Stoppard’s application of chaos theory and quantum science in ROSENCRANTZ AND GUILDENSTERN ARE DEAD, HAPGOOD and ARCADIA; and determine the extent to which Stoppard argues for the importance of human action and choice. ^ Through critical analysis this study examined how Stoppard applies the quantum aspects of: (1) indeterminacy to human epistemology in ROSENCRANTZ AND GUILDENSTERN ARE DEAD; (2) complementarity to human identity in HAPGOOD; and (3) recursive symmetry to human history in ARCADIA. It also examined how Stoppard excavates the complexities of human action, choice and identity through the lens of chaos theory and quantum science. ^ These findings demonstrated that Tom Stoppard is not merely juxtaposing quantum science and human interactions for the sake of drama; rather, by excavating the complexities of human action, choice and identity through the lens of chaos theory and quantum science, Stoppard demonstrates the fundamental connection between individuals and the post-Newtonian universe.^

Public knowledge beyond journalism : infotainment, satire and Australian television

This thesis examines the changing relationships between television, politics, audiences and the public sphere. Premised on the notion that mediated politics is now understood “in new ways by new voices” (Jones, 2005: 4), and appropriating what McNair (2003) calls a “chaos theory” of journalism sociology, this thesis explores how two different contemporary Australian political television programs (Sunrise and The Chaser’s War on Everything) are viewed, understood, and used by audiences. In analysing these programs from textual, industry and audience perspectives, this thesis argues that journalism has been largely thought about in overly simplistic binary terms which have failed to reflect the reality of audiences’ news consumption patterns. The findings of this thesis suggest that both ‘soft’ infotainment (Sunrise) and ‘frivolous’ satire (The Chaser’s War on Everything) are used by audiences in intricate ways as sources of political information, and thus these TV programs (and those like them) should be seen as legitimate and valuable forms of public knowledge production. It therefore might be more worthwhile for scholars to think about, research and teach journalism in the plural: as a series of complementary or antagonistic journalisms, rather than as a single coherent entity.

Dynamics of multi-articular coordination in neurobiological systems

Although previous work in nonlinear dynamics on neurobiological coordination and control has provided valuable insights from studies of single joint movements in humans, researchers have shown increasing interest in coordination of multi-articular actions. Multi-articular movement models have provided valuable insights on neurobiological systems conceptualised as degenerate, adaptive complex systems satisfying the constraints of dynamic environments. In this paper, we overview empirical evidence illustrating the dynamics of adaptive movement behavior in a range of multi-articular actions including kicking, throwing, hitting and balancing. We model the emergence of creativity and the diversity of neurobiological action in the meta-stable region of self organising criticality. We examine the influence on multi-articular actions of decaying and emerging constraints in the context of skill acquisition. We demonstrate how, in this context, transitions between preferred movement patterns exemplify the search for and adaptation of attractor states within the perceptual motor workspace as a function of practice. We conclude by showing how empirical analyses of neurobiological coordination and control have been used to establish a nonlinear pedagogical framework for enhancing acquisition of multi-articular actions.

Analysis of cardiac and epileptic signals using higher order spectra

The theory of nonlinear dyamic systems provides some new methods to handle complex systems. Chaos theory offers new concepts, algorithms and methods for processing, enhancing and analyzing the measured signals. In recent years, researchers are applying the concepts from this theory to bio-signal analysis. In this work, the complex dynamics of the bio-signals such as electrocardiogram (ECG) and electroencephalogram (EEG) are analyzed using the tools of nonlinear systems theory. In the modern industrialized countries every year several hundred thousands of people die due to sudden cardiac death. The Electrocardiogram (ECG) is an important biosignal representing the sum total of millions of cardiac cell depolarization potentials. It contains important insight into the state of health and nature of the disease afflicting the heart. Heart rate variability (HRV) refers to the regulation of the sinoatrial node, the natural pacemaker of the heart by the sympathetic and parasympathetic branches of the autonomic nervous system. Heart rate variability analysis is an important tool to observe the heart's ability to respond to normal regulatory impulses that affect its rhythm. A computerbased intelligent system for analysis of cardiac states is very useful in diagnostics and disease management. Like many bio-signals, HRV signals are non-linear in nature. Higher order spectral analysis (HOS) is known to be a good tool for the analysis of non-linear systems and provides good noise immunity. In this work, we studied the HOS of the HRV signals of normal heartbeat and four classes of arrhythmia. This thesis presents some general characteristics for each of these classes of HRV signals in the bispectrum and bicoherence plots. Several features were extracted from the HOS and subjected an Analysis of Variance (ANOVA) test. The results are very promising for cardiac arrhythmia classification with a number of features yielding a p-value < 0.02 in the ANOVA test. An automated intelligent system for the identification of cardiac health is very useful in healthcare technology. In this work, seven features were extracted from the heart rate signals using HOS and fed to a support vector machine (SVM) for classification. The performance evaluation protocol in this thesis uses 330 subjects consisting of five different kinds of cardiac disease conditions. The classifier achieved a sensitivity of 90% and a specificity of 89%. This system is ready to run on larger data sets. In EEG analysis, the search for hidden information for identification of seizures has a long history. Epilepsy is a pathological condition characterized by spontaneous and unforeseeable occurrence of seizures, during which the perception or behavior of patients is disturbed. An automatic early detection of the seizure onsets would help the patients and observers to take appropriate precautions. Various methods have been proposed to predict the onset of seizures based on EEG recordings. The use of nonlinear features motivated by the higher order spectra (HOS) has been reported to be a promising approach to differentiate between normal, background (pre-ictal) and epileptic EEG signals. In this work, these features are used to train both a Gaussian mixture model (GMM) classifier and a Support Vector Machine (SVM) classifier. Results show that the classifiers were able to achieve 93.11% and 92.67% classification accuracy, respectively, with selected HOS based features. About 2 hours of EEG recordings from 10 patients were used in this study. This thesis introduces unique bispectrum and bicoherence plots for various cardiac conditions and for normal, background and epileptic EEG signals. These plots reveal distinct patterns. The patterns are useful for visual interpretation by those without a deep understanding of spectral analysis such as medical practitioners. It includes original contributions in extracting features from HRV and EEG signals using HOS and entropy, in analyzing the statistical properties of such features on real data and in automated classification using these features with GMM and SVM classifiers.