Numerical Methods of Multifractal Analysis in Information Communication Systems and Networks

In this chapter, the main principles of the theory of fractals and multifractals are stated. A singularity spectrum is introduced for the random telecommunication traffic, concepts of fractal dimensions and scaling functions, and methods used in their determination by means of Wavelet Transform Modulus Maxima (WTMM) are proposed. Algorithm development methods for estimating multifractal spectrum are presented. A method based on multifractal data analysis at network layer level by means of WTMM is proposed for the detection of traffic anomalies in computer and telecommunication networks. The chapter also introduces WTMM as the informative indicator to exploit the distinction of fractal dimen- sions on various parts of a given dataset. A novel approach based on the use of multifractal spectrum parameters is proposed for estimating queuing performance for the generalized multifractal traffic on the input of a buffering device. It is shown that the multifractal character of traffic has significant impact on queuing performance characteristics

Notes on the Circulation of Epistemic Images

Three cases of image circulation in the sciences, two from complex dynamics and one from microscopy, are discussed. The article deals with failed circulations, suspected errors, interdisciplinary communication, notebooks of scientists, the role of media shifts, mathematics and materiality, human perception, pictorial norms and conventions. It analyses how images circulate through different thought collectives and visual cultures. All three examples show different strategies of how images that break with visual traditions have been reintegrated into epistemic circulations and become “boundary objects” that are both robust and flexible

Nonlinear and chaotic dynamics and its application to historical financial markets

Seit ungefähr 15 Jahren beschäftigt sich die ökonomische Forschung mit der Dynamik 'chaotischer' Systeme. Inzwischen hat die Chaosforschung bzw. -theorie einen festen Platz in der Wissenschaft, obgleich dem Enthusiasmus der ersten Phase vorsichtigere Überlegungen über die Leistungsfähigkeit dieses Ansatzes gewichen sind. Der vorliegende Beitrag versucht die Entwicklung knapp zu resümieren und entwickelt einige Ideen über mögliche Anwendungen der Chaos Theorie für die Wirtschaftsgeschichte bzw. deren Theorie. Ein Großteil der Chaosforschung hat sich mit der Analyse von Finanzmärkten beschäftigt. Der Autor gibt einen Überblick über diese Forschungsbemühungen. (ICE2)'For roughly 15 years, economic research has been involved with chaotic systems. During these years chaos theory took a firm place in science, although the enthusiasm of the first decade was followed by a more subdued kind of consideration. This might be the time to sum up some of the results and to develop some ideas concerning possible applications of chaos theory to economic history (and its theory). Since a good portion of the chaos research that has been done until now deals with financial markets, we consider that section of economics.' (author's abstract

Fractals

Volume 3, Issue 1, January 201

On the Super-Additivity and Estimation Biases of Quantile Contributions

Sample measures of top centile contributions to the total (concentration) are downward biased, unstable estimators, extremely sensitive to sample size and concave in accounting for large deviations. It makes them particularly unfit in domains with power law tails, especially for low values of the exponent. These estimators can vary over time and increase with the population size, as shown in this article, thus providing the illusion of structural changes in concentration. They are also inconsistent under aggregation and mixing distributions, as the weighted average of concentration measures for A and B will tend to be lower than that from A U B. In addition, it can be shown that under such fat tails, increases in the total sum need to be accompanied by increased sample size of the concentration measurement. We examine the estimation superadditivity and bias under homogeneous and mixed distributions

Thoughts on Haptic Architecture By a Perceptual Psychologist

Like most people, I do not know much about architecture, but I spend a great deal of time in buildings. I was therefore both intrigued and a little intimidated when I was asked by the editors of Oz to write an article on haptic architecture