ALGORITHMIC INFORMATION THEORY

Natural fluid flow systems exhibit turbulent and chaotic behavior that determines their high-level complexity. Chaos has an accurate mathematical definition, while turbulence is a property of fluid flow without an accurate mathematical definition. Using the Kolmogorov complexity (KC) and its derivative (KC spectrum), permutation entropy (PE), and Lyapunov exponent (LE), we considered how chaos affected the predictability of natural fluid flow systems. This paper applied these measures to investigate the turbulent, complex and chaotic behaviors of monthly streamflow of rivers from Bosnia and Herzegovina, the United States, and the Mendoza Basin (Argentina) and evaluated their time horizons using the Lyapunov time (LT). Based on the measures applied for river streamflow, we derived four modes of the interrelationship between turbulence, complexity, and chaos. Finally, using the measures, we clustered rivers with similar time horizons representing their predictability.

The Discrete Fourier Transform (DFT) has been extended to lossless compression for binary images. Binarisation is key for DFT to compress losslessly because there exist lossy reconstructions (within a specific range of loss values) which are error-corrected during the binarisation step, effectively making the image lossless. In an ironic twist, the quantisation effect which usually introduces errors, has been utilised to remove noise from lossy reconstructions.

Real-world optimisation problems are often very complex. Metaheuristics have been successful in solving many of these problems, but the difficulty in choosing the best approach can be a huge challenge for practitioners. One approach to this dilemma is to use fitness landscape analysis to better understand problems before deciding on approaches to solving the problems. However, despite extensive research on fitness landscape analysis and a large number of developed techniques, very few techniques are used in practice. This could be because fitness landscape analysis in itself can be complex. In an attempt to make fitness landscape analysis techniques accessible, this paper provides an overview of techniques from the 1980s to the present. Attributes that are important for practical implementation are highlighted and ways of adapting techniques to be more feasible or appropriate are suggested. The survey reveals the wide range of factors that can influence problem difficulty, emphasising the need for a shift in focus away from predicting problem hardness towards measuring characteristics. It is hoped that this survey will invoke renewed interest in the field of understanding complex optimisation problems and ultimately lead to better decision making on the use of appropriate metaheuristics.