Applications of fractals to image data compression

Digital image processing is exploited in many diverse applications but the size of digital images places excessive demands on current storage and transmission technology. Image data compression is required to permit further use of digital image processing. Conventional image compression techniques based on statistical analysis have reached a saturation level so it is necessary to explore more radical methods. This thesis is concerned with novel methods, based on the use of fractals, for achieving significant compression of image data within reasonable processing time without introducing excessive distortion. Images are modelled as fractal data and this model is exploited directly by compression schemes. The validity of this is demonstrated by showing that the fractal complexity measure of fractal dimension is an excellent predictor of image compressibility. A method of fractal waveform coding is developed which has low computational demands and performs better than conventional waveform coding methods such as PCM and DPCM. Fractal techniques based on the use of space-filling curves are developed as a mechanism for hierarchical application of conventional techniques. Two particular applications are highlighted: the re-ordering of data during image scanning and the mapping of multi-dimensional data to one dimension. It is shown that there are many possible space-filling curves which may be used to scan images and that selection of an optimum curve leads to significantly improved data compression. The multi-dimensional mapping property of space-filling curves is used to speed up substantially the lookup process in vector quantisation. Iterated function systems are compared with vector quantisers and the computational complexity or iterated function system encoding is also reduced by using the efficient matching algcnithms identified for vector quantisers.

The time dimension of neural network models

This review attempts to provide an insightful perspective on the role of time within neural network models and the use of neural networks for problems involving time. The most commonly used neural network models are defined and explained giving mention to important technical issues but avoiding great detail. The relationship between recurrent and feedforward networks is emphasised, along with the distinctions in their practical and theoretical abilities. Some practical examples are discussed to illustrate the major issues concerning the application of neural networks to data with various types of temporal structure, and finally some highlights of current research on the more difficult types of problems are presented.

The exact sample complexity of PAC-learning problems with unit VC dimension

The Vapnik-Chervonenkis (VC) dimension is a combinatorial measure of a certain class of machine learning problems, which may be used to obtain upper and lower bounds on the number of training examples needed to learn to prescribed levels of accuracy. Most of the known bounds apply to the Probably Approximately Correct (PAC) framework, which is the framework within which we work in this paper. For a learning problem with some known VC dimension, much is known about the order of growth of the sample-size requirement of the problem, as a function of the PAC parameters. The exact value of sample-size requirement is however less well-known, and depends heavily on the particular learning algorithm being used. This is a major obstacle to the practical application of the VC dimension. Hence it is important to know exactly how the sample-size requirement depends on VC dimension, and with that in mind, we describe a general algorithm for learning problems having VC dimension 1. Its sample-size requirement is minimal (as a function of the PAC parameters), and turns out to be the same for all non-trivial learning problems having VC dimension 1. While the method used cannot be naively generalised to higher VC dimension, it suggests that optimal algorithm-dependent bounds may improve substantially on current upper bounds.

Innovation and regional absorptive capacity:the labour market dimension

In 2003, Eurostat published an 'experimental' dataset on regional innovation levels derived from the Second Community Innovation Survey. This dataset, part of the European Innovation Scoreboard, also contains a range of regional labour market indicators. In this paper, we report an exploratory analysis of this data, focussing on how the labour market characteristics of regions shape regions' absorptive capacity (RACAP) and their ability to assimilate knowledge from public and externally conducted R&D. In particular, we aim to establish whether labour market aspects of RACAP are more important for innovation in prosperous or lagging regions of the European Union (EU). © Springer-Verlag 2006.

Coherent propagation and energy transfer in low-dimension nonlinear arrays

We present a theory of coherent propagation and energy or power transfer in a low-dimension array of coupled nonlinear waveguides. It is demonstrated that in the array with nonequal cores (e.g., with the central core) stable steady-state coherent multicore propagation is possible only in the nonlinear regime, with a power-controlled phase matching. The developed theory of energy or power transfer in nonlinear discrete systems is rather generic and has a range of potential applications including both high-power fiber lasers and ultrahigh-capacity optical communication systems. © 2012 American Physical Society.

Hopping transport on a fractal: ac conductivity of porous silicon

We have measured the frequency dependence of the conductivity and the dielectric constant of various samples of porous Si in the regime 1 Hz-100 kHz at different temperatures. The conductivity data exhibit a strong frequency dependence. When normalized to the dc conductivity, our data obey a universal scaling law, with a well-defined crossover, in which the real part of the conductivity sigma' changes from an sqrt(omega) dependence to being proportional to omega. We explain this in terms of activated hopping in a fractal network. The low-frequency regime is governed by the fractal properties of porous Si, whereas the high-frequency dispersion comes from a broad distribution of activation energies. Calculations using the effective-medium approximation for activated hopping on a percolating lattice give fair agreement with the data.

German-Irish corporate relationships:the cultural dimension

The thesis raises the question of whether or not in an age of internationalisation and globalisation, the cultural differences which exist between Germany and Ireland are still relevant to German-Irish corporate relationships or have internationally accepted best practices removed culture from the equation? The first three chapters establish the theoretical framework of the thesis by outlining the broadly culturalist/institutionalist approach, based on the work of Hofstede and Maurice et al, to be pursued, profiling the business cultures of both countries by analysing the components of their respective national institutional frameworks, and the examining existing approaches to the study of mother company-foreign subsidiary relationships. Chapters four to seven constitute the empirical section of the thesis. Using the interviews carried out with two sample groups (Sample Group A: 15 German mother companies and 14 of their Irish operations and Sample Group B: 7 Irish mother companies and 9 of their German operations), the mother companies in both groups are examined to see whether or not they demonstrate characteristics which are in keeping with their national business cultures. Their foreign operations are then analysed as is the mother company-foreign subsidiary relationship to determine whether or not any mother company influences are visible. The general approaches adopted by the two groups of mother companies to their foreign operations are compared and contrasted. Finally, differences in national attitudes and values are identified and their impact assessed. The analysis reveals that despite existing pressures towards convergence, the cultural differences between both countries are still relevant to the relationship particularly at the level of attitudes and values and although similarities in the mother company approaches to their subsidiaries are present, national specificities may nevertheless be detected.

Reduced dimension models for weather forecasting

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Sourcing knowledge for innovation:the international dimension

Drawing knowledge from external sources in the UK, or internationally, has become increasingly important to small and medium-sized firms (SMEs). SMEs cannot generate all they need to know to develop new products and processes within their own companies, they need to look elsewhere for new ideas and expertise. This practice is known as knowledge sourcing. This report provides a detailed review of patterns of knowledge sourcing, and the key factors influencing these patterns, particularly from a small business perspective. We present key findings from a survey of 393 UK companies and analyse the results. We also highlight case studies of UK SMEs that work closely with overseas partners and agents to widen their own knowledge.

An examination of the Prandtl mechanism in large dimension slope failures

An alternative explanation for the modes of failure of large scale failures of open pit walls to those of classical slope stability theory is proposed that makes use of the concept of a transition zone, which is described by a modified Prandtls prism.

The people dimension in logistics and supply chain management:its role and importance

It is widely recognised that the effective application of logistics and supply chain management (SCM) has a vital role to play in European economic recovery. Experience suggests that success in achieving higher levels of supply chain integration (SCI) depends on both physical and technical components (the hard-wiring), as well as human and behavioural components (the soft-wiring). There is significant evidence that the latter has been largely neglected by the logistics and SCM community. Furthermore, it appears that the majority of supply chain improvement initiatives by practitioners have been primarily concerned with technological, structural and process issues. This chapter argues that the difficulties often encountered in attempting to put logistics and SCM theory into practice are largely a consequence of a lack of focus and understanding of the people dimension. Based on this discussion, it offers some suggestions for improvement in this area to supply chain professionals.

Putting supply chain management (SCM) theory into practice:the role and importance of the people dimension

This article deals with a number of supply chain management (SCM) issues: SCM’s “Big Idea” – integration, Divergence of Theory and Practice - the limitations of “hard-wiring”, The “Human Chain”, The Way Forward – asking the right question?