Jonathan Blackledge

Application of the Fractional Diffusion Equation for Predicting Market Behaviour

Most nancial modelling system rely on an underlying hypothesis known as the Ecient Mar- ket Hypothesis (EMH) including the famous Black- Scholes formula for placing an option. However, the EMH has a fundamental aw; it is based on the as- sumption that economic processes are normally dis- tributed and it has long been known that this is not the case. This fundamental assumption leads to a number of shortcomings associated with using the EMH to analyse nancial data which includes fail- ure to predict the future volatility of a market share value. This paper introduces a new nancial risk as- sessment model based on L evy statistics and consid- ers a nancial forecasting system that uses a solution to a non-stationary fractional diusion equation char- acterized by the L evy index. Variation in the L evy index are considered in order to assess the future volatility of nancial data together with the likelihood of the markets become bear or bull dominant thereby providing a solution to securing an investment portfo- lio. The key hypothesis associated with this approach is that a change in the L evy index precedes a change in the nancial signal from which the index is com- puted and can therefore be It is shown that there is a quantitative relationship between L evys charac- teristic function and a random scaling fractal signal obtained through a Greens function solution to the fractional diusion equation. In this sense, the model considered is based on the Fractal Market Hypothe- sis and a case study is presented to illustrate this hy- pothesis by predicting the volatility associated with the foreign exchange markets.

Object Detection and Classification with Applications to Skin Cancer Screening

This paper discusses a new approach to the processes of object detection, recognition and classification in a digital image. The classification method is based on the application of a set of features which include fractal parameters such as the Lacunarity and Fractal Dimension. Thus, the approach used, incorporates the characterisation of an object in terms of its texture. The principal issues associated with object recognition are presented which includes two novel fast segmentation algorithms for which C++ code is provided. The self-learning procedure for designing a decision making engine using fuzzy logic and membership function theory is also presented and a new technique for the creation and extraction of information from a membership function considered. The methods discussed, and the ‘system’ developed, have a range of applications in ‘machine vision’. However, in this publication, we focus on the development and implementation of a skin cancer screening system that can be used in a general practice by non-experts to ‘filter’ normal from abnormal cases so that in the latter case, a patient can be referred to a specialist. A demonstration version of the application developed for this purpose has been made available for this publication which is discussed in Section IX.

Texture Classification using Fractal Geometry for the Diagnosis of Skin Cancers

We present an approach to object detection and recognition in a digital image using a classification method that is based on the application of a set of features that include fractal parameters such as the Lacunarity and Fractal Dimension. The principal issues associated with object recognition are presented and a self-learning procedure for designing a decision making engine using fuzzy logic and membership function theory considered. The methods discussed, and the ‘system’ developed, have a range of applications in ‘machine vision’ and in this publication, we focus on the development and implementation of a skin cancer screening system that can be used in a general practice by non-experts to ‘filter’ normal from abnormal cases so that in the latter case, a patient can be referred to a specialist. The paper provides an overview of the system design and includes a link from which interested readers can download and use a demonstration version of the system developed to date.

Using Virtual Reality to Enhance Electrical Safety and Design in the Built Environment

Electricity and the inherent risks associated with its use in the built environment have long since been a priority for the electrical services industry and also the general public who must live and work in this environment. By its nature virtual reality has the advantage of being safe for both the user and equipment. In addition, it offers the user an opportunity to be exposed to a range of scenarios and conditions that either occur infrequently or are hazardous to replicate. This paper presents a prototype desktop virtual reality model, to enhance electrical safety and design in the built environment. The model presented has the potential to be used as an educational tool for third level students, a design tool for industry, or as a virtual electrical safety manual for the general public. A description of the development of the virtual reality model is presented along with the applications that were developed within the model. The potential for virtual reality is highlighted with areas identified for future development. Based on the development of this prototype model, it appears that there is sufficient evidence to suggest that virtual reality could enhance electrical safety and design in the built environment and also advance training methods used to educate electrical services engineers and electricians.

Relating Fractal Dimension to Branching Behaviour in Filamentous Microorganisms

The productivity of an industrial fermentation process involving a filamentous microbe is heavily dependent on the morphological form adopted by the organism. The development of systems capable of rapidly and accurately characterising morphology within a given process represents a significant challenge to biotechnologists, as the complex phenotypes that are manifested are often not easily quantified. Conventional parameters employed in these analyses are of limited value, as they reveal little about the specific branching behaviour of the organism, which is an important consideration given the demonstrated link between branching frequency and metabolite production. More recently, fractal geometry has been employed in the analysis of microbes, but a clear link between fractal dimension and branching behaviour has not been demonstrated. This study presents an alternative means of enumerating the fractal dimension of fungal mycelial structures, by generating a ‘fractal signal’ from an object boundary. In the analysis of a population of Aspergillus oryzae mycelia, both fractal dimension and hyphal growth unit were found to increase together over time. An extensive analysis of different populations of Penicillium chrysogenum and A. oryzae mycelia, cultivated under a variety of different conditions, revealed a strong correlation between fractal dimension and hyphal growth unit. The technique has the potential to be adapted and applied to any morphological form that may be encountered in a fermentation process, providing a universally applicable process parameter for more complete data acquisition.

Multi-algorithmic Cryptography using Deterministic Chaos with Applications to Mobile Communications

In this extended paper, we present an overview of the principal issues associated with cryptography, providing historically significant examples for illustrative purposes as part of a short tutorial for readers that are not familiar with the subject matter. This is used to introduce the role that nonlinear dynamics and chaos play in the design of encryption engines which utilize different types of Iteration Function Systems (IFS). The design of such encryption engines requires that they conform to the principles associated with diffusion and confusion for generating ciphers that are of a maximum entropy type. For this reason, the role of confusion and diffusion in cryptography is discussed giving a design guide to the construction of ciphers that are based on the use of IFS. We then present the background and operating framework associated with a new product Crypstic which is based on the application of multi-algorithmic IFS to design encryption engines mounted on a USB memory stick using both disinformation and obfuscation to ‘hide’ a forensically inert application. The protocols and procedures associated with the use of this product are also briefly discussed.

A Surface Inspection Machine Vision System that Includes Fractal Texture Analysis

The detection, recognition and classification of features in a digital image is an important component of quality control systems in production and process engineering and industrial systems monitoring, in general. In this paper, a new pattern recognition system is presented that has been designed for the specific task of monitoring the quality of sheet-steel production in a rolling mill. The system is based on using both the Euclidean and Fractal geometric properties of an imaged object to develop training data that is used in conjunction with a supervised learning procedure based on the application of a fuzzy inference engine. Thus, the classification method includes the application of a set of features which include fractal parameters such as the Lacunarity and Fractal Dimension and thereby incorporates the characterisation of an object in terms of texture that, in this application, has metallurgical significance. The principal issues associated with object recognition are presented including a new segmentation algorithm. The selflearning procedure for designing a decision making engine using fuzzy logic and membership function theory is also presented and a new technique for the creation and extraction of information from a membership function considered. The methods discussed, and the system developed, have a range of applications in ‘machine vision’ and automatic inspection. However, in this publication, we focus on the development and implementation of a surface inspection system designed specifically for monitoring surface quality in the manufacture of sheet-steel. For this publication, we include a demonstration version of the system which can be downloaded, installed and utilised by interested readers as discussed in Section VI.

Application of the Fractal Market Hypothesis for Modelling Macroeconomic Time Series

This paper explores the conceptual background to financial time series analysis and financial signal processing in terms of the Efficient Market Hypothesis. By revisiting the principal conventional approaches to market analysis and the reasoning associated with them, we develop a Fractal Market Hypothesis that is based on the application of non-stationary fractional dynamics using an operator of the type ∂ ∂x2 − σ ∂ q(t) ∂tq(t) where σ−1 is the fractional diffusivity and q is the Fourier dimension which, for the topology considered, (i.e. the onedimensional case) is related to the Fractal Dimension 1 < DF < 2 by q = 1−DF + 3/2. We consider an approach that is based on the signal q(t) and its interpretation, including its use as a macroeconomic volatility index. In practice, this is based on the application of a moving window data processor that utilises Orthogonal Linear Regression to compute q from the power spectrum of the windowed data. This is applied to FTSE close-of-day data between 1980 and 2007 which reveals plausible correlations between the behaviour of this market over the period considered and the amplitude fluctuations of q(t) in terms of a macroeconomic model that is compounded in the operator above.

Audio Data Verification and Authentication using Frequency Modulation Based Watermarking

An approach to watermarking digital signals using frequency modulation ‘Chirp Coding’ is considered. The principles underlying this approach are based on the use of a matched filter to reconstruct a ‘chirp stream’ code that is uniquely robust. The method is generic in the sense that it can, in principle, be used for a variety of different signal (the authentication of speech and biomedical signals, for example). Further, by generating a bit stream that is signal dependent, chirp coding provides a method of self-authentication, which has a wide range of applications including copyright protection and digital rights management. However, in this paper, we focus on the application of chirp coding for the verification, authentication and self-authentication of audio signals. We also consider the effect of using a multi-level chirp coding approach to increase the ‘volume’ of data that can be embedded into a host signal. The theoretical and computational aspects of the matched filter with regard to the properties of a chirp are briefly revisited to provide the essential background to the method. Coding and decoding methods are then addressed and the results of different ‘attack strategies’ considered including Objective Difference Grades that are evaluated using Perceptual Evaluation of Audio Quality .

Digital Watermarking and Self-Authentication Using Chirp Coding

This paper discusses a new approach to ‘watermarking’ digital signals using linear frequency modulated or ‘chirp’ coding. The principles underlying this approach are based on the use of a matched filter to provide a reconstruction of a chirped code that is uniquely robust, i.e. in the case of very low signal-to-noise ratios. Chirp coding for authenticating data is generic in the sense that it can be used for a range of data types and applications (the authentication of speech and audio signals, for example). The theoretical and computational aspects of the matched filter and the properties of a chirp are revisited to provide the essential background to the method. Signal code generating schemes are then addressed and details of the coding and decoding techniques considered.