A simplified approach for calculating the moments of action for linear reaction-diffusion equations

The mean action time is the mean of a probability density function that can be interpreted as a critical time, which is a finite estimate of the time taken for the transient solution of a reaction-diffusion equation to effectively reach steady state. For high-variance distributions, the mean action time under-approximates the critical time since it neglects to account for the spread about the mean. We can improve our estimate of the critical time by calculating the higher moments of the probability density function, called the moments of action, which provide additional information regarding the spread about the mean. Existing methods for calculating the nth moment of action require the solution of n nonhomogeneous boundary value problems which can be difficult and tedious to solve exactly. Here we present a simplified approach using Laplace transforms which allows us to calculate the nth moment of action without solving this family of boundary value problems and also without solving for the transient solution of the underlying reaction-diffusion problem. We demonstrate the generality of our method by calculating exact expressions for the moments of action for three problems from the biophysics literature. While the first problem we consider can be solved using existing methods, the second problem, which is readily solved using our approach, is intractable using previous techniques. The third problem illustrates how the Laplace transform approach can be used to study coupled linear reaction-diffusion equations.

Digital signal processing

Signal Processing (SP) is a subject of central importance in engineering and the applied sciences. Signals are information-bearing functions, and SP deals with the analysis and processing of signals (by dedicated systems) to extract or modify information. Signal processing is necessary because signals normally contain information that is not readily usable or understandable, or which might be disturbed by unwanted sources such as noise. Although many signals are non-electrical, it is common to convert them into electrical signals for processing. Most natural signals (such as acoustic and biomedical signals) are continuous functions of time, with these signals being referred to as analog signals. Prior to the onset of digital computers, Analog Signal Processing (ASP) and analog systems were the only tool to deal with analog signals. Although ASP and analog systems are still widely used, Digital Signal Processing (DSP) and digital systems are attracting more attention, due in large part to the significant advantages of digital systems over the analog counterparts. These advantages include superiority in performance,s peed, reliability, efficiency of storage, size and cost. In addition, DSP can solve problems that cannot be solved using ASP, like the spectral analysis of multicomonent signals, adaptive filtering, and operations at very low frequencies. Following the recent developments in engineering which occurred in the 1980's and 1990's, DSP became one of the world's fastest growing industries. Since that time DSP has not only impacted on traditional areas of electrical engineering, but has had far reaching effects on other domains that deal with information such as economics, meteorology, seismology, bioengineering, oceanology, communications, astronomy, radar engineering, control engineering and various other applications. This book is based on the Lecture Notes of Associate Professor Zahir M. Hussain at RMIT University (Melbourne, 2001-2009), the research of Dr. Amin Z. Sadik (at QUT & RMIT, 2005-2008), and the Note of Professor Peter O'Shea at Queensland University of Technology. Part I of the book addresses the representation of analog and digital signals and systems in the time domain and in the frequency domain. The core topics covered are convolution, transforms (Fourier, Laplace, Z. Discrete-time Fourier, and Discrete Fourier), filters, and random signal analysis. There is also a treatment of some important applications of DSP, including signal detection in noise, radar range estimation, banking and financial applications, and audio effects production. Design and implementation of digital systems (such as integrators, differentiators, resonators and oscillators are also considered, along with the design of conventional digital filters. Part I is suitable for an elementary course in DSP. Part II (which is suitable for an advanced signal processing course), considers selected signal processing systems and techniques. Core topics covered are the Hilbert transformer, binary signal transmission, phase-locked loops, sigma-delta modulation, noise shaping, quantization, adaptive filters, and non-stationary signal analysis. Part III presents some selected advanced DSP topics. We hope that this book will contribute to the advancement of engineering education and that it will serve as a general reference book on digital signal processing.

A circuit-breaker restrike diagnostic algorithm using ATP and wavelet transforms

Circuit breaker restrikes are unwanted occurrence, which can ultimately lead to breaker. Before 2008, there was little evidence in the literature of monitoring techniques based on restrike measurement and interpretation produced during switching of capacitor banks and shunt reactor banks. In 2008 a non-intrusive radiometric restrike measurement method, as well a restrike hardware detection algorithm was developed. The limitations of the radiometric measurement method are a band limited frequency response as well as limitations in amplitude determination. Current detection methods and algorithms required the use of wide bandwidth current transformers and voltage dividers. A novel non-intrusive restrike diagnostic algorithm using ATP (Alternative Transient Program) and wavelet transforms is proposed. Wavelet transforms are the most common use in signal processing, which is divided into two tests, i.e. restrike detection and energy level based on deteriorated waveforms in different types of restrike. A ‘db5’ wavelet was selected in the tests as it gave a 97% correct diagnostic rate evaluated using a database of diagnostic signatures. This was also tested using restrike waveforms simulated under different network parameters which gave a 92% correct diagnostic responses. The diagnostic technique and methodology developed in this research can be applied to any power monitoring system with slight modification for restrike detection.

Frame-rate stereopsis using non-parametric transforms and programmable logic

A frame-rate stereo vision system, based on non-parametric matching metrics, is described. Traditional metrics, such as normalized cross-correlation, are expensive in terms of logic. Non-parametric measures require only simple, parallelizable, functions such as comparators, counters and exclusive-or, and are thus very well suited to implementation in reprogrammable logic.

Möbius transforms, coincident Boolean functions and non-coincidence property of Boolean functions

Boolean functions and their Möbius transforms are involved in logical calculation, digital communications, coding theory and modern cryptography. So far, little is known about the relations of Boolean functions and their Möbius transforms. This work is composed of three parts. In the first part, we present relations between a Boolean function and its Möbius transform so as to convert the truth table/algebraic normal form (ANF) to the ANF/truth table of a function in different conditions. In the second part, we focus on the special case when a Boolean function is identical to its Möbius transform. We call such functions coincident. In the third part, we generalize the concept of coincident functions and indicate that any Boolean function has the coincidence property even it is not coincident.

Creative urban regions : harnessing urban technologies to support knowledge city initiatives

In the rapidly growing knowledge economy, the talent and creativity of those around us will be increasingly decisive in shaping economic opportunity. Creativity can be described as the ability to produce new and original ideas and things. In other words, it is any act, idea, or product that changes an existing domain or transforms an existing domain into a new one. From an economic perspective, creativity can be considered as the generation of new ideas that is the major source of innovation and new economic activities. As urban regions have become the localities of key knowledge precincts and knowledge clusters across the globe, the link between a range of new technologies and the development of ‘creative urban regions’ (CURs) has come to the fore. In this sense, creativity has become a buzz concept in knowledge-economy research and policy circles. It has spawned ‘creative milieus,’ ‘creative industries,’ ‘creative cities,’ ‘creative class,’ and ‘creative capital.’ Hence, creativity has become a key concept on the agenda of city managers, development agents, and planners as they search for new forms of urban and economic development. CURs provide vast opportunities for knowledge production and spillover, which lead to the formation of knowledge cities. Urban information and communication technology (ICT) developments support the transformation of cities into knowledge cities. This book, which is a companion volume to Knowledge-Based Urban Development: Planning and Applications in the Information Era (also published by IGI Global) focuses on some of these developments. The Forward and Afterword are written by senior respected academic researchers Robert Stimson of the University of Queensland, Australia, and Zorica Nedovic-Budic of the University of Illinois at Urbana-Champaign, USA. The book is divided into four sections, each one dealing with selected aspects of information and communication technologies and creative urban regions.

The role of extreme sports in lifestyle enhancement and wellness

Alternative sports are fast becoming the physical activity of choice. Participation rates are even outstripping more traditional activities such as golf. At their most extreme there is no second chance, the most likely outcome of a mismanaged error or accident is death. At this level participants enjoy activities such as B.A.S.E. (Buildings, Antennae, Space, Earth) jumping, big wave surfing, waterfall kayaking, extreme skiing, rope-free climbing and extreme mountaineering. Probably the most common explanation for participation in extreme sports is the notion that participation is just a matter of some people‟s need to take unnecessary risks. This study reports on findings that indicate a more positive experience. A phenomenological method was used via unstructured interviews with 15 extreme sports participants (ages 30 – 72 years) and other firsthand accounts. Extreme sport participants directly related their experience to personal transformations that spill over to life in general. Athletes report feelings of deep psychological wellbeing and meaningfulness. The extreme sport experience enables a participant to break through personal barriers and develop an understanding of their own resourcefulness and emotional, cognitive, physical and spiritual capabilities. Furthermore such a breakthrough also seems to trigger a change in personal philosophy or view on life. The extreme sport experience transforms a participant though not in terms of working towards an external (social or cultural) perception of identity or towards some constructed perception of an ideal self, but by touching something within.

Stochastic modelling of financial time series with memory and multifractal scaling

Financial processes may possess long memory and their probability densities may display heavy tails. Many models have been developed to deal with this tail behaviour, which reflects the jumps in the sample paths. On the other hand, the presence of long memory, which contradicts the efficient market hypothesis, is still an issue for further debates. These difficulties present challenges with the problems of memory detection and modelling the co-presence of long memory and heavy tails. This PhD project aims to respond to these challenges. The first part aims to detect memory in a large number of financial time series on stock prices and exchange rates using their scaling properties. Since financial time series often exhibit stochastic trends, a common form of nonstationarity, strong trends in the data can lead to false detection of memory. We will take advantage of a technique known as multifractal detrended fluctuation analysis (MF-DFA) that can systematically eliminate trends of different orders. This method is based on the identification of scaling of the q-th-order moments and is a generalisation of the standard detrended fluctuation analysis (DFA) which uses only the second moment; that is, q = 2. We also consider the rescaled range R/S analysis and the periodogram method to detect memory in financial time series and compare their results with the MF-DFA. An interesting finding is that short memory is detected for stock prices of the American Stock Exchange (AMEX) and long memory is found present in the time series of two exchange rates, namely the French franc and the Deutsche mark. Electricity price series of the five states of Australia are also found to possess long memory. For these electricity price series, heavy tails are also pronounced in their probability densities. The second part of the thesis develops models to represent short-memory and longmemory financial processes as detected in Part I. These models take the form of continuous-time AR(∞) -type equations whose kernel is the Laplace transform of a finite Borel measure. By imposing appropriate conditions on this measure, short memory or long memory in the dynamics of the solution will result. A specific form of the models, which has a good MA(∞) -type representation, is presented for the short memory case. Parameter estimation of this type of models is performed via least squares, and the models are applied to the stock prices in the AMEX, which have been established in Part I to possess short memory. By selecting the kernel in the continuous-time AR(∞) -type equations to have the form of Riemann-Liouville fractional derivative, we obtain a fractional stochastic differential equation driven by Brownian motion. This type of equations is used to represent financial processes with long memory, whose dynamics is described by the fractional derivative in the equation. These models are estimated via quasi-likelihood, namely via a continuoustime version of the Gauss-Whittle method. The models are applied to the exchange rates and the electricity prices of Part I with the aim of confirming their possible long-range dependence established by MF-DFA. The third part of the thesis provides an application of the results established in Parts I and II to characterise and classify financial markets. We will pay attention to the New York Stock Exchange (NYSE), the American Stock Exchange (AMEX), the NASDAQ Stock Exchange (NASDAQ) and the Toronto Stock Exchange (TSX). The parameters from MF-DFA and those of the short-memory AR(∞) -type models will be employed in this classification. We propose the Fisher discriminant algorithm to find a classifier in the two and three-dimensional spaces of data sets and then provide cross-validation to verify discriminant accuracies. This classification is useful for understanding and predicting the behaviour of different processes within the same market. The fourth part of the thesis investigates the heavy-tailed behaviour of financial processes which may also possess long memory. We consider fractional stochastic differential equations driven by stable noise to model financial processes such as electricity prices. The long memory of electricity prices is represented by a fractional derivative, while the stable noise input models their non-Gaussianity via the tails of their probability density. A method using the empirical densities and MF-DFA will be provided to estimate all the parameters of the model and simulate sample paths of the equation. The method is then applied to analyse daily spot prices for five states of Australia. Comparison with the results obtained from the R/S analysis, periodogram method and MF-DFA are provided. The results from fractional SDEs agree with those from MF-DFA, which are based on multifractal scaling, while those from the periodograms, which are based on the second order, seem to underestimate the long memory dynamics of the process. This highlights the need and usefulness of fractal methods in modelling non-Gaussian financial processes with long memory.

The absence of form

what was silent will speak, what is closed will open and will take on a voice Paul Virilio The fundamental problem in dealing with the digital is that we are forced to contend with a fundamental deconstruction of form. A deconstruction that renders our content and practice into a single state that can be openly and easily manipulated, reimagined and mashed together in rapid time to create completely unique artefacts and potentially unwranglable jumbles of data. Once our work is essentially broken down into this series of number sequences, (or bytes), our sound, images, movies and documents – our memory files - we are left with nothing but choice….and this is the key concern. This absence of form transforms our work into new collections and poses unique challenges for the artist seeking opportunities to exploit the potential of digital deconstruction. It is through this struggle with the absent form that we are able to thoroughly explore the latent potential of content, exploit modern abstractions of time and devise approaches within our practice that actively deal with the digital as an essential matter of course.

The Federal circuit in Bilski : the machine-or-transformation test

In a much anticipated judgment, the Federal Circuit has sought to clarify the standards applicable in determining whether a claimed method constitutes patent-eligible subject matter. In Bilski, the Federal Circuit identified a test to determine whether a patentee has made claims that pre-empt the use of a fundamental principle or an abstract idea or whether those claims cover only a particular application of a fundamental principle or abstract idea. It held that the sole test for determining subject matter eligibility for a claimed process under § 101 is that: (1) it is tied to a particular machine or apparatus, or (2) it transforms a particular article into a different state or thing. The court termed this the “machine-or-transformation test.” In so doing it overruled its earlier State Street decision to the extent that it deemed its “useful, tangible and concrete result” test as inadequate to determine whether an alleged invention recites patent-eligible subject matter.