A variable stepsize implementation for stochastic differential equations

Stochastic differential equations (SDEs) arise from physical systems where the parameters describing the system can only be estimated or are subject to noise. Much work has been done recently on developing higher order Runge-Kutta methods for solving SDEs numerically. Fixed stepsize implementations of numerical methods have limitations when, for example, the SDE being solved is stiff as this forces the stepsize to be very small. This paper presents a completely general variable stepsize implementation of an embedded Runge Kutta pair for solving SDEs numerically; in this implementation, there is no restriction on the value used for the stepsize, and it is demonstrated that the integration remains on the correct Brownian path.

Multiscale analysis of protein functions and stochastic modelling of gene transcriptional regulatory networks

Genomic and proteomic analyses have attracted a great deal of interests in biological research in recent years. Many methods have been applied to discover useful information contained in the enormous databases of genomic sequences and amino acid sequences. The results of these investigations inspire further research in biological fields in return. These biological sequences, which may be considered as multiscale sequences, have some specific features which need further efforts to characterise using more refined methods. This project aims to study some of these biological challenges with multiscale analysis methods and stochastic modelling approach. The first part of the thesis aims to cluster some unknown proteins, and classify their families as well as their structural classes. A development in proteomic analysis is concerned with the determination of protein functions. The first step in this development is to classify proteins and predict their families. This motives us to study some unknown proteins from specific families, and to cluster them into families and structural classes. We select a large number of proteins from the same families or superfamilies, and link them to simulate some unknown large proteins from these families. We use multifractal analysis and the wavelet method to capture the characteristics of these linked proteins. The simulation results show that the method is valid for the classification of large proteins. The second part of the thesis aims to explore the relationship of proteins based on a layered comparison with their components. Many methods are based on homology of proteins because the resemblance at the protein sequence level normally indicates the similarity of functions and structures. However, some proteins may have similar functions with low sequential identity. We consider protein sequences at detail level to investigate the problem of comparison of proteins. The comparison is based on the empirical mode decomposition (EMD), and protein sequences are detected with the intrinsic mode functions. A measure of similarity is introduced with a new cross-correlation formula. The similarity results show that the EMD is useful for detection of functional relationships of proteins. The third part of the thesis aims to investigate the transcriptional regulatory network of yeast cell cycle via stochastic differential equations. As the investigation of genome-wide gene expressions has become a focus in genomic analysis, researchers have tried to understand the mechanisms of the yeast genome for many years. How cells control gene expressions still needs further investigation. We use a stochastic differential equation to model the expression profile of a target gene. We modify the model with a Gaussian membership function. For each target gene, a transcriptional rate is obtained, and the estimated transcriptional rate is also calculated with the information from five possible transcriptional regulators. Some regulators of these target genes are verified with the related references. With these results, we construct a transcriptional regulatory network for the genes from the yeast Saccharomyces cerevisiae. The construction of transcriptional regulatory network is useful for detecting more mechanisms of the yeast cell cycle.

Candidate radial-inflow turbines and high-density working fluids for geothermal power systems

Optimisation of Organic Rankine Cycles (ORCs) for binary-cycle geothermal applications could play a major role in the competitiveness of low to moderate temperature geothermal resources. Part of this optimisation process is matching cycles to a given resource such that power output can be maximised. Two major and largely interrelated components of the cycle are the working fluid and the turbine. Both components need careful consideration. Due to the temperature differences in geothermal resources a one-size-fits-all approach to surface power infrastructure is not appropriate. Furthermore, the traditional use of steam as a working fluid does not seem practical due to the low temperatures of many resources. A variety of organic fluids with low boiling points may be utilised as ORC working fluids in binary power cycle loops. Due to differences in thermodynamic properties, certain fluids are able to extract more heat from a given resource than others over certain temperature and pressure ranges. This enables the tailoring of power cycle infrastructure to best match the geothermal resource through careful selection of the working fluid and turbine design optimisation to yield the optimum overall cycle performance. This paper presents the rationale for the use of radial-inflow turbines for ORC applications and the preliminary design of several radial-inflow turbines based on a selection of promising ORC cycles using five different high-density working fluids: R134a, R143a, R236fa, R245fa and n-Pentane at sub- or trans-critical conditions. Numerous studies published compare a variety of working fluids for various ORC configurations. However, there is little information specifically pertaining to the design and implementation of ORCs using realistic radial turbine designs in terms of pressure ratios, inlet pressure, rotor size and rotational speed. Preliminary 1D analysis leads to the generation of turbine designs for the various cycles with similar efficiencies (77%) but large differences in dimensions (139289 mm rotor diameter). The highest performing cycle (R134a) was found to produce 33% more net power from a 150°C resource flowing at 10 kg/s than the lowest performing cycle (n-Pentane).

High strong order methods for non-commutative stochastic ordinary differential equation systems and the Magnus formula

In recent years considerable attention has been paid to the numerical solution of stochastic ordinary differential equations (SODEs), as SODEs are often more appropriate than their deterministic counterparts in many modelling situations. However, unlike the deterministic case numerical methods for SODEs are considerably less sophisticated due to the difficulty in representing the (possibly large number of) random variable approximations to the stochastic integrals. Although Burrage and Burrage [High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations, Applied Numerical Mathematics 22 (1996) 81-101] were able to construct strong local order 1.5 stochastic Runge-Kutta methods for certain cases, it is known that all extant stochastic Runge-Kutta methods suffer an order reduction down to strong order 0.5 if there is non-commutativity between the functions associated with the multiple Wiener processes. This order reduction down to that of the Euler-Maruyama method imposes severe difficulties in obtaining meaningful solutions in a reasonable time frame and this paper attempts to circumvent these difficulties by some new techniques. An additional difficulty in solving SODEs arises even in the Linear case since it is not possible to write the solution analytically in terms of matrix exponentials unless there is a commutativity property between the functions associated with the multiple Wiener processes. Thus in this present paper first the work of Magnus [On the exponential solution of differential equations for a linear operator, Communications on Pure and Applied Mathematics 7 (1954) 649-673] (applied to deterministic non-commutative Linear problems) will be applied to non-commutative linear SODEs and methods of strong order 1.5 for arbitrary, linear, non-commutative SODE systems will be constructed - hence giving an accurate approximation to the general linear problem. Secondly, for general nonlinear non-commutative systems with an arbitrary number (d) of Wiener processes it is shown that strong local order I Runge-Kutta methods with d + 1 stages can be constructed by evaluated a set of Lie brackets as well as the standard function evaluations. A method is then constructed which can be efficiently implemented in a parallel environment for this arbitrary number of Wiener processes. Finally some numerical results are presented which illustrate the efficacy of these approaches. (C) 1999 Elsevier Science B.V. All rights reserved.

Mode matching pursuit for estimating dominant modes in bulk power grid

This study presents a general approach to identify dominant oscillation modes in bulk power system by using wide-area measurement system. To automatically identify the dominant modes without artificial participation, spectral characteristic of power system oscillation mode is applied to distinguish electromechanical oscillation modes which are calculated by stochastic subspace method, and a proposed mode matching pursuit is adopted to discriminate the dominant modes from the trivial modes, then stepwise-refinement scheme is developed to remove outliers of the dominant modes and the highly accurate dominant modes of identification are obtained. The method is implemented on the dominant modes of China Southern Power Grid which is one of the largest AC/DC paralleling grids in the world. Simulation data and field-measurement data are used to demonstrate high accuracy and better robustness of the dominant modes identification approach.

Energy-efficient localization : GPS duty cycling with radio ranging

GPS is a commonly used and convenient technology for determining absolute position in outdoor environments, but its high power consumption leads to rapid battery depletion in mobile devices. An obvious solution is to duty cycle the GPS module, which prolongs the device lifetime at the cost of increased position uncertainty while the GPS is off. This article addresses the trade-off between energy consumption and localization performance in a mobile sensor network application. The focus is on augmenting GPS location with more energy-efficient location sensors to bound position estimate uncertainty while GPS is off. Empirical GPS and radio contact data from a large-scale animal tracking deployment is used to model node mobility, radio performance, and GPS. Because GPS takes a considerable, and variable, time after powering up before it delivers a good position measurement, we model the GPS behaviour through empirical measurements of two GPS modules. These models are then used to explore duty cycling strategies for maintaining position uncertainty within specified bounds. We then explore the benefits of using short-range radio contact logging alongside GPS as an energy-inexpensive means of lowering uncertainty while the GPS is off, and we propose strategies that use RSSI ranging and GPS back-offs to further reduce energy consumption. Results show that our combined strategies can cut node energy consumption by one third while still meeting application-specific positioning criteria.

Influence of all-out and fast start of 5-min cycling time trial performance

Purpose: To examine the influence of two different fast-start pacing strategies on performance and oxygen consumption (V˙O2) during cycle ergometer time trials lasting ∼5 min. Methods: Eight trained male cyclists performed four cycle ergometer time trials whereby the total work completed (113 ± 11.5 kJ; mean ± SD) was identical to the better of two 5-min self-paced familiarization trials. During the performance trials, initial power output was manipulated to induce either an all-out or a fast start. Power output during the first 60 s of the fast-start trial was maintained at 471.0 ± 48.0 W, whereas the all-out start approximated a maximal starting effort for the first 15 s (mean power: 753.6 ± 76.5 W) followed by 45 s at a constant power output (376.8 ± 38.5 W). Irrespective of starting strategy, power output was controlled so that participants would complete the first quarter of the trial (28.3 ± 2.9 kJ) in 60 s. Participants performed two trials using each condition, with their fastest time trial compared. Results: Performance time was significantly faster when cyclists adopted the all-out start (4 min 48 s ± 8 s) compared with the fast start (4 min 51 s ± 8 s; P < 0.05). The first-quarter V˙O2 during the all-out start trial (3.4 ± 0.4 L·min-1) was significantly higher than during the fast-start trial (3.1 ± 0.4 L·min-1; P < 0.05). After removal of an outlier, the percentage increase in first-quarter V˙O2 was significantly correlated (r = -0.86, P < 0.05) with the relative difference in finishing time. Conclusions: An all-out start produces superior middle distance cycling performance when compared with a fast start. The improvement in performance may be due to a faster V˙O2 response rather than time saved due to a rapid acceleration.

Variable structure control for power systems stabilization

The application of variable structure control (VSC) for power systems stabilization is studied in this paper. It is the application, aspects and constraints of VSC which are of particular interest. A variable structure control methodology has been proposed for power systems stabilization. The method is implemented using thyristor controlled series compensators. A three machine power system is stabilized using a switching line control for large disturbances which becomes a sliding control as the disturbance becomes smaller. The results demonstrate the effectiveness of the methodology proposed as an useful tool to suppress the oscillations in power systems.

Flexible high voltage pulsed power supply for plasma applications

Demands for delivering high instantaneous power in a compressed form (pulse shape) have widely increased during recent decades. The flexible shapes with variable pulse specifications offered by pulsed power have made it a practical and effective supply method for an extensive range of applications. In particular, the release of basic subatomic particles (i.e. electron, proton and neutron) in an atom (ionization process) and the synthesizing of molecules to form ions or other molecules are among those reactions that necessitate large amount of instantaneous power. In addition to the decomposition process, there have recently been requests for pulsed power in other areas such as in the combination of molecules (i.e. fusion, material joining), gessoes radiations (i.e. electron beams, laser, and radar), explosions (i.e. concrete recycling), wastewater, exhausted gas, and material surface treatments. These pulses are widely employed in the silent discharge process in all types of materials (including gas, fluid and solid); in some cases, to form the plasma and consequently accelerate the associated process. Due to this fast growing demand for pulsed power in industrial and environmental applications, the exigency of having more efficient and flexible pulse modulators is now receiving greater consideration. Sensitive applications, such as plasma fusion and laser guns also require more precisely produced repetitive pulses with a higher quality. Many research studies are being conducted in different areas that need a flexible pulse modulator to vary pulse features to investigate the influence of these variations on the application. In addition, there is the need to prevent the waste of a considerable amount of energy caused by the arc phenomena that frequently occur after the plasma process. The control over power flow during the supply process is a critical skill that enables the pulse supply to halt the supply process at any stage. Different pulse modulators which utilise different accumulation techniques including Marx Generators (MG), Magnetic Pulse Compressors (MPC), Pulse Forming Networks (PFN) and Multistage Blumlein Lines (MBL) are currently employed to supply a wide range of applications. Gas/Magnetic switching technologies (such as spark gap and hydrogen thyratron) have conventionally been used as switching devices in pulse modulator structures because of their high voltage ratings and considerably low rising times. However, they also suffer from serious drawbacks such as, their low efficiency, reliability and repetition rate, and also their short life span. Being bulky, heavy and expensive are the other disadvantages associated with these devices. Recently developed solid-state switching technology is an appropriate substitution for these switching devices due to the benefits they bring to the pulse supplies. Besides being compact, efficient, reasonable and reliable, and having a long life span, their high frequency switching skill allows repetitive operation of pulsed power supply. The main concerns in using solid-state transistors are the voltage rating and the rising time of available switches that, in some cases, cannot satisfy the application’s requirements. However, there are several power electronics configurations and techniques that make solid-state utilisation feasible for high voltage pulse generation. Therefore, the design and development of novel methods and topologies with higher efficiency and flexibility for pulsed power generators have been considered as the main scope of this research work. This aim is pursued through several innovative proposals that can be classified under the following two principal objectives. • To innovate and develop novel solid-state based topologies for pulsed power generation • To improve available technologies that have the potential to accommodate solid-state technology by revising, reconfiguring and adjusting their structure and control algorithms. The quest to distinguish novel topologies for a proper pulsed power production was begun with a deep and through review of conventional pulse generators and useful power electronics topologies. As a result of this study, it appears that efficiency and flexibility are the most significant demands of plasma applications that have not been met by state-of-the-art methods. Many solid-state based configurations were considered and simulated in order to evaluate their potential to be utilised in the pulsed power area. Parts of this literature review are documented in Chapter 1 of this thesis. Current source topologies demonstrate valuable advantages in supplying the loads with capacitive characteristics such as plasma applications. To investigate the influence of switching transients associated with solid-state devices on rise time of pulses, simulation based studies have been undertaken. A variable current source is considered to pump different current levels to a capacitive load, and it was evident that dissimilar dv/dts are produced at the output. Thereby, transient effects on pulse rising time are denied regarding the evidence acquired from this examination. A detailed report of this study is given in Chapter 6 of this thesis. This study inspired the design of a solid-state based topology that take advantage of both current and voltage sources. A series of switch-resistor-capacitor units at the output splits the produced voltage to lower levels, so it can be shared by the switches. A smart but complicated switching strategy is also designed to discharge the residual energy after each supply cycle. To prevent reverse power flow and to reduce the complexity of the control algorithm in this system, the resistors in common paths of units are substituted with diode rectifiers (switch-diode-capacitor). This modification not only gives the feasibility of stopping the load supply process to the supplier at any stage (and consequently saving energy), but also enables the converter to operate in a two-stroke mode with asymmetrical capacitors. The components’ determination and exchanging energy calculations are accomplished with respect to application specifications and demands. Both topologies were simply modelled and simulation studies have been carried out with the simplified models. Experimental assessments were also executed on implemented hardware and the approaches verified the initial analysis. Reports on details of both converters are thoroughly discussed in Chapters 2 and 3 of the thesis. Conventional MGs have been recently modified to use solid-state transistors (i.e. Insulated gate bipolar transistors) instead of magnetic/gas switching devices. Resistive insulators previously used in their structures are substituted by diode rectifiers to adjust MGs for a proper voltage sharing. However, despite utilizing solid-state technology in MGs configurations, further design and control amendments can still be made to achieve an improved performance with fewer components. Considering a number of charging techniques, resonant phenomenon is adopted in a proposal to charge the capacitors. In addition to charging the capacitors at twice the input voltage, triggering switches at the moment at which the conducted current through switches is zero significantly reduces the switching losses. Another configuration is also introduced in this research for Marx topology based on commutation circuits that use a current source to charge the capacitors. According to this design, diode-capacitor units, each including two Marx stages, are connected in cascade through solid-state devices and aggregate the voltages across the capacitors to produce a high voltage pulse. The polarity of voltage across one capacitor in each unit is reversed in an intermediate mode by connecting the commutation circuit to the capacitor. The insulation of input side from load side is provided in this topology by disconnecting the load from the current source during the supply process. Furthermore, the number of required fast switching devices in both designs is reduced to half of the number used in a conventional MG; they are replaced with slower switches (such as Thyristors) that need simpler driving modules. In addition, the contributing switches in discharging paths are decreased to half; this decrease leads to a reduction in conduction losses. Associated models are simulated, and hardware tests are performed to verify the validity of proposed topologies. Chapters 4, 5 and 7 of the thesis present all relevant analysis and approaches according to these topologies.

Caffeine ingestion and cycling power output in a low or normal muscle glycogen state

Purpose Commencing selected workouts with low muscle glycogen availability augments several markers of training adaptation compared with undertaking the same sessions with normal glycogen content. However, low glycogen availability reduces the capacity to perform high-intensity (>85% of peak aerobic power (V·O2peak)) endurance exercise. We determined whether a low dose of caffeine could partially rescue the reduction in maximal self-selected power output observed when individuals commenced high-intensity interval training with low (LOW) compared with normal (NORM) glycogen availability. Methods Twelve endurance-trained cyclists/triathletes performed four experimental trials using a double-blind Latin square design. Muscle glycogen content was manipulated via exercise–diet interventions so that two experimental trials were commenced with LOW and two with NORM muscle glycogen availability. Sixty minutes before an experimental trial, subjects ingested a capsule containing anhydrous caffeine (CAFF, 3 mg-1·kg-1 body mass) or placebo (PLBO). Instantaneous power output was measured throughout high-intensity interval training (8 × 5-min bouts at maximum self-selected intensity with 1-min recovery). Results There were significant main effects for both preexercise glycogen content and caffeine ingestion on power output. LOW reduced power output by approximately 8% compared with NORM (P < 0.01), whereas caffeine increased power output by 2.8% and 3.5% for NORM and LOW, respectively, (P < 0.01). Conclusion We conclude that caffeine enhanced power output independently of muscle glycogen concentration but could not fully restore power output to levels commensurate with that when subjects commenced exercise with normal glycogen availability. However, the reported increase in power output does provide a likely performance benefit and may provide a means to further enhance the already augmented training response observed when selected sessions are commenced with reduced muscle glycogen availability. It has long been known that endurance training induces a multitude of metabolic and morphological adaptations that improve the resistance of the trained musculature to fatigue and enhance endurance capacity and/or exercise performance (13). Accumulating evidence now suggests that many of these adaptations can be modified by nutrient availability (9–11,21). Growing evidence suggests that training with reduced muscle glycogen using a “train twice every second day” compared with a more traditional “train once daily” approach can enhance the acute training response (29) and markers representative of endurance training adaptation after short-term (3–10 wk) training interventions (8,16,30). Of note is that the superior training adaptation in these previous studies was attained despite a reduction in maximal self-selected power output (16,30). The most obvious factor underlying the reduced intensity during a second training bout is the reduction in muscle glycogen availability. However, there is also the possibility that other metabolic and/or neural factors may be responsible for the power drop-off observed when two exercise bouts are performed in close proximity. Regardless of the precise mechanism(s), there remains the intriguing possibility that the magnitude of training adaptation previously reported in the face of a reduced training intensity (Hulston et al. (16) and Yeo et al.) might be further augmented, and/or other aspects of the training stimulus better preserved, if power output was not compromised. Caffeine ingestion is a possible strategy that might “rescue” the aforementioned reduction in power output that occurs when individuals commence high-intensity interval training (HIT) with low compared with normal glycogen availability. Recent evidence suggests that, at least in endurance-based events, the maximal benefits of caffeine are seen at small to moderate (2–3 mg·kg-1 body mass (BM)) doses (for reviews, see Refs. (3,24)). Accordingly, in this study, we aimed to determine the effect of a low dose of caffeine (3 mg·kg-1 BM) on maximal self-selected power output during HIT commenced with either normal (NORM) or low (LOW) muscle glycogen availability. We hypothesized that even under conditions of low glycogen availability, caffeine would increase maximal self-selected power output and thereby partially rescue the reduction in training intensity observed when individuals commence HIT with low glycogen availability.

The Reef Cycle: Paradise; Paradise Plundered; Paradise Preserved by people Power

This is a musical theatre production with an environmental message addressing a Queensland, Australia tussle between the development of the Galilee Coal Basin and the potential threat to the health of the Great Barrier Reef along the Queensland coast. The drama is enacted by characters representing "goodies" and "baddies" and includes epic poetry, dance, orchestra and drama. The whole performance is enacted in the midst of a post graduate student art exhibition with a coral and coal theme.

Physiological and symptomatic responses to cycling and walking in intermittent claudication

To shed light on the potential efficacy of cycling as a testing modality in the treatment of intermittent claudication (IC), this study compared physiological and symptomatic responses to graded walking and cycling tests in claudicants. Sixteen subjects with peripheral arterial disease (resting ankle: brachial index (ABI) < 0.9) and IC completed a maximal graded treadmill walking (T) and cycle (C) test after three familiarization tests on each mode. During each test, symptoms, oxygen uptake (VO2), minute ventilation (VE), respiratory exchange ratio (RER) and heart rate (HR) were measured, and for 10 min after each test the brachial and ankle systolic pressures were recorded. All but one subject experienced calf pain as the primary limiting symptom during T; whereas the symptoms were more varied during C and included thigh pain, calf pain and dyspnoea. Although maximal exercise time was significantly longer on C than T (690 +/- 67 vs. 495 +/- 57 s), peak VO2, peak VE and peak heart rate during C and T were not different; whereas peak RER was higher during C. These responses during C and T were also positively correlated (P < 0.05) with each other, with the exception of RER. The postexercise systolic pressures were also not different between C and T. However, the peak decline in ankle pressures from resting values after C and T were not correlated with each other. These data demonstrate that cycling and walking induce a similar level of metabolic and cardiovascular strain, but that the primary limiting symptoms and haemodynamic response in an individual's extremity, measured after exercise, can differ substantially between these two modes.

A framework for fully decentralised cycle stealing

Ordinary desktop computers continue to obtain ever more resources – in-creased processing power, memory, network speed and bandwidth – yet these resources spend much of their time underutilised. Cycle stealing frameworks harness these resources so they can be used for high-performance computing. Traditionally cycle stealing systems have used client-server based architectures which place significant limits on their ability to scale and the range of applica-tions they can support. By applying a fully decentralised network model to cycle stealing the limits of centralised models can be overcome. Using decentralised networks in this manner presents some difficulties which have not been encountered in their previous uses. Generally decentralised ap-plications do not require any significant fault tolerance guarantees. High-performance computing on the other hand requires very stringent guarantees to ensure correct results are obtained. Unfortunately mechanisms developed for traditional high-performance computing cannot be simply translated because of their reliance on a reliable storage mechanism. In the highly dynamic world of P2P computing this reliable storage is not available. As part of this research a fault tolerance system has been created which provides considerable reliability without the need for a persistent storage. As well as increased scalability, fully decentralised networks offer the ability for volunteers to communicate directly. This ability provides the possibility of supporting applications whose tasks require direct, message passing style communication. Previous cycle stealing systems have only supported embarrassingly parallel applications and applications with limited forms of communication so a new programming model has been developed which can support this style of communication within a cycle stealing context. In this thesis I present a fully decentralised cycle stealing framework. The framework addresses the problems of providing a reliable fault tolerance sys-tem and supporting direct communication between parallel tasks. The thesis includes a programming model for developing cycle stealing applications with direct inter-process communication and methods for optimising object locality on decentralised networks.