Novel analytical and numerical methods for solving fractional dynamical systems

During the past three decades, the subject of fractional calculus (that is, calculus of integrals and derivatives of arbitrary order) has gained considerable popularity and importance, mainly due to its demonstrated applications in numerous diverse and widespread fields in science and engineering. For example, fractional calculus has been successfully applied to problems in system biology, physics, chemistry and biochemistry, hydrology, medicine, and finance. In many cases these new fractional-order models are more adequate than the previously used integer-order models, because fractional derivatives and integrals enable the description of the memory and hereditary properties inherent in various materials and processes that are governed by anomalous diffusion. Hence, there is a growing need to find the solution behaviour of these fractional differential equations. However, the analytic solutions of most fractional differential equations generally cannot be obtained. As a consequence, approximate and numerical techniques are playing an important role in identifying the solution behaviour of such fractional equations and exploring their applications. The main objective of this thesis is to develop new effective numerical methods and supporting analysis, based on the finite difference and finite element methods, for solving time, space and time-space fractional dynamical systems involving fractional derivatives in one and two spatial dimensions. A series of five published papers and one manuscript in preparation will be presented on the solution of the space fractional diffusion equation, space fractional advectiondispersion equation, time and space fractional diffusion equation, time and space fractional Fokker-Planck equation with a linear or non-linear source term, and fractional cable equation involving two time fractional derivatives, respectively. One important contribution of this thesis is the demonstration of how to choose different approximation techniques for different fractional derivatives. Special attention has been paid to the Riesz space fractional derivative, due to its important application in the field of groundwater flow, system biology and finance. We present three numerical methods to approximate the Riesz space fractional derivative, namely the L1/ L2-approximation method, the standard/shifted Gr¨unwald method, and the matrix transform method (MTM). The first two methods are based on the finite difference method, while the MTM allows discretisation in space using either the finite difference or finite element methods. Furthermore, we prove the equivalence of the Riesz fractional derivative and the fractional Laplacian operator under homogeneous Dirichlet boundary conditions – a result that had not previously been established. This result justifies the aforementioned use of the MTM to approximate the Riesz fractional derivative. After spatial discretisation, the time-space fractional partial differential equation is transformed into a system of fractional-in-time differential equations. We then investigate numerical methods to handle time fractional derivatives, be they Caputo type or Riemann-Liouville type. This leads to new methods utilising either finite difference strategies or the Laplace transform method for advancing the solution in time. The stability and convergence of our proposed numerical methods are also investigated. Numerical experiments are carried out in support of our theoretical analysis. We also emphasise that the numerical methods we develop are applicable for many other types of fractional partial differential equations.

The effects of L1 orthography on processing an artificial logographic script

To date, studies have focused on the acquisition of alphabetic second languages (L2s) in alphabetic first language (L1) users, demonstrating significant transfer effects. The present study examined the process from a reverse perspective, comparing logographic (Mandarin-Chinese) and alphabetic (English) L1 users in the acquisition of an artificial logographic script, in order to determine whether similar language-specific advantageous transfer effects occurred. English monolinguals, English-French bilinguals and Chinese-English bilinguals learned a small set of symbols in an artificial logographic script and were subsequently tested on their ability to process this script in regard to three main perspectives: L2 reading, L2 working memory (WM), and inner processing strategies. In terms of L2 reading, a lexical decision task on the artificial symbols revealed markedly faster response times in the Chinese-English bilinguals, indicating a logographic transfer effect suggestive of a visual processing advantage. A syntactic decision task evaluated the degree to which the new language was mastered beyond the single word level. No L1-specific transfer effects were found for artificial language strings. In order to investigate visual processing of the artificial logographs further, a series of WM experiments were conducted. Artificial logographs were recalled under concurrent auditory and visuo-spatial suppression conditions to disrupt phonological and visual processing, respectively. No L1-specific transfer effects were found, indicating no visual processing advantage of the Chinese-English bilinguals. However, a bilingual processing advantage was found indicative of a superior ability to control executive functions. In terms of L1 WM, the Chinese-English bilinguals outperformed the alphabetic L1 users when processing L1 words, indicating a language experience-specific advantage. Questionnaire data on the cognitive strategies that were deployed during the acquisition and processing of the artificial logographic script revealed that the Chinese-English bilinguals rated their inner speech as lower than the alphabetic L1 users, suggesting that they were transferring their phonological processing skill set to the acquisition and use of an artificial script. Overall, evidence was found to indicate that language learners transfer specific L1 orthographic processing skills to L2 logographic processing. Additionally, evidence was also found indicating that a bilingual history enhances cognitive performance in L2.

Swept frequency biompedance analysis for the determination of body water compartments

Bioelectrical impedance analysis, (BIA), is a method of body composition analysis first investigated in 1962 which has recently received much attention by a number of research groups. The reasons for this recent interest are its advantages, (viz: inexpensive, non-invasive and portable) and also the increasing interest in the diagnostic value of body composition analysis. The concept utilised by BIA to predict body water volumes is the proportional relationship for a simple cylindrical conductor, (volume oc length2/resistance), which allows the volume to be predicted from the measured resistance and length. Most of the research to date has measured the body's resistance to the passage of a 50· kHz AC current to predict total body water, (TBW). Several research groups have investigated the application of AC currents at lower frequencies, (eg 5 kHz), to predict extracellular water, (ECW). However all research to date using BIA to predict body water volumes has used the impedance measured at a discrete frequency or frequencies. This thesis investigates the variation of impedance and phase of biological systems over a range of frequencies and describes the development of a swept frequency bioimpedance meter which measures impedance and phase at 496 frequencies ranging from 4 kHz to 1 MHz. The impedance of any biological system varies with the frequency of the applied current. The graph of reactance vs resistance yields a circular arc with the resistance decreasing with increasing frequency and reactance increasing from zero to a maximum then decreasing to zero. Computer programs were written to analyse the measured impedance spectrum and determine the impedance, Zc, at the characteristic frequency, (the frequency at which the reactance is a maximum). The fitted locus of the measured data was extrapolated to determine the resistance, Ro, at zero frequency; a value that cannot be measured directly using surface electrodes. The explanation of the theoretical basis for selecting these impedance values (Zc and Ro), to predict TBW and ECW is presented. Studies were conducted on a group of normal healthy animals, (n=42), in which TBW and ECW were determined by the gold standard of isotope dilution. The prediction quotients L2/Zc and L2/Ro, (L=length), yielded standard errors of 4.2% and 3.2% respectively, and were found to be significantly better than previously reported, empirically determined prediction quotients derived from measurements at a single frequency. The prediction equations established in this group of normal healthy animals were applied to a group of animals with abnormally low fluid levels, (n=20), and also to a group with an abnormal balance of extra-cellular to intracellular fluids, (n=20). In both cases the equations using L2/Zc and L2/Ro accurately and precisely predicted TBW and ECW. This demonstrated that the technique developed using multiple frequency bioelectrical impedance analysis, (MFBIA), can accurately predict both TBW and ECW in both normal and abnormal animals, (with standard errors of the estimate of 6% and 3% for TBW and ECW respectively). Isotope dilution techniques were used to determine TBW and ECW in a group of 60 healthy human subjects, (male. and female, aged between 18 and 45). Whole body impedance measurements were recorded on each subject using the MFBIA technique and the correlations between body water volumes, (TBW and ECW), and heighe/impedance, (for all measured frequencies), were compared. The prediction quotients H2/Zc and H2/Ro, (H=height), again yielded the highest correlation with TBW and ECW respectively with corresponding standard errors of 5.2% and 10%. The values of the correlation coefficients obtained in this study were very similar to those recently reported by others. It was also observed that in healthy human subjects the impedance measured at virtually any frequency yielded correlations not significantly different from those obtained from the MFBIA quotients. This phenomenon has been reported by other research groups and emphasises the need to validate the technique by investigating its application in one or more groups with abnormalities in fluid levels. The clinical application of MFBIA was trialled and its capability of detecting lymphoedema, (an excess of extracellular fluid), was investigated. The MFBIA technique was demonstrated to be significantly more sensitive, (P<.05), in detecting lymphoedema than the current technique of circumferential measurements. MFBIA was also shown to provide valuable information describing the changes in the quantity of muscle mass of the patient during the course of the treatment. The determination of body composition, (viz TBW and ECW), by MFBIA has been shown to be a significant improvement on previous bioelectrical impedance techniques. The merit of the MFBIA technique is evidenced in its accurate, precise and valid application in animal groups with a wide variation in body fluid volumes and balances. The multiple frequency bioelectrical impedance analysis technique developed in this study provides accurate and precise estimates of body composition, (viz TBW and ECW), regardless of the individual's state of health.

Trading spaces : on the lore and limitations of latent semantic analysis

Two decades after its inception, Latent Semantic Analysis(LSA) has become part and parcel of every modern introduction to Information Retrieval. For any tool that matures so quickly, it is important to check its lore and limitations, or else stagnation will set in. We focus here on the three main aspects of LSA that are well accepted, and the gist of which can be summarized as follows: (1) that LSA recovers latent semantic factors underlying the document space, (2) that such can be accomplished through lossy compression of the document space by eliminating lexical noise, and (3) that the latter can best be achieved by Singular Value Decomposition. For each aspect we performed experiments analogous to those reported in the LSA literature and compared the evidence brought to bear in each case. On the negative side, we show that the above claims about LSA are much more limited than commonly believed. Even a simple example may show that LSA does not recover the optimal semantic factors as intended in the pedagogical example used in many LSA publications. Additionally, and remarkably deviating from LSA lore, LSA does not scale up well: the larger the document space, the more unlikely that LSA recovers an optimal set of semantic factors. On the positive side, we describe new algorithms to replace LSA (and more recent alternatives as pLSA, LDA, and kernel methods) by trading its l2 space for an l1 space, thereby guaranteeing an optimal set of semantic factors. These algorithms seem to salvage the spirit of LSA as we think it was initially conceived.

Error correction in second language writing : teachers’ beliefs, practices, and students’ preferences

Error correction is perhaps the most widely used method for responding to student writing. While various studies have investigated the effectiveness of providing error correction, there has been relatively little research incorporating teachers' beliefs, practices, and students' preferences in written error correction. The current study adopted features of an ethnographic research design in order to explore the beliefs and practices of ESL teachers, and investigate the preferences of L2 students regarding written error correction in the context of a language institute situated in the Brisbane metropolitan district. In this study, two ESL teachers and two groups of adult intermediate L2 students were interviewed and observed. The beliefs and practices of the teachers were elicited through interviews and classroom observations. The preferences of L2 students were elicited through focus group interviews. Responses of the participants were encoded and analysed. Results of the teacher interviews showed that teachers believe that providing written error correction has advantages and disadvantages. Teachers believe that providing written error correction helps students improve their proof-reading skills in order to revise their writing more efficiently. However, results also indicate that providing written error correction is very time consuming. Furthermore, teachers prefer to provide explicit written feedback strategies during the early stages of the language course, and move to a more implicit strategy of providing written error correction in order to facilitate language learning. On the other hand, results of the focus group interviews suggest that students regard their teachers' practice of written error correction as important in helping them locate their errors and revise their writing. However, students also feel that the process of providing written error correction is time consuming. Nevertheless, students want and expect their teachers to provide written feedback because they believe that the benefits they gain from receiving feedback on their writing outweigh the apparent disadvantages of their teachers' written error correction strategies.

Enhancing foreign language learning through listening strategy delivered in L1: an experimental study

Listening used in language teaching refers to a complex process that allows us to understand spoken language. The current study, conducted in Iran with an experimental design, investigated the effectiveness of teaching listening strategies delivered in L1 (Persian) and its effect on listening comprehension in L2. Five listening strategies: Guessing, making inferences, identifying topics, repetition, and note-taking were taught over 14 weeks during a semester. Sixty lower intermediate female participants came from two EFL classrooms in an English language institute. The experimental class (n = 30) who listened to their classroom activities performed better (t value = 10.083) than the control class using a methodology that led learners through five listening strategies in Persian. The same teacher taught the students in the control class (n = 30), who listened to the same classroom listening activities without any of the above listening strategies. A pre and post listening test made by a group of experts in the language institute assessed the effect of teaching listening strategies delivered in L1. Results gathered on the post intervention listening test revealed that listening strategies delivered in L1 led to a statistically significant improvement in their discrete listening scores compared with the control group.

The impact of English as a Foreign Language (EFL) listening comprehension through first language (L1) listening strategy training

Listening is the basic and complementary skill in second language learning. The term listening is used in language teaching to refer to a complex process that allows us to understand spoken language. Listening, the most widely used language skill, is often used in conjunction with the other skills of speaking, reading and writing. Listening is not only a skill area in primary language performance (L1), but is also a critical means of acquiring a second language (L2). Listening is the channel in which we process language in real time – employing pacing, units of encoding and decoding (the 2 processes are central to interpretation and meaning making) and pausing (allows for reflection) that are unique to spoken language. Despite the wide range of areas investigated in listening strategies during training, there is a lack of research looking specifically at how effectively L1 listening strategy training may transfer to L2. To investigate the development of any such transfer patterns the instructional design and implementation of listening strategy of L1 will be critical.

Validation and consistency in the application of a trauma team activation system at a level 1 trauma centre

- The RAH was activated over 2500 trauma calls in 2009. This figure is over twice the number of calls put out by similar services. - Many trauma calls (in particular L2 trauma calls) from the existing system do not warrant activation of the trauma team - Sometimes trauma calls are activated for nontrauma reasons (eg rapid access to radiology, departmental pressures etc) - The excess of trauma calls has several deleterious effects particularly on time management for the trauma service staff: ward rounds/tertiary survey rounds, education, quality improvement, research

Generalized-positioning for mixed-frequency of mixed-GNSS and its preliminary applications

Modernized GPS and GLONASS, together with new GNSS systems, BeiDou and Galileo, offer code and phase ranging signals in three or more carriers. Traditionally, dual-frequency code and/or phase GPS measurements are linearly combined to eliminate effects of ionosphere delays in various positioning and analysis. This typical treatment method has imitations in processing signals at three or more frequencies from more than one system and can be hardly adapted itself to cope with the booming of various receivers with a broad variety of singles. In this contribution, a generalized-positioning model that the navigation system independent and the carrier number unrelated is promoted, which is suitable for both single- and multi-sites data processing. For the synchronization of different signals, uncalibrated signal delays (USD) are more generally defined to compensate the signal specific offsets in code and phase signals respectively. In addition, the ionospheric delays are included in the parameterization with an elaborate consideration. Based on the analysis of the algebraic structures, this generalized-positioning model is further refined with a set of proper constrains to regularize the datum deficiency of the observation equation system. With this new model, uncalibrated signal delays (USD) and ionospheric delays are derived for both GPS and BeiDou with a large dada set. Numerical results demonstrate that, with a limited number of stations, the uncalibrated code delays (UCD) are determinate to a precision of about 0.1 ns for GPS and 0.4 ns for BeiDou signals, while the uncalibrated phase delays (UPD) for L1 and L2 are generated with 37 stations evenly distributed in China for GPS with a consistency of about 0.3 cycle. Extra experiments concerning the performance of this novel model in point positioning with mixed-frequencies of mixed-constellations is analyzed, in which the USD parameters are fixed with our generated values. The results are evaluated in terms of both positioning accuracy and convergence time.

Evidence for allelic association of the dopamine β-hydroxylase gene (DBH) with susceptibility to typical migraine

Migraine is a debilitating neurological disorder characterized by recurrent attacks of severe headache. The disorder is highly prevalent, affecting approximately 12% of Caucasian populations. It is well known that migraine has a strong genetic component, although the type and number of genes involved is not yet clear. However, the calcium channel gene, CACNA1A, on chromosome 19 contains mutations responsible for familial hemiplegic migraine, a rare and severe subtype of migraine. There is also evidence to suggest that serotonin- and dopamine-related genes may be involved in the pathogenesis of migraine. This study employed a linkage and association approach to investigate neurotransmitter-related migraine candidate genes. Polymorphisms within the dopamine beta-hydroxylase (DBH) gene, serotonin transporter gene (SERT), and dopamine receptor gene (DRD2) were tested in 177 unrelated Caucasian migraineurs and 182 control individuals. In addition, an independent sample of 82 families affected with migraine was examined. Unrelated case-control association analysis of a DBH intragenic dinucleotide polymorphism indicated altered allelic distribution between migraine and control groups (L2=16.53, P=0.019). Furthermore, the transmission/disequilibrium test, which was implemented on the family data, also indicated distortion of allele transmission for the same DBH marker (L2=4.44, P=0.035). Together, these results provide evidence for allelic association of the DBH gene with typical migraine susceptibility (Fisher's combined P value=0.006) and indicate that further research into the role of the DBH gene in the etiology of migraine is warranted.

An efficient and effective localization method for networked disjoint top-view cameras

Disjoint top-view networked cameras are among the most commonly utilized networks in many applications. One of the open questions for these cameras' study is the computation of extrinsic parameters (positions and orientations), named extrinsic calibration or localization of cameras. Current approaches either rely on strict assumptions of the object motion for accurate results or fail to provide results of high accuracy without the requirement of the object motion. To address these shortcomings, we present a location-constrained maximum a posteriori (LMAP) approach by applying known locations in the surveillance area, some of which would be passed by the object opportunistically. The LMAP approach formulates the problem as a joint inference of the extrinsic parameters and object trajectory based on the cameras' observations and the known locations. In addition, a new task-oriented evaluation metric, named MABR (the Maximum value of All image points' Back-projected localization errors' L2 norms Relative to the area of field of view), is presented to assess the quality of the calibration results in an indoor object tracking context. Finally, results herein demonstrate the superior performance of the proposed method over the state-of-the-art algorithm based on the presented MABR and classical evaluation metric in simulations and real experiments.

Estimating second language productive vocabulary size: A Capture-Recapture approach

This study provides validity evidence for the Capture-Recapture (CR) method, borrowed from ecology, as a measure of second language (L2) productive vocabulary size (PVS). Two separate “captures” of productive vocabulary were taken using written word association tasks (WAT). At Time 1, 47 bilinguals provided at least 4 associates to each of 30 high-frequency stimulus words in English, their first language (L1), and in French, their L2. A few days later (Time 2), this procedure was repeated with a different set of stimulus words in each language. Since the WAT was used, both Lex30 and CR PVS scores were calculated in each language. Participants also completed an animacy judgment task assessing the speed and efficiency of lexical access. Results indicated that, in both languages, CR and Lex30 scores were significantly positively correlated (evidence of convergent validity). CR scores were also significantly larger in the L1, and correlated significantly with the speed of lexical access in the L2 (evidence of construct validity). These results point to the validity of the technique for estimating relative L2 PVS. However, CR scores are not a direct indication of absolute vocabulary size. A discussion of the method’s underlying assumptions and their implications for interpretation are provided.

Maximum principle and numerical method for the multi-term time–space Riesz–Caputo fractional differential equations

The maximum principle for the space and time–space fractional partial differential equations is still an open problem. In this paper, we consider a multi-term time–space Riesz–Caputo fractional differential equations over an open bounded domain. A maximum principle for the equation is proved. The uniqueness and continuous dependence of the solution are derived. Using a fractional predictor–corrector method combining the L1 and L2 discrete schemes, we present a numerical method for the specified equation. Two examples are given to illustrate the obtained results.