Computationally efficient methods for solving time-variable-order time-space fractional reaction-diffusion equation

Fractional differential equations are becoming more widely accepted as a powerful tool in modelling anomalous diffusion, which is exhibited by various materials and processes. Recently, researchers have suggested that rather than using constant order fractional operators, some processes are more accurately modelled using fractional orders that vary with time and/or space. In this paper we develop computationally efficient techniques for solving time-variable-order time-space fractional reaction-diffusion equations (tsfrde) using the finite difference scheme. We adopt the Coimbra variable order time fractional operator and variable order fractional Laplacian operator in space where both orders are functions of time. Because the fractional operator is nonlocal, it is challenging to efficiently deal with its long range dependence when using classical numerical techniques to solve such equations. The novelty of our method is that the numerical solution of the time-variable-order tsfrde is written in terms of a matrix function vector product at each time step. This product is approximated efficiently by the Lanczos method, which is a powerful iterative technique for approximating the action of a matrix function by projecting onto a Krylov subspace. Furthermore an adaptive preconditioner is constructed that dramatically reduces the size of the required Krylov subspaces and hence the overall computational cost. Numerical examples, including the variable-order fractional Fisher equation, are presented to demonstrate the accuracy and efficiency of the approach.

Time-varying bispectral analysis of auditory evoked multi-channel scalp EEG

Time-varying bispectra, computed using a classical sliding window short-time Fourier approach, are analyzed for scalp EEG potentials evoked by an auditory stimulus and new observations are presented. A single, short duration tone is presented from the left or the right, direction unknown to the test subject. The subject responds by moving the eyes to the direction of the sound. EEG epochs sampled at 200 Hz for repeated trials are processed between -70 ms and +1200 ms with reference to the stimulus. It is observed that for an ensemble of correctly recognized cases, the best matching timevarying bispectra at (8 Hz, 8Hz) are for PZ-FZ channels and this is also largely the case for grand averages but not for power spectra at 8 Hz. Out of 11 subjects, the only exception for time-varying bispectral match was a subject with family history of Alzheimer’s disease and the difference was in bicoherence, not biphase.

Academics’ work and the concept of “profession” : an Australian case study

Universities in Australia and elsewhere have changed considerably in recent years. Inevitably, this has meant that the work of academics has also changed. Academics’ work is of importance because they are key players in universities and universities matter to the nation economically and intellectually in advancing knowledge and its practical application. Through the changes and challenges that have characterised academia in recent years, there is an assumption that academics’ work is representative of a profession. This research study investigates how academics construct their own perspectives regarding the academic "profession". The study is theoretically informed by Freidson’s theory that conceptualises professions as occupations if they are in control of their work rather than it being under the control of either the market or of their employing institutions. Two research questions guide this study. The first question investigates how academics might construct their work in ideal terms and the second one investigates the extent to which such constructions might constitute a "profession". A qualitative case study was conducted within two Australian universities. In all, twenty academics from ten disciplines took part in the study that consisted of a focus group and fifteen individual interviews. The study was conducted in three phases during which a conceptual framework of academics’ work was developed across three versions. This framework acted both a prompt to discussion and as a potential expression of academics’ work. The first version of the framework was developed from the literature during the first phase of the study. This early framework was used during the second phase of the study when five academics took part in a focus group. After the focus group, the second version of the framework was developed and used with fifteen academics in individual interviews during phase three of the study. The third version of the framework was the outcome of a synthesis of the themes that were identified in the data. The discussion data from the focus group and the individual interviews were analysed through a content analysis approach that identified four major themes. The first theme was that academics reported that their work would ideally be located within universities committed to using their expert knowledge to serve the world. The second theme was that academics reported that they wanted sufficient thinking time and reasonable workloads to undertake the intellectual work that they regard as their core responsibility, particularly in relation to undertaking research. They argued against heavy routine administrative workloads and sought a continuation of current flexible working arrangements. The third theme was that teaching qualifications should not be mandated but that there should be a continuation of the present practice of universities offering academics the opportunity to undertake formal teaching qualifications if they wish to. Finally, academics reported that they wanted values that have traditionally mattered to academia to continue to be respected and practised: autonomy, collegiality and collaborative relationships, altruism and service, and intellectual integrity. These themes are sympathetic to Freidson’s theory of professions in all but one matter: the non-mandatory nature of formal qualifications which he regards as absolutely essential for the performance of the complex intellectual work that characterises occupations that are professions. The study places the issue of academic professionalism on the policy agenda for universities wishing to identify academics’ work as a profession. The study contributes a theory-based and data-informed conceptual framework for academics’ work that can be considered in negotiating the nature and extent of their work. The framework provides a means of analysing what "academic professionalism" might mean; it adds specificity to such discussions by exploring a particular definition of profession, namely Freidson’s theory of professions as occupations that are in control of their own work. The study contributes to the development of theories around higher education concepts of academic professionalism and, in so doing, links that theoretical contribution to the wider professions field.

Real-time detection of concealed chemical hazards under ambient light conditions using Raman spectroscopy

Current concerns regarding terrorism and international crime highlight the need for new techniques for detecting unknown and hazardous substances. A novel Raman spectroscopy-based technique, spatially offset Raman spectroscopy (SORS), was recently devised for non-invasively probing the contents of diffusely scattering and opaque containers. Here, we demonstrate a modified portable SORS sensor for detecting concealed substances in-field under different background lighting conditions. Samples including explosive precursors, drugs and an organophosphate insecticide (chemical warfare agent surrogate) were concealed inside diffusely scattering packaging including plastic, paper and cloth. Measurements were carried out under incandescent and fluorescent light as well as under daylight to assess the suitability of the probe for different real-life conditions. In each case, it was possible to identify the substances against their reference Raman spectra in less than one minute. The developed sensor has potential for rapid detection of concealed hazardous substances in airports, mail distribution centers and customs checkpoints.

Exposure to hot and cold temperatures and ambulance attendances in Brisbane, Australia: A time series study

ABSTRACT Objectives: To investigate the effect of hot and cold temperatures on ambulance attendances. Design: An ecological time series study. Setting and participants: The study was conducted in Brisbane, Australia. We collected information on 783 935 daily ambulance attendances, along with data of associated meteorological variables and air pollutants, for the period of 2000–2007. Outcome measures: The total number of ambulance attendances was examined, along with those related to cardiovascular, respiratory and other non-traumatic conditions. Generalised additive models were used to assess the relationship between daily mean temperature and the number of ambulance attendances. Results: There were statistically significant relationships between mean temperature and ambulance attendances for all categories. Acute heat effects were found with a 1.17% (95% CI: 0.86%, 1.48%) increase in total attendances for 1 °C increase above threshold (0–1 days lag). Cold effects were delayed and longer lasting with a 1.30% (0.87%, 1.73%) increase in total attendances for a 1 °C decrease below the threshold (2–15 days lag). Harvesting was observed following initial acute periods of heat effects, but not for cold effects. Conclusions: This study shows that both hot and cold temperatures led to increases in ambulance attendances for different medical conditions. Our findings support the notion that ambulance attendance records are a valid and timely source of data for use in the development of local weather/health early warning systems.

Repeat speeding offenders : time to stop thinking of them as just ‘unlucky normal’ drivers

- Speeding and crash involvement in Australia - Speeding recidivist research in Queensland - Challenges from an Australian perspective - Defining speeding - Community attitudes to speeding - Auditor-General reviews of speed camera programs - Implications for future speed management

Identifying customer behaviour and dwell time using soft biometrics

In a commercial environment, it is advantageous to know how long it takes customers to move between different regions, how long they spend in each region, and where they are likely to go as they move from one location to another. Presently, these measures can only be determined manually, or through the use of hardware tags (i.e. RFID). Soft biometrics are characteristics that can be used to describe, but not uniquely identify an individual. They include traits such as height, weight, gender, hair, skin and clothing colour. Unlike traditional biometrics, soft biometrics can be acquired by surveillance cameras at range without any user cooperation. While these traits cannot provide robust authentication, they can be used to provide identification at long range, and aid in object tracking and detection in disjoint camera networks. In this chapter we propose using colour, height and luggage soft biometrics to determine operational statistics relating to how people move through a space. A novel average soft biometric is used to locate people who look distinct, and these people are then detected at various locations within a disjoint camera network to gradually obtain operational statistics

A stranger's touch : effects of accidental interpersonal touch on consumer evaluations and shopping time

This article examines an unexplored area of consumer research—the effect of accidental interpersonal touch (AIT) from a stranger on consumer evaluations and shopping times. The research presents a field experiment in a retail setting. This study shows that men and women who have been touched by another consumer when examining products report more negative brand evaluations, negative product beliefs, less willingness to pay, and spend less time in-store than their control (no-touch) counterparts. Our findings indicate that the AIT effect is especially negative for touch from a male stranger for both men (same-sex touch) and women (opposite-sex touch). Directions are provided for future study that highlight potential moderators and process explanations underlying the AIT effect.

Alternating direction implicit numerical method for the space and time fractional Bloch-Torrey equation in 3-D

Recently, some authors have considered a new diffusion model–space and time fractional Bloch-Torrey equation (ST-FBTE). Magin et al. (2008) have derived analytical solutions with fractional order dynamics in space (i.e., _ = 1, β an arbitrary real number, 1 < β ≤ 2) and time (i.e., 0 < α < 1, and β = 2), respectively. Yu et al. (2011) have derived an analytical solution and an effective implicit numerical method for solving ST-FBTEs, and also discussed the stability and convergence of the implicit numerical method. However, due to the computational overheads necessary to perform the simulations for nuclear magnetic resonance (NMR) in three dimensions, they present a study based on a two-dimensional example to confirm their theoretical analysis. Alternating direction implicit (ADI) schemes have been proposed for the numerical simulations of classic differential equations. The ADI schemes will reduce a multidimensional problem to a series of independent one-dimensional problems and are thus computationally efficient. In this paper, we consider the numerical solution of a ST-FBTE on a finite domain. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. A fractional alternating direction implicit scheme (FADIS) for the ST-FBTE in 3-D is proposed. Stability and convergence properties of the FADIS are discussed. Finally, some numerical results for ST-FBTE are given.

A new implicit numerical method for the space and time fractional Bloch-Torrey equation

In recent years, it has been found that many phenomena in engineering, physics, chemistry and other sciences can be described very successfully by models using mathematical tools from fractional calculus. Recently, noted a new space and time fractional Bloch-Torrey equation (ST-FBTE) has been proposed (see Magin et al. (2008)), and successfully applied to analyse diffusion images of human brain tissues to provide new insights for further investigations of tissue structures. In this paper, we consider the ST-FBTE on a finite domain. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Firstly, we propose a new effective implicit numerical method (INM) for the STFBTE whereby we discretize the Riesz fractional derivative using a fractional centered difference. Secondly, we prove that the implicit numerical method for the ST-FBTE is unconditionally stable and convergent, and the order of convergence of the implicit numerical method is ( T2 - α + h2 x + h2 y + h2 z ). Finally, some numerical results are presented to support our theoretical analysis.

Numerical methods for solving the multi-term time-fractional wave-diffusion equations

In this paper, the multi-term time-fractional wave diffusion equations are considered. The multiterm time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.

A finite volume method for solving the two-sided time-space fractional advection-dispersion equation

The field of fractional differential equations provides a means for modelling transport processes within complex media which are governed by anomalous transport. Indeed, the application to anomalous transport has been a significant driving force behind the rapid growth and expansion of the literature in the field of fractional calculus. In this paper, we present a finite volume method to solve the time-space two-sided fractional advection dispersion equation on a one-dimensional domain. Such an equation allows modelling different flow regime impacts from either side. The finite volume formulation provides a natural way to handle fractional advection-dispersion equations written in conservative form. The novel spatial discretisation employs fractionally-shifted Gr¨unwald formulas to discretise the Riemann-Liouville fractional derivatives at control volume faces in terms of function values at the nodes, while the L1-algorithm is used to discretise the Caputo time fractional derivative. Results of numerical experiments are presented to demonstrate the effectiveness of the approach.

Evolutionary placement of continuously operating reference stations of network Real-Time Kinematic

Network RTK (Real-Time Kinematic) is a technology that is based on GPS (Global Positioning System) or more generally on GNSS (Global Navigation Satellite System) observations to achieve centimeter-level accuracy positioning in real time. It is enabled by a network of Continuously Operating Reference Stations (CORS). CORS placement is an important problem in the design of network RTK as it directly affects not only the installation and running costs of the network RTK, but also the Quality of Service (QoS) provided by the network RTK. In our preliminary research on the CORS placement, we proposed a polynomial heuristic algorithm for a so-called location-based CORS placement problem. From a computational point of view, the location-based CORS placement is a largescale combinatorial optimization problem. Thus, although the heuristic algorithm is efficient in computation time it may not be able to find an optimal or near optimal solution. Aiming at improving the quality of solutions, this paper proposes a repairing genetic algorithm (RGA) for the location-based CORS placement problem. The RGA has been implemented and compared to the heuristic algorithm by experiments. Experimental results have shown that the RGA produces better quality of solutions than the heuristic algorithm.