Analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations on a finite domain

Generalized fractional partial differential equations have now found wide application for describing important physical phenomena, such as subdiffusive and superdiffusive processes. However, studies of generalized multi-term time and space fractional partial differential equations are still under development. In this paper, the multi-term time-space Caputo-Riesz fractional advection diffusion equations (MT-TSCR-FADE) with Dirichlet nonhomogeneous boundary conditions are considered. The multi-term time-fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0, 1], [1, 2] and [0, 2], respectively. These are called respectively the multi-term time-fractional diffusion terms, the multi-term time-fractional wave terms and the multi-term time-fractional mixed diffusion-wave terms. The space fractional derivatives are defined as Riesz fractional derivatives. Analytical solutions of three types of the MT-TSCR-FADE are derived with Dirichlet boundary conditions. By using Luchko's Theorem (Acta Math. Vietnam., 1999), we proposed some new techniques, such as a spectral representation of the fractional Laplacian operator and the equivalent relationship between fractional Laplacian operator and Riesz fractional derivative, that enabled the derivation of the analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations. © 2012.

Numerical techniques for the variable order time fractional diffusion equation

In this paper we consider the variable order time fractional diffusion equation. We adopt the Coimbra variable order (VO) time fractional operator, which defines a consistent method for VO differentiation of physical variables. The Coimbra variable order fractional operator also can be viewed as a Caputo-type definition. Although this definition is the most appropriate definition having fundamental characteristics that are desirable for physical modeling, numerical methods for fractional partial differential equations using this definition have not yet appeared in the literature. Here an approximate scheme is first proposed. The stability, convergence and solvability of this numerical scheme are discussed via the technique of Fourier analysis. Numerical examples are provided to show that the numerical method is computationally efficient. Crown Copyright © 2012 Published by Elsevier Inc. All rights reserved.

Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain

Multi-term time-fractional differential equations have been used for describing important physical phenomena. However, studies of the multi-term time-fractional partial differential equations with three kinds of nonhomogeneous boundary conditions are still limited. In this paper, a method of separating variables is used to solve the multi-term time-fractional diffusion-wave equation and the multi-term time-fractional diffusion equation in a finite domain. In the two equations, the time-fractional derivative is defined in the Caputo sense. We discuss and derive the analytical solutions of the two equations with three kinds of nonhomogeneous boundary conditions, namely, Dirichlet, Neumann and Robin conditions, respectively.

Capping computation time and storage requirements for appearance-based localization with CAT-SLAM

Appearance-based localization is increasingly used for loop closure detection in metric SLAM systems. Since it relies only upon the appearance-based similarity between images from two locations, it can perform loop closure regardless of accumulated metric error. However, the computation time and memory requirements of current appearance-based methods scale linearly not only with the size of the environment but also with the operation time of the platform. These properties impose severe restrictions on longterm autonomy for mobile robots, as loop closure performance will inevitably degrade with increased operation time. We present a set of improvements to the appearance-based SLAM algorithm CAT-SLAM to constrain computation scaling and memory usage with minimal degradation in performance over time. The appearance-based comparison stage is accelerated by exploiting properties of the particle observation update, and nodes in the continuous trajectory map are removed according to minimal information loss criteria. We demonstrate constant time and space loop closure detection in a large urban environment with recall performance exceeding FAB-MAP by a factor of 3 at 100% precision, and investigate the minimum computational and memory requirements for maintaining mapping performance.

Victims Speak: Comparing Child Sexual Abusers and Their Victims Accounts of Offence Circumstances

This article presents findings from a longitudinal study. The research aimed to explore the effectiveness of a treatment program for offenders which lasted for three years. The research design was structured around the program with interviews and psychometric testing undertaken at key points in time with the same group of respondents. View all notes that sought to evaluate a treatment program for child sexual abusers. A triangulated methodological approach was adopted drawing upon quantitative and qualitative methodological techniques. The focus here is upon one element of this research. 2 2The quantitative element of this research will be published shortly but is referred to in the following reports Davidson 2000, 2003 [research funded by the National Probation Service]. Psychometric testing was undertaken over a four-year period with the men attending the treatment program to explore shifts in the extent of denial, blame attribution, and victim empathy over time. Offender cognitive distortions, general health, and self-esteem were also explored via psychometric testing. An interview-administered survey was undertaken with all sex offenders registered with the Probation Service (those on probation and in custody) in order to gather demographic data, and 117 of 150 offenders responded. View all notes Ninety-one in-depth interviews were conducted over a four-year period with a small, nonrandom sample of twenty-one male offenders who had been convicted of sexual offenses against children. All of the men were subject to probation orders with a psychiatric condition (Criminal Justice Act, 1991). One of the aims of this element of the research was to explore the extent to which evidence of denial could be found in offenders’ accounts of offense circumstance and also to explore the extent to which offenders minimized the nature and extent of abuse perpetrated. Offenders’ accounts of offense circumstances were compared to victim statements, and stark differences emerge. These findings have considerable implications for treatment practice with sex offenders, where victims’ perceptions could be used to directly confront offender denial and minimization.

What health problems overcrowd hospital emergency departments in Queensland and has this changed over time? A case study of two hospitals in Queensland 2001 - 2009

Aim: to describe what health problems patients attending emergency department with and whether this changed over time. Methods: Electronic data was retrieved from EDIS (Emergency Department Information System) and HBCIS (Hospital Based Clinical Information System) in two hospitals in Queensland in the period 2001-2009. The ICD-10 code of patient's diagnosis was then extrapolated and then group into ICD-10 chapters, such that the health problem can be presented. Results: Among the specific health problems, Chapter XIX 'Injury and poisoning' ranked number one consistently (ranging from 22.1% to 31.2% of the total presentations) in both the urban and remote hospitals in Queensland. The top ten specific presenting health problems in both the urban and remote hospital include Chapter XI 'Digestive system', Chapter XIV 'Genitourinary system', Chapter IX 'Circulatory system', and Chapter XIII 'Musculoskeletal system and connective tissue'. Chapter X 'Respiratory system' made the top ten presenting Chapters in both hospitals, but ranked much higher (number four consistently for the eight years, ranging from 6.8% to 8.3%) in the remote hospital. Chapter XV 'Pregnancy childbirth and puerperium' made to the top ten in the urban hospital only while Chapter XII 'Skin and subcutaneous tissue', Chapter I 'Infectious and parasitic diseases' made the top ten in the remote hospital only. Conclusion: The number one health problem presenting to both the urban and remote hospitals in Queensland is Chapter XIX 'Injury and poisoning', and it did not change in the period 211 - 2009.

Development and feasibility of a smartphone, ECG and GPS based system for remotely monitoring exercise in cardiac rehabilitation

Background Despite its efficacy and cost-effectiveness, exercise-based cardiac rehabilitation is undertaken by less than one-third of clinically eligible cardiac patients in every country for which data is available. Reasons for non-participation include the unavailability of hospital-based rehabilitation programs, or excessive travel time and distance. For this reason, there have been calls for the development of more flexible alternatives. Methodology and Principal Findings We developed a system to enable walking-based cardiac rehabilitation in which the patient's single-lead ECG, heart rate, GPS-based speed and location are transmitted by a programmed smartphone to a secure server for real-time monitoring by a qualified exercise scientist. The feasibility of this approach was evaluated in 134 remotely-monitored exercise assessment and exercise sessions in cardiac patients unable to undertake hospital-based rehabilitation. Completion rates, rates of technical problems, detection of ECG changes, pre- and post-intervention six minute walk test (6 MWT), cardiac depression and Quality of Life (QOL) were key measures. The system was rated as easy and quick to use. It allowed participants to complete six weeks of exercise-based rehabilitation near their homes, worksites, or when travelling. The majority of sessions were completed without any technical problems, although periodic signal loss in areas of poor coverage was an occasional limitation. Several exercise and post-exercise ECG changes were detected. Participants showed improvements comparable to those reported for hospital-based programs, walking significantly further on the post-intervention 6 MWT, 637 m (95% CI: 565–726), than on the pre-test, 524 m (95% CI: 420–655), and reporting significantly reduced levels of cardiac depression and significantly improved physical health-related QOL. Conclusions and Significance The system provided a feasible and very flexible alternative form of supervised cardiac rehabilitation for those unable to access hospital-based programs, with the potential to address a well-recognised deficiency in health care provision in many countries. Future research should assess its longer-term efficacy, cost-effectiveness and safety in larger samples representing the spectrum of cardiac morbidity and severity.