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.

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.

A randomised, feasibility trial of a tele-health intervention for Acute Coronary Syndrome patients with depression ('MoodCare')

Background Coronary heart disease (CHD) and depression are leading causes of disease burden globally and the two often co-exist. Depression is common after Myocardial Infarction (MI) and it has been estimated that 15-35% of patients experience depressive symptoms. Co-morbid depression can impair health related quality of life (HRQOL), decrease medication adherence and appropriate utilisation of health services, lead to increased morbidity and suicide risk, and is associated with poorer CHD risk factor profiles and reduced survival. We aim to determine the feasibility of conducting a randomised, multi-centre trial designed to compare a tele-health program (MoodCare) for depression and CHD secondary prevention, with Usual Care (UC). Methods Over 1600 patients admitted after index admission for Acute Coronary Syndrome (ACS) are being screened for depression at six metropolitan hospitals in the Australian states of Victoria and Queensland. Consenting participants are then contacted at two weeks post-discharge for baseline assessment. One hundred eligible participants are to be randomised to an intervention or a usual medical care control group (50 per group). The intervention consists of up to 10 × 30-40 minute structured telephone sessions, delivered by registered psychologists, commencing within two weeks of baseline screening. The intervention focuses on depression management, lifestyle factors (physical activity, healthy eating, smoking cessation, alcohol intake), medication adherence and managing co-morbidities. Data collection occurs at baseline (Time 1), 6 months (post-intervention) (Time 2), 12 months (Time 3) and 24 months follow-up for longer term effects (Time 4). We are comparing depression (Cardiac Depression Scale [CDS]) and HRQOL (Short Form-12 [SF-12]) scores between treatment and UC groups, assessing the feasibility of the program through patient acceptability and exploring long term maintenance effects. A cost-effectiveness analysis of the costs and outcomes for patients in the intervention and control groups is being conducted from the perspective of health care costs to the government. Discussion This manuscript presents the protocol for a randomised, multi-centre trial to evaluate the feasibility of a tele-based depression management and CHD secondary prevention program for ACS patients. The results of this trial will provide valuable new information about potential psychological and wellbeing benefits, cost-effectiveness and acceptability of an innovative tele-based depression management and secondary prevention program for CHD patients experiencing depression.