Stability and convergence of an effective numerical method for the time-space fractional Fokker-Planck equation with a nonlinear source term

Fractional Fokker-Planck equations (FFPEs) have gained much interest recently for describing transport dynamics in complex systems that are governed by anomalous diffusion and nonexponential relaxation patterns. However, effective numerical methods and analytic techniques for the FFPE are still in their embryonic state. In this paper, we consider a class of time-space fractional Fokker-Planck equations with a nonlinear source term (TSFFPE-NST), which involve the Caputo time fractional derivative (CTFD) of order α ∈ (0, 1) and the symmetric Riesz space fractional derivative (RSFD) of order μ ∈ (1, 2). Approximating the CTFD and RSFD using the L1-algorithm and shifted Grunwald method, respectively, a computationally effective numerical method is presented to solve the TSFFPE-NST. The stability and convergence of the proposed numerical method are investigated. Finally, numerical experiments are carried out to support the theoretical claims.

Computationally efficient numerical methods for time- and space-fractional Fokker–Planck equations

Fractional Fokker–Planck equations have been used to model several physical situations that present anomalous diffusion. In this paper, a class of time- and space-fractional Fokker–Planck equations (TSFFPE), which involve the Riemann–Liouville time-fractional derivative of order 1-α (α(0, 1)) and the Riesz space-fractional derivative (RSFD) of order μ(1, 2), are considered. The solution of TSFFPE is important for describing the competition between subdiffusion and Lévy flights. However, effective numerical methods for solving TSFFPE are still in their infancy. We present three computationally efficient numerical methods to deal with the RSFD, and approximate the Riemann–Liouville time-fractional derivative using the Grünwald method. The TSFFPE is then transformed into a system of ordinary differential equations (ODE), which is solved by the fractional implicit trapezoidal method (FITM). Finally, numerical results are given to demonstrate the effectiveness of these methods. These techniques can also be applied to solve other types of fractional partial differential equations.

Analytical and numerical solutions for the time and space-symmetric fractional diffusion equation

We consider a time and space-symmetric fractional diffusion equation (TSS-FDE) under homogeneous Dirichlet conditions and homogeneous Neumann conditions. The TSS-FDE is obtained from the standard diffusion equation by replacing the first-order time derivative by the Caputo fractional derivative and the second order space derivative by the symmetric fractional derivative. Firstly, a method of separating variables is used to express the analytical solution of the tss-fde in terms of the Mittag–Leffler function. Secondly, we propose two numerical methods to approximate the Caputo time fractional derivative, namely, the finite difference method and the Laplace transform method. The symmetric space fractional derivative is approximated using the matrix transform method. Finally, numerical results are presented to demonstrate the effectiveness of the numerical methods and to confirm the theoretical claims.

Quality of child abuse information for measurement and surveillance : linking hospital and child welfare data

National estimates of the prevalence of child abuse-related injuries are obtained from a variety of sectors including welfare, justice, and health resulting in inconsistent estimates across sectors. The International Classification of Diseases (ICD) is used as the international standard for categorising health data and aggregating data for statistical purposes, though there has been limited validation of the quality, completeness or concordance of these data with other sectors. This research study examined the quality of documentation and coding of child abuse recorded in hospital records in Queensland and the concordance of these data with child welfare records. A retrospective medical record review was used to examine the clinical documentation of over 1000 hospitalised injured children from 20 hospitals in Queensland. A data linkage methodology was used to link these records with records in the child welfare database. Cases were sampled from three sub-groups according to the presence of target ICD codes: Definite abuse, Possible abuse, unintentional injury. Less than 2% of cases coded as being unintentional were recoded after review as being possible abuse, and only 5% of cases coded as possible abuse cases were reclassified as unintentional, though there was greater variation in the classification of cases as definite abuse compared to possible abuse. Concordance of health data with child welfare data varied across patient subgroups. This study will inform the development of strategies to improve the quality, consistency and concordance of information between health and welfare agencies to ensure adequate system responses to children at risk of abuse.

Quality of child abuse information in emergency department injury surveillance data : linking hospital and child welfare data

Emergency departments (EDs) are often the first point of contact with an abused child. Despite legal mandate, the reporting of definite or suspected abusive injury to child safety authorities by ED clinicians varies due to a number of factors including training, access to child safety professionals, departmental culture and a fear of ‘getting it wrong’. This study examined the quality of documentation and coding of child abuse captured by ED based injury surveillance data and ED medical records in the state of Queensland and the concordance of these data with child welfare records. A retrospective medical record review was used to examine the clinical documentation of almost 1000 injured children included in the Queensland Injury Surveillance Unit database (QISU) from 10 hospitals in urban and rural centres. Independent experts re-coded the records based on their review of the notes. A data linkage methodology was then used to link these records with records in the state government’s child welfare database. Cases were sampled from three sub-groups according to the surveillance intent codes: Maltreatment by parent, Undetermined and Unintentional injury. Only 0.1% of cases coded as unintentional injury were recoded to maltreatment by parent, while 1.2% of cases coded as maltreatment by parent were reclassified as unintentional and 5% of cases where the intent was undetermined by the triage nurse were recoded as maltreatment by parent. Quality of documentation varied across type of hospital (tertiary referral centre, children’s, urban, regional and remote). Concordance of health data with child welfare data varied across patient subgroups. Outcomes from this research will guide initiatives to improve the quality of intentional child injury surveillance systems.

Making space and place for the knowledge economy : knowledge-based development of Australian cities

The impact of what has been broadly labelled the knowledge economy has been such that, even in the absence of precise measurement, it is the undoubted dynamo of today’s global market, and an essential part of any global city. The socio-economic importance of knowledge production in a knowledge economy is clear, and it is an emerging social phenomenon and research agenda in geographical studies. Knowledge production, and where, how and by whom it is produced, is an urban phenomenon that is poorly understood in an era of strong urbanisation. This paper focuses on knowledge community precincts as the catalytic magnet infrastructures impacting on knowledge production in cities. The paper discusses the increasing importance of knowledge-based urban development within the paradigm of the knowledge economy, and the role of knowledge community precincts as instruments to seed the foundation of knowledge production in cities. This paper explores the knowledge based urban development, and particularly knowledge community precinct development, potentials of Sydney, Melbourne and Brisbane, and benchmarks this against that of Boston, Massachusetts.

Making space and place for knowledge production : socio-spatial development of knowledge community precincts

In the knowledge era the importance of making space and place for knowledge production is clearly understood worldwide by many city administrations that are keen on restructuring their cities as highly competitive and creative places. Consequently, knowledge-based urban development and socio-spatial development of knowledge community precincts have taken their places among the emerging agendas of the urban planning and development practice. This chapter explores these emerging issues and scrutinizes the development of knowledge community precincts that have important economic, social and cultural dimensions on the formation of competitive and creative urban regions. The chapter also sheds light on the new challenges for planning discipline, and discusses the need for and some specifics of a new planning paradigm suitable for dealing with 21st Century’s socio-economic development and urbanization problems.

Distributed orthogonal space-time block codes with adaptive diversity gain

In this paper we present a novel distributed coding protocol for multi-user cooperative networks. The proposed distributed coding protocol exploits the existing orthogonal space-time block codes to achieve higher diversity gain by repeating the code across time and space (available relay nodes). The achievable diversity gain depends on the number of relay nodes that can fully decode the signal from the source. These relay nodes then form space-time codes to cooperatively relay to the destination using number of time slots. However, the improved diversity gain is archived at the expense of the transmission rate. The design principles of the proposed space-time distributed code and the issues related to transmission rate and diversity trade off is discussed in detail. We show that the proposed distributed space-time coding protocol out performs existing distributed codes with a variable transmission rate.

The embodied hybrid space : designing ubiquitous computing towards an amplification of situated real world experiences

The emergence of mobile and ubiquitous computing technology has created what is often referred to as the hybrid space – a virtual layer of digital information and interaction opportunities that sit on top of and augment the physical environment. Embodied media materialise digital information as observable and sometimes interactive parts of the physical environment. The aim of this work is to explore ways to enhance people’s situated real world experience, and to find out what the role and impact of embodied media in achieving this goal can be. The Edge, an initiative of the State Library of Queensland in Brisbane, Australia, and case study of this thesis, envisions to be a physical place for people to meet, explore, experience, learn and teach each other creative practices in various areas related to digital technology and arts. Guided by an Action Research approach, this work applies Lefebvre’s triad of space (1991) to investigate the Edge as a social space from a conceived, perceived and lived point of view. Based on its creators’ vision and goals on the conceived level, different embodied media are iteratively designed, implemented and evaluated towards shaping and amplifying the Edge’s visitor experience on the perceived and lived level.

Using routinely collected hospital data for child maltreatment surveillance : issues, methods and patterns

Background: International data on child maltreatment are largely derived from child protection agencies, and predominantly report only substantiated cases of child maltreatment. This approach underestimates the incidence of maltreatment and makes inter-jurisdictional comparisons difficult. There has been a growing recognition of the importance of health professionals in identifying, documenting and reporting suspected child maltreatment. This study aimed to describe the issues around case identification using coded morbidity data, outline methods for selecting and grouping relevant codes, and illustrate patterns of maltreatment identified. Methods: A comprehensive review of the ICD-10-AM classification system was undertaken, including review of index terms, a free text search of tabular volumes, and a review of coding standards pertaining to child maltreatment coding. Identified codes were further categorised into maltreatment types including physical abuse, sexual abuse, emotional or psychological abuse, and neglect. Using these code groupings, one year of Australian hospitalisation data for children under 18 years of age was examined to quantify the proportion of patients identified and to explore the characteristics of cases assigned maltreatment-related codes. Results: Less than 0.5% of children hospitalised in Australia between 2005 and 2006 had a maltreatment code assigned, almost 4% of children with a principal diagnosis of a mental and behavioural disorder and over 1% of children with an injury or poisoning as the principal diagnosis had a maltreatment code assigned. The patterns of children assigned with definitive T74 codes varied by sex and age group. For males selected as having a maltreatment-related presentation, physical abuse was most commonly coded (62.6% of maltreatment cases) while for females selected as having a maltreatment-related presentation, sexual abuse was the most commonly assigned form of maltreatment (52.9% of maltreatment cases). Conclusion: This study has demonstrated that hospital data could provide valuable information for routine monitoring and surveillance of child maltreatment, even in the absence of population-based linked data sources. With national and international calls for a public health response to child maltreatment, better understanding of, investment in and utilisation of our core national routinely collected data sources will enhance the evidence-base needed to support an appropriate response to children at risk.

Reliability of routinely collected hospital data for child maltreatment surveillance

Background: Internationally, research on child maltreatment-related injuries has been hampered by a lack of available routinely collected health data to identify cases, examine causes, identify risk factors and explore health outcomes. Routinely collected hospital separation data coded using the International Classification of Diseases and Related Health Problems (ICD) system provide an internationally standardised data source for classifying and aggregating diseases, injuries, causes of injuries and related health conditions for statistical purposes. However, there has been limited research to examine the reliability of these data for child maltreatment surveillance purposes. This study examined the reliability of coding of child maltreatment in Queensland, Australia. Methods: A retrospective medical record review and recoding methodology was used to assess the reliability of coding of child maltreatment. A stratified sample of hospitals across Queensland was selected for this study, and a stratified random sample of cases was selected from within those hospitals. Results: In 3.6% of cases the coders disagreed on whether any maltreatment code could be assigned (definite or possible) versus no maltreatment being assigned (unintentional injury), giving a sensitivity of 0.982 and specificity of 0.948. The review of these cases where discrepancies existed revealed that all cases had some indications of risk documented in the records. 15.5% of cases originally assigned a definite or possible maltreatment code, were recoded to a more or less definite strata. In terms of the number and type of maltreatment codes assigned, the auditor assigned a greater number of maltreatment types based on the medical documentation than the original coder assigned (22% of the auditor coded cases had more than one maltreatment type assigned compared to only 6% of the original coded data). The maltreatment types which were the most ‘under-coded’ by the original coder were psychological abuse and neglect. Cases coded with a sexual abuse code showed the highest level of reliability. Conclusion: Given the increasing international attention being given to improving the uniformity of reporting of child-maltreatment related injuries and the emphasis on the better utilisation of routinely collected health data, this study provides an estimate of the reliability of maltreatment-specific ICD-10-AM codes assigned in an inpatient setting.

XML documents clustering using tensor space model - A preliminary study

A hierarchical structure is used to represent the content of the semi-structured documents such as XML and XHTML. The traditional Vector Space Model (VSM) is not sufficient to represent both the structure and the content of such web documents. Hence in this paper, we introduce a novel method of representing the XML documents in Tensor Space Model (TSM) and then utilize it for clustering. Empirical analysis shows that the proposed method is scalable for a real-life dataset as well as the factorized matrices produced from the proposed method helps to improve the quality of clusters due to the enriched document representation with both the structure and the content information.

Flagging Spaces : exploring the myth of the Australian beach as an egalitarian space

The Australian beach is now accepted as a significant part of Australian national culture and identity. However, Huntsman (2001) and Booth (2001) both believe that the beach is dying: “intellectuals have failed to apply to the beach the attention they have lavished on the bush…” (Huntsman 2001, 218). Yet the beach remains a prominent image in contemporary literature and film; authors such as Tim Winton and Robert Drewe frequently set their stories in and around the coast. Although initially considered a space of myth (Fiske, Hodge, and Turner 1987), Meaghan Morris labelled the beach as ‘ordinary’ (1998), and as recently as 2001 in the wake of the Sydney Olympic Games, Bonner, McKee, and Mackay termed the beach ‘tacky’ and ‘familiar’. The beach, it appears, defies an easy categorisation. In fact, I believe the beach is more than merely mythic or ordinary, or a combination of the two. Instead it is an imaginative space, seamlessly shifting its metaphorical meanings dependent on readings of the texts. My studies examine the beach through five common beach myths; this paper will explore the myth of the beach as an egalitarian space. Contemporary Australian national texts no longer conform to these mythical representations – (in fact, was the beach ever a space of equality?), instead creating new definitions for the beach space that continually shifts in meaning. Recent texts such as Tim Winton’s Breath (2008) and Stephen Orr’s Time’s Long Ruin (2010) lay a more complex metaphorical meaning upon the beach space. This paper will explore the beach as a space of egalitarianism in conjunction with recent Australian fiction and films in order to discover how the contemporary beach is represented.

If Big Brother comes to a venue near you! Employee surveillance issues and the communication professional

Todoy's monogers-drowing on the expertise of their IT professiono/s-surveillance.