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.

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.

Educating EFL preservice teachers for teaching astronomy

Malaysia’s Vision 2020 for enhancing its education system includes the development of scientific literacy commencing at the primary school level. This Vision focuses on using English as the Medium of Instruction (EMI) for teaching primary science, as Malaysia has English as a Foreign Language (EFL) in its curriculum. What changes need to occur in preservice teacher education programs for learning about primary science using EMI? This paper investigates the education of Malaysian preservice teachers for learning how to teach one strand in science education (i.e., space, primary astronomy) in an English-language context. Ninety-six second-year preservice teachers from two Malaysian institutes were involved in a 16-week “Earth and Space” course, half the course involved education about primary astronomy. Seventy-five of these preservice teachers provided written responses about the course and their development as potential teachers of primary astronomy using EMI. Preservice teacher assessments and multimedia presentations provided further evidence on learning how to teach primary astronomy. Many of these preservice teachers claimed that learning to teach primary astronomy needs to focus on teaching strategies, content knowledge with easy-to-understand concepts, computer simulations (e.g., Earth Centered Universe, Stellarium, Celestia), other ICT media, and field experiences that use naked-eye observations and telescopes to investigate celestial bodies. Although generally proficient in using ICT, they claimed there were EFL barriers for learning some new terminology. Nevertheless, powerpoints, animations, videos, and simulations were identified as effective ICT tools for providing clear visual representations of abstract concepts and ways to enhance the learning process.

Cultural economic geography and global media studies : the rise of asian media capitals?

This paper considers the scope to develop an approach to the spatial dimensions of media and culture that is informed by cultural-economic geography. I refer to cultural-economic geography as that strand of research in the field of geography that has been informed on the one hand by the ‘cultural turn’ in both geographical and economic thought, and which focuses on the relationship between, space, knowledge and identity in the spheres of production and consumption, and on the other to work by geographers that has sought to map the scale and significance of the cultural or creative industries as new drivers of the global economy. The paper considers the extent to which this work enables those engaged with urban cultural policy to get beyond some of the impasses that have arisen with the development of “creative cities” policies derived from the work of authors such as Richard Florida as well as the business management literature on clusters. It will frame these debates in the context of recent work by Michael Curtin on media capitals, and the question of whether cities in East Asia can emerge as media capitals from outside of the US-Europe-dominated transnational cultural axis.

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.

Recent advances in cancer therapy targeting proteins involved in DNA double-strand break repair

Damage to genetic material represents a persistent and ubiquitous threat to genomic stability. Once DNA damage is detected, a multifaceted signaling network is activated that halts the cell cycle, initiates repair, and in some instances induces apoptotic cell death. In this article, we will review DNA damage surveillance networks, which maintain the stability of our genome, and discuss the efforts underway to identify chemotherapeutic compounds targeting the core components of DNA double-strand breaks (DSB) response pathway. The majority of tumor cells have defects in maintaining genomic stability owing to the loss of an appropriate response to DNA damage. New anticancer agents are exploiting this vulnerability of cancer cells to enhance therapeutic indexes, with limited normal tissue toxicity. Recently inhibitors of the checkpoint kinases Chk1 and Chk2 have been shown to sensitize tumor cells to DNA damaging agents. In addition, the treatment of BRCA1- or BRCA2-deficient tumor cells with poly(ADP-ribose) polymerase (PARP) inhibitors also leads to specific tumor killing. Due to the numerous roles of p53 in genomic stability and its defects in many human cancers, therapeutic agents that restore p53 activity in tumors are the subject of multiple clinical trials. In this article we highlight the proteins mentioned above and catalog several additional players in the DNA damage response pathway, including ATM, DNA-PK, and the MRN complex, which might be amenable to pharmacological interventions and lead to new approaches to sensitize cancer cells to radio- and chemotherapy. The challenge is how to identify those patients most receptive to these treatments.

hSSB1 interacts directly with the MRN complex stimulating its recruitment to DNA double-strand breaks and its endo-nuclease activity

hSSB1 is a recently discovered single-stranded DNA binding protein that is essential for efficient repair of DNA double-strand breaks (DSBs) by the homologous recombination pathway. hSSB1 is required for the efficient recruitment of the MRN complex to sites of DSBs and for the efficient initiation of ATM dependent signalling. Here we explore the interplay between hSSB1 and MRN. We demonstrate that hSSB1 binds directly to NBS1, a component of the MRN complex, in a DNA damage independent manner. Consistent with the direct interaction, we observe that hSSB1 greatly stimulates the endo-nuclease activity of the MRN complex, a process that requires the C-terminal tail of hSSB1. Interestingly, analysis of two point mutations in NBS1, associated with Nijmegen breakage syndrome, revealed weaker binding to hSSB1, suggesting a possible disease mechanism.

hSSB1 rapidly binds at the sites of DNA double-strand breaks and is required for the efficient recruitment of the MRN complex

hSSB1 is a newly discovered single-stranded DNA (ssDNA)-binding protein that is essential for efficient DNA double-strand break signalling through ATM. However, the mechanism by which hSSB1 functions to allow efficient signalling is unknown. Here, we show that hSSB1 is recruited rapidly to sites of double-strand DNA breaks (DSBs) in all interphase cells (G1, S and G2) independently of, CtIP, MDC1 and the MRN complex (Rad50, Mre11, NBS1). However expansion of hSSB1 from the DSB site requires the function of MRN. Strikingly, silencing of hSSB1 prevents foci formation as well as recruitment of MRN to sites of DSBs and leads to a subsequent defect in resection of DSBs as evident by defective RPA and ssDNA generation. Our data suggests that hSSB1 functions upstream of MRN to promote its recruitment at DSBs and is required for efficient resection of DSBs. These findings, together with previous work establish essential roles of hSSB1 in controlling ATM activation and activity, and subsequent DSB resection and homologous recombination (HR).

Phosphorylation of Exo1 modulates homologous recombination repair of DNA double-strand breaks

DNA double-strand break (DSB) repair via the homologous recombination pathway is a multi-stage process, which results in repair of the DSB without loss of genetic information or fidelity. One essential step in this process is the generation of extended single-stranded DNA (ssDNA) regions at the break site. This ssDNA serves to induce cell cycle checkpoints and is required for Rad51 mediated strand invasion of the sister chromatid. Here, we show that human Exonuclease 1 (Exo1) is required for the normal repair of DSBs by HR. Cells depleted of Exo1 show chromosomal instability and hypersensitivity to ionising radiation (IR) exposure. We find that Exo1 accumulates rapidly at DSBs and is required for the recruitment of RPA and Rad51 to sites of DSBs, suggesting a role for Exo1 in ssDNA generation. Interestingly, the phosphorylation of Exo1 by ATM appears to regulate the activity of Exo1 following resection, allowing optimal Rad51 loading and the completion of HR repair. These data establish a role for Exo1 in resection of DSBs in human cells, highlighting the critical requirement of Exo1 for DSB repair via HR and thus the maintenance of genomic stability.