Numerical methods for fractional partial differential equations with Riesz space fractional derivatives

In this paper, we consider the numerical solution of a fractional partial differential equation with Riesz space fractional derivatives (FPDE-RSFD) on a finite domain. Two types of FPDE-RSFD are considered: the Riesz fractional diffusion equation (RFDE) and the Riesz fractional advection–dispersion equation (RFADE). The RFDE is obtained from the standard diffusion equation by replacing the second-order space derivative with the Riesz fractional derivative of order αset membership, variant(1,2]. The RFADE is obtained from the standard advection–dispersion equation by replacing the first-order and second-order space derivatives with the Riesz fractional derivatives of order βset membership, variant(0,1) and of order αset membership, variant(1,2], respectively. Firstly, analytic solutions of both the RFDE and RFADE are derived. Secondly, three numerical methods are provided to deal with the Riesz space fractional derivatives, namely, the L1/L2-approximation method, the standard/shifted Grünwald method, and the matrix transform method (MTM). Thirdly, the RFDE and RFADE are transformed into a system of ordinary differential equations, which is then solved by the method of lines. Finally, numerical results are given, which demonstrate the effectiveness and convergence of the three numerical methods.

The Media City: Media, Architecture and Urban Space

The article reviews the book "The Media City: Media, Architecture and Urban Space," by Scott McQuire.

Learning in the third space : a sociocultural perspective on learning with analogies

Research on analogies in science education has focussed on student interpretation of teacher and textbook analogies, psychological aspects of learning with analogies and structured approaches for teaching with analogies. Few studies have investigated how analogies might be pivotal in students’ growing participation in chemical discourse. To study analogies in this way requires a sociocultural perspective on learning that focuses on ways in which language, signs, symbols and practices mediate participation in chemical discourse. This study reports research findings from a teacher-research study of two analogy-writing activities in a chemistry class. The study began with a theoretical model, Third Space, which informed analyses and interpretation of data. Third Space was operationalized into two sub-constructs called Dialogical Interactions and Hybrid Discourses. The aims of this study were to investigate sociocultural aspects of learning chemistry with analogies in order to identify classroom activities where students generate Dialogical Interactions and Hybrid Discourses, and to refine the operationalization of Third Space. These aims were addressed through three research questions. The research questions were studied through an instrumental case study design. The study was conducted in my Year 11 chemistry class at City State High School for the duration of one Semester. Data were generated through a range of data collection methods and analysed through discourse analysis using the Dialogical Interactions and Hybrid Discourse sub-constructs as coding categories. Results indicated that student interactions differed between analogical activities and mathematical problem-solving activities. Specifically, students drew on discourses other than school chemical discourse to construct analogies and their growing participation in chemical discourse was tracked using the Third Space model as an interpretive lens. Results of this study led to modification of the theoretical model adopted at the beginning of the study to a new model called Merged Discourse. Merged Discourse represents the mutual relationship that formed during analogical activities between the Analog Discourse and the Target Discourse. This model can be used for interpreting and analysing classroom discourse centred on analogical activities from sociocultural perspectives. That is, it can be used to code classroom discourse to reveal students’ growing participation with chemical (or scientific) discourse consistent with sociocultural perspectives on learning.

Recombinant protein production using a Tobacco yellow dwarf virus-based episomal expression vector : control of Rep activity

Over the past decade, plants have been used as expression hosts for the production of pharmaceutically important and commercially valuable proteins. Plants offer many advantages over other expression systems such as lower production costs, rapid scale up of production, similar post-translational modification as animals and the low likelihood of contamination with animal pathogens, microbial toxins or oncogenic sequences. However, improving recombinant protein yield remains one of the greatest challenges to molecular farming. In-Plant Activation (InPAct) is a newly developed technology that offers activatable and high-level expression of heterologous proteins in plants. InPAct vectors contain the geminivirus cis elements essential for rolling circle replication (RCR) and are arranged such that the gene of interest is only expressed in the presence of the cognate viral replication-associated protein (Rep). The expression of Rep in planta may be controlled by a tissue-specific, developmentally regulated or chemically inducible promoter such that heterologous protein accumulation can be spatially and temporally controlled. One of the challenges for the successful exploitation of InPAct technology is the control of Rep expression as even very low levels of this protein can reduce transformation efficiency, cause abnormal phenotypes and premature activation of the InPAct vector in regenerated plants. Tight regulation over transgene expression is also essential if expressing cytotoxic products. Unfortunately, many tissue-specific and inducible promoters are unsuitable for controlling expression of Rep due to low basal activity in the absence of inducer or in tissues other than the target tissue. This PhD aimed to control Rep activity through the production of single chain variable fragments (scFvs) specific to the motif III of Tobacco yellow dwarf virus (TbYDV) Rep. Due to the important role played by the conserved motif III in the RCR, it was postulated that such scFvs can be used to neutralise the activity of the low amount of Rep expressed from a “leaky” inducible promoter, thus preventing activation of the TbYDV-based InPAct vector until intentional induction. Such scFvs could also offer the potential to confer partial or complete resistance to TbYDV, and possibly heterologous viruses as motif III is conserved between geminiviruses. Studies were first undertaken to determine the levels of TbYDV Rep and TbYDV replication-associated protein A (RepA) required for optimal transgene expression from a TbYDV-based InPAct vector. Transient assays in a non-regenerable Nicotiana tabacum (NT-1) cell line were undertaken using a TbYDV-based InPAct vector containing the uidA reporter gene (encoding GUS) in combination with TbYDV Rep and RepA under the control of promoters with high (CaMV 35S) or low (Banana bunchy top virus DNA-R, BT1) activity. The replication enhancer protein of Tomato leaf curl begomovirus (ToLCV), REn, was also used in some co-bombardment experiments to examine whether RepA could be substituted by a replication enhancer from another geminivirus genus. GUS expression was observed both quantitatively and qualitatively by fluorometric and histochemical assays, respectively. GUS expression from the TbYDV-based InPAct vector was found to be greater when Rep was expected to be expressed at low levels (BT1 promoter) rather than high levels (35S promoter). GUS expression was further enhanced when Rep and RepA were co-bombarded with a low ratio of Rep to RepA. Substituting TbYDV RepA with ToLCV REn also enhanced GUS expression but more importantly highest GUS expression was observed when cells were co-transformed with expression vectors directing low levels of Rep and high levels of RepA irrespective of the level of REn. In this case, GUS expression was approximately 74-fold higher than that from a non-replicating vector. The use of different terminators, namely CaMV 35S and Nos terminators, in InPAct vectors was found to influence GUS expression. In the presence of Rep, GUS expression was greater using pInPActGUS-Nos rather than pInPActGUS-35S. The only instance of GUS expression being greater from vectors containing the 35S terminator was when comparing expression from cells transformed with Rep, RepA and REnexpressing vectors and either non-replicating vectors, p35SGS-Nos or p35SGS-35S. This difference was most likely caused by an interaction of viral replication proteins with each other and the terminators. These results indicated that (i) the level of replication associated proteins is critical to high transgene expression, (ii) the choice of terminator within the InPAct vector may affect expression levels and (iii) very low levels of Rep can activate InPAct vectors hence controlling its activity is critical. Prior to generating recombinant scFvs, a recombinant TbYDV Rep was produced in E. coli to act as a control to enable the screening for Rep-specific antibodies. A bacterial expression vector was constructed to express recombinant TbYDV Rep with an Nterminal His-tag (N-His-Rep). Despite investigating several purification techniques including Ni-NTA, anion exchange, hydrophobic interaction and size exclusion chromatography, N-His-Rep could only be partially purified using a Ni-NTA column under native conditions. Although it was not certain that this recombinant N-His-Rep had the same conformation as the native TbYDV Rep and was functional, results from an electromobility shift assay (EMSA) showed that N-His-Rep was able to interact with the TbYDV LIR and was, therefore, possibly functional. Two hybridoma cell lines from mice, immunised with a synthetic peptide containing the TbYDV Rep motif III amino acid sequence, were generated by GenScript (USA). Monoclonal antibodies secreted by the two hybridoma cell lines were first screened against denatured N-His-Rep in Western analysis. After demonstrating their ability to bind N-His-Rep, two scFvs (scFv1 and scFv2) were generated using a PCR-based approach. Whereas the variable heavy chain (VH) from both cell lines could be amplified, only the variable light chain (VL) from cell line 2 was amplified. As a result, scFv1 contained VH and VL from cell line 1, whereas scFv2 contained VH from cell line 2 and VL from cell line 1. Both scFvs were first expressed in E. coli in order to evaluate their affinity to the recombinant TbYDV N-His-Rep. The preliminary results demonstrated that both scFvs were able to bind to the denatured N-His-Rep. However, EMSAs revealed that only scFv2 was able to bind to native N-His-Rep and prevent it from interacting with the TbYDV LIR. Each scFv was cloned into plant expression vectors and co-bombarded into NT-1 cells with the TbYDV-based InPAct GUS expression vector and pBT1-Rep to examine whether the scFvs could prevent Rep from mediating RCR. Although it was expected that the addition of the scFvs would result in decreased GUS expression, GUS expression was found to slightly increase. This increase was even more pronounced when the scFvs were targeted to the cell nucleus by the inclusion of the Simian virus 40 large T antigen (SV40) nuclear localisation signal (NLS). It was postulated that the scFvs were binding to a proportion of Rep, leaving a small amount available to mediate RCR. The outcomes of this project provide evidence that very high levels of recombinant protein can theoretically be expressed using InPAct vectors with judicious selection and control of viral replication proteins. However, the question of whether the scFvs generated in this project have sufficient affinity for TbYDV Rep to prevent its activity in a stably transformed plant remains unknown. It may be that other scFvs with different combinations of VH and VL may have greater affinity for TbYDV Rep. Such scFvs, when expressed at high levels in planta, might also confer resistance to TbYDV and possibly heterologous geminiviruses.

Fundamental solution and discrete random walk model for time-space fractional diffusion equation

In this paper, we consider a time-space fractional diffusion equation of distributed order (TSFDEDO). The TSFDEDO is obtained from the standard advection-dispersion equation by replacing the first-order time derivative by the Caputo fractional derivative of order α∈(0,1], the first-order and second-order space derivatives by the Riesz fractional derivatives of orders β 1∈(0,1) and β 2∈(1,2], respectively. We derive the fundamental solution for the TSFDEDO with an initial condition (TSFDEDO-IC). The fundamental solution can be interpreted as a spatial probability density function evolving in time. We also investigate a discrete random walk model based on an explicit finite difference approximation for the TSFDEDO-IC.

Internet chatrooms : e-space for youth of the risk society

"This book focuses on issues in literacy and technology at the K-12 level in a holistic manner so that the needs of teachers and researchers can be addressed through the use of state-of-the-art perspectives"