Numerical simulation of the Riesz fractional diffusion equation with a nonlinear source term

In this paper, A Riesz fractional diffusion equation with a nonlinear source term (RFDE-NST) is considered. This equation is commonly used to model the growth and spreading of biological species. According to the equivalent of the Riemann-Liouville(R-L) and Gr¨unwald-Letnikov(GL) fractional derivative definitions, an implicit difference approximation (IFDA) for the RFDE-NST is derived. We prove the IFDA is unconditionally stable and convergent. In order to evaluate the efficiency of the IFDA, a comparison with a fractional method of lines (FMOL) is used. Finally, two numerical examples are presented to show that the numerical results are in good agreement with our theoretical analysis.

Mining patterns and factors contributing to crash severity on road curves

Road curves are an important feature of road infrastructure and many serious crashes occur on road curves. In Queensland, the number of fatalities is twice as many on curves as that on straight roads. Therefore, there is a need to reduce drivers’ exposure to crash risk on road curves. Road crashes in Australia and in the Organisation for Economic Co-operation and Development(OECD) have plateaued in the last five years (2004 to 2008) and the road safety community is desperately seeking innovative interventions to reduce the number of crashes. However, designing an innovative and effective intervention may prove to be difficult as it relies on providing theoretical foundation, coherence, understanding, and structure to both the design and validation of the efficiency of the new intervention. Researchers from multiple disciplines have developed various models to determine the contributing factors for crashes on road curves with a view towards reducing the crash rate. However, most of the existing methods are based on statistical analysis of contributing factors described in government crash reports. In order to further explore the contributing factors related to crashes on road curves, this thesis designs a novel method to analyse and validate these contributing factors. The use of crash claim reports from an insurance company is proposed for analysis using data mining techniques. To the best of our knowledge, this is the first attempt to use data mining techniques to analyse crashes on road curves. Text mining technique is employed as the reports consist of thousands of textual descriptions and hence, text mining is able to identify the contributing factors. Besides identifying the contributing factors, limited studies to date have investigated the relationships between these factors, especially for crashes on road curves. Thus, this study proposed the use of the rough set analysis technique to determine these relationships. The results from this analysis are used to assess the effect of these contributing factors on crash severity. The findings obtained through the use of data mining techniques presented in this thesis, have been found to be consistent with existing identified contributing factors. Furthermore, this thesis has identified new contributing factors towards crashes and the relationships between them. A significant pattern related with crash severity is the time of the day where severe road crashes occur more frequently in the evening or night time. Tree collision is another common pattern where crashes that occur in the morning and involves hitting a tree are likely to have a higher crash severity. Another factor that influences crash severity is the age of the driver. Most age groups face a high crash severity except for drivers between 60 and 100 years old, who have the lowest crash severity. The significant relationship identified between contributing factors consists of the time of the crash, the manufactured year of the vehicle, the age of the driver and hitting a tree. Having identified new contributing factors and relationships, a validation process is carried out using a traffic simulator in order to determine their accuracy. The validation process indicates that the results are accurate. This demonstrates that data mining techniques are a powerful tool in road safety research, and can be usefully applied within the Intelligent Transport System (ITS) domain. The research presented in this thesis provides an insight into the complexity of crashes on road curves. The findings of this research have important implications for both practitioners and academics. For road safety practitioners, the results from this research illustrate practical benefits for the design of interventions for road curves that will potentially help in decreasing related injuries and fatalities. For academics, this research opens up a new research methodology to assess crash severity, related to road crashes on curves.

Managing a portfolio of corporate venture units : challenges in achieving within-unit focus and between-unit coordination

Principal Topic: There is increasing recognition that the organizational configurations of corporate venture units should depend on the types of ventures the unit seeks to develop (Burgelman, 1984; Hill and Birkinshaw, 2008). Distinction have been made between internal and external as well as exploitative versus explorative ventures (Hill and Birkinshaw, 2008; Narayan et al., 2009; Schildt et al., 2005). Assuming that firms do not want to limit themselves to a single type of venture, but rather employ a portfolio of ventures, the logical consequence is that firms should employ multiple corporate venture units. Each venture unit tailor-made for the type of venture it seeks to develop. Surprisingly, there is limited attention in the literature for the challenges of managing multiple corporate venture units in a single firm. Maintaining multiple venture units within one firm provides easier access to funding for new ideas (Hamel, 1999). It allows for freedom and flexibility to tie the organizational systems (Rice et al., 2000), autonomy (Hill and Rothaermel, 2003), and involvement of management (Day, 1994; Wadwha and Kotha, 2006) to the requirements of the individual ventures. Yet, the strategic objectives of a venture may change when uncertainty around the venture is resolved (Burgelman, 1984). For example, firms may decide to spin-in external ventures (Chesbrough, 2002) or spun-out ventures that prove strategically unimportant (Burgelman, 1984). This suggests that ventures might need to be transferred between venture units, e.g. from a more internally-driven corporate venture division to a corporate venture capital unit. Several studies suggested that ventures require different managerial skills across their phase of development (Desouza et al., 2007; O'Connor and Ayers, 2005; Kazanjian and Drazin, 1990; Westerman et al., 2006). To facilitate effective transfer between venture units and manage the overall venturing process, it is important that firms set up and manage integrative linkages. Integrative linkages provide synergies and coordination between differentiated units (Lawrence and Lorsch, 1967). Prior findings pointed to the important role of senior management (Westerman et al., 2006; Gilbert, 2006) and a shared organizational vision (Burgers et al., 2009) to coordinate venture units with mainstream businesses. We will draw on these literatures to investigate the key question of how to integratively manage multiple venture units. ---------- Methodology/Key Propositions: In order to seek an answer to the research question, we employ a case study approach that provides unique insights into how firms can break up their venturing process. We selected three Fortune 500 companies that employ multiple venturing units, IBM, Royal Dutch/ Shell and Nokia, and investigated and compared their approaches. It was important that the case companies somewhat differed in the type of venture units they employed as well as the way they integrate and coordinate their venture units. The data are based on extensive interviews and a variety of internal and external company documents to triangulate our findings (Eisenhardt, 1989). The key proposition of the article is that firms can best manage their multiple venture units through an ambidextrous design of loosely coupled units. This provides venture units with sufficient flexibility to employ organizational configurations that best support the type of venture they seek to develop, as well as provides sufficient integration to facilitate smooth transfer of ventures between venture units. Based on the case findings, we develop a generic framework for a new way of managing the venturing process through multiple corporate venture units. ---------- Results and Implications: One of our main findings is that these firms tend to organize their venture units according to phases in the venture development process. That is, they tend to have venture units aimed at incubation of venture ideas as well as units aimed more at the commercialization of ventures into a new business unit for the firm or a start-up. The companies in our case studies tended to coordinate venture units through integrative management skills or a coordinative venture unit that spanned multiple phases. We believe this paper makes two significant contributions. First, we extend prior venturing literature by addressing how firms manage a portfolio of venture units, each achieving different strategic objectives. Second, our framework provides recommendations on how firms should manage such an approach towards venturing. This helps to increase the likelihood of success of their venturing programs.

Bootstrap approaches for estimation and confidence intervals of long term memory processes

In this work, we investigate an alternative bootstrap approach based on a result of Ramsey [F.L. Ramsey, Characterization of the partial autocorrelation function, Ann. Statist. 2 (1974), pp. 1296-1301] and on the Durbin-Levinson algorithm to obtain a surrogate series from linear Gaussian processes with long range dependence. We compare this bootstrap method with other existing procedures in a wide Monte Carlo experiment by estimating, parametrically and semi-parametrically, the memory parameter d. We consider Gaussian and non-Gaussian processes to prove the robustness of the method to deviations from normality. The approach is also useful to estimate confidence intervals for the memory parameter d by improving the coverage level of the interval.

Portfolio size effect in retirement accounts : what does it imply for lifecycle asset allocation funds?

Lifecycle funds offered by retirement plan providers allocate aggressively to risky asset classes when the employee participants are young, gradually switching to more conservative asset classes as they grow older and approach retirement. This approach focuses on maximizing growth of the accumulation fund in the initial years and preserving its value in the later years. The authors simulate terminal wealth outcomes based on conventional lifecycle asset allocation rules as well as on contrarian strategies that reverse the direction of asset switching. The evidence suggests that the growth in portfolio size over time significantly impacts the asset allocation decision. Due to the portfolio size effect that is observed by the authors, the terminal value of accumulation in retirement accounts is influenced more by the asset allocation strategy adopted in later years relative to that adopted in early years. By mechanistically switching to conservative assets in the later years of a plan, lifecycle strategies sacrifice significant growth opportunity and prove counterproductive to the participant's wealth accumulation objective. The authors' conclude that this sacrifice does not seem to be compensated adequately in terms of reducing the risk of potentially adverse outcomes.

Teachers’ attitudes toward reporting child sexual abuse : problems with existing research leading to new scale development

This paper details a systematic literature review identifying problems in extant research relating to teachers’ attitudes towards reporting child sexual abuse, and offers a model for new attitude scale development and testing. Scale development comprised a five-phase process grounded in contemporary attitude theories including: a) developing the initial item pool; b) conducting a panel review; c) refining the scale via an expert focus group; d) building content validity through cognitive interviews; e) assessing internal consistency via field testing. The resulting 21-item scale displayed construct validity in preliminary testing. The scale may prove useful as a research tool, given the theoretical supposition that attitudes may be changed with time, context, experience, and education. Further investigation with a larger sample is warranted.

A hydrogen tethered inhibitor of matrix metalloproteinases

During wound repair, the balance between matrix metalloproteinases (MMPs) and their natural inhibitors (the TIMPs) is crucial for the normal extra cellular matrix turnover. However, the over expression of several MMPs including MMP-1, 2, 3, 8, 9 and MMP-10, combined with abnormally high levels of activation or low expression of TIMPs, may contribute to excessive degradation of connective tissue and formation of chronic ulcers. There are many groups exploring strategies for promoting wound healing involving delivery of growth factors, cells, ECM components and small molecules. Our approach for improving the balance of MMPs is not to add anything more to the wound, but instead to neutralise the over-expressed MMPs using inhibitors tethered to a bandage-like hydrogel. Our in vitro experiments using designed synthetic pseudo peptide inhibitors have been demonstrated to inhibit MMP activity in standard solutions. These inhibitors have also been tethered to polyethylene glycol hydrogels using a facile reaction between the linker unit on the inhibitor and the gel. After tethering the inhibition of MMPs diminishes to some extent and we postulate that this arises due to poor diffusion of the MMPs into the gels. When the tethered inhibitors were tested against chronic wound fluid obtained against patients we observed over 40% inhibition in proteolytic activity suggesting our approach may prove useful in rebalancing MMPs within chronic wounds.

Accurate series solutions for gravity-driven Stokes waves

In the past, high order series expansion techniques have been used to study the nonlinear equations that govern the form of periodic Stokes waves moving steadily on the surface of an inviscid fluid. In the present study, two such series solutions are recomputed using exact arithmetic, eliminating any loss of accuracy due to accumulation of round-off error, allowing a much greater number of terms to be found with confidence. It is shown that higher order behaviour of series generated by the solution casts doubt over arguments that rely on estimating the series’ radius of convergence. Further, the exact nature of the series is used to shed light on the unusual nature of convergence of higher order Pade approximants near the highest wave. Finally, it is concluded that, provided exact values are used in the series, these Pade approximants prove very effective in successfully predicting three turning points in both the dispersion relation and the total energy.

A peptidomimetic inhibitor of matrix metalloproteinases containing a tetherable linker group

Successful wound repair and normal turnover of the extracellular matrix relies on a balance between matrix metalloproteinases (MMPs) and their natural inhibitors (the TIMPs). When over-expression of MMPs and abnormally high levels of activation or low expression of TIMPs are encountered, excessive degradation of connective tissue and the formation of chronic ulcers can occur. One strategy to rebalance MMPs and TIMPs is to use inhibitors. We have designed a synthetic pseudopeptide inhibitor with an amine linker group based on a known high-affinity peptidomimetic MMP inhibitor have demonstrated inhibition of MMP-1, -2, -3 and -9 activity in standard solutions. The inhibitor was also tethered to a polyethylene glycol hydrogel using a facile reaction between the linker unit on the inhibitor and the hydrogel precursors. After tethering, we observed inhibition of the MMPs although there was an increase in the IC50s which was attributed to poor diffusion of the MMPs into the hydrogels, reduced activity of the tethered inhibitor or incomplete incorporation of the inhibitor into the hydrogels. When the tethered inhibitors were tested against chronic wound fluid we observed significant inhibition in proteolytic activity suggesting our approach may prove useful in rebalancing MMPs within chronic wounds.

A modified cementing technique using BoneSource to augment fixation of the acetabulum in a sheep model

Background and purpose Our aim was to prove in an animal model that the use of HA paste at the cement-bone interface in the acetabulum would improve fixation. We examined, in sheep, the effect of interposing a layer of hydroxyapatite cement around the periphery of a polyethylene socket prior to fixing it using polymethylemethacrylate (PMMA). Methods We made a randomized study involving 22 sheep to test whether the application of BoneSource hydroxyapatite material to the surface of the ovine acetabulum prior to cementing a polyethylene cup at hip arthroplasty improved the fixation and the nature of the interface. We studied the gross radiographical appearance of the implant-bone interface and the histological appearance at the interface. Results There were more radiolucencies evident in the control group. Histologically, only sheep randomized into the BoneSource group exhibited a fully osseointegrated interface. Use of the hydroxyapatite material did not confer any detrimental effects. In some cases the material appeared to have been fully resorbed. When the material was evident on histological section, it was incorporated into an osseointegrated interface. There was no giant cell reaction present in any case. There was no evidence of migration of BoneSource to the articulation. Interpretation The application of HA material prior to cementation of a socket produced an improved interface. The technique may be useful in man with to extend the longevity of the cemented implant by protecting the socket interface from the effect of hydrodynamic fluid flow and particulate debris.

Cluster-based Intrusion Detection (CBID) architecture for mobile ad hoc networks

The ad hoc networks are vulnerable to attacks due to distributed nature and lack of infrastructure. Intrusion detection systems (IDS) provide audit and monitoring capabilities that offer the local security to a node and help to perceive the specific trust level of other nodes. The clustering protocols can be taken as an additional advantage in these processing constrained networks to collaboratively detect intrusions with less power usage and minimal overhead. Existing clustering protocols are not suitable for intrusion detection purposes, because they are linked with the routes. The route establishment and route renewal affects the clusters and as a consequence, the processing and traffic overhead increases due to instability of clusters. The ad hoc networks are battery and power constraint, and therefore a trusted monitoring node should be available to detect and respond against intrusions in time. This can be achieved only if the clusters are stable for a long period of time. If the clusters are regularly changed due to routes, the intrusion detection will not prove to be effective. Therefore, a generalized clustering algorithm has been proposed that can run on top of any routing protocol and can monitor the intrusions constantly irrespective of the routes. The proposed simplified clustering scheme has been used to detect intrusions, resulting in high detection rates and low processing and memory overhead irrespective of the routes, connections, traffic types and mobility of nodes in the network. Clustering is also useful to detect intrusions collaboratively since an individual node can neither detect the malicious node alone nor it can take action against that node on its own.

A new future for growth factor complexes as wound therapies?

Background: Topical administration of growth factors (GFs) has displayed some potential in wound healing, but variable efficacy, high doses and costs have hampered their implementation. Moreover, this approach ignores the fact that wound repair is driven by interactions between multiple GFs and extracellular matrix (ECM) proteins. The Problem: Deep dermal partial thickness burn (DDPTB) injuries are the most common burn presentation to pediatric hospitals and also represent the most difficult burn injury to manage clinically. DDPTB often repair with a hypertrophic scar. Wounds that close rapidly exhibit reduced scarring. Thus treatments that shorten the time taken to close DDTPB’s may coincidently reduce scarring. Basic/Clinical Science Advances: We have observed that multi-protein complexes comprised of IGF and IGF-binding proteins bound to the ECM protein vitronectin (VN) significantly enhance cellular functions relevant to wound repair in human skin keratinocytes. These responses require activation of both the IGF-1R and the VN-binding αv integrins. We have recently evaluated the wound healing potential of these GF:VN complexes in a porcine model of DDTPB injury. Clinical Care Relevance: This pilot study demonstrates that GF:VN complexes hold promise as a wound healing therapy. Enhanced healing responses were observed after treatment with nanogram doses of the GF:VN complexes in vitro and in vivo. Critically healing was achieved using substantially less GF than studies in which GFs alone have been used. Conclusion: These data suggest that coupling GFs to ECM proteins, such as VN, may ultimately prove to be an improved technique for the delivery of novel GF-based wound therapies.

A point interpolation method with locally smoothed strain field (PIM-LS2) for mechanics problems using triangular mesh

A point interpolation method with locally smoothed strain field (PIM-LS2) is developed for mechanics problems using a triangular background mesh. In the PIM-LS2, the strain within each sub-cell of a nodal domain is assumed to be the average strain over the adjacent sub-cells of the neighboring element sharing the same field node. We prove theoretically that the energy norm of the smoothed strain field in PIM-LS2 is equivalent to that of the compatible strain field, and then prove that the solution of the PIM- LS2 converges to the exact solution of the original strong form. Furthermore, the softening effects of PIM-LS2 to system and the effects of the number of sub-cells that participated in the smoothing operation on the convergence of PIM-LS2 are investigated. Intensive numerical studies verify the convergence, softening effects and bound properties of the PIM-LS2, and show that the very ‘‘tight’’ lower and upper bound solutions can be obtained using PIM-LS2.

Low sodium haemodialysis reduces interdialytic fluid consumption but paradoxically increases post-dialysis thirst

Background Interdialytic weight gain (IDWG) can be reduced by lowering the dialysate sodium concentration ([Na]) in haemodialysis patients. It has been assumed that this is because thirst is reduced, although this has been difficult to prove. We compared thirst patterns in stable haemodialysis patients with high and low IDWG using a novel technique and compared the effect of low sodium dialysis (LSD) with normal sodium dialysis (NSD). Methods Eight patients with initial high IDWG and seven with low IDWG completed hourly visual analogue ratings of thirst using a modified palmtop computer during the dialysis day and the interdialytic day. The dialysate [Na] was progressively reduced by up to 5 mmol/l over five treatments. Dialysis continued at the lowest attained [Na] for 2 weeks and the measurements were repeated. The dialysate [Na] then returned to baseline and the process was repeated. Results Baseline interdialytic day mean thirst was higher than the dialysis day mean for the high IDWG group (49.9±14.0 vs 36.2±16.6) and higher than the low weight gain group (49.9±14.0 vs 34.1±14.6). This trend persisted on LSD, but there was a pronounced increase in post-dialysis thirst scores for both groups (high IDWG: 46±13 vs 30±21; low IDWG: 48±24 vs 33±18). The high IDWG group demonstrated lower IDWG during LSD than NSD (2.23±0.98 vs 2.86±0.38 kg; P<0.05). Conclusions Our results indicate that patients with high IDWG experience more intense feelings of thirst on the interdialytic day. LSD reduces their IDWG, but paradoxically increases thirst in the immediate post-dialysis period.

Novel analytical and numerical methods for solving fractional dynamical systems

During the past three decades, the subject of fractional calculus (that is, calculus of integrals and derivatives of arbitrary order) has gained considerable popularity and importance, mainly due to its demonstrated applications in numerous diverse and widespread fields in science and engineering. For example, fractional calculus has been successfully applied to problems in system biology, physics, chemistry and biochemistry, hydrology, medicine, and finance. In many cases these new fractional-order models are more adequate than the previously used integer-order models, because fractional derivatives and integrals enable the description of the memory and hereditary properties inherent in various materials and processes that are governed by anomalous diffusion. Hence, there is a growing need to find the solution behaviour of these fractional differential equations. However, the analytic solutions of most fractional differential equations generally cannot be obtained. As a consequence, approximate and numerical techniques are playing an important role in identifying the solution behaviour of such fractional equations and exploring their applications. The main objective of this thesis is to develop new effective numerical methods and supporting analysis, based on the finite difference and finite element methods, for solving time, space and time-space fractional dynamical systems involving fractional derivatives in one and two spatial dimensions. A series of five published papers and one manuscript in preparation will be presented on the solution of the space fractional diffusion equation, space fractional advectiondispersion equation, time and space fractional diffusion equation, time and space fractional Fokker-Planck equation with a linear or non-linear source term, and fractional cable equation involving two time fractional derivatives, respectively. One important contribution of this thesis is the demonstration of how to choose different approximation techniques for different fractional derivatives. Special attention has been paid to the Riesz space fractional derivative, due to its important application in the field of groundwater flow, system biology and finance. We present three numerical methods to approximate the Riesz space fractional derivative, namely the L1/ L2-approximation method, the standard/shifted Gr¨unwald method, and the matrix transform method (MTM). The first two methods are based on the finite difference method, while the MTM allows discretisation in space using either the finite difference or finite element methods. Furthermore, we prove the equivalence of the Riesz fractional derivative and the fractional Laplacian operator under homogeneous Dirichlet boundary conditions – a result that had not previously been established. This result justifies the aforementioned use of the MTM to approximate the Riesz fractional derivative. After spatial discretisation, the time-space fractional partial differential equation is transformed into a system of fractional-in-time differential equations. We then investigate numerical methods to handle time fractional derivatives, be they Caputo type or Riemann-Liouville type. This leads to new methods utilising either finite difference strategies or the Laplace transform method for advancing the solution in time. The stability and convergence of our proposed numerical methods are also investigated. Numerical experiments are carried out in support of our theoretical analysis. We also emphasise that the numerical methods we develop are applicable for many other types of fractional partial differential equations.