Numerical schemes and multivariate extrapolation of a two-dimensional anomalous sub-diffusion equation

Anomalous dynamics in complex systems have gained much interest in recent years. In this paper, a two-dimensional anomalous subdiffusion equation (2D-ASDE) is considered. Two numerical methods for solving the 2D-ASDE are presented. Their stability, convergence and solvability are discussed. A new multivariate extrapolation is introduced to improve the accuracy. Finally, numerical examples are given to demonstrate the effectiveness of the schemes and confirm the theoretical analysis.

Uncertain species distribution: From interpolation to extrapolation

Species distribution models (SDMs) are considered to exemplify Pattern rather than Process based models of a species' response to its environment. Hence when used to map species distribution, the purpose of SDMs can be viewed as interpolation, since species response is measured at a few sites in the study region, and the aim is to interpolate species response at intermediate sites. Increasingly, however, SDMs are also being used to also extrapolate species-environment relationships beyond the limits of the study region as represented by the training data. Regardless of whether SDMs are to be used for interpolation or extrapolation, the debate over how to implement SDMs focusses on evaluating the quality of the SDM, both ecologically and mathematically. This paper proposes a framework that includes useful tools previously employed to address uncertainty in habitat modelling. Together with existing frameworks for addressing uncertainty more generally when modelling, we then outline how these existing tools help inform development of a broader framework for addressing uncertainty, specifically when building habitat models. As discussed earlier we focus on extrapolation rather than interpolation, where the emphasis on predictive performance is diluted by the concerns for robustness and ecological relevance. We are cognisant of the dangers of excessively propagating uncertainty. Thus, although the framework provides a smorgasbord of approaches, it is intended that the exact menu selected for a particular application, is small in size and targets the most important sources of uncertainty. We conclude with some guidance on a strategic approach to identifying these important sources of uncertainty. Whilst various aspects of uncertainty in SDMs have previously been addressed, either as the main aim of a study or as a necessary element of constructing SDMs, this is the first paper to provide a more holistic view.

Efficient simulation of stochastic chemical kinetics with the Stochastic Bulirsch-Stoer extrapolation method

Background Biochemical systems with relatively low numbers of components must be simulated stochastically in order to capture their inherent noise. Although there has recently been considerable work on discrete stochastic solvers, there is still a need for numerical methods that are both fast and accurate. The Bulirsch-Stoer method is an established method for solving ordinary differential equations that possesses both of these qualities. Results In this paper, we present the Stochastic Bulirsch-Stoer method, a new numerical method for simulating discrete chemical reaction systems, inspired by its deterministic counterpart. It is able to achieve an excellent efficiency due to the fact that it is based on an approach with high deterministic order, allowing for larger stepsizes and leading to fast simulations. We compare it to the Euler τ-leap, as well as two more recent τ-leap methods, on a number of example problems, and find that as well as being very accurate, our method is the most robust, in terms of efficiency, of all the methods considered in this paper. The problems it is most suited for are those with increased populations that would be too slow to simulate using Gillespie’s stochastic simulation algorithm. For such problems, it is likely to achieve higher weak order in the moments. Conclusions The Stochastic Bulirsch-Stoer method is a novel stochastic solver that can be used for fast and accurate simulations. Crucially, compared to other similar methods, it better retains its high accuracy when the timesteps are increased. Thus the Stochastic Bulirsch-Stoer method is both computationally efficient and robust. These are key properties for any stochastic numerical method, as they must typically run many thousands of simulations.

The passionate critic

It's hard to be dispassionate about Reyner Banham. For me, and for the plethora of other people with strong opinions about Banham, his writing is compelling, and one’s connection to him as a figure quite personal. For me, frankly, he rocks. As a landscape architect, I gleaned most of my knowledge about Modern architecture from Banham. His Theory and Design in the First Machine Age, along with Rowe and Koetter’s Collage City and Venturi’s Complexity and Contradiction in Architecture were the most influential books in my library, by far. Later, as a budding “real scholar”, I was disappointed to find that, while these authors had serious credibility, the writings themselves were regarded as “polemical” – when in fact what I admired about them most was their ability and willingness to make rough groupings and gross generalizations, and to offer fickle opinions. It spoke to me of a real personal engagement and an active, participatory reading of the architectural culture they discussed. They were at their best in their witty, cutting, but generally pithy, creative prose, such as in Rowe’s extrapolation of the modern citizen as the latest “noble savage”, or Banham railing against conservative social advocates and their response to high density housing: “those who had just re-discovered ‘community’ in the slums would fear megastructure as much as any other kind of large-scale renewal program, and would see to it that the people were never ready.” Any reader of Banham will be able to find a gem that will relate, somehow, personally, to what they are doing right now. For Banham, it was all personal, and the gaps in his scholarship, rather, were the dispassionate places: “Such bias is essential – an unbiased historian is a pointless historian – because history is an essentially critical activity, a constant re-scrutiny and rearrangement of the profession.” Reyner Banham: Historian of the Immediate Future, Nigel Whiteley’s recent “intellectual biography” (the MIT Press, 2002), allowed me to revisit Banham’s passionate mode of criticism and to consider what his legacy might be. The book examines Banham’s body of work, grouped according to his various primary fascinations, as well as his relationship to contemporaneous theoretical movements, such as postmodernism. His mode of practice, as a kind of creative critic, is also considered in some depth. While there are points where the book delves into Banham’s personal life, on the whole Whiteley is very rigorous in considering and theorizing the work itself: more than 750 articles and twelve books. In academic terms, this is good practice. However, considering the entirely personal nature of Banham’s writing itself, this separation seems artificial. Banham, as he himself noted, “didn’t mind a gossip”, and often when reading the book I was curious about what was happening to him at the time. Banham’s was an amazing type of intellectual practice, and one that academics (a term he hated) could do well to learn from. While Whiteley spends a lot of time arguing for his practice to be regarded as such, and makes strong points about both the role of the critic, and the importance of journalism, rather than scholarly publishing, I found myself wondering what his study looked like. What books he had in his library. Did he smoke when he wrote? What sort of teaching load did he have? He is an inspiration to design writers and thinkers, and I, personally, wanted to know how he did it.

Numerical methods for the variable-order fractional advection-diffusion equation with a nonlinear source term

In this paper, we consider a variable-order fractional advection-diffusion equation with a nonlinear source term on a finite domain. Explicit and implicit Euler approximations for the equation are proposed. Stability and convergence of the methods are discussed. Moreover, we also present a fractional method of lines, a matrix transfer technique, and an extrapolation method for the equation. Some numerical examples are given, and the results demonstrate the effectiveness of theoretical analysis.

Numerical simulation for the 3D seepage flow with fractional derivatives in porous media

In this paper, the numerical simulation of the 3D seepage flow with fractional derivatives in porous media is considered under two special cases: non-continued seepage flow in uniform media (NCSFUM) and continued seepage flow in non-uniform media (CSF-NUM). A fractional alternating direction implicit scheme (FADIS) for the NCSF-UM and a modified Douglas scheme (MDS) for the CSF-NUM are proposed. The stability, consistency and convergence of both FADIS and MDS in a bounded domain are discussed. A method for improving the speed of convergence by Richardson extrapolation for the MDS is also presented. Finally, numerical results are presented to support our theoretical analysis.

How useful is expert opinion for predicting the distribution of a species within and beyond the region of expertise? A case study using brush-tailed rock-wallabiesPetrogale penicillata

1. Species' distribution modelling relies on adequate data sets to build reliable statistical models with high predictive ability. However, the money spent collecting empirical data might be better spent on management. A less expensive source of species' distribution information is expert opinion. This study evaluates expert knowledge and its source. In particular, we determine whether models built on expert knowledge apply over multiple regions or only within the region where the knowledge was derived. 2. The case study focuses on the distribution of the brush-tailed rock-wallaby Petrogale penicillata in eastern Australia. We brought together from two biogeographically different regions substantial and well-designed field data and knowledge from nine experts. We used a novel elicitation tool within a geographical information system to systematically collect expert opinions. The tool utilized an indirect approach to elicitation, asking experts simpler questions about observable rather than abstract quantities, with measures in place to identify uncertainty and offer feedback. Bayesian analysis was used to combine field data and expert knowledge in each region to determine: (i) how expert opinion affected models based on field data and (ii) how similar expert-informed models were within regions and across regions. 3. The elicitation tool effectively captured the experts' opinions and their uncertainties. Experts were comfortable with the map-based elicitation approach used, especially with graphical feedback. Experts tended to predict lower values of species occurrence compared with field data. 4. Across experts, consensus on effect sizes occurred for several habitat variables. Expert opinion generally influenced predictions from field data. However, south-east Queensland and north-east New South Wales experts had different opinions on the influence of elevation and geology, with these differences attributable to geological differences between these regions. 5. Synthesis and applications. When formulated as priors in Bayesian analysis, expert opinion is useful for modifying or strengthening patterns exhibited by empirical data sets that are limited in size or scope. Nevertheless, the ability of an expert to extrapolate beyond their region of knowledge may be poor. Hence there is significant merit in obtaining information from local experts when compiling species' distribution models across several regions.

Modelling water droplet movement on a leaf surface

The central aim for the research undertaken in this PhD thesis is the development of a model for simulating water droplet movement on a leaf surface and to compare the model behavior with experimental observations. A series of five papers has been presented to explain systematically the way in which this droplet modelling work has been realised. Knowing the path of the droplet on the leaf surface is important for understanding how a droplet of water, pesticide, or nutrient will be absorbed through the leaf surface. An important aspect of the research is the generation of a leaf surface representation that acts as the foundation of the droplet model. Initially a laser scanner is used to capture the surface characteristics for two types of leaves in the form of a large scattered data set. After the identification of the leaf surface boundary, a set of internal points is chosen over which a triangulation of the surface is constructed. We present a novel hybrid approach for leaf surface fitting on this triangulation that combines Clough-Tocher (CT) and radial basis function (RBF) methods to achieve a surface with a continuously turning normal. The accuracy of the hybrid technique is assessed using numerical experimentation. The hybrid CT-RBF method is shown to give good representations of Frangipani and Anthurium leaves. Such leaf models facilitate an understanding of plant development and permit the modelling of the interaction of plants with their environment. The motion of a droplet traversing this virtual leaf surface is affected by various forces including gravity, friction and resistance between the surface and the droplet. The innovation of our model is the use of thin-film theory in the context of droplet movement to determine the thickness of the droplet as it moves on the surface. Experimental verification shows that the droplet model captures reality quite well and produces realistic droplet motion on the leaf surface. Most importantly, we observed that the simulated droplet motion follows the contours of the surface and spreads as a thin film. In the future, the model may be applied to determine the path of a droplet of pesticide along a leaf surface before it falls from or comes to a standstill on the surface. It will also be used to study the paths of many droplets of water or pesticide moving and colliding on the surface.

Comprehensive standardized data definitions for acute coronary syndrome research in emergency departments in Australasia

Patients with chest discomfort or other symptoms suggestive of acute coronary syndrome (ACS) are one of the most common categories seen in many Emergency Departments (EDs). While the recognition of patients at high-risk of ACS has improved steadily, identifying the majority of chest pain presentations who fall into the low-risk group remains a challenge. Research in this area needs to be transparent, robust, applicable to all hospitals from large tertiary centres to rural and remote sites, and to allow direct comparison between different studies with minimum patient spectrum bias. A standardised approach to the research framework using a common language for data definitions must be adopted to achieve this. The aim was to create a common framework for a standardised data definitions set that would allow maximum value when extrapolating research findings both within Australasian ED practice, and across similar populations worldwide. Therefore a comprehensive data definitions set for the investigation of non-traumatic chest pain patients with possible ACS was developed, specifically for use in the ED setting. This standardised data definitions set will facilitate ‘knowledge translation’ by allowing extrapolation of useful findings into the real-life practice of emergency medicine.

Studies of the radiation chemistry and grafting of a fluoropolymer

The radiation chemistry and the grafting of a fluoropolymer, poly(tetrafluoroethylene-coperfluoropropyl vinyl ether) (PFA), was investigated with the aim of developing a highly stable grafted support for use in solid phase organic chemistry (SPOC). A radiation-induced grafting method was used whereby the PFA was exposed to ionizing radiation to form free radicals capable of initiating graft copolymerization of styrene. To fully investigate this process, both the radiation chemistry of PFA and the grafting of styrene to PFA were examined. Radiation alone was found to have a detrimental effect on PFA when irradiated at 303 K. This was evident from the loss in the mechanical properties due to chain scission reactions. This meant that when radiation was used for the grafting reactions, the total radiation dose needed to be kept as low as possible. The radicals produced when PFA was exposed to radiation were examined using electron spin resonance spectroscopy. Both main-chain (–CF2–C.F–CF2-) and end-chain (–CF2–C.F2) radicals were identified. The stability of the majority of the main-chain radicals when the polymer was heated above the glass transition temperature suggested that they were present mainly in the crystalline regions of the polymer, while the end-chain radicals were predominately located in the amorphous regions. The radical yield at 77 K was lower than the radical yield at 303 K suggesting that cage recombination at low temperatures inhibited free radicals from stabilizing. High-speed MAS 19F NMR was used to identify the non-volatile products after irradiation of PFA over a wide temperature range. The major products observed over the irradiation temperature 303 to 633 K included new saturated chain ends, short fluoromethyl side chains in both the amorphous and crystalline regions, and long branch points. The proportion of the radiolytic products shifted from mainly chain scission products at low irradiation temperatures to extensive branching at higher irradiation temperatures. Calculations of G values revealed that net crosslinking only occurred when PFA was irradiated in the melt. Minor products after irradiation at elevated temperatures included internal and terminal double bonds and CF3 groups adjacent to double bonds. The volatile products after irradiation at 303 K included tetrafluoromethane (CF4) and oxygen-containing species from loss of the perfluoropropyl ether side chains of PFA as identified by mass spectrometry and FTIR spectroscopy. The chemical changes induced by radiation exposure were accompanied by changes in the thermal properties of the polymer. Changes in the crystallinity and thermal stability of PFA after irradiation were examined using DSC and TGA techniques. The equilibrium melting temperature of untreated PFA was 599 K as determined using a method of extrapolation of the melting temperatures of imperfectly formed crystals. After low temperature irradiation, radiation- induced crystallization was prevalent due to scission of strained tie molecules, loss of perfluoropropyl ether side chains, and lowering of the molecular weight which promoted chain alignment and hence higher crystallinity. After irradiation at high temperatures, the presence of short and long branches hindered crystallization, lowering the overall crystallinity. The thermal stability of the PFA decreased with increasing radiation dose and temperature due to the introduction of defect groups. Styrene was graft copolymerized to PFA using -radiation as the initiation source with the aim of preparing a graft copolymer suitable as a support for SPOC. Various grafting conditions were studied, such as the total dose, dose rate, solvent effects and addition of nitroxides to create “living” graft chains. The effect of dose rate was examined when grafting styrene vapour to PFA using the simultaneous grafting method. The initial rate of grafting was found to be independent of the dose rate which implied that the reaction was diffusion controlled. When the styrene was dissolved in various solvents for the grafting reaction, the graft yield was strongly dependent of the type and concentration of the solvent used. The greatest graft yield was observed when the solvent swelled the grafted layers and the substrate. Microprobe Raman spectroscopy was used to map the penetration of the graft into the substrate. The grafted layer was found to contain both poly(styrene) (PS) and PFA and became thicker with increasing radiation dose and graft yield which showed that grafting began at the surface and progressively penetrated the substrate as the grafted layer was swollen. The molecular weight of the grafted PS was estimated by measuring the molecular weight of the non-covalently bonded homopolymer formed in the grafted layers using SEC. The molecular weight of the occluded homopolymer was an order of magnitude greater than the free homopolymer formed in the surrounding solution suggesting that the high viscosity in the grafted regions led to long PS grafts. When a nitroxide mediated free radical polymerization was used, grafting occurred within the substrate and not on the surface due to diffusion of styrene into the substrate at the high temperatures needed for the reaction to proceed. Loading tests were used to measure the capacity of the PS graft to be functionialized with aminomethyl groups then further derivatized. These loading tests showed that samples grafted in a solution of styrene and methanol had superior loading capacity over samples graft using other solvents due to the shallow penetration and hence better accessibility of the graft when methanol was used as a solvent.

A life jacket with holes- : a case study of 'temporary engagement' : a strategy used by Education Queensland to employ beginning secondary teachers

This research investigated the impact of Education Queensland's employment policy and practices for beginning secondary teachers appointed on temporary engagement. The context was the public secondary school sector within the state of Queensland, Australia. The study was set within a context of the changing nature of work from full-time permanent employment towards casual, fixed-term contracts, temporary and part-time employment, a trend reflected in the employment patterns for teachers within Australia. Two broad categories of literature relating to the research problem of this thesis were reviewed, namely the beginning teacher and permanency or tenure. The focus in the research literature on beginning teachers was the professional experiences of teachers within the classroom and school. There was a paucity of research that considered the working and industrial conditions of temporary employment for beginning teachers or the personal and professional implications of this form of employment. The review of the context and literature was conceptualised as a Beginning Temporary Teacher Theoretical Framework which served to inform the study. Using a qualitative case study methodology, the research techniques employed for the thesis were semi-structured interview and document analysis. A simultaneously conducted research project in which the researcher participated entitled 'Winning the Lottery? Beginning Teachers on Temporary Engagement' foregrounded this thesis in terms of refining the research question, contributing to the literature and in the selection of the participants. For this case study the perspectives of four distinct yet inter-related categories of professionals were sought. These included four beginning secondary teachers, three school administrators, a Senior Personnel Officer with Education Queensland, and a representative from the Queensland Teachers' Union. The research findings indicated that none of the beginning teachers or other professionals viewed starting a career in teaching on temporary engagement as the ideal. The negative features identified were the differential treatment received and the high level of uncertainty associated with temporary employment. Differential treatment tended to indicate 'less' entitlements, in terms of access to induction and professional development, recreational and sick leave, acceptance by and expectations of other colleagues, and avenues of redress in grievance cases. Moreover, interviews indicated a high level of uncertainty in terms of starting within the teaching profession, commencing at a new school, and a regular income. In addition, frequent changes in schools and/or cohorts of students exacerbated levels of uncertainty. The beginning teachers reported significantly decreased motivation, self-esteem and sense of belonging, and increased stress levels. There was an even more marked negative impact on those beginning teachers who had experienced a higher number of temporary engagements and schools in their first year of teaching. Conversely, strong staff support and a reasonable length of time in the one school improved the quality of the beginning teachers' experiences. The overall impact of being on temporary engagement resulted in delayed permanent position appointments, decreased commitment to particular schools and to Education Queensland as the employing authority, and for two of the beginning teachers, it produced a desire to seek alternative employment. The implementation of Education Queensland's policies relating to working conditions and entitlements for these temporary beginning teachers at the school level was revealed to be less than satisfactory. There was a tendency towards 'just-in- time' management of the beginning teacher on temporary engagement. The beginning teachers received 'less-than-messages' about access to and use of departmental documentation, support through induction and professional development, and their transition from temporary to permanent employment. To ensure a more systematic, supportive and inclusive process for managing the temporary beginning teacher, a conceptual framework entitled 'Continuums of Tension' was developed. The four continuums included permanent employment - temporary employment; system perspective - individual perspective; teaching as a profession - teaching as a job; and the permanent beginning teacher - university graduate. The general principles of the human resource policies of Education Queensland were based on a commitment to permanent employment, a system's perspective, viewing teaching as a profession and a homogeneous group of permanent beginning teachers. Contrasting with this, the beginning teacher on temporary engagement tended to operate from the position of temporary employment and a perspective that was individually based. Their priorities therefore included the 'occupational' aspects of being a temporary teacher striving to become permanent. Thus there existed a tension or contradiction between the general principles of human resource policies within Education Queensland and the employment experiences of beginning teachers on temporary engagement. The study proposed three actions for resolution to address the aforementioned tensions. The actions included: (a) the effective provision and targeted communication of information; (b) support, induction and professional development; and (c) a coordinated approach between Education Queensland, Queensland Teachers' Union, the Universities and the beginning teacher. These actions are fm1her refined to include: (a) an induction kit to suppm1 the individual through the pre-employment to permanent employee phases, (b) an extrapolation of the roles and responsibilities of Education Queensland personnel charged with supporting the beginning temporary teacher, and (c) a series of recommendations to effect a coordinated approach amongst the key stakeholders. The theoretical and conceptual frameworks have provided a means of addressing the identified needs of the beginning teacher on temporary engagement. As such, this study has contributed to the research literature on teacher employment and professionalism and aims to provide a beginning temporary teacher with managed professional and occupational support.

Pastureland use in the southeastern US: Implications for carbon sequestration

More than 13 Mha of nonfederal land in the southeastern U.S. are devoted to pastureland. Between 1982 and 1992, pastureland increased by 100,000 ha, with nearly 70% converted from cultivated land. We examined the potential for carbon (C) sequestration with improved pasture management and conversion into pastureland from cultivated land. Improved pasture management techniques, such as intensive grazing, fertilization, introduction of improved grass and legume species, and better irrigation systems can lead to sequestration of atmospheric C in soil. Literature values for the influence of changes in pasture management on soil C were summarized for several potential management changes in the Southeast. Soil C sequestration estimates for the Southeast were based on current pasture management practices and evaluated for a range of different adoption rates of improved practices. Conversion into pasture can also potentially sequester significant amounts of atmospheric C in soils. Land-use data from the National Resources Inventory and literature estimates of soil C changes following conversion to pasture were used to estimate historical (1982 to 1992) soil C sequestration in pastures. Potential future sequestration was estimated based on extrapolation of land-use trends between 1982 and 1992. With continued conversion into pasture and improvement of pasture management, southeastern U.S. pasture soils may be a significant C sink for several years.

Remaining useful life prediction using elliptical basis function network and Markov Chain

This paper presents a novel method for remaining useful life prediction using the Elliptical Basis Function (EBF) network and a Markov chain. The EBF structure is trained by a modified Expectation-Maximization (EM) algorithm in order to take into account the missing covariate set. No explicit extrapolation is needed for internal covariates while a Markov chain is constructed to represent the evolution of external covariates in the study. The estimated external and the unknown internal covariates constitute an incomplete covariate set which are then used and analyzed by the EBF network to provide survival information of the asset. It is shown in the case study that the method slightly underestimates the remaining useful life of an asset which is a desirable result for early maintenance decision and resource planning.