952 resultados para Small Signal Stability


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Animal models typically require a known genetic pedigree to estimate quantitative genetic parameters. Here we test whether animal models can alternatively be based on estimates of relatedness derived entirely from molecular marker data. Our case study is the morphology of a wild bird population, for which we report estimates of the genetic variance-covariance matrices (G) of six morphological traits using three methods: the traditional animal model; a molecular marker-based approach to estimate heritability based on Ritland's pairwise regression method; and a new approach using a molecular genealogy arranged in a relatedness matrix (R) to replace the pedigree in an animal model. Using the traditional animal model, we found significant genetic variance for all six traits and positive genetic covariance among traits. The pairwise regression method did not return reliable estimates of quantitative genetic parameters in this population, with estimates of genetic variance and covariance typically being very small or negative. In contrast, we found mixed evidence for the use of the pedigree-free animal model. Similar to the pairwise regression method, the pedigree-free approach performed poorly when the full-rank R matrix based on the molecular genealogy was employed. However, performance improved substantially when we reduced the dimensionality of the R matrix in order to maximize the signal to noise ratio. Using reduced-rank R matrices generated estimates of genetic variance that were much closer to those from the traditional model. Nevertheless, this method was less reliable at estimating covariances, which were often estimated to be negative. Taken together, these results suggest that pedigree-free animal models can recover quantitative genetic information, although the signal remains relatively weak. It remains to be determined whether this problem can be overcome by the use of a more powerful battery of molecular markers and improved methods for reconstructing genealogies.

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Background The onsite treatment of sewage and effluent disposal is widely prevalent in rural and urban fringe areas due to the general unavailability of reticulated wastewater collection systems. Despite the low technology of the systems, failure is common and in many cases leading to adverse public health and environmental consequences. It is important therefore that careful consideration is given to the design and location of onsite sewage treatment systems. This requires an understanding of the factors that influence treatment performance. The use of subsurface absorption systems is the most common form of effluent disposal for onsite sewage treatment, particularly for septic tanks. Also, in the case of septic tanks, a subsurface disposal system is generally an integral component of the sewage treatment process. Site specific factors play a key role in the onsite treatment of sewage. The project The primary aims of the research project were: • to relate treatment performance of onsite sewage treatment systems to soil conditions at site; • to evaluate current research relating to onsite sewage treatment; and, • to identify key issues where currently there is a lack of relevant research. These tasks were undertaken with the objective of facilitating the development of performance based planning and management strategies for onsite sewage treatment. The primary focus of this research project has been on septic tanks. By implication, the investigation has been confined to subsurface soil absorption systems. The design and treatment processes taking place within the septic tank chamber itself did not form a part of the investigation. Five broad categories of soil types prevalent in the Brisbane region have been considered in this project. The number of systems investigated was based on the proportionate area of urban development within the Brisbane region located on each of the different soil types. In the initial phase of the investigation, the majority of the systems evaluated were septic tanks. However, a small number of aerobic wastewater treatment systems (AWTS) were also included. The primary aim was to compare the effluent quality of systems employing different generic treatment processes. It is important to note that the number of each different type of system investigated was relatively small. Consequently, this does not permit a statistical analysis to be undertaken of the results obtained for comparing different systems. This is an important issue considering the large number of soil physico-chemical parameters and landscape factors that can influence treatment performance and their wide variability. The report This report is the last in a series of three reports focussing on the performance evaluation of onsite treatment of sewage. The research project was initiated at the request of the Brisbane City Council. The project component discussed in the current report outlines the detailed soil investigations undertaken at a selected number of sites. In the initial field sampling, a number of soil chemical properties were assessed as indicators to investigate the extent of effluent flow and to help understand what soil factors renovate the applied effluent. The soil profile attributes, especially texture, structure and moisture regime were examined more in an engineering sense to determine the effect of movement of water into and through the soil. It is important to note that it is not only the physical characteristics, but also the chemical characteristics of the soil as well as landscape factors play a key role in the effluent renovation process. In order to understand the complex processes taking place in a subsurface effluent disposal area, influential parameters were identified using soil chemical concepts. Accordingly, the primary focus of this final phase of the research project was to identify linkages between various soil chemical parameters and landscape patterns and their contribution to the effluent renovation process. The research outcomes will contribute to the development of robust criteria for evaluating the performance of subsurface effluent disposal systems. The outcomes The key findings from the soil investigations undertaken are: • Effluent renovation is primarily undertaken by a combination of various soil physico-chemical parameters and landscape factors, thereby making the effluent renovation processes strongly site dependent. • Decisions regarding site suitability for effluent disposal should not be based purely in terms of the soil type. A number of other factors such as the site location in the catena, the drainage characteristics and other physical and chemical characteristics, also exert a strong influence on site suitability. • Sites, which are difficult to characterise in terms of suitability for effluent disposal, will require a detailed soil physical and chemical analysis to be undertaken to a minimum depth of at least 1.2 m. • The Ca:Mg ratio and Exchangeable Sodium Percentage are important parameters in soil suitability assessment. A Ca:Mg ratio of less than 0.5 would generally indicate a high ESP. This in turn would mean that Na and possibly Mg are the dominant exchangeable cations, leading to probable clay dispersion. • A Ca:Mg ratio greater than 0.5 would generally indicate a low ESP in the profile, which in turn indicates increased soil stability. • In higher clay percentage soils, low ESP can have a significant effect. • The presence of high exchangeable Na can be counteracted by the presence of swelling clays, and an exchange complex co-dominated by exchangeable Ca and exchangeable Mg. This aids absorption of cations at depth, thereby reducing the likelihood of dispersion. • Salt is continually added to the soil by the effluent and problems may arise if the added salts accumulate to a concentration that is harmful to the soil structure. Under such conditions, good drainage is essential in order to allow continuous movement of water and salt through the profile. Therefore, for a site to be sustainable, it would have a maximum application rate of effluent. This would be dependent on subsurface characteristics and the surface area available for effluent disposal. • The dosing regime for effluent disposal can play a significant role in the prevention of salt accumulation in the case of poorly draining sites. Though intermittent dosing was not considered satisfactory for the removal of the clogging mat layer, it has positive attributes in the context of removal of accumulated salts in the soil.

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Utilization of multiport-antennas represents an appropriate way for the mitigation of multi-path fading in wireless communication systems. However, to obtain low correlation between the signals from different antenna ports and to prevent gain reduction by cross-talk, large antenna elements spacing is expected. Polarization diversity allows signal separation even with small antenna spacing. Although it is effective, polarization diversity alone does not suffice once the number of antennas exceeds the number of orthogonal polarizations. This paper presents an approach which combines a novel array concept with the use of dual polarization. The theory is verified by a compact dual polarized patch antenna array, which consists of four elements and a decoupling network.

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Purpose: Myopia is a common eye disorder affecting up to 90% of children in South East Asia and 30% of the population worldwide. Myopia of high severity is a leading cause of blindness around the world (4th to 5th most common). Changes and remodelling of the sclera i.e. increase cellular proliferation & increase protein synthesis within scleral cells (↑ scleral DNA) and thinning and lose of extracellular matrix of sclera (↓ scleral GAG synthesis) have been linked to myopic eye growth in animal models. Signals acting on the sclera are thought to originate in the retina, and are modulated by the retinal pigment epithelium (RPE) with limited evidence suggesting that the RPE can modify scleral cell growth in culture. However, the mechanism of retinal signal transmission and the role of posterior eye cup tissue, including the RPE, in mediating changes in scleral fibroblast growth during myopia development are unclear. Retinal transmitter systems are critically involved in pathways regulating eye growth, which ultimately lead to alterations in the sclera if eye size is to change. A dopaminergic agonist and muscarinic antagonists decrease the proliferation of scleral chondrocytes when co-cultured with chick’s retinal pigment epithelium (RPE). GABA receptors have recently been localised to chick sclera. We therefore hypothesised that posterior eye cup tissue from myopic eyes would stimulate and from hyperopic eyes would inhibit growth of scleral fibroblasts in vitro and that GABAergic agents could directly interact with scleral cells or indirectly modify the effects of myopic and hyperopic posterior eye cup tissue on scleral fibroblast growth. Method: Fibroblastic cells obtained from 8-day-old chick sclera were used to establish cell banks. Two major experiments were performed. Experiment 1: To determine if posterior eye cup tissues from myopic eye stimulates and hyperopic eye inhibits scleral cell proliferation, when co-cultured with scleral cells in vitro. This study comprised two linked experiments, i) monocular visual treatments of FDM (form-deprivation myopia), LIM (lens-induced myopia) and LIH (lens-induced hyperopia) with assessment of the effect of full punch eye cup tissue on DNA and GAG synthesis by cultured chick scleral fibroblasts, and ii) binocular visual treatments comprising LIM and LIH with assessment of the effect of individual layers of eye cup tissues (neural retina, RPE and choroid) on cultured chick scleral fibroblasts. Visual treatment was applied for 3 days. Experiment 2: To determine the direct interaction of GABA agents on scleral cell growth and to establish whether GABA agents modify the stimulatory/inhibitory effect of myopic and hyperopic posterior eye cup tissues on cultured scleral cell growth in vitro. Two linked experiments were performed. i) GABA agonists (muscimol and baclofen) and GABA antagonists (bicuculine (-), CGP46381 and TPMPA) were added to scleral cell culture medium to determine their direct effect on scleral cells. ii) GABAergic agents (agonists and antagonists) were administered to scleral fibroblasts co-cultured with posterior eye cup tissue (retina, RPE, retina/RPE, RPE/choroid). Ocular tissues were obtained from chick eyes wearing +15D (LIH) or -15D lenses (LIM) for 3 days. In both experiments, tissues were added to hanging cell culture insert (pore size 1.0ìm) placed over each well of 24 well plates while scleral cells were cultured in DMEM/F12, Glutamax (Gibco) plus 10% FBS and penicillin/streptomycin (50U/ml)) and fungizone (1.25ug/ml) (Gibco), at seeding density of 30,000 cells/well at the bottom of the well and allowed to grow for 3 days. Scleral cells proliferation rate throughout the study was evaluated by determining GAG and DNA content of scleral cells using Dimethylmethylene blue (DMMB) dye and Quant-iTTm Pico Green® dsDNA reagent respectively. Results and analysis: Based on DNA and GAG content, there was no significant difference in tissue effect of LIM and LIH eyes on scleral fibroblast growth (DNA: 8.4 ± 1.1μg versus 9.3 ± 2.3 μg, p=0.23; GAG: 10.13 ± 1.4 μg versus 12.67 ± 1.2 μg, F2,23=6.16, p=0.0005) when tissues were obtained from monocularly treated chick eyes (FDM or +15D lens or -15D lens over right eyes with left eyes untreated) and co-cultured as full punch. When chick eyes were treated binocularly with -15D lens (LIM) right eye and +15D lens (LIH) left eyes and tissue layers were separated, the retina from LIM eyes did not stimulate scleral cell proliferation compared to LIH eyes (DNA: 27.2 ± 6.7 μg versus 23.2 ± 1.5 μg, p=0.23; GAG: 28.1 ±3.7 μg versus 28.7 ± 4.2 μg, p=0.21). Similarly, the LIH and LIM choroid did not produce a differential effect based on DNA (LIM 46.9 ± 6.4 μg versus LIH 53.5 ± 4.7 μg, p=0.18), however the choroid from LIH eyes induced higher scleral GAG content than from LIM eyes (32.5 ± 6.7 μg versus 18.9 ± 1.2 μg, p=0.023). In contrast, the RPE from LIM eyes caused a significant increase in fibroblast proliferation whereas the RPE from LIH eyes was relatively inhibitory (72.4 ± 6.3 μg versus 27.9 ± 2.3 μg, F1, 6=69.99, p=0.0005). GAG data were opposite to DNA data e.g. the RPE from LIH eyes increased (33.7 ± 7.9 μg) while the RPE from LIM eyes decreased (28.2 ± 3.0 μg) scleral cell growth (F1, 6=13.99, p=0.010). Based on DNA content, GABA agents had a small direct effect on scleral cell growth; GABA agonists increased (21.4 ± 1.0% and 18.3 ± 1.0% with muscimol and baclofen, p=0.0021), whereas GABA antagonists decreased fibroblast proliferation (-23.7 ± 0.9% with bicuculine & CGP46381 and -28.1 ± 0.5% with TPMPA, p=0.0004). GABA agents also modified the effect of LIM and LIH tissues (p=0.0005).The increase in proliferation rate of scleral fibroblasts co-cultured with tissues (RPE, retina, RPE/retina and RPE/choroid) from LIM treated eyes was enhanced by GABA agonists (muscimol: 27.4 ± 1.2%, 35.8 ± 1.6%, 8.4 ± 0.3% and 11.9 ± 0.6%; baclofen: 27.0 ± 1.0%, 15.8 ± 1.5%, 16.8 ± 1.2% and 15.4 ± 0.4%, p=0.014) whereas GABA antagonists further reduced scleral fibroblasts growth (bicuculine: -52.5 ± 2.5%, -36.9 ± 1.4%, -37.5 ± 0.6% and -53.7 ± 0.9%; TPMPA: 57.3 ± 1.3%, -15.7 ± 1.2%, -33.5 ± 0.4% and -45.9 ± 1.5%; CGP46381: -51.9 ± 1.6%, -28.5 ± 1.5%, -25.4 ± 2.0% and -45.5 ± 1.9% respectively, p=0.0034). GAG data were opposite to DNA data throughout the experiment e.g. GABA agonists further inhibited while antagonists relatively enhanced scleral fibroblasts growth for both LIM and LIH tissue co-culture. The effect of GABA agents was relatively lower (p=0.0004) for tissue from LIH versus LIM eyes but was in a similar direction. There was a significant drug effect on all four tissue types e.g. RPE, retina, RPE/retina and RPE/choroid for both LIM and LIH tissue co-culture (F20,92=3.928, p=0.0005). However, the effect of GABA agents was greatest in co-culture with RPE tissue (F18,36=4.865, p=0.0005). Summary and Conclusion: 1) Retinal defocus signals are transferred to RPE and choroid which then exert their modifying effect on scleral GAG and DNA synthesis either through growth stimulating factors or directly interacting with scleral cells in process of scleral remodeling during LIM and LIH visual conditions. 2) GABAergic agents affect the proliferation of scleral fibroblasts both directly and when co-cultured with ocular tissues in vitro.

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Immunotherapy is a promising new treatment for patients with advanced prostate and ovarian cancer, but its application is limited by the lack of suitable target antigens that are recognized by CD8+ cytotoxic T lymphocytes (CTL). Human kallikrein 4 (KLK4) is a member of the kallikrein family of serine proteases that is significantly overexpressed in malignant versus healthy prostate and ovarian tissue, making it an attractive target for immunotherapy. We identified a naturally processed, HLA-A*0201-restricted peptide epitope within the signal sequence region of KLK4 that induced CTL responses in vitro in most healthy donors and prostate cancer patients tested. These CTL lysed HLA-A*0201+ KLK4 + cell lines and KLK4 mRNA-transfected monocyte-derived dendritic cells. CTL specific for the HLA-A*0201-restricted KLK4 peptide were more readily expanded to a higher frequency in vitro compared to the known HLA-A*0201-restricted epitopes from prostate cancer antigens; prostate-specific antigen (PSA), prostate-specific membrane antigen (PSMA) and prostatic acid phosphatase (PAP). These data demonstrate that KLK4 is an immunogenic molecule capable of inducing CTL responses and identify it as an attractive target for prostate and ovarian cancer immunotherapy.

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A simple and effective down-sample algorithm, Peak-Hold-Down-Sample (PHDS) algorithm is developed in this paper to enable a rapid and efficient data transfer in remote condition monitoring applications. The algorithm is particularly useful for high frequency Condition Monitoring (CM) techniques, and for low speed machine applications since the combination of the high sampling frequency and low rotating speed will generally lead to large unwieldy data size. The effectiveness of the algorithm was evaluated and tested on four sets of data in the study. One set of the data was extracted from the condition monitoring signal of a practical industry application. Another set of data was acquired from a low speed machine test rig in the laboratory. The other two sets of data were computer simulated bearing defect signals having either a single or multiple bearing defects. The results disclose that the PHDS algorithm can substantially reduce the size of data while preserving the critical bearing defect information for all the data sets used in this work even when a large down-sample ratio was used (i.e., 500 times down-sampled). In contrast, the down-sample process using existing normal down-sample technique in signal processing eliminates the useful and critical information such as bearing defect frequencies in a signal when the same down-sample ratio was employed. Noise and artificial frequency components were also induced by the normal down-sample technique, thus limits its usefulness for machine condition monitoring applications.

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This paper presents an experimental study on the vibration signal patterns associated with a simulated piston slap test of a four-cylinder diesel engine. It is found that a simulated worn-off piston results in an increase in vibration RMS peak amplitudes associated with the major mechanical events of the corresponding cylinder (i.e., inlet and exhaust valve closing and combustion of Cylinder 1). This then led to an increase of overall vibration amplitude of the time domain statistical features such as RMS, Crest Factor, Skewness and Kurtosis in all loading conditions. The simulated worn-off piston not only increased the impact amplitude of piston slap during the engine combustion, it also produced a distinct impulse response during the air induction stroke of the cylinder attributing to an increase of lateral impact force as a result of piston reciprocating motion and the increased clearance between the worn-off piston and the cylinder. The unique signal patterns of piston slap disclosed in this paper can be utilized to assist in the development of condition monitoring tools for automated diagnosis of similar diesel engine faults in practical applications.

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Background: HIV-1 Pr55gag virus-like particles (VLPs) expressed by baculovirus in insect cells are considered to be a very promising HIV-1 vaccine candidate, as they have been shown to elicit broad cellular immune responses when tested in animals, particularly when used as a boost to DNA or BCG vaccines. However, it is important for the VLPs to retain their structure for them to be fully functional and effective. The medium in which the VLPs are formulated and the temperature at which they are stored are two important factors affecting their stability. FINDINGS We describe the screening of 3 different readily available formulation media (sorbitol, sucrose and trehalose) for their ability to stabilise HIV-1 Pr55gag VLPs during prolonged storage. Transmission electron microscopy (TEM) was done on VLPs stored at two different concentrations of the media at three different temperatures (4[degree sign]C, --20[degree sign]C and -70[degree sign]C) over different time periods, and the appearance of the VLPs was compared. VLPs stored in 15% trehalose at -70[degree sign]C retained their original appearance the most effectively over a period of 12 months. VLPs stored in 5% trehalose, sorbitol or sucrose were not all intact even after 1 month storage at the temperatures tested. In addition, we showed that VLPs stored under these conditions were able to be frozen and re-thawed twice before showing changes in their appearance. Conclusions Although the inclusion of other analytical tools are essential to validate these preliminary findings, storage in 15% trehalose at -70[degree sign]C for 12 months is most effective in retaining VLP stability.

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In this paper, we analyse the impact of a (small) heterogeneity of jump type on the most simple localized solutions of a 3-component FitzHugh–Nagumo-type system. We show that the heterogeneity can pin a 1-front solution, which travels with constant (non-zero) speed in the homogeneous setting, to a fixed, explicitly determined, distance from the heterogeneity. Moreover, we establish the stability of this heterogeneous pinned 1-front solution. In addition, we analyse the pinning of 1-pulse, or 2-front, solutions. The paper is concluded with simulations in which we consider the dynamics and interactions of N-front patterns in domains with M heterogeneities of jump type (N = 3, 4, M ≥ 1).

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In this article, we analyze the stability and the associated bifurcations of several types of pulse solutions in a singularly perturbed three-component reaction-diffusion equation that has its origin as a model for gas discharge dynamics. Due to the richness and complexity of the dynamics generated by this model, it has in recent years become a paradigm model for the study of pulse interactions. A mathematical analysis of pulse interactions is based on detailed information on the existence and stability of isolated pulse solutions. The existence of these isolated pulse solutions is established in previous work. Here, the pulse solutions are studied by an Evans function associated to the linearized stability problem. Evans functions for stability problems in singularly perturbed reaction-diffusion models can be decomposed into a fast and a slow component, and their zeroes can be determined explicitly by the NLEP method. In the context of the present model, we have extended the NLEP method so that it can be applied to multi-pulse and multi-front solutions of singularly perturbed reaction-diffusion equations with more than one slow component. The brunt of this article is devoted to the analysis of the stability characteristics and the bifurcations of the pulse solutions. Our methods enable us to obtain explicit, analytical information on the various types of bifurcations, such as saddle-node bifurcations, Hopf bifurcations in which breathing pulse solutions are created, and bifurcations into travelling pulse solutions, which can be both subcritical and supercritical.

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Introduction: Inherent and acquired cisplatin resistance reduces the effectiveness of this agent in the management of non-small cell lung cancer (NSCLC). Understanding the molecular mechanisms underlying this process may result in the development of novel agents to enhance the sensitivity of cisplatin. Methods: An isogenic model of cisplatin resistance was generated in a panel of NSCLC cell lines (A549, SKMES-1, MOR, H460). Over a period of twelve months, cisplatin resistant (CisR) cell lines were derived from original, age-matched parent cells (PT) and subsequently characterized. Proliferation (MTT) and clonogenic survival assays (crystal violet) were carried out between PT and CisR cells. Cellular response to cisplatin-induced apoptosis and cell cycle distribution were examined by FACS analysis. A panel of cancer stem cell and pluripotent markers was examined in addition to the EMT proteins, c-Met and β-catenin. Cisplatin-DNA adduct formation, DNA damage (γH2AX) and cellular platinum uptake (ICP-MS) was also assessed. Results: Characterisation studies demonstrated a decreased proliferative capacity of lung tumour cells in response to cisplatin, increased resistance to cisplatin-induced cell death, accumulation of resistant cells in the G0/G1 phase of the cell cycle and enhanced clonogenic survival ability. Moreover, resistant cells displayed a putative stem-like signature with increased expression of CD133+/CD44+cells and increased ALDH activity relative to their corresponding parental cells. The stem cell markers, Nanog, Oct-4 and SOX-2, were significantly upregulated as were the EMT markers, c-Met and β-catenin. While resistant sublines demonstrated decreased uptake of cisplatin in response to treatment, reduced cisplatin-GpG DNA adduct formation and significantly decreased γH2AX foci were observed compared to parental cell lines. Conclusion: Our results identified cisplatin resistant subpopulations of NSCLC cells with a putative stem-like signature, providing a further understanding of the cellular events associated with the cisplatin resistance phenotype in lung cancer. © 2013 Barr et al.

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The aim of this paper is to provide a comparison of various algorithms and parameters to build reduced semantic spaces. The effect of dimension reduction, the stability of the representation and the effect of word order are examined in the context of the five algorithms bearing on semantic vectors: Random projection (RP), singular value decom- position (SVD), non-negative matrix factorization (NMF), permutations and holographic reduced representations (HRR). The quality of semantic representation was tested by means of synonym finding task using the TOEFL test on the TASA corpus. Dimension reduction was found to improve the quality of semantic representation but it is hard to find the optimal parameter settings. Even though dimension reduction by RP was found to be more generally applicable than SVD, the semantic vectors produced by RP are somewhat unstable. The effect of encoding word order into the semantic vector representation via HRR did not lead to any increase in scores over vectors constructed from word co-occurrence in context information. In this regard, very small context windows resulted in better semantic vectors for the TOEFL test.

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Our understanding of the mechanisms of action of GH and its receptor, the GHR, has advanced significantly in the last decade and has provided some important surprises. It is now clear that the GH-GHR axis activates a number of inter-related signalling pathways, not all of which are dependent on the intracellular tyrosine kinase, JAK2 as originally postulated. JAK2-independent pathways, mediated via the Src family kinases, together with a number of negative regulators of GH signalling and emerging cross-talk mechanisms with other growth factor receptors, provide a complex array of mechanisms that are capable of fine-tuning responses to GH in a cell context dependent manner. Additionally, it is also now clear that GH and the GHR can translocate to the nucleus of target cells and initiate, as yet not well defined, nuclear responses. Continued emphasis on elucidation of these complex mechanisms is critical to provide further insights into the diverse physiological and pathophysiological effects of GH.

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In 2009 and 2010, withdrawal rates from a Pharmacology unit of accelerated QUT nursing students in the first year of their degree, were higher than for continuing students. The cohort of 216 accelerated students in 2011 had university or non-university qualification or equivalent experience and included domestic and international students. A previously tested intervention was introduced in 2011 to improve retention rates and support all Pharmacology students in their first year of nursing. The intervention involved a community website, on-line tutors and an “O week” workshop comprising information about library resources, effective learning strategies and learning tips from a previous student as well as review anatomy, physiology and microbiology lectures. Withdrawal rates for accelerated students in the Pharmacology unit improved and all students found the workshop and review lectures to be informative and valuable. The intervention was therefore successfully transferred to a large, diverse cohort of accelerated nursing students.

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We consider the space fractional advection–dispersion equation, which is obtained from the classical advection–diffusion equation by replacing the spatial derivatives with a generalised derivative of fractional order. We derive a finite volume method that utilises fractionally-shifted Grünwald formulae for the discretisation of the fractional derivative, to numerically solve the equation on a finite domain with homogeneous Dirichlet boundary conditions. We prove that the method is stable and convergent when coupled with an implicit timestepping strategy. Results of numerical experiments are presented that support the theoretical analysis.