A second-order accurate numerical approximation for the Riesz space fractional advection-dispersion equation

In this paper, we consider a space Riesz fractional advection-dispersion equation. The equation is obtained from the standard advection-diffusion equation by replacing the ¯rst-order and second-order space derivatives by the Riesz fractional derivatives of order β 1 Є (0; 1) and β2 Є(1; 2], respectively. Riesz fractional advection and dispersion terms are approximated by using two fractional centered difference schemes, respectively. A new weighted Riesz fractional ¯nite difference approximation scheme is proposed. When the weighting factor Ѳ = 1/2, a second- order accurate numerical approximation scheme for the Riesz fractional advection-dispersion equation is obtained. Stability, consistency and convergence of the numerical approximation scheme are discussed. A numerical example is given to show that the numerical results are in good agreement with our theoretical analysis.

Assessment of tumor prevention in Type 1 Neurofibromatosis using a nitroxide compound

Background Type 1 Neurofibromatosis (NF1) is a genetic disorder linked to mutations of the NF1 gene. Clinical symptoms are varied, but hallmark features of the disease include skin pigmentation anomalies (café au lait macules, skinfold freckling) and dermal neurofibromas. Method These dermal manifestations of NF1 have previously been reported in a mouse model where Nf1+/− mice are topically treated with dimethylbenz[a]anthracene (DMBA) and 12-O-tetradecanoylphorbol-13-acetate (TPA). We adopted this mouse model to test the protective effects of a nitroxide antioxidant, 5-carboxy-1,1,3,3-tetramethylisoindolin-2-yloxyl (CTMIO). Antioxidants have previously been shown to increase longevity in nf1-deficient fruitflies. Doses of 4 μM and 40 μM CTMIO provided ad libitum in drinking water were given to Nf1-deficient mice. Results Consistent with previous reports, Nf1-deficient mice showed a 4.7-fold increase in papilloma formation (P < 0.036). However, neither dose of CTMIO had any significant affect on papilloma formation. A non-significant decrease in skin pigmentation abnormalities was seen with 4 μM but not 40 μM CTMIO. Subsequent analysis of genomic DNA isolated from papillomas indicated that DMBA/TPA induced tumors did not exhibit a local loss of heterozygosity (LOH) at the Nf1 locus. Conclusion These data reveal that oral antioxidant therapy with CTMIO does not reduce tumor formation in a multistage cancer model, but also that this model does not feature LOH for Nf1.

Linear and nonlinear propagation of localised plasmon in metallic nanostructures

A major challenge in modern photonics and nano-optics is the diffraction limit of light which does not allow field localisation into regions with dimensions smaller than half the wavelength. Localisation of light into nanoscale regions (beyond its diffraction limit) has applications ranging from the design of optical sensors and measurement techniques with resolutions as high as a few nanometres, to the effective delivery of optical energy into targeted nanoscale regions such as quantum dots, nano-electronic and nano-optical devices. This field has become a major research direction over the last decade. The use of strongly localised surface plasmons in metallic nanostructures is one of the most promising approaches to overcome this problem. Therefore, the aim of this thesis is to investigate the linear and non-linear propagation of surface plasmons in metallic nanostructures. This thesis will focus on two main areas of plasmonic research –– plasmon nanofocusing and plasmon nanoguiding. Plasmon nanofocusing – The main aim of plasmon nanofocusing research is to focus plasmon energy into nanoscale regions using metallic nanostructures and at the same time achieve strong local field enhancement. Various structures for nanofocusing purposes have been proposed and analysed such as sharp metal wedges, tapered metal films on dielectric substrates, tapered metal rods, and dielectric V-grooves in metals. However, a number of important practical issues related to nanofocusing in these structures still remain unclear. Therefore, one of the main aims of this thesis is to address two of the most important of issues which are the coupling efficiency and heating effects of surface plasmons in metallic nanostructures. The method of analysis developed throughout this thesis is a general treatment that can be applied to a diversity of nanofocusing structures, with results shown here for the specific case of sharp metal wedges. Based on the geometrical optics approximation, it is demonstrated that the coupling efficiency from plasmons generated with a metal grating into the nanofocused symmetric or quasi-symmetric modes may vary between ~50% to ~100% depending on the structural parameters. Optimal conditions for nanofocusing with the view to minimise coupling and dissipative losses are also determined and discussed. It is shown that the temperature near the tip of a metal wedge heated by nanosecond plasmonic pulses can increase by several hundred degrees Celsius. This temperature increase is expected to lead to nonlinear effects, self-influence of the focused plasmon, and ultimately self-destruction of the metal tip. This thesis also investigates a different type of nanofocusing structure which consists of a tapered high-index dielectric layer resting on a metal surface. It is shown that the nanofocusing mechanism that occurs in this structure is somewhat different from other structures that have been considered thus far. For example, the surface plasmon experiences significant backreflection and mode transformation at a cut-off thickness. In addition, the reflected plasmon shows negative refraction properties that have not been observed in other nanofocusing structures considered to date. Plasmon nanoguiding – Guiding surface plasmons using metallic nanostructures is important for the development of highly integrated optical components and circuits which are expected to have a superior performance compared to their electronicbased counterparts. A number of different plasmonic waveguides have been considered over the last decade including the recently considered gap and trench plasmon waveguides. The gap and trench plasmon waveguides have proven to be difficult to fabricate. Therefore, this thesis will propose and analyse four different modified gap and trench plasmon waveguides that are expected to be easier to fabricate, and at the same time acquire improved propagation characteristics of the guided mode. In particular, it is demonstrated that the guided modes are significantly screened by the extended metal at the bottom of the structure. This is important for the design of highly integrated optics as it provides the opportunity to place two waveguides close together without significant cross-talk. This thesis also investigates the use of plasmonic nanowires to construct a Fabry-Pérot resonator/interferometer. It is shown that the resonance effect can be achieved with the appropriate resonator length and gap width. Typical quality factors of the Fabry- Pérot cavity are determined and explained in terms of radiative and dissipative losses. The possibility of using a nanowire resonator for the design of plasmonic filters with close to ~100% transmission is also demonstrated. It is expected that the results obtained in this thesis will play a vital role in the development of high resolution near field microscopy and spectroscopy, new measurement techniques and devices for single molecule detection, highly integrated optical devices, and nanobiotechnology devices for diagnostics of living cells.

Inhibitors of human immunodeficiency virus type 1 reverse transcriptase target distinct phases of early reverse transcription

Early HIV-1 reverse transcription can be separated into initiation and elongation phases. Here we show, using PCR analysis of negative-strand strong-stop DNA [(−)ssDNA] synthesis in intact virus, that different reverse transcriptase (RT) inhibitors affect distinct phases of early natural endogenous reverse transcription (NERT). The effects of nevirapine on NERT were consistent with a mechanism of action including both specific and nonspecific binding events. The nonspecific component of this inhibition targeted the elongation reaction, whereas the specific effect seemed principally to be directed at very early events (initiation or the initiation-elongation switch). In contrast, foscarnet and the nucleoside analog ddATP inhibited both early and late (−)ssDNA synthesis in a similar manner. We also examined compounds that targeted other viral proteins and found that Ro24-7429 (a Tat antagonist) and rosmarinic acid (an integrase inhibitor) also directly inhibited RT. Our results indicate that NERT can be used to identify and evaluate compounds that directly target the reverse transcription complex.

Secondary curve behavior in Lenke Type 1C adolescent idiopathic scoliosis after thoracoscopic selective anterior thoracic fusion

Study Design. Analysis of a case series of 24 Lenke 1C adolescent idiopathic scoliosis (AIS) patients receiving selective thoracoscopic anterior scoliosis correction. Objective. To report the behaviour of the compensatory lumbar curve in a group of Lenke IC AIS patients following thoracoscopic anterior scoliosis correction, and to compare the results of this study with previously published data. Summary of Background Data. Several prior studies have reported spontaneous lumbar curve correction for both anterior and posterior selective fusion in Lenke 1C/King-Moe II patients; however to our knowledge no previous studies have reported outcomes of thoracoscopic anterior correction for this curve type. Methods. All AIS patients with a curve classification of Lenke 1C and a minimum of 24 months follow-up were retrieved from a consecutive series of 190 AIS patients who underwent thoracoscopic anterior instrumented fusion. Cobb angles of the major curve, instrumented levels, compensatory lumbar curve, and T5-T12 kyphosis were recorded, as well as coronal spinal balance, T1 tilt angle and shoulder balance. All radiographic parameters were measured before surgery and at 2, 6, 12 and 24 months after surgery. Results. Twenty-four female patients with right thoracic curves had a mean thoracic Cobb angle of 53.0° before surgery, decreasing to 24.9° two years after surgery. The mean lumbar compensatory Cobb angle was 43.5° before surgery, spontaneously correcting to 25.4° two years after surgery, indicating balance between the thoracic and lumbar scoliotic curves. The lumbar correction achieved (41.8%) compares favourably to previous studies. Conclusions. Selective thoracoscopic anterior fusion allows spontaneous lumbar curve correction and achieves coronal balance of main thoracic and compensatory lumbar curves, good cosmesis and patient satisfaction. Correction and balance are maintained 24 months after surgery.

Don's Party and the AV Jennings type 15 home

Australian housing underwent a watershed when 1960s mass-produced houses slowly started subscribing to a new aesthetic of continuous living spaces, known as the ‘open plan’ home. This created a new landscape for Australian playwrights to observe and explore in their work when representing domesticity on the stage. Instead of representing a single room of the house on the stage, plays such as ‘Don’s Party’, started to work with a number of openly connected spaces bound by doorways to private sections of the house or to specific outdoor areas. In representing this dialectic between interior and the exterior, private and public spaces in the home, the continuous spaces of the AV Jennings house in ‘Don’s Party’ acted to blur these conditions creating an outer interior. These connected spaces became the place for an outward performance on the family’s interiority, while simultaneously presenting a boundary to an inner interior in the offstage spaces of the home. This paper focuses on the play 'Don's Party' by David Williamson and how the spatial arrangements of the AV Jennings home, in which it was set, influenced the playwright. The research includes a textual analysis of the play, biographical research and interviews with the playwright alongside an analysis of the spatial arrangements of AV Jennings houses.

Practical stability of approximating discrete-time filters with respect to model mismatch

This paper establishes practical stability results for an important range of approximate discrete-time filtering problems involving mismatch between the true system and the approximating filter model. Practical stability is established in the sense of an asymptotic bound on the amount of bias introduced by the model approximation. Our analysis applies to a wide range of estimation problems and justifies the common practice of approximating intractable infinite dimensional nonlinear filters by simpler computationally tractable filters.

The relationship between Bayesian motor unit number estimation and histological measurements of motor neurons in wild-type and SOD1 G93A mice

Objective: To assess the relationship between Bayesian MUNE and histological motor neuron counts in wild-type mice and in an animal model of ALS. Methods: We performed Bayesian MUNE paired with histological counts of motor neurons in the lumbar spinal cord of wild-type mice and transgenic SOD1 G93A mice that show progressive weakness over time. We evaluated the number of acetylcholine endplates that were innervated by a presynaptic nerve. Results: In wild-type mice, the motor unit number in the gastrocnemius muscle estimated by Bayesian MUNE was approximately half the number of motor neurons in the region of the spinal cord that contains the cell bodies of the motor neurons supplying the hindlimb crural flexor muscles. In SOD1 G93A mice, motor neuron numbers declined over time. This was associated with motor endplate denervation at the end-stage of disease. Conclusion: The number of motor neurons in the spinal cord of wild-type mice is proportional to the number of motor units estimated by Bayesian MUNE. In SOD1 G93A mice, there is a lower number of estimated motor units compared to the number of spinal cord motor neurons at the end-stage of disease, and this is associated with disruption of the neuromuscular junction. Significance: Our finding that the Bayesian MUNE method gives estimates of motor unit numbers that are proportional to the numbers of motor neurons in the spinal cord supports the clinical use of Bayesian MUNE in monitoring motor unit loss in ALS patients. © 2012 International Federation of Clinical Neurophysiology.