Efficient preconditioning of the method of lines for solving nonlinear two-sided space-fractional diffusion equations

A standard method for the numerical solution of partial differential equations (PDEs) is the method of lines. In this approach the PDE is discretised in space using �finite di�fferences or similar techniques, and the resulting semidiscrete problem in time is integrated using an initial value problem solver. A significant challenge when applying the method of lines to fractional PDEs is that the non-local nature of the fractional derivatives results in a discretised system where each equation involves contributions from many (possibly every) spatial node(s). This has important consequences for the effi�ciency of the numerical solver. First, since the cost of evaluating the discrete equations is high, it is essential to minimise the number of evaluations required to advance the solution in time. Second, since the Jacobian matrix of the system is dense (partially or fully), methods that avoid the need to form and factorise this matrix are preferred. In this paper, we consider a nonlinear two-sided space-fractional di�ffusion equation in one spatial dimension. A key contribution of this paper is to demonstrate how an eff�ective preconditioner is crucial for improving the effi�ciency of the method of lines for solving this equation. In particular, we show how to construct suitable banded approximations to the system Jacobian for preconditioning purposes that permit high orders and large stepsizes to be used in the temporal integration, without requiring dense matrices to be formed. The results of numerical experiments are presented that demonstrate the effectiveness of this approach.

Identification and simultaneous analysis of harmane, harmol, isovitexin and vitexin in Passiflora incarnata extracts with a novel HLPC method

A high performance liquid chromatographic method for the simultaneous analysis of two flavonoids (iso-vitexin and vitexin), and three indole alkaloids (harmane, harmine, and harmol) was developed. This method was then utilised to quantitate levels of these five constituents in methanolic extracts of Australian Passiflora incarnata. HPLC analysis was performed using a Waters™ Novapak C18 (150 × 4 mm, 4 μm) column, with a gradient solvent system of methanol-water-acetic acid. Detection was achieved by PDA UV (254 nm) and fluorescence (excitation 254 nm, emission 414 nm), utilising the external standard method to obtain quantification.

Simultaneous determination of aldrin, dieldrin, endrin, heptachlor, and p,p'-DDT in medicinal plant extracts using a novel high performance liquid chromatography method

A high performance liquid chromatographic method for the simultaneous determination of five organochlorine pesticides (aldrin, p,p’-DDT, dieldrin, endrin, and heptachlor) was developed. The method was used to determine the levels of these pesticides in medicinal plant samples. Analysis was carried out using a Merck LiChrospher 100 RP C18 (5 μm) column with a gradient solvent system of acetonitrile-water and PDA UV detection (224 nm). Quantification was carried out by the external standard method. The limit of detection for the utilized method was below the local legal limits (ANZFA) for similar plant materials for all 5 pesticides excepting endrin. Medicinal plant extracts were further analyzed by conventional GC-ECD and GC-NPD means using SPE and GPC cleanup as required.

Comparison of methods for processing drinking water samples for the isolation of Myocbacterium avium and intracellulare

Several protocols for isolation of mycobacteria from water exist, but there is no established standard method. This study compared methods of processing potable water samples for the isolation of Mycobacterium avium and Mycobacterium intracellulare using spiked sterilized water and tap water decontaminated using 0.005% cetylpyridinium chloride (CPC). Samples were concentrated by centrifugation or filtration and inoculated onto Middlebrook 7H10 and 7H11 plates and Lowenstein-Jensen slants and into mycobacterial growth indicator tubes with or without polymyxin, azlocillin, nalidixic acid, trimethoprim, and amphotericin B. The solid media were incubated at 32°C, at 35°C, and at 35°C with CO2 and read weekly. The results suggest that filtration of water for the isolation of mycobacteria is a more sensitive method for concentration than centrifugation. The addition of sodium thiosulfate may not be necessary and may reduce the yield. Middlebrook M7H10 and 7H11 were equally sensitive culture media. CPC decontamination, while effective for reducing growth of contaminants, also significantly reduces mycobacterial numbers. There was no difference at 3 weeks between the different incubation temperatures.

Corneal sensitivity as an ophthalmic marker of diabetic neuropathy

Purpose. The objective of this study was to explore the discriminative capacity of non-contact corneal esthesiometry (NCCE) when compared with the neuropathy disability score (NDS) score—a validated, standard method of diagnosing clinically significant diabetic neuropathy. Methods. Eighty-one participants with type 2 diabetes, no history of ocular disease, trauma, or surgery and no history of systemic disease that may affect the cornea were enrolled. Participants were ineligible if there was history of neuropathy due to non-diabetic cause or current diabetic foot ulcer or infection. Corneal sensitivity threshold was measured on the eye of dominant hand side at a distance of 10 mm from the center of the cornea using a stimulus duration of 0.9 s. The NDS was measured producing a score ranging from 0 to 10. To determine the optimal cutoff point of corneal sensitivity that identified the presence of neuropathy (diagnosed by NDS), the Youden index and “closest-to-(0,1)” criteria were used. Results. The receiver-operator characteristic curve for NCCE for the presence of neuropathy (NDS ≥3) had an area under the curve of 0.73 (p = 0.001) and, for the presence of moderate neuropathy (NDS ≥6), area of 0.71 (p = 0.003). By using the Youden index, for an NDS ≥3, the sensitivity of NCCE was 70% and specificity was 75%, and a corneal sensitivity threshold of 0.66 mbar or higher indicated the presence of neuropathy. When NDS ≥6 (indicating risk of foot ulceration) was applied, the sensitivity was 52% with a specificity of 85%. Conclusions. NCCE is a sensitive test for the diagnosis of minimal and more advanced diabetic neuropathy and may serve as a useful surrogate marker for diabetic and perhaps other neuropathies.

Comparison of antigen detection and quantitative PCR in the detection of chlamydial infection in koalas (Phascolarctos cinereus)

The gold standard method for detecting chlamydial infection in domestic and wild animals is PCR, but the technique is not suited to testing animals in the field when a rapid diagnosis is frequently required. The objective of this study was to compare the results of a commercially available enzyme immunoassay test for Chlamydia against a quantitative Chlamydia pecorum-specific PCR performed on swabs collected from the conjunctival sac, nasal cavity and urogenital sinuses of naturally infected koalas (Phascolarctos cinereus). The level of agreement for positive results between the two assays was low (43.2%). The immunoassay detection cut-off was determined as approximately 400 C. pecorum copies, indicating that the test was sufficiently sensitive to be used for the rapid diagnosis of active chlamydial infections.

A banded preconditioner for the two-sided, nonlinear space-fractional diffusion equation

The method of lines is a standard method for advancing the solution of partial differential equations (PDEs) in time. In one sense, the method applies equally well to space-fractional PDEs as it does to integer-order PDEs. However, there is a significant challenge when solving space-fractional PDEs in this way, owing to the non-local nature of the fractional derivatives. Each equation in the resulting semi-discrete system involves contributions from every spatial node in the domain. This has important consequences for the efficiency of the numerical solver, especially when the system is large. First, the Jacobian matrix of the system is dense, and hence methods that avoid the need to form and factorise this matrix are preferred. Second, since the cost of evaluating the discrete equations is high, it is essential to minimise the number of evaluations required to advance the solution in time. In this paper, we show how an effective preconditioner is essential for improving the efficiency of the method of lines for solving a quite general two-sided, nonlinear space-fractional diffusion equation. A key contribution is to show, how to construct suitable banded approximations to the system Jacobian for preconditioning purposes that permit high orders and large stepsizes to be used in the temporal integration, without requiring dense matrices to be formed. The results of numerical experiments are presented that demonstrate the effectiveness of this approach.

Tackling the health burden from household air pollution (HAP) : development and implementation of new WHO Guidelines

Household air pollution (HAP), arising mainly from the combustion of solid and other polluting fuels, is responsible for a very substantial public health burden, most recently estimated as causing 3.5 million premature deaths in 2010. These patterns of household fuel use have also important negative impacts on safety, prospects for poverty reduction and the environment, including climate change. Building on previous air quality guidelines, the WHO is developing new guidelines focused on household fuel combustion, covering cooking, heating and lighting, and although global, the key focus is low and middle income countries reflecting the distribution of disease burden. As discussed in this paper, currently in development, the guidelines will include reviews of a wide range of evidence including fuel use in homes, emissions from stoves and lighting, household air pollution and exposure levels experienced by populations, health risks, impacts of interventions on HAP and exposure, and also key factors influencing sustainable and equitable adoption of improved stoves and cleaner fuels. GRADE, the standard method used for guidelines evidence review may not be well suited to the variety and nature of evidence required for this project, and a modified approach is being developed and tested. Work on the guidelines is being carried out in close collaboration with the UN Foundation Global Alliance on Clean cookstoves, allowing alignment with specific tools including recently developed international voluntary standards for stoves, and the development of country action plans. Following publication, WHO plans to work closely with a number of countries to learn from implementation efforts, in order to further strengthen support and guidance. A case study on the situation and policy actions to date in Bhutan provide an illustration of the challenges and opportunities involved, and the timely importance of the new guidelines and associated research, evaluation and policy development agendas.

Steps towards the validation of the Trendelenburg test : The effect of experimentally reduced hip abductor muscle function on frontal plane mechanics

Introduction: The Trendelenburg Test (TT) is used to assess the functional strength of the hip abductor muscles (HABD), their ability to control frontal plane motion of the pelvis, and the ability of the lumbopelvic complex to transfer load into single leg stance. Rationale: Although a standard method to perform the test has been described for use within clinical populations, no study has directly investigated Trendelenburg’s hypotheses. Purpose: To investigate the validity of the TT using an ultrasound guided nerve block (UNB) of the superior gluteal nerve and determine whether the reduction in HABD strength would result in the theorized mechanical compensatory strategies measured during the TT. Methods: Quasi-experimental design using a convenience sample of nine healthy males. Only subjects with no current or previous injury to the lumbar spine, pelvis, or lower extremities, and no previous surgeries were included. Force dynamometry was used to evaluation HABD strength (%BW). 2D mechanics were used to evaluate contralateral pelvic drop (cMPD), change in contralateral pelvic drop (∆cMPD), ipsilateral hip adduction (iHADD) and ipsilateral trunk sway (TRUNK) measured in degrees (°). All measures were collected prior to and following a UNB on the superior gluteal nerve performed by an interventional radiologist. Results: Subjects’ age was median 31yrs (IQR:22-32yrs); and weight was median 73kg (IQR:67-81kg). An average 52% reduction of HABD strength (z=2.36,p=0.02) resulted following the UNB. No differences were found in cMPD or ∆cMPD (z=0.01,p= 0.99, z=-0.67,p=0.49). Individual changes in biomechanics show no consistency between subjects and non-systematic changes across the group. One subject demonstrated the mechanical compensations described by Trendelenburg. Discussion: The TT should not be used as screening measure for HABD strength in populations demonstrating strength greater than 30%BW but reserved for use with populations with marked HABD weakness. Importance: This study presents data regarding a critical level of HABD strength required to support the pelvis during the TT.

EdU, a new thymidine analogue for labelling proliferating cells in the nervous system

The standard method of labelling proliferating cells uses the thymidine analogue, bromodeoxyuridine (BrdU), which incorporates into the DNA during S-phase of the cell cycle. A disadvantage of this method is that the immunochemical processing requires pre-treatment of the cells and tissue with heat or acid to reveal the antigen. This pre-treatment reduces reliability of the method and degrades the specimen, reducing the ability for multiple immuno-fluorescence labelling at high resolution. We report here the utility of a novel thymidine analogue, ethynyl deoxyuridine (EdU), detected with a fluorescent azide via the “click” chemistry reaction (the Huisgen 1,3-dipolar cycloaddition reaction of an organic azide to a terminal acetylene). The detection of EdU requires no heat or acid treatment and the incorporated EdU is covalently conjugated to fluorescent probe. The reaction is quick and compatible with fluorescence immunochemistry and other fluorescent probes. We show here that EdU is non-toxic in vitro and in vivo and can be used in place of BrdU to label cells during neurogenesis and the progeny identified at least 30 days later. The fluorescent labelling of EdU, markedly improves the detection of proliferating cells and allows concurrent high resolution fluorescence immunochemistry.

Using ICD-10-AM codes to characterise hospital-acquired complications

This paper describes the limitations of using the International Statistical Classification of Diseases and Related Health Problems, Tenth Revision, Australian Modification (ICD-10-AM) to characterise patient harm in hospitals. Limitations were identified during a project to use diagnoses flagged by Victorian coders as hospital-acquired to devise a classification of 144 categories of hospital acquired diagnoses (the Classification of Hospital Acquired Diagnoses or CHADx). CHADx is a comprehensive data monitoring system designed to allow hospitals to monitor their complication rates month-to-month using a standard method. Difficulties in identifying a single event from linear sequences of codes due to the absence of code linkage were the major obstacles to developing the classification. Obstetric and perinatal episodes also presented challenges in distinguishing condition onset, that is, whether conditions were present on admission or arose after formal admission to hospital. Used in the appropriate way, the CHADx allows hospitals to identify areas for future patient safety and quality initiatives. The value of timing information and code linkage should be recognised in the planning stages of any future electronic systems.

A tale of two solvers: Eager and lazy approaches to bit-vectors

The standard method for deciding bit-vector constraints is via eager reduction to propositional logic. This is usually done after first applying powerful rewrite techniques. While often efficient in practice, this method does not scale on problems for which top-level rewrites cannot reduce the problem size sufficiently. A lazy solver can target such problems by doing many satisfiability checks, each of which only reasons about a small subset of the problem. In addition, the lazy approach enables a wide range of optimization techniques that are not available to the eager approach. In this paper we describe the architecture and features of our lazy solver (LBV). We provide a comparative analysis of the eager and lazy approaches, and show how they are complementary in terms of the types of problems they can efficiently solve. For this reason, we propose a portfolio approach that runs a lazy and eager solver in parallel. Our empirical evaluation shows that the lazy solver can solve problems none of the eager solvers can and that the portfolio solver outperforms other solvers both in terms of total number of problems solved and the time taken to solve them.

In response: Changes in ultraviolet transmittance of hydrogel and silicone hydrogel contact lenses induced by wear

We thank Dr Shedden and Dr Pall for their insightful comments and the opportunity to clarify a number of points from our work.1 The “protection factor” (PF) expressed as the inverse of the transmittance of contact lens (CL) material (1/Tλ), where T is the percentage transmittance of ultraviolet radiation (UVR) in a given waveband (UVC, UVB or UVA) of the UV spectrum for contact lenses is the standard method for reporting PF values and as such there should not be any controversy. We have calculated the PF for each wavelength across the entire UV spectrum (UVC, UVB, UVA) as presented in figure 3 of our previous publication.1 In that article, we were simply stating the observation when transmission in the UVC spectra band is considered especially because appreciable amounts of potentially carcinogenic short UV wavelengths was shown to be present in sunlight in our region three decades ago2 and these short wavelength photons are reported to be more biologically damaging to ocular tissues.3 In addition, the depletion of the Ozone layer is still continuing. Nevertheless, we understand the concern of the authors that the results of the PF might be confusing to those who are not familiar with the science of UVR and as such we have made some revisions to the findings of the calculated PF...

Salt in the desert: A comparison of clinical versus serum-calculated osmolality determination of dehydration

Background: Clinicians frequently use their own judgement to assess patient’s hydration status although there is limited evidence for the diagnostic utility of any individual clinical symptom. Hence, the aim of this study was to compare the diagnostic accuracy of clinically assessed dehydration in older hospital patients (using multiple symptoms), versus dehydration measured using serum-calculated osmolality (CO) as the reference standard. Method: Participants were 44 hospital patients aged ≥ 60 years. Dehydration was assessed clinically and pathologically (CO) within 24 hours of admission and at study exit. Indicators of diagnostic accuracy were calculated. Results: Clinicians identified 27% of patients as dehydrated at admission, and 19% at exit, compared to 19% and 16% using CO. Agreement between the measures was fair at admission and poor at exit. Clinical assessment showed poor sensitivity for predicting dehydration with reasonable specificity. Conclusions: Compared to the use of CO, clinical assessment of dehydration in older patients was poor. Given that failure to identify dehydration in this population may have serious consequences, we recommend that clinicians do not rely upon their own assessments without also using the reference standard.

User-centered video quality assessment for scalable video coding of H.264/AVC standard

Scalable video coding of H.264/AVC standard enables adaptive and flexible delivery for multiple devices and various network conditions. Only a few works have addressed the influence of different scalability parameters (frame rate, spatial resolution, and SNR) on the user perceived quality within a limited scope. In this paper, we have conducted an experiment of subjective quality assessment for video sequences encoded with H.264/SVC to gain a better understanding of the correlation between video content and UPQ at all scalable layers and the impact of rate-distortion method and different scalabilities on bitrate and UPQ. Findings from this experiment will contribute to a user-centered design of adaptive delivery of scalable video stream.