A bidomain threshold model of propagating calcium waves

We present a bidomain fire-diffuse-fire model that facilitates mathematical analysis of propagating waves of elevated intracellular calcium (Ca) in living cells. Modelling Ca release as a threshold process allows the explicit construction of travelling wave solutions to probe the dependence of Ca wave speed on physiologically important parameters such as the threshold for Ca release from the endoplasmic reticulum (ER) to the cytosol, the rate of Ca resequestration from the cytosol to the ER, and the total [Ca] (cytosolic plus ER). Interestingly, linear stability analysis of the bidomain fire-diffuse-fire model predicts the onset of dynamic wave instabilities leading to the emergence of Ca waves that propagate in a back-and-forth manner. Numerical simulations are used to confirm the presence of these so-called "tango waves" and the dependence of Ca wave speed on the total [Ca]. The original publication is available at www.springerlink.com (Journal of Mathematical Biology)

Self-exciting threshold binomial autoregressive processes

We introduce a new class of integer-valued self-exciting threshold models, which is based on the binomial autoregressive model of order one as introduced by McKenzie (Water Resour Bull 21:645–650, 1985. doi:10.1111/j.1752-1688.1985. tb05379.x). Basic probabilistic and statistical properties of this class of models are discussed. Moreover, parameter estimation and forecasting are addressed. Finally, the performance of these models is illustrated through a simulation study and an empirical application to a set of measle cases in Germany.

Instabilities in threshold-diffusion equations with delay

The introduction of delays into ordinary or partial differential equation models is well known to facilitate the production of rich dynamics ranging from periodic solutions through to spatio-temporal chaos. In this paper we consider a class of scalar partial differential equations with a delayed threshold nonlinearity which admits exact solutions for equilibria, periodic orbits and travelling waves. Importantly we show how the spectra of periodic and travelling wave solutions can be determined in terms of the zeros of a complex analytic function. Using this as a computational tool to determine stability we show that delays can have very different effects on threshold systems with negative as opposed to positive feedback. Direct numerical simulations are used to confirm our bifurcation analysis, and to probe some of the rich behaviour possible for mixed feedback.

Iterated responsive threshold search for the quadratic multiple knapsack problem

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Supra-treatment threshold neonatal jaundice: Incidence in HIV-exposed compared to non-exposed neonates at Queen Elizabeth Central Hospital in Blantyre, Malawi

Introduction Jaundice is the yellowish pigmentation of the skin, sclera, and mucous membranes resulting from bilirubin deposition. Children born to mothers with HIV are more likely to be born premature, with low birth weight, and to become septic—all risk factors for neonatal jaundice. Further, there has been a change in the prevention of mother-to-child transmission (PMTCT) of HIV guidelines from single-dose nevirapine to a six-week course, all of which theoretically put HIV-exposed newborns at greater risk of developing neonatal jaundice. Aim We carried out a study to determine the incidence of severe and clinical neonatal jaundice in HIV-exposed neonates admitted to the Chatinkha Nursery (CN) neonatal unit at Queen Elizabeth Central Hospital (QECH) in Blantyre. Methods Over a period of four weeks, the incidence among non-exposed neonates was also determined for comparison between the two groups of infants. Clinical jaundice was defined as transcutaneous bilirubin levels greater than 5 mg/dL and severe jaundice as bilirubin levels above the age-specific treatment threshold according the QECH guidelines. Case notes of babies admitted were retrieved and information on birth date, gestational age, birth weight, HIV status of mother, type of feeding, mode of delivery, VDRL status of mother, serum bilirubin, duration of stay in CN, and outcome were extracted. Results Of the 149 neonates who were recruited, 17 (11.4%) were HIV-exposed. One (5.88%) of the 17 HIV-exposed and 19 (14.4%) of 132 HIVnon- exposed infants developed severe jaundice requiring therapeutic intervention (p = 0.378). Eight (47%) of the HIV-exposed and 107 (81%) of the non-exposed neonates had clinical jaundice of bilirubin levels greater than 5 mg/dL (p < 0.001). Conclusions The study showed a significant difference in the incidence of clinical jaundice between the HIV-exposed and HIV-non-exposed neonates. Contrary to our hypothesis, however, the incidence was greater in HIVnon- exposed than in HIV-exposed infants.

INTEGRATED THRESHOLD-ACTIVATED FEEDBACK MICROSYSTEM FOR REAL-TIME CHARACTERIZATION, SENSING AND TREATMENT OF BACTERIAL BIOFILMS

Biofilms are the primary cause of clinical bacterial infections and are impervious to typical amounts of antibiotics, necessitating very high doses for treatment. Therefore, it is highly desirable to develop new alternate methods of treatment that can complement or replace existing approaches using significantly lower doses of antibiotics. Current standards for studying biofilms are based on end-point studies that are invasive and destroy the biofilm during characterization. This dissertation presents the development of a novel real-time sensing and treatment technology to aid in the non-invasive characterization, monitoring and treatment of bacterial biofilms. The technology is demonstrated through the use of a high-throughput bifurcation based microfluidic reactor that enables simulation of flow conditions similar to indwelling medical devices. The integrated microsystem developed in this work incorporates the advantages of previous in vitro platforms while attempting to overcome some of their limitations. Biofilm formation is extremely sensitive to various growth parameters that cause large variability in biofilms between repeated experiments. In this work we investigate the use of microfluidic bifurcations for the reduction in biofilm growth variance. The microfluidic flow cell designed here spatially sections a single biofilm into multiple channels using microfluidic flow bifurcation. Biofilms grown in the bifurcated device were evaluated and verified for reduced biofilm growth variance using standard techniques like confocal microscopy. This uniformity in biofilm growth allows for reliable comparison and evaluation of new treatments with integrated controls on a single device. Biofilm partitioning was demonstrated using the bifurcation device by exposing three of the four channels to various treatments. We studied a novel bacterial biofilm treatment independent of traditional antibiotics using only small molecule inhibitors of bacterial quorum sensing (analogs) in combination with low electric fields. Studies using the bifurcation-based microfluidic flow cell integrated with real-time transduction methods and macro-scale end-point testing of the combination treatment showed a significant decrease in biomass compared to the untreated controls and well-known treatments such as antibiotics. To understand the possible mechanism of action of electric field-based treatments, fundamental treatment efficacy studies focusing on the effect of the energy of the applied electrical signal were performed. It was shown that the total energy and not the type of the applied electrical signal affects the effectiveness of the treatment. The linear dependence of the treatment efficacy on the applied electrical energy was also demonstrated. The integrated bifurcation-based microfluidic platform is the first microsystem that enables biofilm growth with reduced variance, as well as continuous real-time threshold-activated feedback monitoring and treatment using low electric fields. The sensors detect biofilm growth by monitoring the change in impedance across the interdigitated electrodes. Using the measured impedance change and user inputs provided through a convenient and simple graphical interface, a custom-built MATLAB control module intelligently switches the system into and out of treatment mode. Using this self-governing microsystem, in situ biofilm treatment based on the principles of the bioelectric effect was demonstrated by exposing two of the channels of the integrated bifurcation device to low doses of antibiotics.

Voltage and current spectra for matrix power converters

Matrix power converters are used for transforming one alternating-current power supply to another, with different peak voltage and frequency. There are three input lines, with sinusoidally varying voltages which are 120◦ out of phase one from another, and the output is to be delivered as a similar three-phase supply. The matrix converter switches rapidly, to connect each output line in sequence to each of the input lines in an attempt to synthesize the prescribed output voltages. The switching is carried out at high frequency and it is of practical importance to know the frequency spectra of the output voltages and of the input and output currents. We determine in this paper these spectra using a new method, which has significant advantages over the prior default method (a multiple Fourier series technique), leading to a considerably more direct calculation. In particular, the determination of the input current spectrum is feasible here, whereas it would be a significantly more daunting procedure using the prior method instead.

Nonlinear development of matrix-converter instabilities

Matrix converters convert a three-phase alternating-current power supply to a power supply of a different peak voltage and frequency, and are an emerging technology in a wide variety of applications. However, they are susceptible to an instability, whose behaviour is examined herein. The desired “steady-state” mode of operation of the matrix converter becomes unstable in a Hopf bifurcation as the output/input voltage transfer ratio, q, is increased through some threshold value, qc. Through weakly nonlinear analysis and direct numerical simulation of an averaged model, we show that this bifurcation is subcritical for typical parameter values, leading to hysteresis in the transition to the oscillatory state: there may thus be undesirable large-amplitude oscillations in the output voltages even when q is below the linear stability threshold value qc.

Threshold behaviour and final outcome of an epidemic on a random network with household structure

This paper considers a stochastic SIR (susceptible-infective-removed) epidemic model in which individuals may make infectious contacts in two ways, both within 'households' (which for ease of exposition are assumed to have equal size) and along the edges of a random graph describing additional social contacts. Heuristically-motivated branching process approximations are described, which lead to a threshold parameter for the model and methods for calculating the probability of a major outbreak, given few initial infectives, and the expected proportion of the population who are ultimately infected by such a major outbreak. These approximate results are shown to be exact as the number of households tends to infinity by proving associated limit theorems. Moreover, simulation studies indicate that these asymptotic results provide good approximations for modestly-sized finite populations. The extension to unequal sized households is discussed briefly.

Interface properties and capacitance-voltage behaviour of diamond devices prepared by microwave-assisted CVD

Free standing diamond films were used to study the effect of diamond surface morphology and microstructure on the electrical properties of Schottky barrier diodes. By using free standing films both the rough top diamond surface and the very smooth bottom surface are available for post-metal deposition. Rectifying electrical contacts were then established either with the smooth or the rough surface. The estimate of doping density from the capacitance-voltage plots shows that the smooth surface has a lower doping density when compared with the top layers of the same film. The results also show that surface roughness does not contribute significantly to the frequency dispersion of the small signal capacitance. The electrical properties of an abrupt asymmetric n(+)(silicon)-p(diamond) junction have also been measured. The I-V curves exhibit at low temperatures a plateau near zero bias, and show inversion of rectification. Capacitance-voltage characteristics show a capacitance minimum with forward bias, which is dependent on the environment conditions. It is proposed that this anomalous effect arises from high level injection of minority carriers into the bulk.

Threshold values of sagittal abdominal diameter for the detection of cardio-metabolic risk factors in Northeastern Mexico: a cross-sectional study

Background: The use of sagittal abdominal diameter (SAD) has been proposed for screening cardio-metabolic risk factors; however, its accuracy can be influenced by the choice of thresholds values. Aim: To determine the SAD threshold values for cardio-metabolic risk factors in Mexican adults; to assess whether parallel and serial SAD testing can improve waist circumference (WC) sensitivity and specificity; and to analyze the effect of considering SAD along with WC and body mass index (BMI) in detecting cardio-metabolic risk. Methods: This cross-sectional study was conducted during 2012-2014 in Northeast Mexico (n = 269). Data on anthropometric, clinical, and biochemical measurements were collected. Sex-adjusted receiver-operating characteristic curves (ROC) were obtained using hypertension, dysglycemia, dyslipidemia and insulin resistance as individual outcomes and metabolic syndrome as a composite outcome. Age-adjusted odds ratios and 95% confidence intervals (CI) were estimated using logistic regression. Results: The threshold value for SAD with acceptable combination of sensitivity and specificity was 24.6 cm in men and 22.5 cm in women. Parallel SAD testing improved WC sensitivity and serial testing improved WC specificity. The co-occurrence of high WC/high SAD increased the risk for insulin resistance by 2.4-fold (95% CI: 1.1-5.3), high BMI/high SAD by 4.3-fold (95% CI: 1.7-11.9) and SAD alone by 2.2-fold (95% CI: 1.2.-4.2). Conclusions: The use of SAD together with traditional obesity indices such as WC and BMI has advantages over using either of these indices alone. SAD may be a powerful screening tool for interventions for high-risk individuals.

Implications of low breakdown voltage of component subcells on external quantum efficiency measurements of multijunction solar cells

The electrical and optical coupling between subcells in a multijunction solar cell affects its external quantum efficiency (EQE) measurement. In this study, we show how a low breakdown voltage of a component subcell impacts the EQE determination of a multijunction solar cell and demands the use of a finely adjusted external voltage bias. The optimum voltage bias for the EQE measurement of a Ge subcell in two different GaInP/GaInAs/Ge triple-junction solar cells is determined both by sweeping the external voltage bias and by tracing the I–V curve under the same light bias conditions applied during the EQE measurement. It is shown that the I–V curve gives rapid and valuable information about the adequate light and voltage bias needed, and also helps to detect problems associated with non-ideal I–V curves that might affect the EQE measurement. The results also show that, if a non-optimum voltage bias is applied, a measurement artifact can result. Only when the problems associated with a non-ideal I–V curve and/or a low breakdown voltage have been discarded, the measurement artifacts, if any, can be attributed to other effects such as luminescent coupling between subcells.

Interface properties and capacitance-voltage behaviour of diamond devices prepared by microwave-assisted CVD

Free standing diamond films were used to study the effect of diamond surface morphology and microstructure on the electrical properties of Schottky barrier diodes. By using free standing films both the rough top diamond surface and the very smooth bottom surface are available for post-metal deposition. Rectifying electrical contacts were then established either with the smooth or the rough surface. The estimate of doping density from the capacitance-voltage plots shows that the smooth surface has a lower doping density when compared with the top layers of the same film. The results also show that surface roughness does not contribute significantly to the frequency dispersion of the small signal capacitance. The electrical properties of an abrupt asymmetric n(+)(silicon)-p(diamond) junction have also been measured. The I-V curves exhibit at low temperatures a plateau near zero bias, and show inversion of rectification. Capacitance-voltage characteristics show a capacitance minimum with forward bias, which is dependent on the environment conditions. It is proposed that this anomalous effect arises from high level injection of minority carriers into the bulk.