Infinite product expansion of the Fokker-Planck equation with steady-state solution

We present an analytical technique for solving Fokker–Planck equations that have a steady-state solution by representing the solution as an infinite product rather than, as usual, an infinite sum. This method has many advantages: automatically ensuring positivity of the resulting approximation, and by design exactly matching both the short- and long-term behaviour. The efficacy of the technique is demonstrated via comparisons with computations of typical examples

Thermoelectric effects in a rectangular Aharonov-Bohm geometry

The thermoelectric transport properties of a rectangular Aharonov-Bohm ring at low temperature are investigated using a theoretical approach based on Green's functions. The oscillations in the transmission coefficient as the field is varied can be used to tune the thermoelectric response of the ring. Large magnitude thermopowers are obtainable which, in conjunction with low conductance, can result in a high thermoelectric figure of merit. The effects of single site impurities and more general Anderson disorder are considered explicitly in the context of evaluating their effect on the Fano-type resonances in the transmission coefficient. Importantly, it is shown that even for moderate levels of disorder the thermoelectric figure of merit can remain significant, increasing the appeal of such structures from the perspective of specialist thermoelectric applications

Fast physical models for Si LDMOS power transistor characterization

A new nonlinear, process-oriented, quasi-two-dimensional (Q2D) model is described for microwave laterally diffused MOS (LDMOS) power transistors. A set of one-dimensional energy transport equations are solved across a two-dimensional cross-section in a “current-driven” form. The model accounts for avalanche breakdown and gate conduction, and accurately predicts DC and microwave characteristics at execution speeds sufficiently fast for circuit simulation applications

Analytical approximation to the multidimensional Fokker--Planck equation with steady state

The Fokker--Planck equation is a key ingredient of many models in physics, and related subjects, and arises in a diverse array of settings. Analytical solutions are limited to special cases, and resorting to numerical simulation is often the only route available; in high dimensions, or for parametric studies, this can become unwieldy. Using asymptotic techniques, that draw upon the known Ornstein--Uhlenbeck (OU) case, we consider a mean-reverting system and obtain its representation as a product of terms, representing short-term, long-term, and medium-term behaviour. A further reduction yields a simple explicit formula, both intuitive in terms of its physical origin and fast to evaluate. We illustrate a breadth of cases, some of which are `far' from the OU model, such as double-well potentials, and even then, perhaps surprisingly, the approximation still gives very good results when compared with numerical simulations. Both one- and two-dimensional examples are considered

Long- and short-time asymptotics of the first-passage time of the Ornstein-Uhlenbeck and other mean-reverting processes

The first-passage problem of the Ornstein–Uhlenbeck process to a boundary is a long-standing problem with no known closed-form solution except in specific cases. Taking this as a starting-point, and extending to a general mean-reverting process, we investigate the long- and short-time asymptotics using a combination of Hopf–Cole and Laplace transform techniques. As a result we are able to give a single formula that is correct in both limits, as well as being exact in certain special cases. We demonstrate the results using a variety of other models

Fully automated grey and white matter segmentation of the cervical cord in vivo

We propose and validate a new fully automated spinal cord (SC) segmentation technique that incorporates two different multi-atlas segmentation propagation and fusion techniques: Optimized PatchMatch Label fusion (OPAL) and Similarity and Truth Estimation for Propagated Segmentations (STEPS). We collaboratively join the advantages of each method to obtain the most accurate SC segmentation. The new method reaches the inter-rater variability, providing automatic segmentations equivalents to inter-rater segmentations in terms of DSC 0.97 for whole cord for any subject

Fully automated grey and white matter spinal cord segmentation

Axonal loss in the spinal cord is one of the main contributing factors to irreversible clinical disability in multiple sclerosis (MS). In vivo axonal loss can be assessed indirectly by estimating a reduction in the cervical cross-sectional area (CSA) of the spinal cord over time, which is indicative of spinal cord atrophy, and such a measure may be obtained by means of image segmentation using magnetic resonance imaging (MRI). In this work, we propose a new fully automated spinal cord segmentation technique that incorporates two different multi-atlas segmentation propagation and fusion techniques: The Optimized PatchMatch Label fusion (OPAL) algorithm for localising and approximately segmenting the spinal cord, and the Similarity and Truth Estimation for Propagated Segmentations (STEPS) algorithm for segmenting white and grey matter simultaneously. In a retrospective analysis of MRI data, the proposed method facilitated CSA measurements with accuracy equivalent to the inter-rater variability, with a Dice score (DSC) of 0.967 at C2/C3 level. The segmentation performance for grey matter at C2/C3 level was close to inter-rater variability, reaching an accuracy (DSC) of 0.826 for healthy subjects and 0.835 people with clinically isolated syndrome MS

Acute spinal cord injury: monitoring the lumbar cerebrospinal fluid provides limited information about the injury site

In some centers, monitoring the lumbar cerebrospinal fluid (CSF) is used to guide management of patients with acute traumatic spinal cord injuries (TSCI) and draining lumbar CSF to improve spinal cord perfusion. Here, we investigate whether the lumbar CSF provides accurate information about the injury site and the effect of draining lumbar CSF on injury site perfusion. In 13 TSCI patients, we simultaneously monitored lumbar CSF pressure (CSFP) and intraspinal pressure (ISP) from the injury site. Using CSFP or ISP, we computed spinal cord perfusion pressure (SCPP), vascular pressure reactivity index (sPRx) and optimum SCPP (SCPPopt). We also assessed the effect on ISP of draining 10mL CSF. Metabolites at the injury site were compared with metabolites in the lumbar CSF. We found that ISP was pulsatile, but CSFP had low pulse pressure and was non-pulsatile 21% of the time. There was weak or no correlation between CSFP versus ISP (R=-0.11), SCPP(csf) versus SCPP(ISP) (R=0.39) and sPRx(csf) versus sPRx(ISP) (R=0.45). CSF drainage caused no significant change in ISP in 7/12 patients, a significant drop by <5mmHg in 4/12 patients and by ~8mmHg in 1/12 patient. Metabolite concentrations in the CSF versus injury site did not correlate for lactate (R=0.00), pyruvate (R=-0.12) or lactate-to-pyruvate ratio (R=-0.05) with weak correlations noted for glucose (R=0.31), glutamate (R=0.61) and glycerol (R=0.56). We conclude that, after a severe TSCI, monitoring from the lumbar CSF provides only limited information about the injury site and that lumbar CSF drainage does not effectively reduce ISP in most patients

Process-orientated physics-based modeling of microwave power transistors: Small- and large-signal characterization

The coupling between charge transport, heat and energy flow required to model high frequency power devices is developed in the context of a computationally efficient physics-based model, which has been successfully applied to microwave laterally diffused MOS transistors. The accurate prediction of small-and large-signal microwave characteristics, and the physical insight gained, can be used in the process-orientated optimization and process sensitivity analysis of LDMOS power FETs. The charge-based model is well-suited to non-linear CAD implementation for applications such as power amplifier design. © 2012 IEEE

The usefulness of a free self-test for screening albuminuria in the general population: a cross-sectional survey

<p>Abstract</p> <p>Background</p> <p>In this study we evaluated the usefulness of a free self-test for screening albuminuria in the general population.</p> <p>Methods</p> <p>Dutch adults were invited by the Dutch Kidney Foundation to order a free albuminuria self-test, consisting of three semi quantitative dipstick tests, via the Internet. Results were classified in negative, low-positive and high-positive. In case of a positive test result, the tester was recommended to visit a GP for supplementary examination and/or treatment. Participants of the programme were sent a questionnaire for evaluation by e-mail eight weeks after receiving the self-test.</p> <p>Results</p> <p>During the first 30 days of the self-test programme, 996,927 self-tests were ordered. In total, 71,714 participants completed the questionnaire: 79% had a negative test result and 21% had a positive test result (20% low-positive and 1% high-positive). Of the positive testers, 25% visited a GP after testing for albuminuria. Among the 3,983 participants who visited a GP, 193 new diseases were detected: 25 chronic renal failure, 152 hypertension and 31 diabetes mellitus.</p> <p>Conclusion</p> <p>Using a free self-test for screening albuminuria in the general population resulted in a large response and a number of newly detected diseases. However, we found a very high percentage of positive testers of which probably a large part is false positive. Furthermore, only a small part of the positive testers visited a GP for additional examination and/or treatment. The efficiency of such a campaign could be increased by embedding the testing in health care to reduce the number of false-positive results and to ensure follow-up and treatment in case of a positive test result.</p