Behavior of different numerical schemes for population genetic drift problems

In this paper, we focus on numerical methods for the genetic drift problems, which is governed by a degenerated convection-dominated parabolic equation. Due to the degeneration and convection, Dirac singularities will always be developed at boundary points as time evolves. In order to find a \emph{complete solution} which should keep the conservation of total probability and expectation, three different schemes based on finite volume methods are used to solve the equation numerically: one is a upwind scheme, the other two are different central schemes. We observed that all the methods are stable and can keep the total probability, but have totally different long-time behaviors concerning with the conservation of expectation. We prove that any extra infinitesimal diffusion leads to a same artificial steady state. So upwind scheme does not work due to its intrinsic numerical viscosity. We find one of the central schemes introduces a numerical viscosity term too, which is beyond the common understanding in the convection-diffusion community. Careful analysis is presented to prove that the other central scheme does work. Our study shows that the numerical methods should be carefully chosen and any method with intrinsic numerical viscosity must be avoided.Comment: 17 pages, 8 figure

Infinite-dimensional Kalman Filtering and Sensor Placement Problem

One of the central problems in engineering is to estimate the state of a stochastic dynamic system from limited noisy measurements. A Kalman filter is commonly used for state estimation, which produces an unbiased optimal estimate that minimizes the variance of the estimation error. Many physical processes, such as diffusion and beam vibrations, can be described by partial differential equations. These governing equations may be reformulated mathematically as infinite-dimensional dynamic systems. In this work, the derivation of the Kalman filter for infinite-dimensional linear dynamic systems is reviewed, and the sensor placement problem for Kalman filtering is considered. The optimality criterion for sensor selection and location is to minimize the steady-state error variance, which is shown to be the nuclear norm of an operator that solves an algebraic Riccati equation. Three partial differential equation models are examined: one-dimensional diffusion, simply supported Euler-Bernoulli beam with Kelvin-Voigt damping, and two-dimensional diffusion on an L-shaped region. Optimal sensor locations are calculated for the three models. The sensor noise effects on the state estimation are investigated with the assumption that all the selected sensors are placed optimally. Results show that using multiple low quality sensors can lead to as good an estimate as using a single high quality sensor, provided that enough sensors are used. In particular, for the one-dimensional diffusion equation, approximately proportional relations between the square root of sensor noise variance and the estimation error are observed in simulations

Sensor Choice for Minimum Error Variance Estimation

© 2016 IEEE, Morris, K. A., & Özer, A. ö. (2014). Modeling and Stabilizability of Voltage-Actuated Piezoelectric Beams with Magnetic Effects. SIAM Journal on Control and Optimization, 52(4), 2371–2398. https://doi.org/10.1137/130918319A Kalman filter is optimal in that the variance of the error is minimized by the estimator. It is shown here, in an infinite-dimensional context, that the solution to an operator Riccati equation minimizes the steady-state error variance. This extends a result previously known for lumped parameter systems to distributed parameter systems. It is shown then that minimizing the trace of the Riccati operator is a reasonable criterion for choosing sensor locations. It is then shown that multiple inaccurate sensors, that is, those with large noise variance, can provide as good an estimate as a single highly accurate (but probably more expensive) sensor. Optimal sensor location is then combined with estimator design. A framework for calculation of the best sensor locations using approximations is established and sensor location as well as choice is investigated with three examples. Simulations indicate that the sensor locations do affect the quality of the estimation and that multiple low quality sensors can lead to better estimation than a single high quality sensor.NSERC Discovery Grant US AFOSR grant || FA 9550-16-1-006

Postconditioning inhibits myocardial apoptosis during prolonged reperfusion via a JAK2-STAT3-Bcl-2 pathway

<p>Abstract</p> <p>Background</p> <p>Postconditioning (PostC) inhibits myocardial apoptosis after ischemia-reperfusion (I/R) injury. The JAK2-STAT3 pathway has anti-apoptotic effects and plays an essential role in the late protection of preconditioning. Our aim was to investigate the anti-apoptotic effect of PostC after prolonged reperfusion and the role of the JAK2-STAT3 pathway in the anti-apoptotic effect of PostC.</p> <p>Methods</p> <p>Wistar rats were subjected to 30 minutes ischemia and 2 or 24 hours (h) reperfusion, with or without PostC (three cycles of 10 seconds reperfusion and 10 seconds reocclusion at the onset of reperfusion). Separate groups of rats were treated with a JAK2 inhibitor (AG490) or a PI3K inhibitor (wortmannin) 5 minutes before PostC. Immunohistochemistry was used to analyze Bcl-2 protein levels after reperfusion. mRNA levels of Bcl-2 were detected by qRT-PCR. TTC staining was used to detect myocardial infarction size. Myocardial apoptosis was evaluated by TUNEL staining. Western-blot was used to detect p-STAT3 and p-Akt levels after reperfusion.</p> <p>Results</p> <p>There was more myocardial apoptosis at 24 h <it>vs </it>2 h after reperfusion in all groups. PostC significantly reduced myocardial apoptosis and elevated Bcl-2 levels at both 2 and 24 hours after reperfusion. PostC increased p-STAT3 and p-Akt levels after reperfusion. Administration of AG490 reduced p-STAT3 and p-Akt levels and attenuated the anti-apoptotic effect of PostC. Wortmannin also reduced p-Akt levels and attenuated the anti-apoptotic effect of PostC but had no effect on p-STAT3 levels. AG490 abrogated the up-regulation of Bcl-2 by PostC.</p> <p>Conclusion</p> <p>PostC may reduce myocardial apoptosis during prolonged reperfusion via a JAK2-STAT3-Bcl-2 pathway. As a downstream target of JAK2 signaling, activation of PI3K/Akt pathway may be necessary in the protection of PostC.</p

Biosynthesis, characterization, and antifungal activity of plant-mediated silver nanoparticles using Cnidium monnieri fruit extract

The present study describes a novel method for green synthesis of silver nanoparticles using Cnidium monnieri (CM-AgNPs). Cnidium monnieri fruit is an excellent anti tinea drug that can be used externally to treat superficial fungal infections in the human body. The aqueous ethanolic extract of Cnidium monnieri fruit was prepared and employed in the synthesis of stable silver nanoparticles via biological reduction method. The synthesis conditions of CM-AgNPs was systematically optimized using Box–Behnken design. CM-AgNPs were well characterized by UV-spectroscopy and X-ray powder diffraction (XRD), and it was confirmed that the synthesized particles were AgNPs. The possible functional groups required for the reduction and stabilization of CM-AgNPs in the extract were identified through FTIR spectrum. The size of CM-AgNPs structure was confirmed to be approximately 44.6 nm in polydisperse spherical shape through scanning electron microscopy (SEM), transmission electron microscopy (TEM), and laser dynamic light scattering (DLS). Further, the minimum inhibitory concentration 90% (MIC90) ratios values of Cm-AgNPs against Trichophyton rubrum (7 d), T. mentagrophytes (7 d) and Candida albicans (24 h) were 3.125, 3.125, and 0.78125 μg/mL, respectively, determined by the broth micro dilution method. Finally, the result was concluded that the synthesized AgNPs could be further evaluated in large scale as a potential human topical antifungal agent

Development and validation of multivariable prediction models for adverse COVID-19 outcomes in patients with IBD

Objectives Develop an individualised prognostic risk prediction tool for predicting the probability of adverse COVID-19 outcomes in patients with inflammatory bowel disease (IBD). Design and setting This study developed and validated prognostic penalised logistic regression models using reports to the international Surveillance Epidemiology of Coronavirus Under Research Exclusion for Inflammatory Bowel Disease voluntary registry from March to October 2020. Model development was done using a training data set (85% of cases reported 13 March–15 September 2020), and model validation was conducted using a test data set (the remaining 15% of cases plus all cases reported 16 September–20 October 2020). Participants We included 2709 cases from 59 countries (mean age 41.2 years (SD 18), 50.2% male). All submitted cases after removing duplicates were included. Primary and secondary outcome measures COVID-19 related: (1) Hospitalisation+: composite outcome of hospitalisation, ICU admission, mechanical ventilation or death; (2) Intensive Care Unit+ (ICU+): composite outcome of ICU admission, mechanical ventilation or death; (3) Death. We assessed the resulting models’ discrimination using the area under the curve of the receiver operator characteristic curves and reported the corresponding 95% CIs. Results Of the submitted cases, a total of 633 (24%) were hospitalised, 137 (5%) were admitted to the ICU or intubated and 69 (3%) died. 2009 patients comprised the training set and 700 the test set. The models demonstrated excellent discrimination, with a test set area under the curve (95% CI) of 0.79 (0.75 to 0.83) for Hospitalisation+, 0.88 (0.82 to 0.95) for ICU+ and 0.94 (0.89 to 0.99) for Death. Age, comorbidities, corticosteroid use and male gender were associated with a higher risk of death, while the use of biological therapies was associated with a lower risk. Conclusions Prognostic models can effectively predict who is at higher risk for COVID-19-related adverse outcomes in a population of patients with IBD. A free online risk calculator (https://covidibd.org/covid-19-risk-calculator/) is available for healthcare providers to facilitate discussion of risks due to COVID-19 with patients with IBD