Linear implicit approximations of invariant measures of semi-linear SDEs with non-globally Lipschitz coefficients

This article investigates the weak approximation towards the invariant measure of semi-linear stochastic differential equations (SDEs) under non-globally Lipschitz coefficients. For this purpose, we propose a linear-theta-projected Euler (LTPE) scheme, which also admits an invariant measure, to handle the potential influence of the linear stiffness. Under certain assumptions, both the SDE and the corresponding LTPE method are shown to converge exponentially to the underlying invariant measures, respectively. Moreover, with time-independent regularity estimates for the corresponding Kolmogorov equation, the weak error between the numerical invariant measure and the original one can be guaranteed with an order one. Numerical experiments are provided to verify our theoretical findings.Comment: 45 pages, 7 figure

Linear implicit approximations of invariant measures of semi-linear SDEs with non-globally Lipschitz coefficients

This article investigates the weak approximation towards the invariant measure of semi-linear stochastic differential equations (SDEs) under non-globally Lipschitz coefficients. For this purpose, we propose a linear-theta-projected Euler (LTPE) scheme, which also admits an invariant measure, to handle the potential influence of the linear stiffness. Under certain assumptions, both the SDE and the corresponding LTPE method are shown to converge exponentially to the underlying invariant measures, respectively. Moreover, with time-independent regularity estimates for the corresponding Kolmogorov equation, the weak error between the numerical invariant measure and the original one can be guaranteed with convergence of order one. In terms of computational complexity, the proposed ergodicity preserving scheme with the nonlinearity explicitly treated has a significant advantage over the ergodicity preserving implicit Euler method in the literature. Numerical experiments are provided to verify our theoretical findings

Robust estimation of bacterial cell count from optical density

Optical density (OD) is widely used to estimate the density of cells in liquid culture, but cannot be compared between instruments without a standardized calibration protocol and is challenging to relate to actual cell count. We address this with an interlaboratory study comparing three simple, low-cost, and highly accessible OD calibration protocols across 244 laboratories, applied to eight strains of constitutive GFP-expressing E. coli. Based on our results, we recommend calibrating OD to estimated cell count using serial dilution of silica microspheres, which produces highly precise calibration (95.5% of residuals <1.2-fold), is easily assessed for quality control, also assesses instrument effective linear range, and can be combined with fluorescence calibration to obtain units of Molecules of Equivalent Fluorescein (MEFL) per cell, allowing direct comparison and data fusion with flow cytometry measurements: in our study, fluorescence per cell measurements showed only a 1.07-fold mean difference between plate reader and flow cytometry data

Review on A big data-based innovative knowledge teaching evaluation system in universities

With the widespread use of digital technologies such as big data, cloud computing and artificial intelligence in higher education, how to establish a scientific and systematic evaluation system to turn the traditional classroom with the one-way transmission of knowledge into an interactive space for exchanging ideas and inspiring wisdom has become an essential task for human resource management in universities, and a key to improving teaching quality. However, due to the debate between scientism and humanism in teaching evaluation, studies related to teaching performance have been isolated from human resource management, resulting in the lack of a systematic vision and framework for such studies. Relevant studies are still limited to the evaluation contents of different evaluation subjects. Evaluations also tend to focus only on the teaching process, ignoring the objectives of talent training, making it difficult for evaluations to play a goal-oriented role and hindering the further development of relevant studies. Therefore, this paper draws on human resource management methodologies and analyzes knowledge teaching evaluation system characteristics in colleges and universities in a big data context to construct a “multiple evaluations, trinity and four-step closed-loop” big data-based knowledge teaching evaluation system. “Trinity” represents evaluation from three performance dimensions: teaching effect, teaching behavior and teaching ability. “Multiple evaluations” represents the design of teaching performance indicators based on teaching data, breaking the barriers between different evaluation subjects. “Four-step closed-loop” draws on performance management theory to standardize the teaching performance management process from four aspects: planning, implementation, evaluation, and feedback. This evaluation system provides a systematic methodology for unifying the theory and practice of innovative knowledge teaching evaluation system in universities in a big data context