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Excitation–emission-spectral unmixing-based fluorescence resonance energy transfer (ExEm-spFRET) microscopy exhibits excellent robustness in living cells. We here develop an automatic ExEm-spFRET microscope with 3.04 s of time resolution for a quantitative FRET imaging. The user-friendly interface software has been designed to operate in two modes: administrator and user. Automatic background recognition, subtraction, and cell segmentation were integrated into the software, which enables FRET calibration or measurement in a one-click operation manner. In administrator mode, both correction factors and spectral fingerprints are only calibrated periodically for a stable system. In user mode, quantitative ExEm-spFRET imaging is directly implemented for FRET samples. We implemented quantitative ExEm-spFRET imaging for living cells expressing different tandem constructs (C80Y, C40Y, C10Y, and C4Y, respectively) and obtained consistent results for at least 3 months, demonstrating the stability of our microscope. Next, we investigated Bcl-xL-Bad interaction by using ExEm-spFRET imaging and FRET two-hybrid assay and found that the Bcl-xL-Bad complexes exist mainly in Bad-Bcl-xL trimers in healthy cells and Bad-Bcl-xL2 trimers in apoptotic cells. We also performed time-lapse FRET imaging on our system for living cells expressing Yellow Cameleon 3.6 (YC3.6) to monitor ionomycin-induced rapid extracellular Ca2+ influx with a time interval of 5 s for total 250 s.
Accurate predetermination of the quantum yield ratio (QA/QD) and the extinction coefficient ratio (KA/KD) between acceptor and donor is a prerequisite for quantitative fluorescence resonance energy transfer (FRET) imaging. We here propose a method to measure KA/KD and QA/QD by measuring the excitation–emission spectra (ExEm-spectra) of one dish of cells expressing m (≥3) kinds of FRET constructs. The ExEm-spectra images are unmixed to obtain the weight maps of donor (WD), acceptor (WA), and acceptor sensitization (WS). For each cell, the frequency distribution plots of the WS/WD and WS/WA images are fitted by using a single-Gaussian function to obtain the peak values of WS/WD (SD) and WS/WA (SA). The statistical frequency-SD/SA plots from all cells are fitted by using a multi-Gaussian function to obtain the peak values of both SD and SA, and then the ranges of WS/WD (RSD) and WS/WA (RSA) for each FRET construct are predetermined. Based on the predetermined RSD and RSA values of FRET constructs, our method is capable of automatically classifying cells expressing different FRET constructs. Finally, the WS/WD–WA/WD plot from different kinds of cells is linearly fitted to obtain KA/KD and QA/QD values.
Understanding factors associated with post-discharge sleep quality among COVID-19 survivors is important for intervention development.
This study investigated sleep quality and its correlates among COVID-19 patients 6 months after their most recent hospital discharge.
Healthcare providers at hospitals located in five different Chinese cities contacted adult COVID-19 patients discharged between 1 February and 30 March 2020. A total of 199 eligible patients provided verbal informed consent and completed the interview. Using score on the single-item Sleep Quality Scale as the dependent variable, multiple linear regression models were fitted.
Among all participants, 10.1% reported terrible or poor sleep quality, and 26.6% reported fair sleep quality, 26.1% reported worse sleep quality when comparing their current status with the time before COVID-19, and 33.7% were bothered by a sleeping disorder in the past 2 weeks. After adjusting for significant background characteristics, factors associated with sleep quality included witnessing the suffering (adjusted B = −1.15, 95% CI = −1.70, −0.33) or death (adjusted B = −1.55, 95% CI = −2.62, −0.49) of other COVID-19 patients during hospital stay, depressive symptoms (adjusted B = −0.26, 95% CI = −0.31, −0.20), anxiety symptoms (adjusted B = −0.25, 95% CI = −0.33, −0.17), post-traumatic stress disorders (adjusted B = −0.16, 95% CI = −0.22, −0.10) and social support (adjusted B = 0.07, 95% CI = 0.04, 0.10).
COVID-19 survivors reported poor sleep quality. Interventions and support services to improve sleep quality should be provided to COVID-19 survivors during their hospital stay and after hospital discharge.
The chapter focuses on network flow problems, which form a very important part of practical applications. Routing, distribution, and scheduling problems often belong to this category of formulations, while a large number of other optimization problems encountered in diverse areas of applications may contain elements of network flow problems.
Quadratic multidimensional functions play a very important role in the understanding of general nonlinear functions. Convexity of quadratic functions is linked in a natural way from its geometrical definition all the way to the properties of its matrix eigenspectrum. Indeed, to second order expansion, and close to the expansion point, any nonlinear function can be approximated by a quadratic – thus providing a crucial link and understanding of the local behaviour and convexity properties of general functions.
The chapter introduces basic optimization concepts, and motivates the use of optimization models and methods to engineering and scientific practice applications. It establishes key concepts, such as the types of variables, arguments to an optimization problem as continuous, integer and control functions (for optimal control problems). Further, it introduces types of optimization problems according to their formulation (such as multiobjective, bilevel, stochastic optimization problems)
This chapter introduces concepts of norm-1 and infinity norm fitting, both in terms of their own merit as useful fitting techniques, apart from least squares, but also importantly to teach how optimization problems that seem hard to solve (such as by being non-differentiable) can be reformulated effectively into easier ones that can be handled by standard solution methods – in this case by LP solvers.
Unconstrained multivariate gradient-based minimization is introduced by means of search direction-producing methods, focusing on steepest descent and Newton's method. Issues with both methods are discussed, highlighting what happens in the case of locally nonconvex functions, particularly in Newton's method. Linesearch is introduced, effectively rendering multidimensional optimization into a sequence of one-dimensional searches along the ray of the search directions produced. Linesearch criteria are discussed, such as the Armijo first condition, and efficient ways to cut the step size are discussed.
Duality theory has a central role in constrained optimization, both from a theoretical point of view and to enable understanding of solution methods and problem reformulations for special classes of problems. Such applications are presented in the next chapter on Lagrangian relaxation and Lagrangian decomposition. In this chapter, the fundamental background for duality theory is presented along with a basic introduction of key concepts related to it.
Convexity is of paramount importance in optimization theory. This chapter adopts a simple and intuitive description, highlighting the importance of these properties to guarantee global optimality, and paves the way to understanding nonconvex optimization problems in later chapters.
This chapter is the main chapter of the book that introduces in detail how modern Interior Point Methods work, what they are based on, and the associated numerical-computational implementation schemes involved. The difference between primal barrier methods and primal-dual barrier methods is presented and discussed, showing why nowadays mostly primal-dual methods are used in general optimization solvers.
This chapter is a first introduction to penalty and barrier methods, as a direct way to transform generally constrained optimization problems to unconstrained ones. This is done through the appropriate choice of penalty and barrier functions, with the various problems facing such methods highlighted in intuitive and illustrative ways via discussion and graphical examples. The chapter also prepares the reader for the much more advanced material that follows in the next chapter.
This chapter is a standard section in most introductory material on optimization. It examines three basic one-dimensional optimization methods, highlighting connections between them and leading to the one-dimensional Newton's method as the method of choice.
This chapter focuses on the formulation of LP problems as a means to teach how to derive mathematical programming formulations for basic descriptions, specifications, and data related to associated processes that are to be optimized. It focuses on basic blending type problems, production planning, with special focus given to network flow problems that cover a wide range of applications. This topic is revisited in more detail in chapter 14.
Decomposition of optimization problems is a fundamental technique to reduce the computational cost and enable efficient solution of very large-scale models. Key decomposition approaches are presented in this chapter, discussing primal and dual decomposition methods, Generalized Benders Decomposition, and related applications.
This is a basic and standard chapter on motivating and illustrating Linear Programming problems via geometrical construction of feasible regions and objective function contours. It establishes the context of Linear Programming and motivates the material of the next chapter via numerous illustrative examples.