BCH Two-step Auxiliary Variable Integration with MplusAutomation

This R tutorial automates the BCH two-step axiliary variable procedure (Bolk, Croon, Hagenaars, 2004) using the MplusAutomation package (Hallquist & Wiley, 2018) to estimate models and extract relevant parameters. To learn more about auxiliary variable integration methods and why multi-step methods are necessary for producing un-biased estimates see Asparouhov & Muthén (2014). The name of this mehtod, BCH, stands for Bolck, Croon, & Hagenaars, the authors who developed this method (Bolk, Croon, Hagenaars, 2004). This tutorial utilizes the public-use data repository named the Longitudinal Survey of American Youth (LSAY; Miller et al., 1992). The applied example used in this tutorial is based off the example presented in the seminal chapter on mixture modeling by Katherine Masyn (2013). This tutorial contains the 9 math indicators from this original study as well as two auxiliary variables.

3-Step ML Auxiliary Variable Integration Using MplusAutomation

This R tutorial automates the 3-step ML axiliary variable procedure using the MplusAutomation package (Hallquist & Wiley, 2018) to estimate models and extract relevant parameters. To learn more about auxiliary variable integration methods and why multi-step methods are necessary for producing un-biased estimates see Asparouhov & Muthén (2014). The motivation for writing this tutorial is that conducting the 3-step manually is highly error prone as it requires pulling logit values estimated in the step-1 model and adding them in the model statement of the step-2 model (i.e., lots of copying & pasting). In contrast, this approach is fully replicable and provides clear documentation which translates to more reliable research.

Estimating the Highest Time-Step in Numerical Methods to Enhance the Optimization of Chaotic Oscillators

The execution time that takes to perform numerical simulation of a chaotic oscillator mainly depends on the time-step h. This paper shows that the optimization of chaotic oscillators can be enhanced by estimating the highest h in either one-step or multi-step methods. Four chaotic oscillators are used as a case study, and the optimization of their Kaplan-Yorke dimension (DKY) is performed by applying three metaheuristics, namely: particle swarm optimization (PSO), many optimizing liaison (MOL), and differential evolution (DE) algorithms. Three representative one-step and three multi-step methods are used to solve the four chaotic oscillators, for which the estimation of the highest h is obtained from their stability analysis. The optimization results show the effectiveness of using a high h value for the six numerical methods in reducing execution time while maximizing the positive Lyapunov exponent (LE+) and DKY of the chaotic oscillators by applying PSO, MOL, and DE algorithms.

Stabilised explicit Adams-type methods

In this work we present explicit Adams-type multi-step methods with extended stability intervals, which are analogous to the stabilised Chebyshev Runge – Kutta methods. It is proved that for any k ≥ 1 there exists an explicit k-step Adams-type method of order one with stability interval of length 2k. The first order methods have remarkably simple expressions for their coefficients and error constant. A damped modification of these methods is derived. In the general case, to construct a k-step method of order p it is necessary to solve a constrained optimisation problem in which the objective function and p constraints are second degree polynomials in k variables. We calculate higher-order methods up to order six numerically and perform some numerical experiments to confirm the accuracy and stability of the methods.

Fabrication of Porous Lead Bromide Films by Introducing Indium Tribromide for Efficient Inorganic CsPbBr3 Perovskite Solar Cells

In the process of preparing CsPbBr3 films by two-step or multi-step methods, due to the low solubility of CsBr in organic solvents, the prepared perovskite films often have a large number of holes, which is definitely not conducive to the performance of CsPbBr3 perovskite solar cells (PSCs). In response to this problem, this article proposed a method of introducing InBr3 into the PbBr2 precursor to prepare a porous PbBr2 film to increase the reaction efficiency between CsBr and PbBr2 and achieve the purpose of In (Ⅲ) incorporation, which not only optimized the morphology of the produced CsPbBr3 film but also enhanced the charge extraction and transport capabilities, which was ascribed to the reduction of the trap state density and impurity phases in the perovskite films, improving the performance of CsPbBr3 PSCs. At the optimal InBr3 concentration of 0.21 M, the InBr3:CsPbBr3 perovskite solar cell exhibited a power conversion efficiency of 6.48%, which was significantly higher than that of the pristine device.

Genome Editing in Bacteria: CRISPR-Cas and Beyond

Genome editing in bacteria encompasses a wide array of laborious and multi-step methods such as suicide plasmids. The discovery and applications of clustered regularly interspaced short palindromic repeats (CRISPR)-Cas based technologies have revolutionized genome editing in eukaryotic organisms due to its simplicity and programmability. Nevertheless, this system has not been as widely favored for bacterial genome editing. In this review, we summarize the main approaches and difficulties associated with CRISPR-Cas-mediated genome editing in bacteria and present some alternatives to circumvent these issues, including CRISPR nickases, Cas12a, base editors, CRISPR-associated transposases, prime-editing, endogenous CRISPR systems, and the use of pre-made ribonucleoprotein complexes of Cas proteins and guide RNAs. Finally, we also address fluorescent-protein-based methods to evaluate the efficacy of CRISPR-based systems for genome editing in bacteria. CRISPR-Cas still holds promise as a generalized genome-editing tool in bacteria and is developing further optimization for an expanded application in these organisms. This review provides a rarely offered comprehensive view of genome editing. It also aims to familiarize the microbiology community with an ever-growing genome-editing toolbox for bacteria.

Improved second-order unconditionally stable schemes of linear multi-step and equivalent single-step integration methods

Second-order unconditionally stable schemes of linear multi-step methods, and their equivalent single-step methods, are developed in this paper. The parameters of the linear two-, three-, and four-step methods are determined for optimal accuracy, unconditional stability and tunable algorithmic dissipation. The linear three- and four-step schemes are presented for the first time. As an alternative, corresponding single-step methods, spectrally equivalent to the multi-step ones, are developed by introducing the required intermediate variables. Their formulations are equivalent to that of the corresponding multi-step methods; their use is more convenient, owing to being self-starting. Compared with existing second-order methods, the proposed ones, especially the linear four-step method and its alternative single-step one, show higher accuracy for a given degree of algorithmic dissipation. The accuracy advantage and other properties of the newly developed schemes are demonstrated by several illustrative examples.

Accuracy of Symmetric Multi-Step Methods for the Numerical Modelling of Satellite Motion

Stability of high-order linear multistep St¨ormer-Cowell and symmetric methods are discussed in detail in this paper. Efficient algorithms for obtaining intervals of absolute stability and periodicity are given for these methods. To demonstrate the accuracy of numerical integration of the orbit over an interval about one year two model problems are considered. First problem is the 3D Kepler problem. Second one is a specially designed 3D model problem that has the exact solution and simulates the Earth-Moon-satellite system