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Prime editing enables the introduction of virtually any small-sized genetic change without requiring donor DNA or double-strand breaks. However, evaluation of prime editing efficiency requires time-consuming experiments, and the factors that affect efficiency have not been extensively investigated. In this study, we performed high-throughput evaluation of prime editor 2 (PE2) activities in human cells using 54,836 pairs of prime editing guide RNAs (pegRNAs) and their target sequences. The resulting data sets allowed us to identify factors affecting PE2 efficiency and to develop three computational models to predict pegRNA efficiency. For a given target sequence, the computational models predict efficiencies of pegRNAs with different lengths of primer binding sites and reverse transcriptase templates for edits of various types and positions. Testing the accuracy of the predictions using test data sets that were not used for training, we found Spearman’s correlations between 0.47 and 0.81. Our computational models and information about factors affecting PE2 efficiency will facilitate practical application of prime editing. Prime editing is optimized by a method to choose the most efficient guide RNA.

Background Statistical methods that use the mid- p approach are useful tools to analyze categorical data, particularly for small and moderate sample sizes. Mid- p tests strike a balance between overly conservative exact methods and asymptotic methods that frequently violate the nominal level. Here, we examine a mid- p version of the McNemar exact conditional test for the analysis of paired binomial proportions. Methods We compare the type I error rates and power of the mid- p test with those of the asymptotic McNemar test (with and without continuity correction), the McNemar exact conditional test, and an exact unconditional test using complete enumeration. We show how the mid- p test can be calculated using eight standard software packages, including Excel. Results The mid- p test performs well compared with the asymptotic, asymptotic with continuity correction, and exact conditional tests, and almost as good as the vastly more complex exact unconditional test. Even though the mid- p test does not guarantee preservation of the significance level, it did not violate the nominal level in any of the 9595 scenarios considered in this article. It was almost as powerful as the asymptotic test. The exact conditional test and the asymptotic test with continuity correction did not perform well for any of the considered scenarios. Conclusions The easy-to-calculate mid- p test is an excellent alternative to the complex exact unconditional test. Both can be recommended for use in any situation. We also recommend the asymptotic test if small but frequent violations of the nominal level is acceptable.

This paper proposes asymptotic and exact methods for testing the equality of correlations for multiple bilateral data under Dallal’s model. Three asymptotic test statistics are derived for large samples. Since they are not applicable to small data, several conditional and unconditional exact methods are proposed based on these three statistics. Numerical studies are conducted to compare all these methods with regard to type I error rates (TIEs) and powers. The results show that the asymptotic score test is the most robust, and two exact tests have satisfactory TIEs and powers. Some real examples are provided to illustrate the effectiveness of these tests.

Consider a credit portfolio with the investments in various sectors and exposed to an external stochastic environment. The portfolio loss due to defaults is of critical importance for social and economic security particularly in times of financial distress. We argue that the dependences among obligors within sectors (intradependence) and across sectors (interdependence) may coexist and influence the portfolio loss. To quantify the portfolio loss, we develop a multi-sector structural model in which a multivariate regular variation structure is employed to model the intradependence within sectors, and the interdependence across sectors is implied in the arbitrarily dependent macroeconomic factors, although, given them, obligors in different sectors are conditionally independent. We establish some sharp asymptotic formulas for the tail probability and the (tail) distortion risk measures of the portfolio loss. Our results show that the portfolio loss is mainly driven by the latent variables and the recovery rate function, and is also potentially affected by the macroeconomic factors and the intradependence within sectors. Moreover, we implement intensive numerical studies to examine the accuracy of the obtained approximations and conduct some sensitivity analysis.

Gwet’s first-order agreement coefficient (AC1) is widely used to assess the agreement between raters. This paper proposes several asymptotic statistics for a homogeneity test of stratified AC1 in large sample sizes. These statistics may have unsatisfactory performance, especially for small samples and a high value of AC1. Furthermore, we propose three exact methods for small pieces. A likelihood ratio statistic is recommended in large sample sizes based on the numerical results. The exact E approaches under likelihood ratio and score statistics are more robust in the case of small sample scenarios. Moreover, the exact E method is effective to a high value of AC1. We apply two real examples to illustrate the proposed methods.

This article completes our studies on the formal construction of asymptotic approximations for statistics based on a random number of observations. Second order Chebyshev–Edgeworth expansions of asymptotically normally or chi-squared distributed statistics from samples with negative binomial or Pareto-like distributed random sample sizes are obtained. The results can have applications for a wide spectrum of asymptotically normally or chi-square distributed statistics. Random, non-random, and mixed scaling factors for each of the studied statistics produce three different limit distributions. In addition to the expected normal or chi-squared distributions, Student’s t-, Laplace, Fisher, gamma, and weighted sums of generalized gamma distributions also occur.

Matrix population models require the population to be divided into discrete stage classes. In many cases, especially when classes are defined by a continuous variable, such as length or mass, there are no natural breakpoints, and the division is artificial. We introduce the \"integral projection model,\" which eliminates the need for division into discrete classes, without requiring any additional biological assumptions. Like a traditional matrix model, the integral projection model provides estimates of the asymptotic growth rate, stable size distribution, reproductive values, and sensitivities of the growth rate to changes in vital rates. However, where the matrix model represents the size distributions, reproductive value, and sensitivities as step functions (constant within a stage class), the integral projection model yields smooth curves for each of these as a function of individual size. We describe a method for fitting the model to data, and we apply this method to data on an endangered plant species, northern monkshood (Aconitum noveboracense), with individuals classified by stem diameter. The matrix and integral models yield similar estimates of the asymptotic growth rate, but the reproductive values and sensitivities in the matrix model are sensitive to the choice of stage classes. The integral projection model avoids this problem and yields size-specific sensitivities that are not affected by stage duration. These general properties of the integral projection model will make it advantageous for other populations where there is no natural division of individuals into stage classes.

We present fully sequential procedures for steady-state simulation that are designed to select the best of a finite number of simulated systems when \"best\" is defined by the largest or smallest long-run average performance. We also provide a framework for establishing the asymptotic validity of such procedures and prove the validity of our procedures. An example based on the M/M /1 queue is given.

Firms compete in supply functions when they offer a schedule of prices and quantities into a market; for example, this occurs in many wholesale electricity markets. We study the equilibrium behaviour when firms differ, both with regard to their costs and their capacities. We characterize strong equilibrium solutions in which, given the other players' supply functions, optimal profits are achieved for every demand realisation. If the demand can be low enough for it to be met economically with supply from just one firm, then the supply function equilibria are ordered in a natural way. We consider equilibria in which, for the highest levels of demand, all but one of the firms have reached their capacity limit. We show that there can be at most one supply function equilibrium with this property. We also propose a new numerical method to find asymmetric supply function equilibria, using piecewise-linear approximations and a discretization of the demand distribution. We show that this approach has good theoretical convergence behaviour. Finally, we present numerical results from an implementation using GAMS to demonstrate that the approach is effective in practice.

Recent research demonstrates that the well-documented feeble link between exchange rates and economic fundamentals can be reconciled with conventional exchange rate theories under the assumption that the discount factor is near unity (Engel and West 2005). We provide empirical evidence that this assumption is valid, lending further support to the above explanation of the empirical disconnect between nominal exchange rates and fundamentals.