We unify various nonparametric hypothesis testing problems in a framework of permutation testing, enabling hypothesis testing on multi-sample, multidimensional data and contingency tables. Most of the functions available in the R environment to implement permutation tests are single functions constructed for specific test problems; to facilitate the use of the package, the package encapsulates similar tests in a categorized manner, greatly improving ease of use. We will all provide functions for self-selected permutation scoring methods and self-selected p-value calculation methods (asymptotic, exact, and sampling). For two-sample tests, we will provide mean tests and estimate drift sizes; we will provide tests on variance; we will provide paired-sample tests; we will provide correlation coefficient tests under three measures. For multi-sample problems, we will provide both ordinary and ordered alternative test problems. For multidimensional data, we will implement multivariate means (including ordered alternatives) and multivariate pairwise tests based on four statistics; the components with significant differences are also calculated. For contingency tables, we will perform permutation chi-square test or ordered alternative.

The top-performing ensemble-based Penalized Cox Regression (ePCR) framework developed during the DREAM 9.5 mCRPC Prostate Cancer Challenge <https://www.synapse.org/ProstateCancerChallenge> presented in Guinney J, Wang T, Laajala TD, et al. (2017) <doi:10.1016/S1470-2045(16)30560-5> is provided here-in, together with the corresponding follow-up work. While initially aimed at modeling the most advanced stage of prostate cancer, metastatic Castration-Resistant Prostate Cancer (mCRPC), the modeling framework has subsequently been extended to cover also the non-metastatic form of advanced prostate cancer (CRPC). Readily fitted ensemble-based model S4-objects are provided, and a simulated example dataset based on a real-life cohort is provided from the Turku University Hospital, to illustrate the use of the package. Functionality of the ePCR methodology relies on constructing ensembles of strata in patient cohorts and averaging over them, with each ensemble member consisting of a highly optimized penalized/regularized Cox regression model. Various cross-validation and other modeling schema are provided for constructing novel model objects.

The current version provides functions to compute, print and summarize the Index of Sensitivity to Nonignorability (ISNI) in the generalized linear model for independent data, and in the marginal multivariate Gaussian model and the mixed-effects models for continuous and binary longitudinal/clustered data. It allows for arbitrary patterns of missingness in the regression outcomes caused by dropout and/or intermittent missingness. One can compute the sensitivity index without estimating any nonignorable models or positing specific magnitude of nonignorability. Thus ISNI provides a simple quantitative assessment of how robust the standard estimates assuming missing at random is with respect to the assumption of ignorability. For a tutorial, download at <https://huixie.people.uic.edu/Research/ISNI_R_tutorial.pdf>. For more details, see Troxel Ma and Heitjan (2004) and Xie and Heitjan (2004) <doi:10.1191/1740774504cn005oa> and Ma Troxel and Heitjan (2005) <doi:10.1002/sim.2107> and Xie (2008) <doi:10.1002/sim.3117> and Xie (2012) <doi:10.1016/j.csda.2010.11.021> and Xie and Qian (2012) <doi:10.1002/jae.1157>.

Measure of the Effect ('MOTE') is an effect size calculator, including a wide variety of effect sizes in the mean differences family (all versions of d) and the variance overlap family (eta, omega, epsilon, r). MOTE provides non-central confidence intervals for each effect size, relevant test statistics, and output for reporting in APA Style (American Psychological Association, 2010, <ISBN:1433805618>) with LaTeX'. In research, an over-reliance on p-values may conceal the fact that a study is under-powered (Halsey, Curran-Everett, Vowler, & Drummond, 2015 <doi:10.1038/nmeth.3288>). A test may be statistically significant, yet practically inconsequential (Fritz, Scherndl, & Kühberger, 2012 <doi:10.1177/0959354312436870>). Although the American Psychological Association has long advocated for the inclusion of effect sizes (Wilkinson & American Psychological Association Task Force on Statistical Inference, 1999 <doi:10.1037/0003-066X.54.8.594>), the vast majority of peer-reviewed, published academic studies stop short of reporting effect sizes and confidence intervals (Cumming, 2013, <doi:10.1177/0956797613504966>). MOTE simplifies the use and interpretation of effect sizes and confidence intervals.

Provide a variety of Q-matrix validation methods for the generalized cognitive diagnosis models, including the method based on the generalized deterministic input, noisy, and gate model (G-DINA) by de la Torre (2011) <DOI:10.1007/s11336-011-9207-7> discrimination index (the GDI method) by de la Torre and Chiu (2016) <DOI:10.1007/s11336-015-9467-8>, the Hull method by Najera et al. (2021) <DOI:10.1111/bmsp.12228>, the stepwise Wald test method (the Wald method) by Ma and de la Torre (2020) <DOI:10.1111/bmsp.12156>, the multiple logistic regressionâ based Qâ matrix validation method (the MLR-B method) by Tu et al. (2022) <DOI:10.3758/s13428-022-01880-x>, the beta method based on signal detection theory by Li and Chen (2024) <DOI:10.1111/bmsp.12371> and Q-matrix validation based on relative fit index by Chen et al. (2013) <DOI:10.1111/j.1745-3984.2012.00185.x>. Different research methods and iterative procedures during Q-matrix validating are available <DOI:10.3758/s13428-024-02547-5>.

This package provides functions are provided for prior specification in divergence time estimation using fossils as well as other kinds of data. It provides tools for interacting with the input and output of Bayesian platforms in evolutionary biology such as BEAST2', MrBayes', RevBayes', or MCMCTree'. It Implements a simple measure similarity between probability density functions for comparing prior and posterior Bayesian densities, as well as code for calculating the combination of distributions using conflation of Hill (2008). Functions for estimating the origination time in collections of distributions using the x-intercept (e.g., Draper and Smith, 1998) and stratigraphic intervals (Marshall 2010) are also available. Hill, T. 2008. "Conflations of probability distributions". Transactions of the American Mathematical Society, 363:3351-3372. <doi:10.48550/arXiv.0808.1808>, Draper, N. R. and Smith, H. 1998. "Applied Regression Analysis". 1--706. Wiley Interscience, New York. <DOI:10.1002/9781118625590>, Marshall, C. R. 2010. "Using confidence intervals to quantify the uncertainty in the end-points of stratigraphic ranges". Quantitative Methods in Paleobiology, 291--316. <DOI:10.1017/S1089332600001911>.

This package provides a constrained generalized additive model is fitted by the cgam routine. Given a set of predictors, each of which may have a shape or order restrictions, the maximum likelihood estimator for the constrained generalized additive model is found using an iteratively re-weighted cone projection algorithm. The ShapeSelect routine chooses a subset of predictor variables and describes the component relationships with the response. For each predictor, the user needs only specify a set of possible shape or order restrictions. A model selection method chooses the shapes and orderings of the relationships as well as the variables. The cone information criterion (CIC) is used to select the best combination of variables and shapes. A genetic algorithm may be used when the set of possible models is large. In addition, the cgam routine implements a two-dimensional isotonic regression using warped-plane splines without additivity assumptions. It can also fit a convex or concave regression surface with triangle splines without additivity assumptions. See Liao X, Meyer MC (2019)<doi:10.18637/jss.v089.i05> for more details.

This package provides three estimators for tensor response regression (TRR) and tensor predictor regression (TPR) models with tensor envelope structure. The three types of estimation approaches are generic and can be applied to any envelope estimation problems. The full Grassmannian (FG) optimization is often associated with likelihood-based estimation but requires heavy computation and good initialization; the one-directional optimization approaches (1D and ECD algorithms) are faster, stable and does not require carefully chosen initial values; the SIMPLS-type is motivated by the partial least squares regression and is computationally the least expensive. For details of TRR, see Li L, Zhang X (2017) <doi:10.1080/01621459.2016.1193022>. For details of TPR, see Zhang X, Li L (2017) <doi:10.1080/00401706.2016.1272495>. For details of 1D algorithm, see Cook RD, Zhang X (2016) <doi:10.1080/10618600.2015.1029577>. For details of ECD algorithm, see Cook RD, Zhang X (2018) <doi:10.5705/ss.202016.0037>. For more details of the package, see Zeng J, Wang W, Zhang X (2021) <doi:10.18637/jss.v099.i12>.

Multidimensional scaling (MDS) methods that aim at pronouncing the clustered appearance of the configuration (Rusch, Mair & Hornik, 2021, <doi:10.1080/10618600.2020.1869027>). They achieve this by transforming proximities/distances with explicit power functions and penalizing the fitting criterion with a clusteredness index, the OPTICS Cordillera (Rusch, Hornik & Mair, 2018, <doi:10.1080/10618600.2017.1349664>). There are two variants: One for finding the configuration directly (COPS-C) with given explicit power transformations and implicit ratio, interval and non-metric optimal scaling transformations (Borg & Groenen, 2005, ISBN:978-0-387-28981-6), and one for using the augmented fitting criterion to find optimal hyperparameters for the explicit transformations (P-COPS). The package contains various functions, wrappers, methods and classes for fitting, plotting and displaying a large number of different MDS models (most of the functionality in smacofx) in the COPS framework. The package further contains a function for pattern search optimization, the ``Adaptive Luus-Jaakola Algorithm (Rusch, Mair & Hornik, 2021,<doi:10.1080/10618600.2020.1869027>) and a functions to calculate the phi-distances for count data or histograms.

Fits time-varying effect models (TVEM). These are a kind of application of varying-coefficient models in the context of longitudinal data, allowing the strength of linear, logistic, or Poisson regression relationships to change over time. These models are described further in Tan, Shiyko, Li, Li & Dierker (2012) <doi:10.1037/a0025814>. We thank Kaylee Litson, Patricia Berglund, Yajnaseni Chakraborti, and Hanjoo Kim for their valuable help with testing the package and the documentation. The development of this package was part of a research project supported by National Institutes of Health grants P50 DA039838 from the National Institute of Drug Abuse and 1R01 CA229542-01 from the National Cancer Institute and the NIH Office of Behavioral and Social Science Research. Content is solely the responsibility of the authors and does not necessarily represent the official views of the funding institutions mentioned above. This software is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

This package provides a multiple-testing procedure for high-dimensional mediation hypotheses. Mediation analysis is of rising interest in epidemiology and clinical trials. Among existing methods for mediation analyses, the popular joint significance (JS) test yields an overly conservative type I error rate and therefore low power. In the R package HDMT we implement a multiple-testing procedure that accurately controls the family-wise error rate (FWER) and the false discovery rate (FDR) when using JS for testing high-dimensional mediation hypotheses. The core of our procedure is based on estimating the proportions of three component null hypotheses and deriving the corresponding mixture distribution of null p-values. Results of the data examples include better-behaved quantile-quantile plots and improved detection of novel mediation relationships on the role of DNA methylation in genetic regulation of gene expression. With increasing interest in mediation by molecular intermediaries such as gene expression, the proposed method addresses an unmet methodological challenge. Methods used in the package refer to James Y. Dai, Janet L. Stanford & Michael LeBlanc (2020) <doi:10.1080/01621459.2020.1765785>.

Miscellaneous functions and data used in psychological research and teaching. Keng currently has a built-in dataset depress, and could (1) scale a vector; (2) divide a vector into three groups, (3) compute the cut-off values of Pearson's r with known sample size; (4) test the significance and compute the post-hoc power for Pearson's r with known sample size; (5) conduct a priori power analysis and plan the sample size for Pearson's r; (6) compare lm()'s fitted outputs using R-squared, f_squared, post-hoc power, and PRE (Proportional Reduction in Error, also called partial R-squared or partial Eta-squared); (7) calculate PRE from partial correlation, Cohen's f, or f_squared; (8) conduct a priori power analysis and plan the sample size for one or a set of predictors in regression analysis; (9) conduct post-hoc power analysis for one or a set of predictors in regression analysis with known sample size; (10) randomly pick numbers for Chinese Super Lotto and Double Color Balls; (11) assess course objective achievement in Outcome-Based Education.

This package implements the covariate balancing propensity score (CBPS) proposed by Imai and Ratkovic (2014) <DOI:10.1111/rssb.12027>. The propensity score is estimated such that it maximizes the resulting covariate balance as well as the prediction of treatment assignment. The method, therefore, avoids an iteration between model fitting and balance checking. The package also implements optimal CBPS from Fan et al. (in-press) <DOI:10.1080/07350015.2021.2002159>, several extensions of the CBPS beyond the cross-sectional, binary treatment setting. They include the CBPS for longitudinal settings so that it can be used in conjunction with marginal structural models from Imai and Ratkovic (2015) <DOI:10.1080/01621459.2014.956872>, treatments with three- and four-valued treatment variables, continuous-valued treatments from Fong, Hazlett, and Imai (2018) <DOI:10.1214/17-AOAS1101>, propensity score estimation with a large number of covariates from Ning, Peng, and Imai (2020) <DOI:10.1093/biomet/asaa020>, and the situation with multiple distinct binary treatments administered simultaneously. In the future it will be extended to other settings including the generalization of experimental and instrumental variable estimates.

Evaluates the probability density function, cumulative distribution function, quantile function, random numbers, survival function, hazard rate function, and maximum likelihood estimates for the following distributions: Bell exponential, Bell extended exponential, Bell Weibull, Bell extended Weibull, Bell-Fisk, Bell-Lomax, Bell Burr-XII, Bell Burr-X, complementary Bell exponential, complementary Bell extended exponential, complementary Bell Weibull, complementary Bell extended Weibull, complementary Bell-Fisk, complementary Bell-Lomax, complementary Bell Burr-XII and complementary Bell Burr-X distribution. Related work includes: a) Fayomi A., Tahir M. H., Algarni A., Imran M. and Jamal F. (2022). "A new useful exponential model with applications to quality control and actuarial data". Computational Intelligence and Neuroscience, 2022. <doi:10.1155/2022/2489998>. b) Alanzi, A. R., Imran M., Tahir M. H., Chesneau C., Jamal F. Shakoor S. and Sami, W. (2023). "Simulation analysis, properties and applications on a new Burr XII model based on the Bell-X functionalities". AIMS Mathematics, 8(3): 6970-7004. <doi:10.3934/math.2023352>. c) Algarni A. (2022). "Group Acceptance Sampling Plan Based on New Compounded Three-Parameter Weibull Model". Axioms, 11(9): 438. <doi:10.3390/axioms11090438>.

Determination of absolute protein quantities is necessary for multiple applications, such as mechanistic modeling of biological systems. Quantitative liquid chromatography tandem mass spectrometry (LC-MS/MS) proteomics can measure relative protein abundance on a system-wide scale. To estimate absolute quantitative information using these relative abundance measurements requires additional information such as heavy-labeled references of known concentration. Multiple methods have been using different references and strategies; some are easily available whereas others require more effort on the users end. Hence, we believe the field might benefit from making some of these methods available under an automated framework, which also facilitates validation of the chosen strategy. We have implemented the most commonly used absolute label-free protein abundance estimation methods for LC-MS/MS modes quantifying on either MS1-, MS2-levels or spectral counts together with validation algorithms to enable automated data analysis and error estimation. Specifically, we used Monte-carlo cross-validation and bootstrapping for model selection and imputation of proteome-wide absolute protein quantity estimation. Our open-source software is written in the statistical programming language R and validated and demonstrated on a synthetic sample.

Species Distribution Modeling (SDM) is a practical methodology that aims to estimate the area of distribution of a species. However, most of the work has focused on estimating static expressions of the correlation between environmental variables. The outputs of correlative species distribution models can be interpreted as maps of the suitable environment for a species but not generally as maps of its actual distribution. Soberón and Peterson (2005) <doi:10.17161/bi.v2i0.4> presented the BAM scheme, a heuristic framework that states that the occupied area of a species occurs on sites that have been accessible through dispersal (M) and have both favorable biotic (B) and abiotic conditions (A). The bamm package implements classes and functions to operate on each element of the BAM and by using a cellular automata model where the occupied area of a species at time t is estimated by the multiplication of three binary matrices: one matrix represents movements (M), another abiotic -niche- tolerances (A), and a third, biotic interactions (B). The theoretical background of the package can be found in Soberón and Osorio-Olvera (2023) <doi:10.1111/jbi.14587>.

This package provides functions that support estimating, assessing and mapping regional disaggregated indicators. So far, estimation methods comprise direct estimation, the model-based unit-level approach Empirical Best Prediction (see "Small area estimation of poverty indicators" by Molina and Rao (2010) <doi:10.1002/cjs.10051>), the area-level model (see "Estimates of income for small places: An application of James-Stein procedures to Census Data" by Fay and Herriot (1979) <doi:10.1080/01621459.1979.10482505>) and various extensions of it (adjusted variance estimation methods, log and arcsin transformation, spatial, robust and measurement error models), as well as their precision estimates. The assessment of the used model is supported by a summary and diagnostic plots. For a suitable presentation of estimates, map plots can be easily created. Furthermore, results can easily be exported to excel. For a detailed description of the package and the methods used see "The R Package emdi for Estimating and Mapping Regionally Disaggregated Indicators" by Kreutzmann et al. (2019) <doi:10.18637/jss.v091.i07> and the second package vignette "A Framework for Producing Small Area Estimates Based on Area-Level Models in R".

Bundles functions used to analyze the harmfulness of trial errors in criminal trials. Functions in the Scientific Analysis of Trial Errors ('sate') package help users estimate the probability that a jury will find a defendant guilty given jurors preferences for a guilty verdict and the uncertainty of that estimate. Users can also compare actual and hypothetical trial conditions to conduct harmful error analysis. The conceptual framework is discussed by Barry Edwards, A Scientific Framework for Analyzing the Harmfulness of Trial Errors, UCLA Criminal Justice Law Review (2024) <doi:10.5070/CJ88164341> and Barry Edwards, If The Jury Only Knew: The Effect Of Omitted Mitigation Evidence On The Probability Of A Death Sentence, Virginia Journal of Social Policy & the Law (2025) <https://vasocialpolicy.org/wp-content/uploads/2025/05/Edwards-If-The-Jury-Only-Knew.pdf>. The relationship between individual jurors verdict preferences and the probability that a jury returns a guilty verdict has been studied by Davis (1973) <doi:10.1037/h0033951>; MacCoun & Kerr (1988) <doi:10.1037/0022-3514.54.1.21>, and Devine et el. (2001) <doi:10.1037/1076-8971.7.3.622>, among others.

Supporting functionality to run caret with spatial or spatial-temporal data. caret is a frequently used package for model training and prediction using machine learning. CAST includes functions to improve spatial or spatial-temporal modelling tasks using caret'. It includes the newly suggested Nearest neighbor distance matching cross-validation to estimate the performance of spatial prediction models and allows for spatial variable selection to selects suitable predictor variables in view to their contribution to the spatial model performance. CAST further includes functionality to estimate the (spatial) area of applicability of prediction models. Methods are described in Meyer et al. (2018) <doi:10.1016/j.envsoft.2017.12.001>; Meyer et al. (2019) <doi:10.1016/j.ecolmodel.2019.108815>; Meyer and Pebesma (2021) <doi:10.1111/2041-210X.13650>; Milà et al. (2022) <doi:10.1111/2041-210X.13851>; Meyer and Pebesma (2022) <doi:10.1038/s41467-022-29838-9>; Linnenbrink et al. (2024) <doi:10.5194/gmd-17-5897-2024>; Schumacher et al. (2025) <doi:10.5194/gmd-18-10185-2025>. The package is described in detail in Meyer et al. (2026) <doi:10.1007/978-3-031-99665-8_11>.

In practice, it is difficult to determine the number of decomposition modes, K, for Variational Mode Decomposition (VMD). To overcome this issue, this study offers Spearman Variational Mode Decomposition (SVMD), a method that uses the Spearman correlation coefficient to calculate the ideal mode number. Unlike the Pearson correlation coefficient, which only returns a perfect value when X and Y are linearly connected, the Spearman correlation can be calculated without knowing the probability distributions of X and Y. The Spearman correlation coefficient, also called Spearman's rank correlation coefficient, is a subset of a wider correlation coefficient. As VMD decomposes a signal, the Spearman correlation coefficient between the reconstructed and original sequences rises as the mode number K increases. Once the signal has been fully decomposed, subsequent increases in K cause the correlation to gradually level off. When the correlation reaches a specific level, VMD is said to have adequately decomposed the signal. Numerous experiments revealed that a threshold of 0.997 produces the best denoising effect, so the threshold is set at 0.997. This package has been developed using concept of Yang et al. (2021)<doi:10.1016/j.aej.2021.01.055>.

This package provides functions to implement the methods of the Flood Estimation Handbook (FEH), associated updates and the revitalised flood hydrograph model (ReFH). Currently the package uses NRFA peak flow dataset version 14. Aside from FEH functionality, further hydrological functions are available. Most of the methods implemented in this package are described in one or more of the following: "Flood Estimation Handbook", Centre for Ecology & Hydrology (1999, ISBN:0 948540 94 X). "Flood Estimation Handbook Supplementary Report No. 1", Kjeldsen (2007, ISBN:0 903741 15 7). "Regional Frequency Analysis - an approach based on L-moments", Hosking & Wallis (1997, ISBN: 978 0 521 01940 8). "Making better use of local data in flood frequency estimation", Environment Agency (2017, ISBN: 978 1 84911 387 8). "Sampling uncertainty of UK design flood estimation" , Hammond (2021, <doi:10.2166/nh.2021.059>). "The FEH 2025 statistical method update", UK Centre for Ecology and Hydrology (2025). "Low flow estimation in the United Kingdom", Institute of Hydrology (1992, ISBN 0 948540 45 1). Data from the UK National River Flow Archive (<https://nrfa.ceh.ac.uk/>, terms and conditions: <https://nrfa.ceh.ac.uk/help/costs-terms-and-conditions>).

Abstract of Manuscript. Differential gene expression analysis using RNA sequencing (RNA-seq) data is a standard approach for making biological discoveries. Ongoing large-scale efforts to process and normalize publicly available gene expression data enable rapid and systematic reanalysis. While several powerful tools systematically process RNA-seq data, enabling their reanalysis, few resources systematically recompute differentially expressed genes (DEGs) generated from individual studies. We developed a robust differential expression analysis pipeline to recompute 3162 human DEG lists from The Cancer Genome Atlas, Genotype-Tissue Expression Consortium, and 142 studies within the Sequence Read Archive. After measuring the accuracy of the recomputed DEG lists, we built the Differential Expression Enrichment Tool (DEET), which enables users to interact with the recomputed DEG lists. DEET, available through CRAN and RShiny, systematically queries which of the recomputed DEG lists share similar genes, pathways, and TF targets to their own gene lists. DEET identifies relevant studies based on shared results with the userâ s gene lists, aiding in hypothesis generation and data-driven literature review. Sokolowski, Dustin J., et al. "Differential Expression Enrichment Tool (DEET): an interactive atlas of human differential gene expression." Nucleic Acids Research Genomics and Bioinformatics (2023).

R implementation of Quantile Data Envelopment Analysis. The package qDEA allows a user specified proportion of observations to lie external to a given Decision Making Units's (DMU's)reference hyperplane. qDEA can be used to detect and address influential outliers or to implement quantile benchmarking, as discussed in Atwood and Shaik (2020). Quantile benchmarking is accomplished by using heuristic procedures to find a DMU's closest input-output projection point in a specified direction while allowing a specified proportion of observations to lie external to the projected point's hyperplane. The qDEA package accommodates standard (DEA) and quantile DEA estimation, returns to scale CRS(constant),VRS(variable),DRS(decreasing) or IRS(increasing), the use of directional vectors, bias correction through subsample bootstrapping and subsample size selection procedures. The user can also recover each DMU's reference DMUs and external DMUs if desired. The implemented procedures are based on discussions in: Atwood and Shaik (2020) <doi:10.1016/j.ejor.2020.03.054> Atwood and Shaik (2018) <doi:10.1007/978-3-319-68678-3_4> Walden and Atwood (2023) <doi:10.1086/724932> Walden and Atwood (2025) <doi:10.1086/736554>.

Implementation of a scalable, highly configurable, and e(x)tended architecture for (e)volutionary and (g)enetic (a)lgorithms. Multiple representations (binary, real-coded, permutation, and derivation-tree), a rich collection of genetic operators, as well as an extended processing pipeline are provided for genetic algorithms (Goldberg, D. E. (1989, ISBN:0-201-15767-5)), differential evolution (Price, Kenneth V., Storn, Rainer M. and Lampinen, Jouni A. (2005) <doi:10.1007/3-540-31306-0>), simulated annealing (Aarts, E., and Korst, J. (1989, ISBN:0-471-92146-7)), grammar-based genetic programming (Geyer-Schulz (1997, ISBN:978-3-7908-0830-X)), grammatical evolution (Ryan, C., O'Neill, M., and Collins, J. J. (2018) <doi:10.1007/978-3-319-78717-6>), and grammatical differential evolution (O'Neill, M. and Brabazon, A. (2006) in Arabinia, H. (2006, ISBN:978-193-241596-3). All algorithms reuse basic adaptive mechanisms for performance optimization. For xega''s architecture, see Geyer-Schulz, A. (2025) <doi:10.5445/IR/1000187255>. Sequential or parallel execution (on multi-core machines, local clusters, and high-performance computing environments) is available for all algorithms. See <https://github.com/ageyerschulz/xega/tree/main/examples/executionModel>.