* Lyapunov Exponents and Kaplan-Yorke Dimension* (

**GPoM.FDLyapu**)

Estimation of the spectrum of Lyapunov Exponents and the Kaplan-Yorke dimension of any low-dimensional model of polynomial form. It can be applied, for example, to systems such as the chaotic Lorenz-1963 system or the hyperchaotic Rossler-1979 system. It can also be applied to dynamical models in Ordinary Differential Equations (ODEs) directly obtained from observational time series using the ‘GPoM’ package. The approach used is semi-formal, the Jacobian matrix being estimated automatically from the polynomial equations. Two methods are made available; one introduced by Wolf et al. (1985) <doi:10.1016/0167-2789(85)90011-9> and the other one introduced by Grond et al. (2003) <doi:10.1016/S0960-0779(02)00479-4>. The package is provided with an interface for a more intuitive usage, it can also be run without the interface. This platform is developed at the Centre d’Etudes Spatiales de la Biosphere (CESBIO), UMR 5126 UPS/CNRS/CNES/IRD, 18 av. Edouard Belin, 31401 TOULOUSE, FRANCE. The developments were funded by the French program Les Enveloppes Fluides et l’Environnement (LEFE, MANU, projects GloMo, SpatioGloMo and MoMu). The French programs Defi InFiNiTi (CNRS) and PNTS (CNRS) are also acknowledged (projects Crops’I Chaos and Musc & SlowFast).

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**Logistic Bayesian Lasso for Rare (or Common) Haplotype Association****LBLGXE**)

This function takes a dataset of haplotypes and environmental covariates with one binary phenotype in which rows for individuals of uncertain phase have been augmented by ‘pseudo-individuals’ who carry the possible multilocus genotypes consistent with the single-locus phenotypes. Bayesian lasso is used to find the posterior distributions of logistic regression coefficients, which are then used to calculate Bayes Factor and credible set to test for association with haplotypes, environmental covariates and interactions. The model can handle complex sampling data, in particular, frequency matched cases and controls with controls obtained using stratified sampling. This version can also be applied to a dataset with no environmental covariate and two correlated binary phenotypes.

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**Testing for Symmetry of Data and Model Residuals****symmetry**)

Implementations of a large number of tests for symmetry and their bootstrap variants, which can be used for testing the symmetry of random samples around a known or unknown mean. Functions are also there for testing the symmetry of model residuals around zero. Currently, the supported models are linear models and generalized autoregressive conditional heteroskedasticity (GARCH) models (fitted with the ‘fGarch’ package). All tests are implemented using the ‘Rcpp’ package which ensures great performance of the code.

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**Pin, Discover and Share Resources****pins**)

Pin remote resources into a local cache to work offline, improve speed and avoid recomputing; discover and share resources with others in ‘GitHub’, ‘Kaggle’ or ‘RStudio Connect’. Resources can be anything from ‘CSV’, ‘JSON’, or image files to arbitrary R objects.