The human microbiota composition is associated with a number of diseases including obesity, inflammatory bowel disease, and bacterial vaginosis. Thus, microbiome research has the potential to reshape clinical and therapeutic approaches. However, raw microbiome count data require careful pre-processing steps that take into account both the sparsity of counts and the large number of taxa that are being measured. Filtering is defined as removing taxa that are present in a small number of samples and have small counts in the samples where they are observed. Despite progress in the number and quality of filtering approaches, there is no consensus on filtering standards and quality assessment. This can adversely affect downstream analyses and reproducibility of results across platforms and software. We introduce PERFect, a novel permutation filtering approach designed to address two unsolved problems in microbiome data processing: (i) define and quantify loss due to filtering by implementing thresholds and (ii) introduce and evaluate a permutation test for filtering loss to provide a measure of excessive filtering. Methods are assessed on three "mock experiment" data sets, where the true taxa compositions are known, and are applied to two publicly available real microbiome data sets. The method correctly removes contaminant taxa in "mock" data sets, quantifies and visualizes the corresponding filtering loss, providing a uniform data-driven filtering criteria for real microbiome data sets. In real data analyses PERFect tends to remove more taxa than existing approaches; this likely happens because the method is based on an explicit loss function, uses statistically principled testing, and takes into account correlation between taxa. The PERFect software is freely available at https://github.com/katiasmirn/PERFect.

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Development of methods to design optimal Gough-Stewart platform geometries capable of meeting desired specifications is of high interest. Computationally intensive methods have been used to treat this problem in various settings. This paper uses analytic methods to characterize all orthogonal Gough-Stewart platforms (OGSPs) and to study their properties over a small workspace. This characterization is used to design optimal OGSPs for precision applications that achieve a desired hyperellipsoid of velocities. Some examples demonstrating the versatility of this theory are discussed.

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