First, an ordinal representation scheme for permutations is defined. Next, an “unranking” algorithm that can generate a permutation of n items according to its ordinal representation is designed. By using this algorithm, all permutations can be systematically generated in lexicographic order. Finally, a “ranking” algorithm that can convert a permutation to its ordinal representation is designed...

The coin package implements a unified approach for conditional inference procedures commonly known as permutation tests. The theoretical basis of design and implementation is the unified framework for permutation tests given by Strasser and Weber (1999). For a very flexible formulation of multivariate linear statistics, Strasser and Weber (1999) derived the conditional expectation and covarianc...

7 We propose a novel, efficient approach for obtaining high-quality experimental designs for 8 event-related functional magnetic resonance imaging (ER-fMRI). Our approach combines a 9 greedy hillclimbing algorithm and a cyclic permutation method. When searching for optimal 10 ER-fMRI designs, the proposed approach focuses only on a promising restricted class of 11 designs with equal frequency o...

By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. Thus every permutation matrix over C is a quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a fai...

MOTIVATION Permutation testing is very popular for analyzing microarray data to identify differentially expressed (DE) genes; estimating false discovery rates (FDRs) is a very popular way to address the inherent multiple testing problem. However, combining these approaches may be problematic when sample sizes are unequal. RESULTS With unbalanced data, permutation tests may not be suitable bec...

Several permutation strategies are often possible for tests of individual terms in analysis-of-variance (ANOVA) designs. These include restricted permutations, permutation of whole groups of units, permutation of some form of residuals or some combination of these. It is unclear, especially for complex designs involving random factors, mixed models or nested hierarchies, just which permutation ...

In this paper, we present a new blockwise permutation test approach based on the moments of the test statistic. The method is of importance to neuroimaging studies. In order to preserve the exchangeability condition required in permutation tests, we divide the entire set of data into certain exchangeability blocks. In addition, computationally efficient moments-based permutation tests are perfo...

This paper deals with the approach of using multiscale permutation entropy as a tool for feature selection for fault diagnosis in ball bearings. The coefficients obtained from the wavelet transformation of the vibration signals of the bearings are used for the calculation of statistical parameters. Based on the minimum multiscale permutation entropy criteria, the best scale is selected and stat...

We develop the technique of reduced word manipulation to give a range of results concerning reduced words and permutations more generally. We prove a broad connection between pattern containment and reduced words, which specializes to our previous work for vexillary permutations. We also analyze general tilings of Elnitsky’s polygon, and demonstrate that these are closely related to the pattern...