Many papers on parallel random permutation algorithms assume the input size n to be a power of two and imply that these algorithms can be easily generalized to arbitrary n, e.g., by padding the input array to a power of two. We show that this simplifying assumption is not necessarily correct since it may result in a bias (i.e., not all possible permutations are generated with equal likelihood)....

Several approximate permutation tests have been proposed for tests of partial regression coefficients in a linear model based on sample partial correlations. This paper begins with an explanation and notation for an exact test. It then compares the distributions of the test statistics under the various permutation methods proposed, and shows that the partial correlations under permutation are a...

The present paper deals with permutations induced by tame automorphisms over finite fields. The first main result is a formula for determining the sign of the permutation induced by a given elementary automorphism over a finite field. The second main result is a formula for determining the sign of the permutation induced by a given affine automorphism over a finite field. We also give a combini...

BACKGROUND AND PURPOSE Developing improved methods for analysis of the modified Rankin Scale (mRS) remains a critical issue for the stroke research community. A recently proposed permutation-based approach is assumption-free and easily interpretable but computationally intensive and does not provide confidence intervals to quantify the precision of the effect size estimate. We aimed to develop ...

Statistical parametric mapping (SPM) analysis of fMRI data requires specifying correctly the temporal and spatial noise covariance structure. This is a difficult if not impossible task. When these assumptions are not satisfied, statistical inference can be invalid or inefficient. Permutation tests are free of strong assumptions on the distribution of signal noise. We propose permutation tests o...

Assessing genome-wide statistical significance is an important and difficult problem in multipoint linkage analysis. Due to multiple tests on the same genome, the usual pointwise significance level based on the chi-square approximation is inappropriate. Permutation is widely used to determine genome-wide significance. Theoretical approximations are available for simple experimental crosses. In ...

This paper presents an efficient block-wise image encryption method based on multiple chaotic maps. The image is divided into four overlapping blocks and each block is permutated with Cat map and its parameters are controlled by Henon map using multiple keys. Due to overlapping division of blocks, it produces effect of double permutation in the middle portion of overlapped image in single permu...

Frequency domain independent component analysis has a scaling indeterminacy and a permutation problem. The scaling indeterminacy can be solved by use of a decomposed spectrum. For the permutation problem, we have proposed the rules in terms of gain ratio and phase difference derived from the decomposed spectra and the source’s coarse directions. The present paper experimentally clarifies that t...

Many papers on parallel random permutation algorithms assume the input size n to be a power of two and imply that these algorithms can be easily generalized to arbitrary n. We show that this simplifying assumption is not necessarily correct since it may result in a bias. Many of these algorithms are, however, consistent, i.e., iterating them ultimately converges against an unbiased permutation....

Normal approximations for descents and inversions of permutations of the set {1, 2, . . . , n} are well known. We consider the number of inversions of a permutation π(1), π(2), . . . , π(n) of a multiset with n elements, which is the number of pairs (i, j) with 1 ≤ i < j ≤ n and π(i) > π(j). The number of descents is the number of i in the range 1 ≤ i < n such that π(i) > π(i + 1). We prove tha...