We evaluate four association tests for rare variants-the combined multivariate and collapsing (CMC) method, two weighted-sum methods, and a variable threshold method-by applying them to the simulated data sets of unrelated individuals in the Genetic Analysis Workshop 17 (GAW17) data. The family-wise error rate (FWER) and average power are used as criteria for evaluation. Our results show that w...

Inspired by work of McKay, Morse, and Wilf, we give an exact count of the involutions in Sn which contain a given permutation τ ∈ Sk as a subsequence; this number depends on the patterns of the first j values of τ for 1 ≤ j ≤ k. We then use this to define a partition of Sk, analogous to Wilf-classes in the study of pattern avoidance, and examine properties of this equivalence. In the process, w...

Sorting by reversals is an important problem in inferring the evolutionary relationship between two genomes. The problem of sorting unsigned permutation has been proven to be NP-hard. The best guaranteed error bounded is the 3/2approximation algorithm. However, the problem of sorting signed permutation can be solved easily. Fast algorithms have been developed both for finding the sorting sequen...

Let W ( ) be either the number of descents or inversions of a permutation 2 Sn. Stein's method is applied to bound the sup-norm distance between the distribution of W and the standard normal distribution. This appears to be the rst use of Stein's method in theory of permutation statistics. The construction of an exchangeable pair (W;W 0) used in Stein's method is non-trivial and may be of indep...

In this paper, we analyze a knapsack schemes. The one is suggested by Su, which is relied on a new method entitled permutation combination method. We demonstrate that this permutation method is useless to the security of the scheme. Since the special super increasing construction, we can break this scheme employ the algorithm provided by Shamir scheme. Finally, we provide an enhanced version of...

An alternative permutation decoding method is described which can be used for any binary systematic encoding scheme, regardless whether the code is linear or not. Thus, the method can be applied to some important codes such as Z2Z4-linear codes, which are binary and, in general, nonlinear codes in the usual sense. For this, it is proved that these codes allow a systematic encoding scheme. As pa...

Invented in the 1960’s, permutation codes have reemerged in recent years as a topic of great interest because of properties making them attractive for certain modern technological applications. In 2011 a decoding method called LP (linear programming) decoding was introduced for a class of permutation codes with a Euclidean distance induced metric. In this paper we comparatively analyze the Eucl...

This paper proposes a cooperative games model for the permutation flow shop scheduling problem (PFSP) with multiple customer tasks. Here, customers create alliances through cooperation in case of delayed and early delivery penalty constraints, tasks alliance are rescheduled to seek maximum cost savings. A new <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www...

This paper deals with the amount of disorder that is left in a permutation after one of its elements has been selected with quickselect with or without median-of-three pivoting. Five measures of disorder are considered: inversions, cycles of length less than or equal to some m, cycles of any length, expected cycle length, and the distance to the identity permutation. “Grand averages” for each m...