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...

We investigate the relative computational powers of a mesh with static buses and a mesh with half-duplex wrap-arounds. The latter model is like a torus, except that any wrap-around link of the architecture can only transmit data in one of the two directions at any clock tick. We show that the permutation routing problem can be solved as efficiently on a linear array augmented with a half-duplex...

In this paper we demonstrate the power of reconfiguration by presenting efficient randomized algorithms for both packet routing and sorting on a reconfigurable mesh connected computer. The run times of these algorithms are better than the best achievable time bounds on a conventional mesh. Many variations of the reconfigurable mesh can be found in the literature. We define yet another variation...

MOTIVATION Array CGH technologies enable the simultaneous measurement of DNA copy number for thousands of sites on a genome. We developed the circular binary segmentation (CBS) algorithm to divide the genome into regions of equal copy number. The algorithm tests for change-points using a maximal t-statistic with a permutation reference distribution to obtain the corresponding P-value. The numbe...

MOTIVATION A gene set test is a differential expression analysis in which a P-value is assigned to a set of genes as a unit. Gene set tests are valuable for increasing statistical power, organizing and interpreting results and for relating expression patterns across different experiments. Existing methods are based on permutation. Methods that rely on permutation of probes unrealistically assum...

Fulton introduced the essential set of a permutation, together with a rank function. In this paper we study some combinatorial aspects of the essential set: We present an algorithm that retrieves a permutation from its ranked essential set. Thereby we can characterize the class of ranked sets that arise as ranked essential sets of permutations, answering a question of Fulton. Several classes of...

this paper presents a new audio encryption algorithm based on permutation and residue number system. in the current approach, signal samples are combined with residue number system through permutation; therefore, a specific noise is generated. then, the audio signal is combined with the noise, generated by the algorithm, to produce a silence signal. for this purpose, the algorithm uses a predef...

A permutation class is splittable if it is contained in the merge of two of its proper subclasses. We characterise the unsplittable subclasses of the class of separable permutations both structurally and in terms of their bases.

Ready access to emerging databases of gene annotation and functional pathways has shifted assessments of differential expression in DNA microarray studies from single genes to groups of genes with shared biological function. This paper takes a critical look at existing methods for assessing the differential expression of a group of genes (functional category), and provides some suggestions for ...