Related papers: Permutation patterns in genome rearrangement probl…

A consecutive pattern in a permutation $\pi$ is another permutation $\sigma$ determined by the relative order of a subsequence of contiguous entries of $\pi$. Traditional notions such as descents, runs and peaks can be viewed as particular…

Genomic data sets are growing dramatically as the cost of sequencing continues to decline and small sequencing devices become available. Enormous community databases store and share this data with the research community, but some of these…

Let $\pi=(\pi_1,\pi_2,\hdots,\pi_n)$ be permutation of the elements $1,2,\hdots,n. $ Positive integer $k\leq2^{n-1}$ we call index of $\pi,$ if in its binary notation as $n$-digital binary number, the 1's correspond to the ascent points. We…

We study two related probabilistic models of permutations and trees biased by their number of descents. Here, a descent in a permutation $\sigma$ is a pair of consecutive elements $\sigma(i), \sigma(i+1)$ such that $\sigma(i) >…

A sequence of reversals that takes a signed permutation to the identity is perfect if at no step a common interval is broken. Determining a parsimonious perfect sequence of reversals that sorts a signed permutation is NP-hard. Here we show…

A wide range of applications and research has been done with genome-scale metabolic models. In this work we describe a methodology for comparing metabolic networks constructed from genome-scale metabolic models and how to apply this…

The problem of reconstructing strings from substring information has found many applications due to its importance in genomic data sequencing and DNA- and polymer-based data storage. One practically important and challenging paradigm…

Skewed probit regression is but one example of a statistical model that generalizes a simpler model, like probit regression. All skew-symmetric distributions and link functions arise from symmetric distributions by incorporating a skewness…

In the mixture models problem it is assumed that there are $K$ distributions $\theta_{1},\ldots,\theta_{K}$ and one gets to observe a sample from a mixture of these distributions with unknown coefficients. The goal is to associate instances…

The dynamics of recombination in genetics leads to an interesting nonlinear differential equation, which has a natural generalization to a measure valued version. The latter can be solved explicitly under rather general circumstances. It…

Finding the minimum distance of linear codes is an NP-hard problem. Traditionally, this computation has been addressed by means of the design of algorithms that find, by a clever exhaustive search, a linear combination of some generating…

In this paper, we study the occurrence of patterns in the cycle structures of permutations.

In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions.…

A central theme in phylogenetics is the reconstruction and analysis of evolutionary trees from a given set of data. To determine the optimal search methods for reconstructing trees, it is crucial to understand the size and structure of the…

Billey, Jockusch, and Stanley characterized 321-avoiding permutations by a property of their reduced decompositions. This paper generalizes that result with a detailed study of permutations via their reduced decompositions and the notion of…

During evolution of microorganisms genomes underwork have different changes in their lengths, gene orders, and gene contents. Investigating these structural rearrangements helps to understand how genomes have been modified over time. Some…

We study the expansions of permutation statistics in the basis of functions counting occurrences of a fixed pattern in a permutation. We show the finiteness of these pattern expansions for a class of permutation statistics including the…

Permutation resemblance measures the distance of a function from being a permutation. Here we show how to determine the permutation resemblance through linear integer programming techniques. We also present an algorithm for constructing…

We address the problem of filling missing entries in a kernel Gram matrix, given a related full Gram matrix. We attack this problem from the viewpoint of regression, assuming that the two kernel matrices can be considered as explanatory…

Gene and protein networks are very important to model complex large-scale systems in molecular biology. Inferring or reverseengineering such networks can be defined as the process of identifying gene/protein interactions from experimental…