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- Murray Patterson, Yongmei Liu, Eugenia Ternovska, Arvind Gupta
- IJCAI
- 2007

Mitchell and Ternovska [49, 50] propose a constraint programming framework for search problems that is based on classical logic extended with inductive definitions. They formulate a search problem as the problem of model expansion (MX). In this framework, the problem is encoded in a logic, an instance of the problem is represented by a finite structure, and… (More)

- Ján Manuch, Murray Patterson, Roland Wittler, Cédric Chauve, Eric Tannier
- BMC Bioinformatics
- 2012

Recovering the structure of ancestral genomes can be formalized in terms of properties of binary matrices such as the Consecutive-Ones Property (C1P). The Linearization Problem asks to extract, from a given binary matrix, a maximum weight subset of rows that satisfies such a property. This problem is in general intractable, and in particular if the… (More)

- Roland Wittler, Ján Manuch, Murray Patterson, Jens Stoye
- Journal of Computational Biology
- 2010

In comparative genomics, differences or similarities of gene orders are determined to predict functional relations of genes or phylogenetic relations of genomes. For this purpose, various combinatorial models can be used to specify gene clusters--groups of genes that are co-located in a set of genomes. Several approaches have been proposed to reconstruct… (More)

- Murray Patterson, Tobias Marschall, +4 authors Alexander Schönhuth
- RECOMB
- 2014

- Cédric Chauve, Ján Manuch, Murray Patterson
- Electronic Notes in Discrete Mathematics
- 2009

Motivated by problems of comparative genomics and paleogenomics, we introduce the Gapped Consecutive-Ones Property Problem (k,δ)-C1P: given a binary matrix M and two integers k and δ, can the columns of M be permuted such that each row contains at most k sequences of 1's and no two consecutive sequences of 1's are separated by a gap of more than δ 0's. The… (More)

- Nigel Jollands, Jonathan Lermit, Murray Patterson
- 2003

Aggregate indices can assist decision-making by summarising a complex array of information. However, little research has been conducted on aggregate environmental indicators. The purpose of this paper is to address the debate surrounding aggregate environmental indices. In doing so, the paper highlights the strengths and weaknesses of aggregate indices for… (More)

A binary matrix has the Consecutive-Ones Property (C1P) if its columns can be ordered in such a way that all 1's in each row are consecutive. We consider here a variant of the C1P where columns can appear multiple times in the ordering. Although the general problem of deciding the C1P with multiplicity is NP-complete, we present here a case of interest in… (More)

- Murray Patterson, Tobias Marschall, +4 authors Alexander Schönhuth
- Journal of Computational Biology
- 2015

The human genome is diploid, which requires assigning heterozygous single nucleotide polymorphisms (SNPs) to the two copies of the genome. The resulting haplotypes, lists of SNPs belonging to each copy, are crucial for downstream analyses in population genetics. Currently, statistical approaches, which are oblivious to direct read information, constitute… (More)

- Murray Patterson, Gergely J. Szöllosi, Vincent Daubin, Eric Tannier
- BMC Bioinformatics
- 2013

Models of ancestral gene order reconstruction have progressively integrated different evolutionary patterns and processes such as unequal gene content, gene duplications, and implicitly sequence evolution via reconciled gene trees. These models have so far ignored lateral gene transfer, even though in unicellular organisms it can have an important… (More)

- Cédric Chauve, Murray Patterson, Ashok Rajaraman
- IWOCA
- 2013

The Consecutive-Ones Property (C1P) is a classical concept in discrete mathematics that has been used in several genomics applications , from physical mapping of contemporary genomes to the assembly of ancient genomes. A common issue in genome assembly concerns repeats , genomic sequences that appear in several locations of a genome. Handling repeats leads… (More)