Reconstruction of permutations distorted by single transposition errors

The reconstruction problem for permutations on $n$ elements from their erroneous patterns which are distorted by transpositions is presented in this paper. It is shown that for any $n \geq 3$ an unknown permutation is uniquely reconstructible from 4 distinct permutations at transposition distance at most one from the unknown permutation. The {\it transposition distance} between two permutations is defined as the least number of transpositions needed to transform one into the other. The proposed approach is based on the investigation of structural properties of a corresponding Cayley graph. In the case of at most two transposition errors it is shown that $\frac32(n-2)(n+1)$ erroneous patterns are required in order to reconstruct an unknown permutation. Similar results are obtained for two particular cases when permutations are distorted by given transpositions. These results confirm some bounds for regular graphs which are also presented in this paper.Comment: 5 pages, Report of paper presented at ISIT-200

Reconstruction Codes for DNA Sequences with Uniform Tandem-Duplication Errors

DNA as a data storage medium has several advantages, including far greater data density compared to electronic media. We propose that schemes for data storage in the DNA of living organisms may benefit from studying the reconstruction problem, which is applicable whenever multiple reads of noisy data are available. This strategy is uniquely suited to the medium, which inherently replicates stored data in multiple distinct ways, caused by mutations. We consider noise introduced solely by uniform tandem-duplication, and utilize the relation to constant-weight integer codes in the Manhattan metric. By bounding the intersection of the cross-polytope with hyperplanes, we prove the existence of reconstruction codes with greater capacity than known error-correcting codes, which we can determine analytically for any set of parameters.Comment: 11 pages, 2 figures, Latex; version accepted for publicatio

Gene order rearrangement methods for the reconstruction of phylogeny

The study of phylogeny, i.e. the evolutionary history of species, is a central problem in biology and a key for understanding characteristics of contemporary species. Many problems in this area can be formulated as combinatorial optimisation problems which makes it particularly interesting for computer scientists. The reconstruction of the phylogeny of species can be based on various kinds of data, e.g. morphological properties or characteristics of the genetic information of the species. Maximum parsimony is a popular and widely used method for phylogenetic reconstruction aiming for an explanation of the observed data requiring the least evolutionary changes. A certain property of the genetic information gained much interest for the reconstruction of phylogeny in recent time: the organisation of the genomes of species, i.e. the arrangement of the genes on the chromosomes. But the idea to reconstruct phylogenetic information from gene arrangements has a long history. In Dobzhansky and Sturtevant (1938) it was already pointed out that “a comparison of the different gene arrangements in the same chromosome may, in certain cases, throw light on the historical relationships of these structures, and consequently on the history of the species as a whole”. This kind of data is promising for the study of deep evolutionary relationships because gene arrangements are believed to evolve slowly (Rokas and Holland, 2000). This seems to be the case especially for mitochondrial genomes which are available for a wide range of species (Boore, 1999). The development of methods for the reconstruction of phylogeny from gene arrangement data has made considerable progress during the last years. Prominent examples are the computation of parsimonious evolutionary scenarios, i.e. a shortest sequence of rearrangements transforming one arrangement of genes into another or the length of such a minimal scenario (Hannenhalli and Pevzner, 1995b; Sankoff, 1992; Watterson et al., 1982); the reconstruction of parsimonious phylogenetic trees from gene arrangement data (Bader et al., 2008; Bernt et al., 2007b; Bourque and Pevzner, 2002; Moret et al., 2002a); or the computation of the similarities of gene arrangements (Bergeron et al., 2008a; Heber et al., 2009). 1 1 Introduction The central theme of this work is to provide efficient algorithms for modified versions of fundamental genome rearrangement problems using more plausible rearrangement models. Two types of modified rearrangement models are explored. The first type is to restrict the set of allowed rearrangements as follows. It can be observed that certain groups of genes are preserved during evolution. This may be caused by functional constraints which prevented the destruction (Lathe et al., 2000; Sémon and Duret, 2006; Xie et al., 2003), certain properties of the rearrangements which shaped the gene orders (Eisen et al., 2000; Sankoff, 2002; Tillier and Collins, 2000), or just because no destructive rearrangement happened since the speciation of the gene orders. It can be assumed that gene groups, found in all studied gene orders, are not acquired independently. Accordingly, these gene groups should be preserved in plausible reconstructions of the course of evolution, in particular the gene groups should be present in the reconstructed putative ancestral gene orders. This can be achieved by restricting the set of rearrangements, which are allowed for the reconstruction, to those which preserve the gene groups of the given gene orders. Since it is difficult to determine functionally what a gene group is, it has been proposed to consider common combinatorial structures of the gene orders as gene groups (Marcotte et al., 1999; Overbeek et al., 1999). The second considered modification of the rearrangement model is extending the set of allowed rearrangement types. Different types of rearrangement operations have shuffled the gene orders during evolution. It should be attempted to use the same set of rearrangement operations for the reconstruction otherwise distorted or even wrong phylogenetic conclusions may be obtained in the worst case. Both possibilities have been considered for certain rearrangement problems before. Restricted sets of allowed rearrangements have been used successfully for the computation of parsimonious rearrangement scenarios consisting of inversions only where the gene groups are identified as common intervals (Bérard et al., 2007; Figeac and Varré, 2004). Extending the set of allowed rearrangement operations is a delicate task. On the one hand it is unknown which rearrangements have to be regarded because this is part of the phylogeny to be discovered. On the other hand, efficient exact rearrangement methods including several operations are still rare, in particular when transpositions should be included. For example, the problem to compute shortest rearrangement scenarios including transpositions is still of unknown computational complexity. Currently, only efficient approximation algorithms are known (e.g. Bader and Ohlebusch, 2007; Elias and Hartman, 2006). Two problems have been studied with respect to one or even both of these possibilities in the scope of this work. The first one is the inversion median problem. Given the gene orders of some taxa, this problem asks for potential ancestral gene orders such that the corresponding inversion scenario is parsimonious, i.e. has a minimum length. Solving this problem is an essential component 2 of algorithms for computing phylogenetic trees from gene arrangements (Bourque and Pevzner, 2002; Moret et al., 2002a, 2001). The unconstrained inversion median problem is NP-hard (Caprara, 2003). In Chapter 3 the inversion median problem is studied under the additional constraint to preserve gene groups of the input gene orders. Common intervals, i.e. sets of genes that appear consecutively in the gene orders, are used for modelling gene groups. The problem of finding such ancestral gene orders is called the preserving inversion median problem. Already the problem of finding a shortest inversion scenario for two gene orders is NP-hard (Figeac and Varré, 2004). Mitochondrial gene orders are a rich source for phylogenetic investigations because they are known for more than 1 000 species. Four rearrangement operations are reported at least in the literature to be relevant for the study of mitochondrial gene order evolution (Boore, 1999): That is inversions, transpositions, inverse transpositions, and tandem duplication random loss (TDRL). Efficient methods for a plausible reconstruction of genome rearrangements for mitochondrial gene orders using all four operations are presented in Chapter 4. An important rearrangement operation, in particular for the study of mitochondrial gene orders, is the tandem duplication random loss operation (e.g. Boore, 2000; Mauro et al., 2006). This rearrangement duplicates a part of a gene order followed by the random loss of one of the redundant copies of each gene. The gene order is rearranged depending on which copy is lost. This rearrangement should be regarded for reconstructing phylogeny from gene order data. But the properties of this rearrangement operation have rarely been studied (Bouvel and Rossin, 2009; Chaudhuri et al., 2006). The combinatorial properties of the TDRL operation are studied in Chapter 5. The enumeration and counting of sorting TDRLs, that is TDRL operations reducing the distance, is studied in particular. Closed formulas for computing the number of sorting TDRLs and methods for the enumeration are presented. Furthermore, TDRLs are one of the operations considered in Chapter 4. An interesting property of this rearrangement, distinguishing it from other rearrangements, is its asymmetry. That is the effects of a single TDRL can (in the most cases) not be reversed with a single TDRL. The use of this property for phylogeny reconstruction is studied in Section 4.3. This thesis is structured as follows. The existing approaches obeying similar types of modified rearrangement models as well as important concepts and computational methods to related problems are reviewed in Chapter 2. The combinatorial structures of gene orders that have been proposed for identifying gene groups, in particular common intervals, as well as the computational approaches for their computation are reviewed in Section 2.2. Approaches for computing parsimonious pairwise rearrangement scenarios are outlined in Section 2.3. Methods for the computation genome rearrangement scenarios obeying biologically motivated constraints, as introduced above, are detailed in Section 2.4. The approaches for the inversion median problem are covered in Section 2.5. Methods for the reconstruction of phylogenetic trees from gene arrangement data are briefly outlined in Section 2.6.3 1 Introduction Chapter 3 introduces the new algorithms CIP, ECIP, and TCIP for solving the preserving inversion median problem. The efficiency of the algorithm is empirically studied for simulated as well as mitochondrial data. The description of algorithms CIP and ECIP is based on Bernt et al. (2006b). TCIP has been described in Bernt et al. (2007a, 2008b). But the theoretical foundation of TCIP is extended significantly within this work in order to allow for more than three input permutations. Gene order rearrangement methods that have been developed for the reconstruction of the phylogeny of mitochondrial gene orders are presented in the fourth chapter. The presented algorithm CREx computes rearrangement scenarios for pairs of gene orders. CREx regards the four types of rearrangement operations which are important for mitochondrial gene orders. Based on CREx the algorithm TreeREx for assigning rearrangement events to a given tree is developed. The quality of the CREx reconstructions is analysed in a large empirical study for simulated gene orders. The results of TreeREx are analysed for several mitochondrial data sets. Algorithms CREx and TreeREx have been published in Bernt et al. (2008a, 2007c). The analysis of the mitochondrial gene orders of Echinodermata was included in Perseke et al. (2008). Additionally, a new and simple method is presented to explore the potential of the CREx method. The new method is applied to the complete mitochondrial data set. The problem of enumerating and counting sorting TDRLs is studied in Chapter 5. The theoretical results are covered to a large extent by Bernt et al. (2009b). The missing combinatorial explanation for some of the presented formulas is given here for the first time. Therefor, a new method for the enumeration and counting of sorting TDRLs has been developed (Bernt et al., 2009a)

A novel sex-determining QTL in Nile tilapia (Oreochromis niloticus)

Background: Fish species often exhibit significant sexual dimorphism for commercially important traits. Accordingly, the control of phenotypic sex, and in particular the production of monosex cultures, is of particular interest to the aquaculture industry. Sex determination in the widely farmed Nile tilapia (Oreochromis niloticus) is complex, involving genomic regions on at least three chromosomes (chromosomes 1, 3 and 23) and interacting in certain cases with elevated early rearing temperature as well. Thus, sex ratios may vary substantially from 50%. Results: This study focused on mapping sex-determining quantitative trait loci (QTL) in families with skewed sex ratios. These included four families that showed an excess of males (male ratio varied between 64% and 93%) when reared at standard temperature (28°C) and a fifth family in which an excess of males (96%) was observed when fry were reared at 36°C for ten days from first feeding. All the samples used in the current study were genotyped for two single-nucleotide polymorphisms (rs397507167 and rs397507165) located in the expected major sex-determining region in linkage group 1 (LG 1). The only misassigned individuals were phenotypic males with the expected female genotype, suggesting that those offspring had undergone sex-reversal with respect to the major sex-determining locus. We mapped SNPs identified from double digest Restriction-site Associated DNA (ddRAD) sequencing in these five families. Three genetic maps were constructed consisting of 641, 175 and 1,155 SNPs from the three largest families. QTL analyses provided evidence for a novel genome-wide significant QTL in LG 20. Evidence was also found for another sex-determining QTL in the fifth family, in the proximal region of LG 1. Conclusions: Overall, the results from this study suggest that these previously undetected QTLs are involved in sex determination in the Nile tilapia, causing sex reversal (masculinisation) with respect to the XX genotype at the major sex-determining locus in LG 1

Exploring aspects of memory in healthy ageing and following stroke

Memory is critical for everyday functioning. Remembering an event with rich detail requires the ability to remember the temporal order of occurrences within the event and spatial locations associated with it. But it remains unclear whether it also requires memory for the perspective from which we encoded the event, whether these three aspects of memory are affected following stroke, and which are the key brain regions upon which they rely. These questions are explored in this thesis. In the first study presented here, I examined young and elderly healthy subjects with an autobiographical memory interview and a 2D spatial memory task assessing self-perspective, and found no correlation between performance on these tasks. In the second experimental study, by assessing stroke patients on a 3D spatio-temporal memory task, I found that damage to the right intraparietal sulcus was associated with poorer memory for temporal order. However, voxelwise analyses detected no association between parietal lobe regions and accuracy in the egocentric condition of this task, or between medial temporal lobe regions and accuracy in the allocentric condition, one possible reason being that performance was near ceiling. In the third experimental study, by assessing a considerably larger group of stroke patients on a spatial memory task, I found that, as a group, patients performed worse than healthy controls, and performance was correlated with an activities of daily living scale. A spatial memory network was identified in right (but not left) hemisphere stroke patients. These findings provide evidence that spatial memory impairment is common after stroke, highlight its potential functional relevance, and increase our understanding of which regions are critical for remembering temporal order and spatial information. Furthermore, they suggest a dissociation between the mechanisms underpinning recall of 2D scenes over relatively short intervals versus remembering of real-life events across periods of many years.Open Acces

Tevatron-for-LHC Report: Preparations for Discoveries

This is the "TeV4LHC" report of the "Physics Landscapes" Working Group, focused on facilitating the start-up of physics explorations at the LHC by using the experience gained at the Tevatron. We present experimental and theoretical results that can be employed to probe various scenarios for physics beyond the Standard Model.Comment: 222 pp., additional contribution added, typos/layout correcte

About Phase: Synthetic Aperture Radar and the Phase Retrieval Problem

Synthetic aperture radar (SAR) uses relative motion to produce fine resolution images from microwave frequencies and is a useful tool for regular monitoring and mapping applications. Unfortunately, if target distance is estimated poorly, then phase errors are incurred in the data, producing a blurry reconstruction of the image. In this thesis, we introduce a new multistatic methodology for determining these phase errors from interferometry-inspired combinations of signals. To motivate this, we first consider a more general problem called phase retrieval, in which a signal is reconstructed from linear measurements whose phases are either unreliable or unavailable. We make significant theoretical progress on the phase retrieval problem, to include characterizing injectivity in the complex case, devising the theory of almost injectivity, and performing a stability analysis. We then apply certain ideas from phase retrieval to resolve phase errors in SAR. Specifically, we use bistatic techniques to measure relative phases, and then we apply a graph-theoretic phase retrieval algorithm to recover the phase errors. We conclude by devising an image reconstruction procedure based on this algorithm, and we provide simulations that demonstrate stability to noise