Solution Counting for CSP and SAT with Large Tree-Width

Рассмотрена проблема подсчета количества решений задачи совместимости ограничений (Constraint Satisfaction Problem). Для ее решения был адаптирован метод обратного прослеживания с ацикличным представлением графа ограничений (Backtracking with Tree-Decomposition). Предложен точный алгоритм, сложность которого экспоненциально зависит от ширины дерева, и приближенный алгоритм, экспоненциально зависящий от размера максимальной клики.The problem of counting the number of solutions of a CSP is considered. For solving the problem the Backtracking with a Tree-Decomposition method was adapted. The exact algorithm is suggested which has the worst-time complexity exponential in a tree width, as well as iterative algorithm that has computational complexity exponential in a maximum clique size.Розглянуто проблему підрахунку кількості розв’язків задачі сумісності обмежень (Constraint Satisfaction Problem). Для її розв’язку було адаптовано метод зворотного простеження з ациклічним поданням графа обмежень (Backtracking with Tree-Decomposition). Запропоновано точний алгоритм, складність якого експоненційно залежить від ширини дерева, і наближений алгоритм, експоненційно залежний від розміру максимальної кліки

A high resolution radiation hybrid map of bovine chromosome 14 identifies scaffold rearrangement in the latest bovine assembly

<p>Abstract</p> <p>Background</p> <p>Radiation hybrid (RH) maps are considered to be a tool of choice for fine mapping closely linked loci, considering that the resolution of linkage maps is determined by the number of informative meiosis and recombination events which may require very large mapping populations. Accurately defining the marker order on chromosomes is crucial for correct identification of quantitative trait loci (QTL), haplotype map construction and refinement of candidate gene searches.</p> <p>Results</p> <p>A 12 k Radiation hybrid map of bovine chromosome 14 was constructed using 843 single nucleotide polymorphism markers. The resulting map was aligned with the latest version of the bovine assembly (Btau_3.1) as well as other previously published RH maps. The resulting map identified distinct regions on Bovine chromosome 14 where discrepancies between this RH map and the bovine assembly occur. A major region of discrepancy was found near the centromere involving the arrangement and order of the scaffolds from the assembly. The map further confirms previously published conserved synteny blocks with human chromosome 8. As well, it identifies an extra breakpoint and conserved synteny block previously undetected due to lower marker density. This conserved synteny block is in a region where markers between the RH map presented here and the latest sequence assembly are in very good agreement.</p> <p>Conclusion</p> <p>The increase of publicly available markers shifts the rate limiting step from marker discovery to the correct identification of their order for further use by the research community. This high resolution map of bovine chromosome 14 will facilitate identification of regions in the sequence assembly where additional information is required to resolve marker ordering.</p

A high resolution radiation hybrid map of bovine chromosome 14 identifies scaffold rearrangement in the latest bovine assembly

<p>Abstract</p> <p>Background</p> <p>Radiation hybrid (RH) maps are considered to be a tool of choice for fine mapping closely linked loci, considering that the resolution of linkage maps is determined by the number of informative meiosis and recombination events which may require very large mapping populations. Accurately defining the marker order on chromosomes is crucial for correct identification of quantitative trait loci (QTL), haplotype map construction and refinement of candidate gene searches.</p> <p>Results</p> <p>A 12 k Radiation hybrid map of bovine chromosome 14 was constructed using 843 single nucleotide polymorphism markers. The resulting map was aligned with the latest version of the bovine assembly (Btau_3.1) as well as other previously published RH maps. The resulting map identified distinct regions on Bovine chromosome 14 where discrepancies between this RH map and the bovine assembly occur. A major region of discrepancy was found near the centromere involving the arrangement and order of the scaffolds from the assembly. The map further confirms previously published conserved synteny blocks with human chromosome 8. As well, it identifies an extra breakpoint and conserved synteny block previously undetected due to lower marker density. This conserved synteny block is in a region where markers between the RH map presented here and the latest sequence assembly are in very good agreement.</p> <p>Conclusion</p> <p>The increase of publicly available markers shifts the rate limiting step from marker discovery to the correct identification of their order for further use by the research community. This high resolution map of bovine chromosome 14 will facilitate identification of regions in the sequence assembly where additional information is required to resolve marker ordering.</p

Modelling the conference paper assignment problem

In this paper we describe different constraints and models for the conference paper assignment problem. While the core problem is a simple flow problem, additional constraints often arise to tailor a solution to specific wishes, or to increase perceived fairness for reviewers and/or submissions. We show some results from actual conferences paper assignments, and also investigate scalability of the method for large-scale events

Efficient and Accurate Construction of Genetic Linkage Maps from the Minimum Spanning Tree of a Graph

Genetic linkage maps are cornerstones of a wide spectrum of biotechnology applications, including map-assisted breeding, association genetics, and map-assisted gene cloning. During the past several years, the adoption of high-throughput genotyping technologies has been paralleled by a substantial increase in the density and diversity of genetic markers. New genetic mapping algorithms are needed in order to efficiently process these large datasets and accurately construct high-density genetic maps. In this paper, we introduce a novel algorithm to order markers on a genetic linkage map. Our method is based on a simple yet fundamental mathematical property that we prove under rather general assumptions. The validity of this property allows one to determine efficiently the correct order of markers by computing the minimum spanning tree of an associated graph. Our empirical studies obtained on genotyping data for three mapping populations of barley (Hordeum vulgare), as well as extensive simulations on synthetic data, show that our algorithm consistently outperforms the best available methods in the literature, particularly when the input data are noisy or incomplete. The software implementing our algorithm is available in the public domain as a web tool under the name MSTmap

Gene Regulatory Network Reconstruction Using Bayesian Networks, the Dantzig Selector, the Lasso and Their Meta-Analysis

Modern technologies and especially next generation sequencing facilities are giving a cheaper access to genotype and genomic data measured on the same sample at once. This creates an ideal situation for multifactorial experiments designed to infer gene regulatory networks. The fifth “Dialogue for Reverse Engineering Assessments and Methods” (DREAM5) challenges are aimed at assessing methods and associated algorithms devoted to the inference of biological networks. Challenge 3 on “Systems Genetics” proposed to infer causal gene regulatory networks from different genetical genomics data sets. We investigated a wide panel of methods ranging from Bayesian networks to penalised linear regressions to analyse such data, and proposed a simple yet very powerful meta-analysis, which combines these inference methods. We present results of the Challenge as well as more in-depth analysis of predicted networks in terms of structure and reliability. The developed meta-analysis was ranked first among the teams participating in Challenge 3A. It paves the way for future extensions of our inference method and more accurate gene network estimates in the context of genetical genomics

Mapping quantitative trait loci (QTL) in sheep. I. A new male framework linkage map and QTL for growth rate and body weight

A male sheep linkage map comprising 191 microsatellites was generated from a single family of 510 Awassi-Merino backcross progeny. Except for ovine chromosomes 1, 2, 10 and 17, all other chromosomes yielded a LOD score difference greater than 3.0 between the best and second-best map order. The map is on average 11% longer than the Sheep Linkage Map v4.7 male-specific map. This map was employed in quantitative trait loci (QTL) analyses on body-weight and growth-rate traits between birth and 98 weeks of age. A custom maximum likelihood program was developed to map QTL in half-sib families for non-inbred strains (QTL-MLE) and is freely available on request. The new analysis package offers the advantage of enabling QTL × fixed effect interactions to be included in the model. Fifty-four putative QTL were identified on nine chromosomes. Significant QTL with sex-specific effects (i.e. QTL × sex interaction) in the range of 0.4 to 0.7 SD were found on ovine chromosomes 1, 3, 6, 11, 21, 23, 24 and 26

A Large Maize (Zea mays L.) SNP Genotyping Array: Development and Germplasm Genotyping, and Genetic Mapping to Compare with the B73 Reference Genome

SNP genotyping arrays have been useful for many applications that require a large number of molecular markers such as high-density genetic mapping, genome-wide association studies (GWAS), and genomic selection. We report the establishment of a large maize SNP array and its use for diversity analysis and high density linkage mapping. The markers, taken from more than 800,000 SNPs, were selected to be preferentially located in genes and evenly distributed across the genome. The array was tested with a set of maize germplasm including North American and European inbred lines, parent/F1 combinations, and distantly related teosinte material. A total of 49,585 markers, including 33,417 within 17,520 different genes and 16,168 outside genes, were of good quality for genotyping, with an average failure rate of 4% and rates up to 8% in specific germplasm. To demonstrate this array's use in genetic mapping and for the independent validation of the B73 sequence assembly, two intermated maize recombinant inbred line populations – IBM (B73×Mo17) and LHRF (F2×F252) – were genotyped to establish two high density linkage maps with 20,913 and 14,524 markers respectively. 172 mapped markers were absent in the current B73 assembly and their placement can be used for future improvements of the B73 reference sequence. Colinearity of the genetic and physical maps was mostly conserved with some exceptions that suggest errors in the B73 assembly. Five major regions containing non-colinearities were identified on chromosomes 2, 3, 6, 7 and 9, and are supported by both independent genetic maps. Four additional non-colinear regions were found on the LHRF map only; they may be due to a lower density of IBM markers in those regions or to true structural rearrangements between lines. Given the array's high quality, it will be a valuable resource for maize genetics and many aspects of maize breeding

The Imprinted Gene DIO3 Is a Candidate Gene for Litter Size in Pigs

Genomic imprinting is an important epigenetic phenomenon, which on the phenotypic level can be detected by the difference between the two heterozygote classes of a gene. Imprinted genes are important in both the development of the placenta and the embryo, and we hypothesized that imprinted genes might be involved in female fertility traits. We therefore performed an association study for imprinted genes related to female fertility traits in two commercial pig populations. For this purpose, 309 SNPs in fifteen evolutionary conserved imprinted regions were genotyped on 689 and 1050 pigs from the two pig populations. A single SNP association study was used to detect additive, dominant and imprinting effects related to four reproduction traits; total number of piglets born, the number of piglets born alive, the total weight of the piglets born and the total weight of the piglets born alive. Several SNPs showed significant () additive and dominant effects and one SNP showed a significant imprinting effect. The SNP with a significant imprinting effect is closely linked to DIO3, a gene involved in thyroid metabolism. The imprinting effect of this SNP explained approximately 1.6% of the phenotypic variance, which corresponded to approximately 15.5% of the additive genetic variance. In the other population, the imprinting effect of this QTL was not significant (), but had a similar effect as in the first population. The results of this study indicate a possible association between the imprinted gene DIO3 and female fertility traits in pigs

Integrative mapping analysis of chicken microchromosome 16 organization

<p>Abstract</p> <p>Background</p> <p>The chicken karyotype is composed of 39 chromosome pairs, of which 9 still remain totally absent from the current genome sequence assembly, despite international efforts towards complete coverage. Some others are only very partially sequenced, amongst which microchromosome 16 (GGA16), particularly under-represented, with only 433 kb assembled for a full estimated size of 9 to 11 Mb. Besides the obvious need of full genome coverage with genetic markers for QTL (Quantitative Trait Loci) mapping and major genes identification studies, there is a major interest in the detailed study of this chromosome because it carries the two genetically independent <it>MHC </it>complexes <it>B </it>and <it>Y</it>. In addition, GGA16 carries the ribosomal RNA (<it>rRNA</it>) genes cluster, also known as the <it>NOR </it>(nucleolus organizer region). The purpose of the present study is to construct and present high resolution integrated maps of GGA16 to refine its organization and improve its coverage with genetic markers.</p> <p>Results</p> <p>We developed 79 STS (Sequence Tagged Site) markers to build a physical RH (radiation hybrid) map and 34 genetic markers to extend the genetic map of GGA16. We screened a BAC (Bacterial Artificial Chromosome) library with markers for the <it>MHC-B</it>, <it>MHC-Y </it>and <it>rRNA </it>complexes. Selected clones were used to perform high resolution FISH (Fluorescent <it>In Situ </it>Hybridization) mapping on giant meiotic lampbrush chromosomes, allowing meiotic mapping in addition to the confirmation of the order of the three clusters along the chromosome. A region with high recombination rates and containing PO41 repeated elements separates the two <it>MHC </it>complexes.</p> <p>Conclusions</p> <p>The three complementary mapping strategies used refine greatly our knowledge of chicken microchromosome 16 organisation. The characterisation of the recombination hotspots separating the two <it>MHC </it>complexes demonstrates the presence of PO41 repetitive sequences both in tandem and inverted orientation. However, this region still needs to be studied in more detail.</p