Molecular studies of Arabidopsis and Brassica with focus on resistance to Leptosphaeria maculans

Blackleg caused by Leptosphaeria maculans is a widespread fungal disease on B~assica napus (oilseed rape). In contrast, Arabidopsis thaliana and B. nigra are in general highly resistant. This study presents results from genomic interaction between the A. thaliana and B. napus genome with focus on L. maculans resistance. Identification and partial characterization of A. thaliana resistance in accessions, L. maculans susceptible mutants, and signaling pathways were also performed. Finally, a resistance gene to L. maculans from B. nigra was cloned and transferred to B. napus. Chromosome counts and RFLP analyses of A. thaliana DNA content in A. thaliana (+) B. napus back-crossed progeny were performed. The results showed that in BC,, originating from symmetric hybrids, the frequency of retained A. thaliana loci was reduced to 42%. The average chromosome number decreased from 48 in BC1 to 39 in BC2. These results can be compared with the asymmetric hybrid derived BC,, that had 16% loci present and an average chromosome number of 38. Clearly, symmetric hybrid offspring retained most DNA as complete chromosomes whereas asymmetric hybrid offspring contained mostly DNA fragments. Pathogen screening of the hybrid offspring revealed both cotyledon and adult leaf resistance to L. maculans. The adult leaf resistance was localized to chromosome 3 from A. thaliana, on two areas on each side of the centromere. A. thaliana resistance was examined in 171 accessions from 27 countries. Only four accessions displayed any susceptibility. To further explore the underlying causes of the resistance, a set of L. maculans disease susceptible mutants (lms) were isolated. Two of the mutants, lmsl and lms5 have been mapped to chromosome 2 and 1, respectively. The resistance was further analyzed with respect to defense signaling and effector molecules. The results indicated that resistance in A . thaliana against L . maculans depended on camalexin and is independent on salicylic acid, jasmonic acid or ethylene response. In contrast, lmsl produced wild type level of camalexin and higher expression levels than wild type of P R l , and PDFl.2. The results suggest the possibility of at least two independent resistance factors in A. thaliana. A gene conferring resistance to L. maculans, L m l , was cloned from B. nigra. Sequence analysis revealed a novel protein with two putative trans-membrane motifs and homology to the nin protein of Lotus japonicus and to A. thaliana sequences of unknown function. The knowledge gained in A. thaliana and from Lml will promote a further understanding of the mechanisms underlying resistance to L. macula

Random triangle removal

Starting from a complete graph on $n$ vertices, repeatedly delete the edges of a uniformly chosen triangle. This stochastic process terminates once it arrives at a triangle-free graph, and the fundamental question is to estimate the final number of edges (equivalently, the time it takes the process to finish, or how many edge-disjoint triangles are packed via the random greedy algorithm). Bollob\'as and Erd\H{o}s (1990) conjectured that the expected final number of edges has order $n^{3/2}$, motivated by the study of the Ramsey number $R(3,t)$. An upper bound of $o(n^2)$ was shown by Spencer (1995) and independently by R\"odl and Thoma (1996). Several bounds were given for variants and generalizations (e.g., Alon, Kim and Spencer (1997) and Wormald (1999)), while the best known upper bound for the original question of Bollob\'as and Erd\H{o}s was $n^{7/4+o(1)}$ due to Grable (1997). No nontrivial lower bound was available. Here we prove that with high probability the final number of edges in random triangle removal is equal to $n^{3/2+o(1)}$, thus confirming the 3/2 exponent conjectured by Bollob\'as and Erd\H{o}s and matching the predictions of Spencer et al. For the upper bound, for any fixed $\epsilon>0$ we construct a family of $\exp(O(1/\epsilon))$ graphs by gluing $O(1/\epsilon)$ triangles sequentially in a prescribed manner, and dynamically track all homomorphisms from them, rooted at any two vertices, up to the point where $n^{3/2+\epsilon}$ edges remain. A system of martingales establishes concentration for these random variables around their analogous means in a random graph with corresponding edge density, and a key role is played by the self-correcting nature of the process. The lower bound builds on the estimates at that very point to show that the process will typically terminate with at least $n^{3/2-o(1)}$ edges left.Comment: 42 pages, 4 figures. Supercedes arXiv:1108.178

Labor Contracts and the Taft-Hartley Act

The amount of information stored on the internet grows daily and naturally the requirements on the systems used to search for and analyse information increases. As a part in meeting the raised requirements this study investigates if it is possible for a automatised text analysis system to distinguish certain groups and categories of words in a text, and more specifically investigate if it is possible to distinguish words with a high information value from words with a low information value. This is important to enable optimizations of systems for global surveillance and information retrieval. The study is carried out using word spaces, which are often used in text analysis to model language. The distributional character of certain categories of words is examined by studying the intrinsic dimensionality of the space, locally around different words. Based on the result from the study of the intrinsic dimensionality, where there seems to be differences in the distributional character between categories of words, an algorithm is implemented for classifying words based on the dimensionality data. The classification algorithm is tested for different categories. The result strengthens the thesis that there could exist useful differences between the distributional character of different categories of words.I takt med att allt mer information finns tillgänglig på internet växer kraven som ställs på system som används för att söka efter och analysera information. I den här rapporten undersöks huruvida det är möjligt för ett systemför automatiserad textanalys att avgöra vilka ord som är relevanta och informationsbärande i ett sammanhang. Detta är viktigt för att möjlig göra optimering och effektivisering av exempelvis informationssöknings- och omvärldsbevakningssystem. Undersökningen genomförs med hjälp av ordrumsmodeller för att modellera språk. Den distributionella karaktären hos termerna undersöks genom att studeraden intrinsiska dimensionaliteten lokalt i rummet kring olika termer. Baserat på resultaten av denna undersökning, som tycks visa på att det fanns skillnader i den distributionella karaktären hos olika kategorier av ord, implementeras en algoritm för att klassificera ord baserat på dimensionaliteten. Klassificeringsalgoritmen testas för olika kategorier. Resultatet stärker tesen om att det kan finnas vissa användbara skillnader mellan den distributionella karaktären hos olika kategorier av ord

Dynamic concentration of the triangle-free process

The triangle-free process begins with an empty graph on n vertices and iteratively adds edges chosen uniformly at random subject to the constraint that no triangle is formed. We determine the asymptotic number of edges in the maximal triangle-free graph at which the triangle-free process terminates. We also bound the independence number of this graph, which gives an improved lower bound on the Ramsey numbers R(3,t): we show R(3,t) > (1-o(1)) t^2 / (4 log t), which is within a 4+o(1) factor of the best known upper bound. Our improvement on previous analyses of this process exploits the self-correcting nature of key statistics of the process. Furthermore, we determine which bounded size subgraphs are likely to appear in the maximal triangle-free graph produced by the triangle-free process: they are precisely those triangle-free graphs with density at most 2.Comment: 75 pages, 1 figur

Dense subgraphs in the H-free process

The H-free process starts with the empty graph on n vertices and adds edges chosen uniformly at random, one at a time, subject to the condition that no copy of H is created, where H is some fixed graph. When H is strictly 2-balanced, we show that for some c,d>0, with high probability as $n \to \infty$, the final graph of the H-free process contains no subgraphs F on $v_F \leq n^{d}$ vertices with maximum density $\max_{J \subseteq F}\{e_J/v_J\} \geq c$. This extends and generalizes results of Gerke and Makai for the C_3-free process.Comment: 7 pages, revised versio

The game chromatic number of random graphs

Given a graph G and an integer k, two players take turns coloring the vertices of G one by one using k colors so that neighboring vertices get different colors. The first player wins iff at the end of the game all the vertices of G are colored. The game chromatic number \chi_g(G) is the minimum k for which the first player has a winning strategy. In this paper we analyze the asymptotic behavior of this parameter for a random graph G_{n,p}. We show that with high probability the game chromatic number of G_{n,p} is at least twice its chromatic number but, up to a multiplicative constant, has the same order of magnitude. We also study the game chromatic number of random bipartite graphs