Extremal numbers for odd cycles

We describe the C_{2k+1}-free graphs on n vertices with maximum number of edges. The extremal graphs are unique except for n = 3k-1, 3k, 4k-2, or 4k-1. The value of ex(n,C_{2k+1}) can be read out from the works of Bondy, Woodall, and Bollobas, but here we give a new streamlined proof. The complete determination of the extremal graphs is also new. We obtain that the bound for n_0(C_{2k+1}) is 4k in the classical theorem of Simonovits, from which the unique extremal graph is the bipartite Turan graph.Comment: 6 page

Periodical Cicadas Are Coming in May!

Millions of 17-cicadas will come out in southern Iowa in May 1963; 20,000 - 40,000 may emerge around a single tree. They won\u27t sting or bite humans and animals or do much damage, but they will make a lot of noise

Insect and Rodent Prospects for 1960

Weather conditions during the growing season pretty much determine the size of the insect problem in any given year. Keeping this in mind, here are the prospects for 1960- depending on the weather

Extremal Numbers for Odd Cycles

We describe the C 2k+1-free graphs on n vertices with maximum number of edges. The extremal graphs are unique for n ∉ {3k − 1, 3k, 4k − 2, 4k − 1}. The value of ex(n, C 2k+1) can be read out from the works of Bondy [3], Woodall [14], and Bollobás [1], but here we give a new streamlined proof. The complete determination of the extremal graphs is also new. We obtain that the bound for n 0(C 2k+1) is 4k in the classical theorem of Simonovits, from which the unique extremal graph is the bipartite Turán graph

iTriplet, a rule-based nucleic acid sequence motif finder

<p>Abstract</p> <p>Background</p> <p>With the advent of high throughput sequencing techniques, large amounts of sequencing data are readily available for analysis. Natural biological signals are intrinsically highly variable making their complete identification a computationally challenging problem. Many attempts in using statistical or combinatorial approaches have been made with great success in the past. However, identifying highly degenerate and long (>20 nucleotides) motifs still remains an unmet challenge as high degeneracy will diminish statistical significance of biological signals and increasing motif size will cause combinatorial explosion. In this report, we present a novel rule-based method that is focused on finding degenerate and long motifs. Our proposed method, named iTriplet, avoids costly enumeration present in existing combinatorial methods and is amenable to parallel processing.</p> <p>Results</p> <p>We have conducted a comprehensive assessment on the performance and sensitivity-specificity of iTriplet in analyzing artificial and real biological sequences in various genomic regions. The results show that iTriplet is able to solve challenging cases. Furthermore we have confirmed the utility of iTriplet by showing it accurately predicts polyA-site-related motifs using a dual Luciferase reporter assay.</p> <p>Conclusion</p> <p>iTriplet is a novel rule-based combinatorial or enumerative motif finding method that is able to process highly degenerate and long motifs that have resisted analysis by other methods. In addition, iTriplet is distinguished from other methods of the same family by its parallelizability, which allows it to leverage the power of today's readily available high-performance computing systems.</p

The Effect of Collective Bargaining Legislation on Strikes and Wages

Using Canadian data on large, private-sector contract negotiations from January 1967 to March 1993, we find that wages and strikes are substantially influenced by labor policy. In particular, we find that prohibiting the use of replacement workers during strikes is associated with significantly higher wages, and more frequent and longer strikes. This is consistent with private information theories of bargaining. We estimate the welfare consequences of a ban on replacement workers, as well as other labor policies. Despite the higher dispute costs, union workers are better off with a ban on replacement workers. The higher wage more than compensates for the more frequent and longer strikes.