Fragmentation of bacteriophage S13 replicative from DNA by restriction endonucleases from Hemophilus influenzae and Hemophilus aegyptius.

The restriction enzymes Hind from Hemophilus influenzae and HaeIII from Hemophilus aegyptius cleave bacteriophage S13 replicative form (RF) DNA into 13 and 10 specific fragments, respectively. The sizes of these fragments were estimated by gel electrophoresis, electron microscopy, and pyrimidine isostich analysis. The Hind and HaeIII fragments were ordered relative to each other by cross digestion and a physical map of the S13 genome constructed. Comparison of the Hind cleavage patterns of S13 RF DNA and X174 RF DNA showed the majority of the fragments from the two DNAs coincided with each other except for three of the thirteen S13 fragments and three of the thirteen X174 fragments. Comparison of the HaeIII patterns of the two DNAs revealed a lack of coincidence of one S13 fragment only and two X174 fragments. From the data obtained by the cleavage of the two DNAs by Hind and HaeIII, a correlation between the physical restriction enzyme cleavage maps and the genetic map of the two phages was made. The differences in cleavage of the two DNAs by the restriction enzymes have been explained by changes in two restriction enzyme sites in the AB region and one change of site in the F region of the genetic map of the two bacteriophages

Constructive Dimension and Turing Degrees

This paper examines the constructive Hausdorff and packing dimensions of Turing degrees. The main result is that every infinite sequence S with constructive Hausdorff dimension dim_H(S) and constructive packing dimension dim_P(S) is Turing equivalent to a sequence R with dim_H(R) <= (dim_H(S) / dim_P(S)) - epsilon, for arbitrary epsilon > 0. Furthermore, if dim_P(S) > 0, then dim_P(R) >= 1 - epsilon. The reduction thus serves as a *randomness extractor* that increases the algorithmic randomness of S, as measured by constructive dimension. A number of applications of this result shed new light on the constructive dimensions of Turing degrees. A lower bound of dim_H(S) / dim_P(S) is shown to hold for the Turing degree of any sequence S. A new proof is given of a previously-known zero-one law for the constructive packing dimension of Turing degrees. It is also shown that, for any regular sequence S (that is, dim_H(S) = dim_P(S)) such that dim_H(S) > 0, the Turing degree of S has constructive Hausdorff and packing dimension equal to 1. Finally, it is shown that no single Turing reduction can be a universal constructive Hausdorff dimension extractor, and that bounded Turing reductions cannot extract constructive Hausdorff dimension. We also exhibit sequences on which weak truth-table and bounded Turing reductions differ in their ability to extract dimension.Comment: The version of this paper appearing in Theory of Computing Systems, 45(4):740-755, 2009, had an error in the proof of Theorem 2.4, due to insufficient care with the choice of delta. This version modifies that proof to fix the error

Erasmus Computing Grid: Het bouwen van een 20 Tera-FLOPS Virtuele Supercomputer.

Het Erasmus Medisch Centrum en de Hogeschool Rotterdam zijn in 2005 een samenwerking begonnen teneinde de ongeveer 95% onbenutte rekencapaciteit van hun computers beschikbaar te maken voor onderzoek en onderwijs. Deze samenwerking heeft geleid tot het Erasmus Computing GRID (ECG), een virtuele supercomputer met na voltooiing een rekencapaciteit van 20 Teraflops. Dit artikel schetst enige achtergronden van grid computing, beschrijft een aantal toepassingen die mogelijk zijn met een grid infrastructuur en geeft de wijze weer waarop het ECG wordt vormgegeven. In het verlengde hiervan bevat het een pleidooi om grid computing binnen het onderwijs een betere basis te geven om op die manier vanuit het onderwijs een substantiële bijdrage te leveren aan het versterken van (rekenintensief) onderzoek

Efficient Triangle Counting in Large Graphs via Degree-based Vertex Partitioning

The number of triangles is a computationally expensive graph statistic which is frequently used in complex network analysis (e.g., transitivity ratio), in various random graph models (e.g., exponential random graph model) and in important real world applications such as spam detection, uncovering of the hidden thematic structure of the Web and link recommendation. Counting triangles in graphs with millions and billions of edges requires algorithms which run fast, use small amount of space, provide accurate estimates of the number of triangles and preferably are parallelizable. In this paper we present an efficient triangle counting algorithm which can be adapted to the semistreaming model. The key idea of our algorithm is to combine the sampling algorithm of Tsourakakis et al. and the partitioning of the set of vertices into a high degree and a low degree subset respectively as in the Alon, Yuster and Zwick work treating each set appropriately. We obtain a running time $O \left(m + \frac{m^{3/2} \Delta \log{n}}{t \epsilon^2} \right)$ and an $\epsilon$ approximation (multiplicative error), where $n$ is the number of vertices, $m$ the number of edges and $\Delta$ the maximum number of triangles an edge is contained. Furthermore, we show how this algorithm can be adapted to the semistreaming model with space usage $O\left(m^{1/2}\log{n} + \frac{m^{3/2} \Delta \log{n}}{t \epsilon^2} \right)$ and a constant number of passes (three) over the graph stream. We apply our methods in various networks with several millions of edges and we obtain excellent results. Finally, we propose a random projection based method for triangle counting and provide a sufficient condition to obtain an estimate with low variance.Comment: 1) 12 pages 2) To appear in the 7th Workshop on Algorithms and Models for the Web Graph (WAW 2010

Cyclotomic integers, fusion categories, and subfactors

Dimensions of objects in fusion categories are cyclotomic integers, hence number theoretic results have implications in the study of fusion categories and finite depth subfactors. We give two such applications. The first application is determining a complete list of numbers in the interval (2, 76/33) which can occur as the Frobenius-Perron dimension of an object in a fusion category. The smallest number on this list is realized in a new fusion category which is constructed in the appendix written by V. Ostrik, while the others are all realized by known examples. The second application proves that in any family of graphs obtained by adding a 2-valent tree to a fixed graph, either only finitely many graphs are principal graphs of subfactors or the family consists of the A_n or D_n Dynkin diagrams. This result is effective, and we apply it to several families arising in the classification of subfactors of index less then 5.Comment: 47 pages, with an appendix by Victor Ostri