1,373 research outputs found
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
and an approximation (multiplicative error), where is the number
of vertices, the number of edges and 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 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
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