40,863 research outputs found
Looking for vertex number one
Given an instance of the preferential attachment graph , we
would like to find vertex 1, using only 'local' information about the graph;
that is, by exploring the neighborhoods of small sets of vertices. Borgs et. al
gave an an algorithm which runs in time , which is local in the
sense that at each step, it needs only to search the neighborhood of a set of
vertices of size . We give an algorithm to find vertex 1, which
w.h.p. runs in time and which is local in the strongest sense
of operating only on neighborhoods of single vertices. Here
is any function that goes to infinity with .Comment: As accepted for AA
The Isomorphism Problem for Computable Abelian p-Groups of Bounded Length
Theories of classification distinguish classes with some good structure
theorem from those for which none is possible. Some classes (dense linear
orders, for instance) are non-classifiable in general, but are classifiable
when we consider only countable members. This paper explores such a notion for
classes of computable structures by working out a sequence of examples.
We follow recent work by Goncharov and Knight in using the degree of the
isomorphism problem for a class to distinguish classifiable classes from
non-classifiable. In this paper, we calculate the degree of the isomorphism
problem for Abelian -groups of bounded Ulm length. The result is a sequence
of classes whose isomorphism problems are cofinal in the hyperarithmetical
hierarchy. In the process, new back-and-forth relations on such groups are
calculated.Comment: 15 page
The Lefthanded Local Lemma characterizes chordal dependency graphs
Shearer gave a general theorem characterizing the family \LLL of dependency
graphs labeled with probabilities which have the property that for any
family of events with a dependency graph from \LLL (whose vertex-labels are
upper bounds on the probabilities of the events), there is a positive
probability that none of the events from the family occur.
We show that, unlike the standard Lov\'asz Local Lemma---which is less
powerful than Shearer's condition on every nonempty graph---a recently proved
`Lefthanded' version of the Local Lemma is equivalent to Shearer's condition
for all chordal graphs. This also leads to a simple and efficient algorithm to
check whether a given labeled chordal graph is in \LLL.Comment: 12 pages, 1 figur
PAC Learning, VC Dimension, and the Arithmetic Hierarchy
We compute that the index set of PAC-learnable concept classes is
-complete within the set of indices for all concept classes of
a reasonable form. All concept classes considered are computable enumerations
of computable classes, in a sense made precise here. This family of
concept classes is sufficient to cover all standard examples, and also has the
property that PAC learnability is equivalent to finite VC dimension
The biosynthesis of galactolipids in red clover (Trifolium pratense) : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Biochemistry
Galactolipids occur in all cells capable of the photosynthetic evolution of oxygen. The main galactolipids are monogalactosyl diglyceride (MGDG), digalactosyldiglyceride (DGDG) and sulfolipid (SL), MGDG being the most abundant. These three together form the major nonpigment lipids in both leaves and green algae, accounting for about 40% of the total lipids. Nearly all of the cellular MGDG of plants is present in the chloroplasts and is concentrated in the lamellae. Galactolipids contain unusually high percentages of polyunsaturated acids (MGDG contains greater than 90% in some plants), the major one being α-linolenic acid (9,12,15-octadecatrienoic acid; 18:3). Thus in higher plants most of the MGDG is monogalactosyl dilinolenoyl glycerol. MGDG may be the actual substrate of the desaturation reactions of α-linolenic biosynthesis
Shem, Shem, I Know Your Name: Tracing the Significance of Naming in Genesis
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