29,344 research outputs found
The Digrams of Webster\u27s Unabridged Dictionary
For many years word buffs at these laboratories have made a game out of finding words which contain strange digrams (pairs of letters side-by-side). The problem, as originally posed by M.D. McIlroy, was to complete a table with 26 rows and 26 columns, labeled by the letters A, B, ... , Z. The space where row L crossed column L\u27 was to be filled by a word containing the digram LL\u27
Recommended from our members
Economic modelling using constraint logic programming
This paper investigates the use of constraint logic programming (CLP) in economic modelling
through the design and implementation of two economic models. The first model, the Desai-
Henry model contains only linear equations while the second model, constructed by the author,
contains non-linear elements. In order to implement the second model, a non-linear constraint
solver was constructed. This was necessary because, although CLP is a very powerful
programming paradigm, currently available implementations lack any on-linear constraint
solving mechanisms
Modelling alternative strategies for delivering hepatitis B vaccine in prisons : the impact on the vaccination coverage of the injecting drug user population
Since 2001 hepatitis B vaccination has been offered to prisoners on reception into prisons in
England and Wales. However, short campaigns of vaccinating the entire population of individual
prisons have achieved high vaccination coverage for limited periods, suggesting that short
campaigns may be a preferable way of vaccinating prisoners. A model is used that describes the
flow of prisoners through prisons stratified by injecting status to compare a range of vaccination
scenarios that describe vaccination on prison reception or via regular short campaigns. Model
results suggest that vaccinating on prison reception can capture a greater proportion of the
injecting drug user (IDU) population than the comparable campaign scenarios (63% vs. 55 . 6%
respectively). Vaccination on prison reception is also more efficient at capturing IDUs for
vaccination than vaccination via a campaign, although vaccination via campaigns may have a
role with some infections for overall control
The algebra of rewriting for presentations of inverse monoids
We describe a formalism, using groupoids, for the study of rewriting for
presentations of inverse monoids, that is based on the Squier complex
construction for monoid presentations. We introduce the class of pseudoregular
groupoids, an example of which now arises as the fundamental groupoid of our
version of the Squier complex. A further key ingredient is the factorisation of
the presentation map from a free inverse monoid as the composition of an
idempotent pure map and an idempotent separating map. The relation module of a
presentation is then defined as the abelianised kernel of this idempotent
separating map. We then use the properties of idempotent separating maps to
derive a free presentation of the relation module. The construction of its
kernel - the module of identities - uses further facts about pseudoregular
groupoids.Comment: 22 page
Accuracy thresholds of topological color codes on the hexagonal and square-octagonal lattices
Accuracy thresholds of quantum error correcting codes, which exploit
topological properties of systems, defined on two different arrangements of
qubits are predicted. We study the topological color codes on the hexagonal
lattice and on the square-octagonal lattice by the use of mapping into the spin
glass systems. The analysis for the corresponding spin glass systems consists
of the duality, and the gauge symmetry, which has succeeded in deriving
locations of special points, which are deeply related with the accuracy
thresholds of topological error correcting codes. We predict that the accuracy
thresholds for the topological color codes would be for the
hexagonal lattice and for the square-octagonal lattice,
where denotes the error probability on each qubit. Hence both of them are
expected to be slightly lower than the probability for the
quantum Gilbert-Varshamov bound with a zero encoding rate.Comment: 6 pages, 4 figures, the previous title was "Threshold of topological
color code". This is the published version in Phys. Rev.
- …