303,522 research outputs found
Stepwise Projection: Toward Brane Setups for Generic Orbifold Singularities
The construction of brane setups for the exceptional series E6,E7,E8 of SU(2)
orbifolds remains an ever-haunting conundrum. Motivated by techniques in some
works by Muto on non-Abelian SU(3) orbifolds, we here provide an algorithmic
outlook, a method which we call stepwise projection, that may shed some light
on this puzzle. We exemplify this method, consisting of transformation rules
for obtaining complex quivers and brane setups from more elementary ones, to
the cases of the D-series and E6 finite subgroups of SU(2). Furthermore, we
demonstrate the generality of the stepwise procedure by appealing to Frobenius'
theory of Induced Representations. Our algorithm suggests the existence of
generalisations of the orientifold plane in string theory.Comment: 22 pages, 3 figure
Universal Gate Set for Continuous-Variable Quantum Computation with Microwave Circuits
We provide an explicit construction of a universal gate set for
continuous-variable quantum computation with microwave circuits. Such a
universal set has been first proposed in quantum-optical setups, but its
experimental implementation has remained elusive in that domain due to the
difficulties in engineering strong nonlinearities. Here, we show that a
realistic microwave architecture allows to overcome this difficulty. As an
application, we show that this architecture allows to generate a cubic phase
state with an experimentally feasible procedure. This work highlights a
practical advantage of microwave circuits with respect to optical systems for
the purpose of engineering non-Gaussian states, and opens the quest for
continuous-variable algorithms based on a few repetitions of elementary gates
from the continuous-variable universal set.Comment: 6+6 pages, 2 figure
Capturing CFLs with Tree Adjoining Grammars
We define a decidable class of TAGs that is strongly equivalent to CFGs and
is cubic-time parsable. This class serves to lexicalize CFGs in the same manner
as the LCFGs of Schabes and Waters but with considerably less restriction on
the form of the grammars. The class provides a normal form for TAGs that
generate local sets in much the same way that regular grammars provide a normal
form for CFGs that generate regular sets.Comment: 8 pages, 3 figures. To appear in proceedings of ACL'9
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