4,364 research outputs found
Quantum matchgate computations and linear threshold gates
The theory of matchgates is of interest in various areas in physics and
computer science. Matchgates occur in e.g. the study of fermions and spin
chains, in the theory of holographic algorithms and in several recent works in
quantum computation. In this paper we completely characterize the class of
boolean functions computable by unitary two-qubit matchgate circuits with some
probability of success. We show that this class precisely coincides with that
of the linear threshold gates. The latter is a fundamental family which appears
in several fields, such as the study of neural networks. Using the above
characterization, we further show that the power of matchgate circuits is
surprisingly trivial in those cases where the computation is to succeed with
high probability. In particular, the only functions that are
matchgate-computable with success probability greater than 3/4 are functions
depending on only a single bit of the input
An exact quantification of backreaction in relativistic cosmology
An important open question in cosmology is the degree to which the
Friedmann-Lemaitre-Robertson-Walker (FLRW) solutions of Einstein's equations
are able to model the large-scale behaviour of the locally inhomogeneous
observable universe. We investigate this problem by considering a range of
exact n-body solutions of Einstein's constraint equations. These solutions
contain discrete masses, and so allow arbitrarily large density contrasts to be
modelled. We restrict our study to regularly arranged distributions of masses
in topological 3-spheres. This has the benefit of allowing straightforward
comparisons to be made with FLRW solutions, as both spacetimes admit a discrete
group of symmetries. It also provides a time-symmetric hypersurface at the
moment of maximum expansion that allows the constraint equations to be solved
exactly. We find that when all the mass in the universe is condensed into a
small number of objects (<10) then the amount of backreaction in dust models
can be large, with O(1) deviations from the predictions of the corresponding
FLRW solutions. When the number of masses is large (>100), however, then our
measures of backreaction become small (<1%). This result does not rely on any
averaging procedures, which are notoriously hard to define uniquely in general
relativity, and so provides (to the best of our knowledge) the first exact and
unambiguous demonstration of backreaction in general relativistic cosmological
modelling. Discrete models such as these can therefore be used as laboratories
to test ideas about backreaction that could be applied in more complicated and
realistic settings.Comment: 13 pages, 9 figures. Corrections made to Tables IV and
Detecting and Characterizing Small Dense Bipartite-like Subgraphs by the Bipartiteness Ratio Measure
We study the problem of finding and characterizing subgraphs with small
\textit{bipartiteness ratio}. We give a bicriteria approximation algorithm
\verb|SwpDB| such that if there exists a subset of volume at most and
bipartiteness ratio , then for any , it finds a set
of volume at most and bipartiteness ratio at most
. By combining a truncation operation, we give a local
algorithm \verb|LocDB|, which has asymptotically the same approximation
guarantee as the algorithm \verb|SwpDB| on both the volume and bipartiteness
ratio of the output set, and runs in time
, independent of the size of the
graph. Finally, we give a spectral characterization of the small dense
bipartite-like subgraphs by using the th \textit{largest} eigenvalue of the
Laplacian of the graph.Comment: 17 pages; ISAAC 201
Introduction: politicised iconicity, adaptable stardom and Generation X celebrity in the contemporary mediascape
Distributed Drug Discovery, Part 2: Global Rehearsal of Alkylating Agents for the Synthesis of Resin-Bound Unnatural Amino Acids and Virtual D3 Catalog Construction
Optical energies of AllnN epilayers
Optical energy gaps are measured for high-quality Al1−xInxN-on-GaN epilayers with a range of compositions around the lattice match point using photoluminescence and photoluminescence excitation spectroscopy. These data are combined with structural data to determine the compositional dependence of emission and absorption energies. The trend indicates a very large bowing parameter of 6 eV and differences with earlier reports are discussed. Very large Stokes' shifts of 0.4-0.8 eV are observed in the composition range 0.13<x<0.24, increasing approximately linearly with InN fraction despite the change of sign of the piezoelectric fiel
A Hypergraph Dictatorship Test with Perfect Completeness
A hypergraph dictatorship test is first introduced by Samorodnitsky and
Trevisan and serves as a key component in their unique games based \PCP
construction. Such a test has oracle access to a collection of functions and
determines whether all the functions are the same dictatorship, or all their
low degree influences are Their test makes queries and has
amortized query complexity but has an inherent loss of
perfect completeness. In this paper we give an adaptive hypergraph dictatorship
test that achieves both perfect completeness and amortized query complexity
.Comment: Some minor correction
Failure mechanism of AlN nanocaps used to protect rare earth-implanted GaN during high temperature annealing
The structural properties of nanometric AlN caps, grown on GaN to prevent dissociation during high temperature annealing after Eu implantation, have been characterized by scanning electron microscopy and electron probe microanalysis. The caps provide good protection up to annealing temperatures of at least 1300 degrees C, but show localized failure in the form of irregularly shaped holes with a lateral size of 1-2 µm which extend through the cap into the GaN layer beneath. Compositional micrographs, obtained using wavelength dispersive x-ray analysis, suggest that these holes form when GaN dissociates and ejects through cracks already present in the as-grown AlN caps due to the large lattice mismatch between the two materials. Implantation damage enhances the formation of the holes during annealing. Simultaneous room temperature cathodoluminescence mapping showed that the Eu luminescence is reduced in N-poor regions. Hence, exposed GaN dissociates first by outdiffusion of nitrogen through AlN cracks, thereby opening a hole in the cap through which Ga subsequently evaporates
Distributed Drug Discovery, Part 3: Using D3 Methodology to Synthesize Analogs of an Anti-Melanoma Compound
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