16,683 research outputs found
Strengths and Weaknesses of Quantum Computing
Recently a great deal of attention has focused on quantum computation
following a sequence of results suggesting that quantum computers are more
powerful than classical probabilistic computers. Following Shor's result that
factoring and the extraction of discrete logarithms are both solvable in
quantum polynomial time, it is natural to ask whether all of NP can be
efficiently solved in quantum polynomial time. In this paper, we address this
question by proving that relative to an oracle chosen uniformly at random, with
probability 1, the class NP cannot be solved on a quantum Turing machine in
time . We also show that relative to a permutation oracle chosen
uniformly at random, with probability 1, the class cannot be
solved on a quantum Turing machine in time . The former bound is
tight since recent work of Grover shows how to accept the class NP relative to
any oracle on a quantum computer in time .Comment: 18 pages, latex, no figures, to appear in SIAM Journal on Computing
(special issue on quantum computing
CCS from industrial sources
The literature concerning the application of CCS to industry is reviewed. Costs are presented for different sectors including ``high purity'' (processes which inherently produce a high concentration of CO2), cement, iron and steel, refinery and biomass. The application of CCS to industry is a field which has had much less attention than its application to the electricity production sector. Costs range from less than 2011 100/tCO 2 . In the words of a synthesis report from the United Nations Industrial Development Organisation (UNIDO) ``This area has so far not been the focus of discussions and therefore much attention needs to be paid to the application of CCS to industrial sources if the full potential of CCS is to be unlocked''
Deriving Boltzmann Equations from Kadanoff-Baym Equations in Curved Space-Time
To calculate the baryon asymmetry in the baryogenesis via leptogenesis
scenario one usually uses Boltzmann equations with transition amplitudes
computed in vacuum. However, the hot and dense medium and, potentially, the
expansion of the universe can affect the collision terms and hence the
generated asymmetry. In this paper we derive the Boltzmann equation in the
curved space-time from (first-principle) Kadanoff-Baym equations. As one
expects from general considerations, the derived equations are covariant
generalizations of the corresponding equations in Minkowski space-time. We find
that, after the necessary approximations have been performed, only the
left-hand side of the Boltzmann equation depends on the space-time metric. The
amplitudes in the collision term on the right--hand side are independent of the
metric, which justifies earlier calculations where this has been assumed
implicitly. At tree level, the matrix elements coincide with those computed in
vacuum. However, the loop contributions involve additional integrals over the
the distribution function.Comment: 14 pages, 5 figures, extended discussion of the constraint equations
and the solution for the spectral functio
Telescopes don't make catalogues!
Astronomical instruments make intensity measurements; any precise
astronomical experiment ought to involve modeling those measurements. People
make catalogues, but because a catalogue requires hard decisions about
calibration and detection, no catalogue can contain all of the information in
the raw pixels relevant to most scientific investigations. Here we advocate
making catalogue-like data outputs that permit investigators to test hypotheses
with almost the power of the original image pixels. The key is to provide users
with approximations to likelihood tests against the raw image pixels. We
advocate three options, in order of increasing difficulty: The first is to
define catalogue entries and associated uncertainties such that the catalogue
contains the parameters of an approximate description of the image-level
likelihood function. The second is to produce a K-catalogue sampling in
"catalogue space" that samples a posterior probability distribution of
catalogues given the data. The third is to expose a web service or equivalent
that can re-compute on demand the full image-level likelihood for any
user-supplied catalogue.Comment: presented at ELSA 2010: Gaia, at the frontiers of astrometr
Orthosymplectically invariant functions in superspace
The notion of spherically symmetric superfunctions as functions invariant
under the orthosymplectic group is introduced. This leads to dimensional
reduction theorems for differentiation and integration in superspace. These
spherically symmetric functions can be used to solve orthosymplectically
invariant Schroedinger equations in superspace, such as the (an)harmonic
oscillator or the Kepler problem. Finally the obtained machinery is used to
prove the Funk-Hecke theorem and Bochner's relations in superspace.Comment: J. Math. Phy
Quantum Weakly Nondeterministic Communication Complexity
We study the weakest model of quantum nondeterminism in which a classical
proof has to be checked with probability one by a quantum protocol. We show the
first separation between classical nondeterministic communication complexity
and this model of quantum nondeterministic communication complexity for a total
function. This separation is quadratic.Comment: 12 pages. v3: minor correction
Orbit closures in the enhanced nilpotent cone
We study the orbits of in the enhanced nilpotent cone
, where is the variety of nilpotent
endomorphisms of . These orbits are parametrized by bipartitions of , and we prove that the closure ordering corresponds to a natural partial
order on bipartitions. Moreover, we prove that the local intersection
cohomology of the orbit closures is given by certain bipartition analogues of
Kostka polynomials, defined by Shoji. Finally, we make a connection with Kato's
exotic nilpotent cone in type C, proving that the closure ordering is the same,
and conjecturing that the intersection cohomology is the same but with degrees
doubled.Comment: 32 pages. Update (August 2010): There is an error in the proof of
Theorem 4.7, in this version and the almost-identical published version. See
the corrigendum arXiv:1008.1117 for independent proofs of later results that
depend on that statemen
Simplifying responsible research and innovation â a tool building in societal readiness into research
Researchers and research funders are increasingly seeking to ensure their work is aligned to societal needs and to prevent it from having foreseeable negative impacts, particularly in fast moving and ethically sensitive fields. In this post, Stefan de Jong, Michael J. Bernstein and Ingeborg Meijer, describe their work developing a tool that facilitates researchers and research funders to incorporate responsible research and innovation values into their work
The Low-Energy Theorem of Pion Photoproduction in Soliton Models of the Nucleon
We derive an analytic expression for the Kroll-Ruderman amplitude up to the
order 1/N_C for general Skyrme-type models of the nucleon. Due to the
degeneracy of intermediate N- and Delta-states we find deviations from the
standard low-energy theorem for the photoproduction of neutral pions.Comment: 17 pages, LATEX, SI-93-TP3S
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