1,131 research outputs found
On variables with few occurrences in conjunctive normal forms
We consider the question of the existence of variables with few occurrences
in boolean conjunctive normal forms (clause-sets). Let mvd(F) for a clause-set
F denote the minimal variable-degree, the minimum of the number of occurrences
of variables. Our main result is an upper bound mvd(F) <= nM(surp(F)) <=
surp(F) + 1 + log_2(surp(F)) for lean clause-sets F in dependency on the
surplus surp(F).
- Lean clause-sets, defined as having no non-trivial autarkies, generalise
minimally unsatisfiable clause-sets.
- For the surplus we have surp(F) <= delta(F) = c(F) - n(F), using the
deficiency delta(F) of clause-sets, the difference between the number of
clauses and the number of variables.
- nM(k) is the k-th "non-Mersenne" number, skipping in the sequence of
natural numbers all numbers of the form 2^n - 1.
We conjecture that this bound is nearly precise for minimally unsatisfiable
clause-sets.
As an application of the upper bound we obtain that (arbitrary!) clause-sets
F with mvd(F) > nM(surp(F)) must have a non-trivial autarky (so clauses can be
removed satisfiability-equivalently by an assignment satisfying some clauses
and not touching the other clauses). It is open whether such an autarky can be
found in polynomial time.
As a future application we discuss the classification of minimally
unsatisfiable clause-sets depending on the deficiency.Comment: 14 pages. Revision contains more explanations, and more information
regarding the sharpness of the boun
Coupled superconducting qudit-resonator system: Energy spectrum, state population, and state transition under microwave drive
Superconducting quantum multilevel systems coupled to resonators have recently been considered in some
applications such as microwave lasing and high-fidelity quantum logical gates. In this work, using an rf-SQUID
type phase qudit coupled to a microwave coplanar waveguide resonator, we study both theoretically and
experimentally the energy spectrum of the system when the qudit level spacings are varied around the resonator
frequency by changing the magnetic flux applied to the qudit loop. We show that the experimental result can
be well described by a theoretical model that extends from the usual two-level Jaynes-Cummings system to the
present four-level system. It is also shown that due to the small anharmonicity of the phase device a simplified
model capturing the leading state interactions fits the experimental spectra very well. Furthermore we use the
Lindblad master equation containing various relaxation and dephasing processes to calculate the level populations
in the simpler qutrit-resonator system, which allows a clear understanding of the dynamics of the system under
the microwave drive. Our results help to better understand and perform the experiments of coupled multilevel
and resonator systems and can be applied in the case of transmon or Xmon qudits having similar anharmonicity
to the present phase device.This work was supported by the Ministry of Science and Technology of China (Grants No. 2014CB921202, No. 2015CB921104, and No. 2016YFA0300601),the National Natural Science Foundation of China (Grants No. 91321208 and No. 11674380)the Key Research Program of the Chinese Academy of Sciences (Grant No. XDPB08-3)S.H. acknowledges support by the US NSF (PHY-1314861)
Effect of nanostructuration on compressibility of cubic BN
Compressibility of high-purity nanostructured cBN has been studied under
quasi-hydrostatic conditions at 300 K up to 35 GPa using diamond anvil cell and
angle-dispersive synchrotron X-ray powder diffraction. A data fit to the Vinet
equation of state yields the values of the bulk modulus B0 of 375(4) GPa with
its first pressure derivative B0' of 2.3(3). The nanometer grain size (\sim20
nm) results in decrease of the bulk modulus by ~9%
The Case for Quantum Key Distribution
Quantum key distribution (QKD) promises secure key agreement by using quantum
mechanical systems. We argue that QKD will be an important part of future
cryptographic infrastructures. It can provide long-term confidentiality for
encrypted information without reliance on computational assumptions. Although
QKD still requires authentication to prevent man-in-the-middle attacks, it can
make use of either information-theoretically secure symmetric key
authentication or computationally secure public key authentication: even when
using public key authentication, we argue that QKD still offers stronger
security than classical key agreement.Comment: 12 pages, 1 figure; to appear in proceedings of QuantumComm 2009
Workshop on Quantum and Classical Information Security; version 2 minor
content revision
Detection of relic gravitational waves in the CMB: Prospects for CMBPol mission
Detection of relic gravitational waves, through their imprint in the cosmic
microwave background radiation, is one of the most important tasks for the
planned CMBPol mission. In the simplest viable theoretical models the
gravitational wave background is characterized by two parameters, the
tensor-to-scalar ratio and the tensor spectral index . In this paper,
we analyze the potential joint constraints on these two parameters, and
, using the potential observations of the CMBPol mission, which is
expected to detect the relic gravitational waves if . The
influence of the contaminations, including cosmic weak lensing, various
foreground emissions, and systematical errors, is discussed.Comment: 26 pages, 19 figures, 4 tables; JCAP in pres
Perturbations in electromagnetic dark energy
It has been recently proposed that the presence of a temporal electromagnetic
field on cosmological scales could explain the phase of accelerated expansion
that the universe is currently undergoing. The field contributes as a
cosmological constant and therefore, the homogeneous cosmology produced by such
a model is exactly the same as that of CDM. However, unlike a
cosmological constant term, electromagnetic fields can acquire perturbations
which in principle could affect CMB anisotropies and structure formation. In
this work, we study the evolution of inhomogeneous scalar perturbations in this
model. We show that provided the initial electromagnetic fluctuations generated
during inflation are small, the model is perfectly compatible with both CMB and
large scale structure observations at the same level of accuracy as
CDM.Comment: 12 pages, 3 figures. Added new comments to match the published
versio
Can residuals of the Solar system foreground explain low multipole anomalies of the CMB ?
The low multipole anomalies of the Cosmic Microwave Background has received
much attention during the last few years. It is still not ascertained whether
these anomalies are indeed primordial or the result of systematics or
foregrounds. An example of a foreground, which could generate some non-Gaussian
and statistically anisotropic features at low multipole range, is the very
symmetric Kuiper Belt in the outer solar system. In this paper, expanding upon
the methods presented by Maris et al. (2011), we investigate the contributions
from the Kuiper Belt objects (KBO) to the WMAP ILC 7 map, whereby we can
minimize the contrast in power between even and odd multipoles in the CMB,
discussed discussed by Kim & Naselsky (2010). We submit our KBO de-correlated
CMB signal to several tests, to analyze its validity, and find that
incorporation of the KBO emission can decrease the quadrupole-octupole
alignment and parity asymmetry problems, provided that the KBO signals has a
non-cosmological dipole modulation, associated with the statistical anisotropy
of the ILC 7 map. Additionally, we show that the amplitude of the dipole
modulation, within a 2 sigma interval, is in agreement with the corresponding
amplitudes, discussed by Lew (2008).Comment: 24 pages, 9 figures, 5 tables. Matches version in JCA
Contributions from SUSY-FCNC couplings to the interpretation of the HyperCP events for the decay \Sigma^+ \to p \mu^+ \mu^-
The observation of three events for the decay
with a dimuon invariant mass of MeV by the HyperCP collaboration
imply that a new particle X may be needed to explain the observed dimuon
invariant mass distribution. We show that there are regions in the SUSY-FCNC
parameter space where the in the NMSSM can be used to explain the
HyperCP events without contradicting all the existing constraints from the
measurements of the kaon decays, and the constraints from the
mixing are automatically satisfied once the constraints from kaon decays are
satisfied.Comment: 18 pages, 7 figure
Selection of Wavelet Subbands Using Genetic Algorithm for Face Recognition
Abstract. In this paper, a novel representation called the subband face is proposed for face recognition. The subband face is generated from selected subbands obtained using wavelet decomposition of the original face image. It is surmised that certain subbands contain information that is more significant for discriminating faces than other subbands. The problem of subband selection is cast as a combinatorial optimization problem and genetic algorithm (GA) is used to find the optimum subband combination by maximizing Fisher ratio of the training features. The performance of the GA selected subband face is evaluated using three face databases and compared with other wavelet-based representations.
Equation of state and phonon frequency calculations of diamond at high pressures
The pressure-volume relationship and the zone-center optical phonon frequency
of cubic diamond at pressures up to 600 GPa have been calculated based on
Density Functional Theory within the Local Density Approximation and the
Generalized Gradient Approximation. Three different approaches, viz. a
pseudopotential method applied in the basis of plane waves, an all-electron
method relying on Augmented Plane Waves plus Local Orbitals, and an
intermediate approach implemented in the basis of Projector Augmented Waves
have been used. All these methods and approximations yield consistent results
for the pressure derivative of the bulk modulus and the volume dependence of
the mode Grueneisen parameter of diamond. The results are at variance with
recent precise measurements up to 140 GPa. Possible implications for the
experimental pressure determination based on the ruby luminescence method are
discussed.Comment: 10 pages, 6 figure
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