24,313 research outputs found
Lower Bounds in the Preprocessing and Query Phases of Routing Algorithms
In the last decade, there has been a substantial amount of research in
finding routing algorithms designed specifically to run on real-world graphs.
In 2010, Abraham et al. showed upper bounds on the query time in terms of a
graph's highway dimension and diameter for the current fastest routing
algorithms, including contraction hierarchies, transit node routing, and hub
labeling. In this paper, we show corresponding lower bounds for the same three
algorithms. We also show how to improve a result by Milosavljevic which lower
bounds the number of shortcuts added in the preprocessing stage for contraction
hierarchies. We relax the assumption of an optimal contraction order (which is
NP-hard to compute), allowing the result to be applicable to real-world
instances. Finally, we give a proof that optimal preprocessing for hub labeling
is NP-hard. Hardness of optimal preprocessing is known for most routing
algorithms, and was suspected to be true for hub labeling
Semileptonic B Decays and Determination of |Vub|
Semileptonic decays of the B mesons provide an excellent probe for the weak
and strong interactions of the bottom quark. The large data samples collected
at the B Factories have pushed the experimental studies of the semileptonic B
decays to a new height and stimulated significant theoretical developments. I
review recent progresses in this fast-evolving field, with an emphasis on the
determination of the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element
|Vub|.Comment: 16 pages, 4 figures, accepted by Mod. Phys. Lett.
On The Expected Photon Spectrum in B -> X_s + gamma and Its Uses
Measuring the photon energy spectrum in radiative B decays provides essential
help for gaining theoretical control over semileptonic B transitions. The
hadronic recoil mass distribution in B -> X_u \ell\nu promises the best
environment for determining |V_ub|. The theoretical uncertainties are largest
in the domain of low values of the lepton pair mass q^2. Universality relations
allow to describe this domain reliably in terms of the photon spectrum in B ->
X_s + \gamma. A method is proposed to incorporate 1/m_b corrections into this
relation. The low-E_\gamma tail in radiative decays is important in the context
of extracting |V_ub|. We argue that CLEO's recent fit to the spectrum
underestimates the fraction of the photon spectrum below 2 GeV. Potentially
significant uncertainties enter in the theoretical evaluation of the integrated
end-point lepton spectrum or the B -> X_u \ell\nu width with a too high value
of the lower cut on q^2 in alternative approaches to |V_ub|.Comment: 24 pages, 6 figures, LaTeX. Revised: Complete version. Numerical
predictions are improved and the estimate for the decay fraction revised. The
theoretical expectations for the decay fraction and the spectrum itself are
given on the plot
Shape-Function Effects and Split Matching in B-> Xs l+ l-
We derive the triply differential spectrum for the inclusive rare decay B ->
Xs l+ l- in the shape function region, in which Xs is jet-like with . Experimental cuts make this a relevant region. The
perturbative and non-perturbative parts of the matrix elements can be defined
with the Soft-Collinear Effective Theory, which is used to incorporate alphas
corrections consistently. We show that, with a suitable power counting for the
dilepton invariant mass, the same universal jet and shape functions appear as
in B-> Xs gamma and B-> Xu l nu decays. Parts of the usual alphas(m_b)
corrections go into the jet function at a lower scale, and parts go into the
non-perturbative shape function. For B -> Xs l+ l-, the perturbative series in
alphas are of a different character above and below mu=mb. We introduce a
``split matching'' method that allows the series in these regions to be treated
independently.Comment: 33 pages; journal versio
Linearly polarized GHz magnetization dynamics of spin helix modes in the ferrimagnetic insulator CuOSeO
Linear dichroism -- the polarization dependent absorption of electromagnetic
waves -- is routinely exploited in applications as diverse as structure
determination of DNA or polarization filters in optical technologies. Here
filamentary absorbers with a large length-to-width ratio are a prerequisite.
For magnetization dynamics in the few GHz frequency regime strictly linear
dichroism was not observed for more than eight decades. Here, we show that the
bulk chiral magnet CuOSeO exhibits linearly polarized magnetization
dynamics at an unexpectedly small frequency of about 2 GHz. Unlike optical
filters that are assembled from filamentary absorbers, the magnet provides
linear polarization as a bulk material for an extremely wide range of
length-to-width ratios. In addition, the polarization plane of a given mode can
be switched by 90 via a tiny variation in width. Our findings shed a
new light on magnetization dynamics in that ferrimagnetic ordering combined
with anisotropic exchange interaction offers strictly linear polarization and
cross-polarized modes for a broad spectrum of sample shapes. The discovery
allows for novel design rules and optimization of microwave-to-magnon
transduction in emerging microwave technologies.Comment: 20 pages, 4 figure
Collisionless energy absorption in the short-pulse intense laser-cluster interaction
In a previous Letter [Phys. Rev. Lett. 96, 123401 (2006)] we have shown by
means of three-dimensional particle-in-cell simulations and a simple
rigid-sphere model that nonlinear resonance absorption is the dominant
collisionless absorption mechanism in the intense, short-pulse laser cluster
interaction. In this paper we present a more detailed account of the matter. In
particular we show that the absorption efficiency is almost independent of the
laser polarization. In the rigid-sphere model, the absorbed energy increases by
many orders of magnitude at a certain threshold laser intensity. The
particle-in-cell results display maximum fractional absorption around the same
intensity. We calculate the threshold intensity and show that it is
underestimated by the common over-barrier ionization estimate.Comment: 12 pages, 13 figures, RevTeX
Increasing the Reliability of Adaptive Quadrature Using Explicit Interpolants
We present two new adaptive quadrature routines. Both routines differ from
previously published algorithms in many aspects, most significantly in how they
represent the integrand, how they treat non-numerical values of the integrand,
how they deal with improper divergent integrals and how they estimate the
integration error. The main focus of these improvements is to increase the
reliability of the algorithms without significantly impacting their efficiency.
Both algorithms are implemented in Matlab and tested using both the "families"
suggested by Lyness and Kaganove and the battery test used by Gander and
Gautschi and Kahaner. They are shown to be more reliable, albeit in some cases
less efficient, than other commonly-used adaptive integrators.Comment: 32 pages, submitted to ACM Transactions on Mathematical Softwar
Perturbations in the relaxation mechanism for a large cosmological constant
Recently, a mechanism for relaxing a large cosmological constant (CC) has
been proposed [arxiv:0902.2215], which permits solutions with low Hubble rates
at late times without fine-tuning. The setup is implemented in the LXCDM
framework, and we found a reasonable cosmological background evolution similar
to the LCDM model with a fine-tuned CC. In this work we analyse analytically
the perturbations in this relaxation model, and we show that their evolution is
also similar to the LCDM model, especially in the matter era. Some tracking
properties of the vacuum energy are discussed, too.Comment: 18 pages, LaTeX; discussion improved, accepted by CQ
Scalable design of tailored soft pulses for coherent control
We present a scalable scheme to design optimized soft pulses and pulse
sequences for coherent control of interacting quantum many-body systems. The
scheme is based on the cluster expansion and the time dependent perturbation
theory implemented numerically. This approach offers a dramatic advantage in
numerical efficiency, and it is also more convenient than the commonly used
Magnus expansion, especially when dealing with higher order terms. We
illustrate the scheme by designing 2nd-order pi-pulses and a 6th-order 8-pulse
refocusing sequence for a chain of qubits with nearest-neighbor couplings. We
also discuss the performance of soft-pulse refocusing sequences in suppressing
decoherence due to low-frequency environment.Comment: 4 pages, 2 tables. (modified first table, references added, minor
text changes
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