1,827 research outputs found
On the Link between Gaussian Homotopy Continuation and Convex Envelopes
Abstract. The continuation method is a popular heuristic in computer vision for nonconvex optimization. The idea is to start from a simpli-fied problem and gradually deform it to the actual task while tracking the solution. It was first used in computer vision under the name of graduated nonconvexity. Since then, it has been utilized explicitly or im-plicitly in various applications. In fact, state-of-the-art optical flow and shape estimation rely on a form of continuation. Despite its empirical success, there is little theoretical understanding of this method. This work provides some novel insights into this technique. Specifically, there are many ways to choose the initial problem and many ways to progres-sively deform it to the original task. However, here we show that when this process is constructed by Gaussian smoothing, it is optimal in a specific sense. In fact, we prove that Gaussian smoothing emerges from the best affine approximation to Vese’s nonlinear PDE. The latter PDE evolves any function to its convex envelope, hence providing the optimal convexification
Study of and decays and determination of the CKM angle
We report a study of the suppressed and favored
decays, where the neutral meson is detected
through its decays to the and CP-even and
final states. The measurement is carried out using a proton-proton
collision data sample collected by the LHCb experiment, corresponding to an
integrated luminosity of 3.0~fb. We observe the first significant
signals in the CP-even final states of the meson for both the suppressed
and favored modes, as well as
in the doubly Cabibbo-suppressed final state of the decay. Evidence for the ADS suppressed decay , with , is also presented. From the observed
yields in the , and their
charge conjugate decay modes, we measure the value of the weak phase to be
. This is one of the most precise
single-measurement determinations of to date.Comment: 22 pages, 9 figures; All figures and tables, along with any
supplementary material and additional information, are available at
https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2015-020.htm
Observation of resonances consistent with pentaquark states in decays
Observations of exotic structures in the channel, that we refer to
as pentaquark-charmonium states, in decays are
presented. The data sample corresponds to an integrated luminosity of 3/fb
acquired with the LHCb detector from 7 and 8 TeV pp collisions. An amplitude
analysis is performed on the three-body final-state that reproduces the
two-body mass and angular distributions. To obtain a satisfactory fit of the
structures seen in the mass spectrum, it is necessary to include two
Breit-Wigner amplitudes that each describe a resonant state. The significance
of each of these resonances is more than 9 standard deviations. One has a mass
of MeV and a width of MeV, while the second
is narrower, with a mass of MeV and a width of MeV. The preferred assignments are of opposite parity, with one
state having spin 3/2 and the other 5/2.Comment: 48 pages, 18 figures including the supplementary material, v2 after
referee's comments, now 19 figure
Study of the production of and hadrons in collisions and first measurement of the branching fraction
The product of the () differential production
cross-section and the branching fraction of the decay () is
measured as a function of the beauty hadron transverse momentum, ,
and rapidity, . The kinematic region of the measurements is and . The measurements use a data sample
corresponding to an integrated luminosity of collected by the
LHCb detector in collisions at centre-of-mass energies in 2011 and in 2012. Based on previous LHCb
results of the fragmentation fraction ratio, , the
branching fraction of the decay is
measured to be \begin{equation*} \mathcal{B}(\Lambda_b^0\rightarrow J/\psi
pK^-)= (3.17\pm0.04\pm0.07\pm0.34^{+0.45}_{-0.28})\times10^{-4},
\end{equation*} where the first uncertainty is statistical, the second is
systematic, the third is due to the uncertainty on the branching fraction of
the decay , and the
fourth is due to the knowledge of . The sum of the
asymmetries in the production and decay between and
is also measured as a function of and .
The previously published branching fraction of , relative to that of , is updated.
The branching fractions of are determined.Comment: 29 pages, 19figures. All figures and tables, along with any
supplementary material and additional information, are available at
https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2015-032.htm
Evidence for the strangeness-changing weak decay
Using a collision data sample corresponding to an integrated luminosity
of 3.0~fb, collected by the LHCb detector, we present the first search
for the strangeness-changing weak decay . No
hadron decay of this type has been seen before. A signal for this decay,
corresponding to a significance of 3.2 standard deviations, is reported. The
relative rate is measured to be
, where and
are the and fragmentation
fractions, and is the branching
fraction. Assuming is bounded between 0.1 and
0.3, the branching fraction would lie
in the range from to .Comment: 7 pages, 2 figures, All figures and tables, along with any
supplementary material and additional information, are available at
https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2015-047.htm
Search for hidden-sector bosons in decays
A search is presented for hidden-sector bosons, , produced in the decay
, with and
. The search is performed using -collision data
corresponding to 3.0 fb collected with the LHCb detector. No significant
signal is observed in the accessible mass range
MeV, and upper limits are placed on the branching fraction product
as
a function of the mass and lifetime of the boson. These limits are of
the order of for lifetimes less than 100 ps over most of the
range, and place the most stringent constraints to date on many
theories that predict the existence of additional low-mass bosons.Comment: All figures and tables, along with supplementary material, are
available at
https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2015-036.htm
Study of boson production in association with beauty and charm
The associated production of a boson with a jet originating from either a
light parton or heavy-flavor quark is studied in the forward region using
proton-proton collisions. The analysis uses data corresponding to integrated
luminosities of 1.0 and collected with the LHCb detector
at center-of-mass energies of 7 and 8 TeV, respectively. The bosons are
reconstructed using the decay and muons with a transverse
momentum, , larger than 20 GeV in the pseudorapidity range
GeV
and . The sum of the muon and jet momenta must satisfy
GeV. The fraction of jet events that originate from beauty
and charm quarks is measured, along with the charge asymmetries of the
and production cross-sections. The ratio of the jet to
jet production cross-sections is also measured using the
decay. All results are in agreement with Standard Model predictions
Measurements of long-range near-side angular correlations in TeV proton-lead collisions in the forward region
Two-particle angular correlations are studied in proton-lead collisions at a
nucleon-nucleon centre-of-mass energy of TeV, collected
with the LHCb detector at the LHC. The analysis is based on data recorded in
two beam configurations, in which either the direction of the proton or that of
the lead ion is analysed. The correlations are measured in the laboratory
system as a function of relative pseudorapidity, , and relative
azimuthal angle, , for events in different classes of event
activity and for different bins of particle transverse momentum. In
high-activity events a long-range correlation on the near side, , is observed in the pseudorapidity range . This
measurement of long-range correlations on the near side in proton-lead
collisions extends previous observations into the forward region up to
. The correlation increases with growing event activity and is found
to be more pronounced in the direction of the lead beam. However, the
correlation in the direction of the lead and proton beams are found to be
compatible when comparing events with similar absolute activity in the
direction analysed.Comment: All figures and tables, along with any supplementary material and
additional information, are available at
https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2015-040.htm
Measurement of the branching fraction ratio
Using collision data collected by LHCb at center-of-mass energies
= 7 TeV and 8 TeV, corresponding to an integrated luminosity of 3
fb, the ratio of the branching fraction of the decay relative to that of the
decay is measured to be 0.268 0.032 (stat) 0.007 (syst) 0.006
(BF). The first uncertainty is statistical, the second is systematic, and the
third is due to the uncertainties on the branching fractions of the and decays. This
measurement is consistent with the previous LHCb result, and the statistical
uncertainty is halved.Comment: 17 pages including author list, 2 figure
Amplitude analysis of decays
The Dalitz plot distribution of decays
is studied using a data sample corresponding to of
collision data recorded by the LHCb experiment during 2011 and 2012. The data
are described by an amplitude model that contains contributions from
intermediate , , and
resonances. The model also contains components to describe broad structures,
including the and resonances, in the
S-wave and the S- and P-waves. The masses and widths of the
and resonances are measured, as are the complex
amplitudes and fit fractions for all components included in the amplitude
model. The model obtained will be an integral part of a future determination of
the angle of the CKM quark mixing matrix using decays.Comment: 33 pages, 12 figures; updated for publicatio
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