1,788 research outputs found
Sampling Theorem and Discrete Fourier Transform on the Riemann Sphere
Using coherent-state techniques, we prove a sampling theorem for Majorana's
(holomorphic) functions on the Riemann sphere and we provide an exact
reconstruction formula as a convolution product of samples and a given
reconstruction kernel (a sinc-type function). We also discuss the effect of
over- and under-sampling. Sample points are roots of unity, a fact which allows
explicit inversion formulas for resolution and overlapping kernel operators
through the theory of Circulant Matrices and Rectangular Fourier Matrices. The
case of band-limited functions on the Riemann sphere, with spins up to , is
also considered. The connection with the standard Euler angle picture, in terms
of spherical harmonics, is established through a discrete Bargmann transform.Comment: 26 latex pages. Final version published in J. Fourier Anal. App
Efficient Syntax-Driven Lumping of Differential Equations
We present an algorithm to compute exact aggregations of a class of systems of ordinary differential equations (ODEs). Our approach consists in an extension of Paige and Tarjanâs seminal solution to the coarsest refinement problem by encoding an ODE system into a suitable discrete-state representation. In particular, we consider a simple extension of the syntax of elementary chemical reaction networks because (i) it can express ODEs with derivatives given by polynomials of degree at most two, which are relevant in many applications in natural sciences and engineering; and (ii) we can build on two recently introduced bisimulations, which yield two complementary notions of ODE lumping. Our algorithm computes the largest bisimulations in O(râ
sâ
logs)O(râ
sâ
logâĄs) time, where r is the number of monomials and s is the number of variables in the ODEs. Numerical experiments on real-world models from biochemistry, electrical engineering, and structural mechanics show that our prototype is able to handle ODEs with millions of variables and monomials, providing significant model reductions
What Does Brain Response to Neutral Faces Tell Us about Major Depression? Evidence from Machine Learning and fMRI
Introduction: A considerable number of previous studies have shown abnormalities in the processing of emotional faces in major depression. Fewer studies, however, have focused specifically on abnormal processing of neutral faces despite evidence that depressed patients are slow and less accurate at recognizing neutral expressions in comparison with healthy controls. The current study aimed to investigate whether this misclassification described behaviourally for neutral faces also occurred when classifying patterns of brain activation to neutral faces for these patients. Methods: Two independent depressed samples: (1) Nineteen medication-free patients with depression and 19 healthy volunteers and (2) Eighteen depressed individuals and 18 age and gender-ratio-matched healthy volunteers viewed emotional faces (sad/neutral; happy/neutral) during an fMRI experiment. We used a new pattern recognition framework: first, we trained the classifier to discriminate between two brain states (e.g. viewing happy faces vs. viewing neutral faces) using data only from healthy controls (HC). Second, we tested the classifier using patterns of brain activation of a patient and a healthy control for the same stimuli. Finally, we tested if the classifier's predictions (predictive probabilities) for emotional and neutral face classification were different for healthy controls and depressed patients. Results: Predictive probabilities to patterns of brain activation to neutral faces in both groups of patients were significantly lower in comparison to the healthy controls. This difference was specific to neutral faces. There were no significant differences in predictive probabilities to patterns of brain activation to sad faces (sample 1) and happy faces (samples 2) between depressed patients and healthy controls. Conclusions: Our results suggest that the pattern of brain activation to neutral faces in depressed patients is not consistent with the pattern observed in healthy controls subject to the same stimuli. This difference in brain activation might underlie the behavioural misinterpretation of the neutral faces content by the depressed patients. © 2013 Oliveira et al
Differential branching fraction and angular analysis of the decay B0âKâ0ÎŒ+ÎŒâ
The angular distribution and differential branching fraction of the decay B 0â K â0 ÎŒ + ÎŒ â are studied using a data sample, collected by the LHCb experiment in pp collisions at sâ=7 TeV, corresponding to an integrated luminosity of 1.0 fbâ1. Several angular observables are measured in bins of the dimuon invariant mass squared, q 2. A first measurement of the zero-crossing point of the forward-backward asymmetry of the dimuon system is also presented. The zero-crossing point is measured to be q20=4.9±0.9GeV2/c4 , where the uncertainty is the sum of statistical and systematic uncertainties. The results are consistent with the Standard Model predictions
Observation of two new baryon resonances
Two structures are observed close to the kinematic threshold in the mass spectrum in a sample of proton-proton collision data, corresponding
to an integrated luminosity of 3.0 fb recorded by the LHCb experiment.
In the quark model, two baryonic resonances with quark content are
expected in this mass region: the spin-parity and
states, denoted and .
Interpreting the structures as these resonances, we measure the mass
differences and the width of the heavier state to be
MeV,
MeV,
MeV, where the first and second
uncertainties are statistical and systematic, respectively. The width of the
lighter state is consistent with zero, and we place an upper limit of
MeV at 95% confidence level. Relative
production rates of these states are also reported.Comment: 17 pages, 2 figure
Observation of the decay
The decay is observed for the first
time, using proton-proton collisions collected with the LHCb detector
corresponding to an integrated luminosity of 3fb. A signal yield of
decays is reported with a significance of 6.2 standard deviations.
The ratio of the branching fraction of \B_c \rightarrow J/\psi K^+ K^- \pi^+
decays to that of decays is measured to be
, where the first uncertainty is statistical and the
second is systematic.Comment: 18 pages, 2 figure
Measurement of the mass and lifetime of the baryon
A proton-proton collision data sample, corresponding to an integrated
luminosity of 3 fb collected by LHCb at and 8 TeV, is used
to reconstruct , decays. Using the , decay mode for calibration, the lifetime ratio and absolute
lifetime of the baryon are measured to be \begin{align*}
\frac{\tau_{\Omega_b^-}}{\tau_{\Xi_b^-}} &= 1.11\pm0.16\pm0.03, \\
\tau_{\Omega_b^-} &= 1.78\pm0.26\pm0.05\pm0.06~{\rm ps}, \end{align*} where the
uncertainties are statistical, systematic and from the calibration mode (for
only). A measurement is also made of the mass difference,
, and the corresponding mass, which
yields \begin{align*} m_{\Omega_b^-}-m_{\Xi_b^-} &= 247.4\pm3.2\pm0.5~{\rm
MeV}/c^2, \\ m_{\Omega_b^-} &= 6045.1\pm3.2\pm 0.5\pm0.6~{\rm MeV}/c^2.
\end{align*} These results are consistent with previous measurements.Comment: 11 pages, 5 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-2016-008.htm
Measurement of the lifetime
Using a data set corresponding to an integrated luminosity of ,
collected by the LHCb experiment in collisions at centre-of-mass energies
of 7 and 8 TeV, the effective lifetime in the
decay mode, , is measured to be ps. Assuming
conservation, corresponds to the lifetime of the light
mass eigenstate. This is the first measurement of the effective
lifetime in this decay mode.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-2016-017.htm
Study of charmonium production in b -hadron decays and first evidence for the decay Bs0
Using decays to Ï-meson pairs, the inclusive production of charmonium states in b-hadron decays is studied with pp collision data corresponding to an integrated luminosity of 3.0 fbâ1, collected by the LHCb experiment at centre-of-mass energies of 7 and 8 TeV. Denoting byBC ⥠B(b â C X) Ă B(C â ÏÏ) the inclusive branching fraction of a b hadron to a charmonium state C that decays into a pair of Ï mesons, ratios RC1C2 ⥠BC1 /BC2 are determined as RÏc0ηc(1S) = 0.147 ± 0.023 ± 0.011, RÏc1ηc(1S) =0.073 ± 0.016 ± 0.006, RÏc2ηc(1S) = 0.081 ± 0.013 ± 0.005,RÏc1 Ïc0 = 0.50 ± 0.11 ± 0.01, RÏc2 Ïc0 = 0.56 ± 0.10 ± 0.01and Rηc(2S)ηc(1S) = 0.040 ± 0.011 ± 0.004. Here and below the first uncertainties are statistical and the second systematic.Upper limits at 90% confidence level for the inclusive production of X(3872), X(3915) and Ïc2(2P) states are obtained as RX(3872)Ïc1 < 0.34, RX(3915)Ïc0 < 0.12 andRÏc2(2P)Ïc2 < 0.16. Differential cross-sections as a function of transverse momentum are measured for the ηc(1S) andÏc states. The branching fraction of the decay B0s â ÏÏÏ is measured for the first time, B(B0s â ÏÏÏ) = (2.15±0.54±0.28±0.21B)Ă10â6. Here the third uncertainty is due to the branching fraction of the decay B0s â ÏÏ, which is used for normalization. No evidence for intermediate resonances is seen. A preferentially transverse Ï polarization is observed.The measurements allow the determination of the ratio of the branching fractions for the ηc(1S) decays to ÏÏ and p p asB(ηc(1S)â ÏÏ)/B(ηc(1S)â p p) = 1.79 ± 0.14 ± 0.32
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