31,486 research outputs found
Asymptotic Generalization Bound of Fisher's Linear Discriminant Analysis
Fisher's linear discriminant analysis (FLDA) is an important dimension
reduction method in statistical pattern recognition. It has been shown that
FLDA is asymptotically Bayes optimal under the homoscedastic Gaussian
assumption. However, this classical result has the following two major
limitations: 1) it holds only for a fixed dimensionality , and thus does not
apply when and the training sample size are proportionally large; 2) it
does not provide a quantitative description on how the generalization ability
of FLDA is affected by and . In this paper, we present an asymptotic
generalization analysis of FLDA based on random matrix theory, in a setting
where both and increase and . The
obtained lower bound of the generalization discrimination power overcomes both
limitations of the classical result, i.e., it is applicable when and
are proportionally large and provides a quantitative description of the
generalization ability of FLDA in terms of the ratio and the
population discrimination power. Besides, the discrimination power bound also
leads to an upper bound on the generalization error of binary-classification
with FLDA
Detecting the orbital character of the spin fluctuation in the Iron-based superconductors with the resonant inelastic X-ray scattering spectroscopy
The orbital distribution of the spin fluctuation in the iron-based
superconductors(IBSs) is the key information needed to understand the
magnetism, superconductivity and electronic nematicity in these multi-orbital
systems. In this work, we propose that the resonant inelastic X-ray
scattering(RIXS) technique can be used to probe selectively the spin
fluctuation on different Fe orbitals. In particular, the spin fluctuation
on the three orbitals, namely, the , and the
orbital, can be selectively probed in the
scattering geometry by aligning the direction of the outgoing photon in the
, and direction. Such orbital-resolved information on the spin
fluctuation is invaluable for the study of the orbital-selective physics in the
IBSs and can greatly advance our understanding on the relation between orbital
ordering and spin nematicity in the IBSs and the orbital-selective pairing
mechanism in these multi-orbital systems.Comment: 6 pages with new and more informative figures, the explicit form of
the RIXS matrix element is provided, and the discussion part has been
rewritte
Vanishing pseudogap around in an electron-doped high- superconductor: a simple picture
Recent ARPES measurement on electron-doped cuprate
finds
that the pseudogap along the boundary of the antiferromagnetic Brillouin
zone(AFBZ) exhibits dramatic momentum dependence. In particular, the pseudogap
vanishes in a finite region around the anti-nodal point, in which a single
broadened peak emerges at the un-renormalized quasiparticle energy. Such an
observation is argued to be inconsistent with the antiferromagnetic(AFM)
band-folding picture, which predicts a constant pseudogap along the AFBZ
boundary. On the other hand, it is claimed that the experimental results are
consistent with the prediction of the cluster dynamical mean field
theory(CDMFT) simulation on the Hubbard model, in which the pseudogap is
interpreted as a s-wave splitting between the Hubbard bands and the in-gap
states. Here we show that the observed momentum dependence of the pseudogap is
indeed consistent with AFM band-folding picture, provided that we assume the
existence of a strongly momentum dependent quasiparticle scattering rate. More
specifically, we show that the quasiparticle scattering rate acts to reduce the
spectral gap induced by AFM band-folding effect. The new quasiparticle poles
corresponding to the AF-split bands can even be totally eliminated when the
scattering rate exceeds the bare band folding gap, leaving the system with a
single pole at the un-renormalized quasiparticle energy. We predict that the
pseudogap should close in a square root fashion as we move toward
along the AFBZ boundary. Our results illustrates again that the quasiparticle
scattering rate can play a much more profound role than simply broadening the
quasiparticle peak in the quasiparticle dynamics of strongly correlated
electron systems.Comment: 5 pages, 2 figures, new references adde
Is a molecular state
Assuming the newly observed to be a molecular state of , we calculate the partial widths of and within the light front
model (LFM). is the channel by which was
observed, our calculation indicates that it is indeed one of the dominant modes
whose width can be in the range of a few MeV depending on the model parameters.
Similar to and , Voloshin suggested that there should be a
resonance at 4030 MeV which can be a molecular state of .
Then we go on calculating its decay rates to all the aforementioned final
states and as well the . It is found that if is a
molecular state of , the partial width of
is rather small, but the rate of
is even larger than . The
implications are discussed and it is indicated that with the luminosity of BES
and BELLE, the experiments may finally determine if is a molecular
state or a tetraquark.Comment: 17 pages, 6 figures, 3 table
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