35,375 research outputs found
Multiscale change-point segmentation: beyond step functions.
Modern multiscale type segmentation methods are known to detect multiple change-points with high statistical accuracy, while allowing for fast computation. Underpinning (minimax) estimation theory has been developed mainly for models that assume the signal as a piecewise constant function. In this paper, for a large collection of multiscale segmentation methods (including various existing procedures), such theory will be extended to certain function classes beyond step functions in a nonparametric regression setting. This extends the interpretation of such methods on the one hand and on the other hand reveals these methods as robust to deviation from piecewise constant functions. Our main finding is the adaptation over nonlinear approximation classes for a universal thresholding, which includes bounded variation functions, and (piecewise) Holder functions of smoothness order 0 < alpha <= 1 as special cases. From this we derive statistical guarantees on feature detection in terms of jumps and modes. Another key finding is that these multiscale segmentation methods perform nearly (up to a log-factor) as well as the oracle piecewise constant segmentation estimator (with known jump locations), and the best piecewise constant approximants of the (unknown) true signal. Theoretical findings are examined by various numerical simulations
From the Complete Yang Model to Snyder's Model, de Sitter Special Relativity and Their Duality
By means of Dirac procedure, we re-examine Yang's quantized space-time model,
its relation to Snyder's model, the de Sitter special relativity and their
UV-IR duality. Starting from a dimensionless dS_5-space in a 5+1-d Mink-space a
complete Yang model at both classical and quantum level can be presented and
there really exist Snyder's model, the dS special relativity and the duality.Comment: 7 papge
Multiple Superconducting Gaps, Anisotropic Spin Fluctuations and Spin-Orbit Coupling in Iron-Pnictides
This article reviews the NMR and NQR studies on iron-based high-temperature
superconductors by the IOP/Okayama group. It was found that the electron pairs
in the superconducting state are in the spin-singlet state with multiple
fully-opened energy gaps. The antiferromagnetic spin fluctuations in the normal
state are found to be closely correlated with the superconductivity. Also the
antiferromagnetic spin fluctuations are anisotropic in the spin space, which is
different from the case in copper oxide superconductors. This anisotropy
originates from the spin-orbit coupling and is an important reflection of the
multiple-bands nature of this new class of superconductors.Comment: 20 pages, 16 figure
Astrometry via Close Approach Events: Applications to Main-Belt Asteroid (702) Alauda
The release of Gaia catalog is revolutionary to the astronomy of solar system
objects. After some effects such as atmospheric refraction and CCD geometric
distortion have been taken into account, the astrometric precision for
ground-based telescopes can reach the level of tens of milli-arcseconds. If an
object approaches a reference star in a small relative angular distance (less
than 100 arcseconds), which is called close approach event in this work, the
relative positional precision between the object and reference star will be
further improved since the systematic effects of atmospheric turbulence and
local telescope optics can be reduced. To obtain the precise position of a
main-belt asteroid in an close approach event, a second-order angular velocity
model with time is supposed in the sky plane. By fitting the relationship
between the relative angular distance and observed time, we can derive the time
of maximum approximation and calculate the corresponding position of the
asteroid. In practice, 5 nights' CCD observations including 15 close approach
events of main-belt asteroid (702) Alauda are taken for testing by the 1m
telescope at Yunnan Observatory, China. Compared with conventional solutions,
our results show that the positional precision significantly improves, which
reaches better than 4 milli-arcseconds, and 1 milli-arcsecond in the best case
when referenced for JPL ephemeris in both right ascension and declination.Comment: 11 pages, 22 figure
A typing error in Tokeshi's test of bimodality
Copyright © 2003 Blackwell PublishingâOne way to describe patterns of species distribution is to plot the frequency histograms using speciesârange-size data (Gaston, 1994; Brown, 1995; Gaston & Blackburn, 2000). Usually the untransformed geographical ranges of species are distributed following a âhollow curveâ, i.e. most species have narrow ranges and very few have widespread distributions. This highly âright-skewedâ curve has been regarded as unimodal (e.g. Gaston, 1994). In some cases, however, the species-range-size distribution shows a bimodal pattern (Hanski, 1982; Brown, 1984, 1995; Gaston, 1994; Gaston & Blackburn, 2000), in which to the left-hand mode is added a right hand mode generated by the widespread group of species that occur in almost all sampled sites. The âcore-satellite species hypothesisâ (Hanski, 1982) and the âresource usage modelâ (Brown, 1984, 1995) were proposed to explain the finding that a few species are regionally common (widespread) and locally abundant (the âcoreâ species in Hanskiâs model; the generalists or broad-niched species in Brownâs model), while most species can be regarded as having smaller ranges and low local abundances (the âsatelliteâ species in Hanskiâs model; the specialists or narrow-niched species in Brownâs model). [âŠ]
Hydration-induced anisotropic spin fluctuations in Na_{x}CoO_{2}\cdot1.3H_{2}O superconductor
We report ^{59}Co NMR studies in single crystals of cobalt oxide
superconductor Na_{0.42}CoO_{2}\cdot1.3H_{2}O (T_c=4.25K) and its parent
compound Na_{0.42}CoO_{2}. We find that both the magnitude and the temperature
(T) dependence of the Knight shifts are identical in the two compounds above
T_c. The spin-lattice relaxation rate (1/T_1) is also identical above T_0
\sim60 K for both compounds. Below T_0, the unhydrated sample is found to be a
non-correlated metal that well conforms to Fermi liquid theory, while spin
fluctuations develop in the superconductor. These results indicate that water
intercalation does not change the density of states but its primary role is to
bring about spin fluctuations. Our result shows that, in the hydrated
superconducting compound, the in-plane spin fluctuation around finite wave
vector is much stronger than that along the c-axis, which indicates that the
spin correlation is quasi-two-dimensional.Comment: 4 pages, 5 figure
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