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 Publishing“One way to describe patterns of species distribution is to plot the frequency histograms using species–range-size data (Gaston, 1994; Brown, 1995; Gaston & Blackburn, 2000). Usually the untransformed geographical ranges of species are distributed following a ‘hollow curve’, i.e. most species have narrow ranges and very few have widespread distributions. This highly ‘right-skewed’ 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 ‘core-satellite species hypothesis’ (Hanski, 1982) and the ‘resource usage model’ (Brown, 1984, 1995) were proposed to explain the finding that a few species are regionally common (widespread) and locally abundant (the ‘core’ species in Hanski’s model; the generalists or broad-niched species in Brown’s model), while most species can be regarded as having smaller ranges and low local abundances (the ‘satellite’ species in Hanski’s model; the specialists or narrow-niched species in Brown’s model). […]

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