Theory of functional principal components analysis for discretely observed data

For discretely observed functional data, estimating eigenfunctions with diverging index is essential in nearly all methods based on functional principal components analysis. In this paper, we propose a new approach to handle each term appeared in the perturbation series and overcome the summability issue caused by the estimation bias. We obtain the moment bounds for eigenfunctions and eigenvalues for a wide range of the sampling rate. We show that under some mild assumptions, the moment bound for the eigenfunctions with diverging indices is optimal in the minimax sense. This is the first attempt at obtaining an optimal rate for eigenfunctions with diverging index for discretely observed functional data. Our results fill the gap in theory between the ideal estimation from fully observed functional data and the reality that observations are taken at discrete time points with noise, which has its own merits in models involving inverse problem and deserves further investigation

Evolution of pore structure, submaceral composition and produced gases of two Chinese coals during thermal treatment

This research was funded by the Research Program for Excellent Doctoral Dissertation Supervisor of Beijing (grant no. YB20101141501), the Fundamental Research Funds for Central Universities (grant no. 35832015136) and Key Project of Coal-based Science and Technology in Shanxi Province-CBM accumulation model and reservoir evaluation in Shanxi province (grant no. MQ2014-01).Peer reviewedPostprin

LHC Search of New Higgs Boson via Resonant Di-Higgs Production with Decays into 4W

Searching for new Higgs particle beyond the observed light Higgs boson h(125GeV) will unambiguously point to new physics beyond the standard model. We study the resonant production of a CP-even heavy Higgs state $H^0$ in the di-Higgs channel via, $gg\to H^0\to h^0h^0\to WW^*WW^*$, at the LHC Run-2 and the high luminosity LHC (HL-LHC). We analyze two types of the $4W$ decay modes, one with the same-sign di-leptons ($4W\to\ell^\pm\nu\ell^\pm\nu 4q$) and the other with tri-leptons ($4W\to\ell^\pm\nu\ell^\mp\nu\ell^\pm\nu 2q$). We perform a full simulation for the signals and backgrounds, and estimate the discovery potential of the heavy Higgs state at the LHC Run-2 and the HL-LHC, in the context of generical two-Higgs-doublet models (2HDM). We determine the viable parameter space of the 2HDM as allowed by the theoretical constraints and the current experimental limits. We systematically analyze the allowed parameter space of the 2HDM which can be effectively probed by the heavy Higgs searches of the LHC, and further compare this with the viable parameter region under the current theoretical and experimental bounds.Comment: v3: JHEP published version, 34pp, 10 Figs(36 plots) and 9 Tables. Only minor typos fixed, references added. v2: JHEP version. All results and conclusions un-changed, discussions and references added. (This update is much delayed due to author's traveling and flu.

A Practical Guide for X-Ray Diffraction Characterization of Ga(Al, In)N Alloys

Ga(In, Al)N alloys are used as an active layer or cladding layer in light emitting diodes and laser diodes. x-ray diffraction is extensively used to evaluate the crystalline quality, the chemical composition and the residual strain in Ga(Al,In)N thin films, which directly determine the emission wavelength and the device performance. Due to the minor mismatch in lattice parameters between Ga(Al, In)N alloy and a GaN virtual substrate, x-ray diffraction comes to a problem to separate the signal from Ga(Al,In)N alloy and GaN. We give a detailed comparison on different diffraction planes. In order to balance the intensity and peak separation between Ga(Al,In)N alloy and GaN, (0004) and (1015) planes make the best choice for symmetric scan and asymmetric scan, respectively.Comment: 9 pages, 5 figure

The Ages of Optically Bright Sub-Clusters in the Serpens Star-Forming Region

The Serpens Molecular Cloud is one of the most active star-forming regions within 500 pc, with over one thousand of YSOs at different evolutionary stages. The ages of the member stars inform us about the star formation history of the cloud. In this paper, we develop a spectral energy distribution (SED) fitting method for nearby evolved (diskless) young stars from members of the Pleiades to estimate their ages, with a temperature scale adopted from APOGEE spectra. When compared with literature temperatures of selected YSOs in Orion, the SED fits to cool (<5000 K) stars have temperatures that differ by an average of <~ 50 K and have a scatter of ~ 210 K for both disk-hosting and diskless stars. We then apply this method to YSOs in the Serpens Molecular Cloud to estimate ages of optical members previously identified from Gaia DR2 astrometry data. The optical members in Serpens are concentrated in different subgroups with ages from ~4 Myr to ~22 Myr; the youngest clusters, W40 and Serpens South, are dusty regions that lack enough optical members to be included in this analysis. These ages establish that the Serpens Molecular Cloud has been forming stars for much longer than has been inferred from infrared surveys.Comment: 28 pages, 22 figures, accepted for publication in The Astrophysical Journa

Advancements in Optical See-through Near-Eye Display

With the development of optical design and manufacturing, the optical see-through near-eye display becomes a promising research topic in recent decades, which can be applied in medical devices, education, aviation, entertainment et al. Typical products include Head-mounted Displays (HMDs) and Augmented Reality (AR) glasses. The optical display system of AR devices mainly consists of a miniature projecting module and an optical imaging module. In this chapter, the display systems used by AR glasses on the market, including various mini-display screens and optical imaging elements, have been systematically summarized. Therein, the differences in optical combinators are the key part to distinguish various AR display systems. Thus, it is essential to figure out the advantages and disadvantages of each optical imaging technology applied in this area. Besides, the characteristics of the projectors are crucial to the quality of the images