Multiple Change-point Detection: a Selective Overview

Very long and noisy sequence data arise from biological sciences to social science including high throughput data in genomics and stock prices in econometrics. Often such data are collected in order to identify and understand shifts in trend, e.g., from a bull market to a bear market in finance or from a normal number of chromosome copies to an excessive number of chromosome copies in genetics. Thus, identifying multiple change points in a long, possibly very long, sequence is an important problem. In this article, we review both classical and new multiple change-point detection strategies. Considering the long history and the extensive literature on the change-point detection, we provide an in-depth discussion on a normal mean change-point model from aspects of regression analysis, hypothesis testing, consistency and inference. In particular, we present a strategy to gather and aggregate local information for change-point detection that has become the cornerstone of several emerging methods because of its attractiveness in both computational and theoretical properties.Comment: 26 pages, 2 figure

Label-free analysis of protein biomarkers using pattern-optimized graphene-nanopyramid SERS for rapid diagnosis of Alzheimer’s disease

The quantitative and highly sensitive detection of biomarkers such as Tau proteins and Aβ polypeptides is considered one of the most effective methods for the early diagnosis of Alzheimer’s disease (AD). Surface-enhanced Raman spectroscopy (SERS) detection is a promising method that faces, however, challenges like insufficient sensitivity due to the non-optimized nanostructures for specialized analyte sizes and insufficient control of the location of SERS hot spots. Thus, the SERS detection of AD biomarkers is restricted. We reported here an in-depth study of the analytical Raman enhancement factor (EF) of the wafer-scale graphene-Au nanopyramid hybrid SERS substrates using a combination of both theoretical calculation and experimental measurements. Experimental results show that larger nanopyramids and smaller gap spacing lead to a larger SERS EF, with an optimized analytical EF up to 1.1 × 1010. The hybrid SERS substrate exhibited detection limits of 10–15 M for Tau and phospho-Tau (P-Tau) proteins and 10–14 M for Aβ polypeptides, respectively. Principal component analysis correctly categorized the SERS spectra of different biomarkers at ultralow concentrations (10–13 M) using the optimized substrate. Amide III bands at 1200–1300 cm–1 reflect different structural conformations of proteins or polypeptides. Tau and P-Tau proteins are inherently disordered with a few α-helix residuals. The structure of Aβ42 polypeptides transitioned from the α-helix to the β-sheet as the concentration increased. These results demonstrate that the hybrid SERS method could be a simple and effective way for the label-free detection of protein biomarkers to enable the rapid early diagnosis of AD and other diseases

Properties of Functions in the Wiener Class BVp[a,b] for 0<p<1

We will investigate properties of functions in the Wiener class BVp[a,b] with 0<p<1. We prove that any function in BVp[a,b] (0<p<1) can be expressed as the difference of two increasing functions in BVp[a,b]. We also obtain the explicit form of functions in BVp[a,b] and show that their derivatives are equal to zero a.e. on [a,b]

Assessment of nonequilibrium air-chemistry models on species formation in hypersonic shock layer

The present study aims to assess the performance of chemical rate models for species formation in the reacting shock layer flows over the blunt-cone hypersonic vehicles. Three 11-species nonequilibrium chemical models for air, Gupta 90, Park 93 and Ozawa's modified models, are assessed. Two controlling temperature expressions ((TTv0.5)-T-0.5 and (TTv0.3)-T-0.7) for dissociation reactions are taken into account in these chemical kinetic models. To further examine the performance of these models for predictions of nonequilibrium effects and species formations in the shock layer, two typical flight cases are adopted: (1) the NO formation in reacting flows over the Bow-shock Ultraviolent (BSUV) vehicle at Mach number 17.7, and (2) the electron formation over the Radio Attenuation Measurements (RAM) C-II vehicle at Mach number 23.9 and 25.9. Firstly, comparisons of interested parameters between the computed results in different rate models and available reference data are carried out. Secondly, the reasons for the difference of species formations in these models are discussed. Results show that both the chemical rate model and the weight factor of the controlling temperature have a distinctive influence on species concentration and distribution in the shock layer. The weight factor determines the level of the vibrational-electronic temperature and the reaction release heat in nonequilibrium processes. With the increasing of the weight factor, the NO concentration increases and the electron density decreases in the same rate model. The spectral integration within the wavelengths of 205-255 nm shows that the prediction accuracy of the Park-0.5 and Ozawa-0.7 models is relatively high. Numerical results also indicate that the Ozawa-0.7 model may be an all-round model to predict electron formation in the shock layer. (C) 2018 Elsevier Ltd. All rights reserved

Approximation Properties of Chebyshev Polynomials in the Legendre Norm

In this paper, we present some important approximation properties of Chebyshev polynomials in the Legendre norm. We mainly discuss the Chebyshev interpolation operator at the Chebyshev&ndash;Gauss&ndash;Lobatto points. The cases of single domain and multidomain for both one dimension and multi-dimensions are considered, respectively. The approximation results in Legendre norm rather than in the Chebyshev weighted norm are given, which play a fundamental role in numerical analysis of the Legendre&ndash;Chebyshev spectral method. These results are also useful in Clenshaw&ndash;Curtis quadrature which is based on sampling the integrand at Chebyshev points

Water Uptake Patterns of Alfalfa under Winter Irrigation in Cold and Arid Grassland

Crop reduction caused by cryogenesis and drought is a serious and global problem. The environmental stress caused by low temperature and drought during the overwintering stage of forage is the key factor leading to this low yield. In cold and arid grassland, winter irrigation can effectively alleviate the stress of alfalfa during overwintering, improve the survival rate of alfalfa, and significantly increase the yield. However, the water uptake patterns of alfalfa under winter irrigation are not clear, which are important to explore the mechanism of alleviating environmental stress by winter irrigation. In this research, the stable isotope compositions of all probable water sources and alfalfa xylem water were measured after winter irrigation. A graphical method was applied to identify the main soil layers with water uptake by the alfalfa roots. The contribution rate of available water sources to alfalfa xylem water was quantified by the MixSIAR (Bayesian isotope analysis mixing model in R) model. The results indicated that alfalfa absorbed soil water when the soil water content was high enough in the root layer when under high water volume freezing irrigation (irrigation in early winter when soil is freezing) but not under low and medium water volume freezing irrigation. Alfalfa gradually began to absorb soil water on the third day after thawing irrigation (irrigation in late winter when the soil is thawing) and showed different water uptake characteristics under low, medium, and high water volume. Thawing irrigation also accelerated the regeneration of alfalfa