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

An Interacting model of Dark Energy in Brans-Dicke theory

In this paper it is shown that in non-minimally coupled Brans-Dicke theory containing a self-interacting potential, a suitable conformal transformation can automatically give rise to an interaction between the normal matter and the Brans-Dicke scalar field. Considering the scalar field in the Einstein frame as the quintessence matter, it has been shown that such a non-minimal coupling between the matter and the scalar field can give rise to a late time accelerated expansion for the universe preceded by a decelerated expansion for very high values of the Brans-Dicke parameter $\omega$. We have also studied the observational constraints on the model parameters considering the Hubble and Supernova data.Comment: 12 pages, 15 figures. Accepted for publication in Astrophysics and Space Scienc

Nonparametric estimation of genewise variance for microarray data

Estimation of genewise variance arises from two important applications in microarray data analysis: selecting significantly differentially expressed genes and validation tests for normalization of microarray data. We approach the problem by introducing a two-way nonparametric model, which is an extension of the famous Neyman--Scott model and is applicable beyond microarray data. The problem itself poses interesting challenges because the number of nuisance parameters is proportional to the sample size and it is not obvious how the variance function can be estimated when measurements are correlated. In such a high-dimensional nonparametric problem, we proposed two novel nonparametric estimators for genewise variance function and semiparametric estimators for measurement correlation, via solving a system of nonlinear equations. Their asymptotic normality is established. The finite sample property is demonstrated by simulation studies. The estimators also improve the power of the tests for detecting statistically differentially expressed genes. The methodology is illustrated by the data from microarray quality control (MAQC) project.Comment: Published in at http://dx.doi.org/10.1214/10-AOS802 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Bose-Einstein Condensation with Entangled Order Parameter

We propose a practically accessible non-mean-field ground state of Bose-Einstein condensation (BEC), which occurs in an interspecies two-particle entangled state, and is thus described by an entangled order parameter. A suitably defined entanglement entropy is used as the characterization of the non-mean-field nature, and is found to persist in a wide parameter regime. The interspecies entanglement leads to novel interference terms in the dynamical equations governing the single particle orbital wavefunctions. Experimental feasibility and several methods of probe are discussed. We urge the study of multi-channel scattering between different species of atoms.Comment: V1: 5 pages, 4 figures. Accepted by Phys. Rev. Lett.; V2: A couple of very minor typos corrected, publishe

Quantization and Corrections of Adiabatic Particle Transport in a Periodic Ratchet Potential

We study the transport of an overdamped particle adiabatically driven by an asymmetric potential which is periodic in both space and time. We develop an adiabatic perturbation theory after transforming the Fokker-Planck equation into a time-dependent hermitian problem, and reveal an analogy with quantum adiabatic particle transport. An analytical expression is obtained for the ensemble average of the particle velocity in terms of the Berry phase of the Bloch states. Its time average is shown to be quantized as a Chern number in the deterministic or tight-binding limit, with exponentially small corrections. In the opposite limit, where the thermal energy dominates the ratchet potential, a formula for the average velocity is also obtained, showing a second order dependence on the potential.Comment: 8 page

Superconducting phase with a chiral ff-wave pairing symmetry and Majorana fermions induced in a hole-doped semiconductor

We show that a chiral $f+if$-wave superconducting pairing may be induced in the lowest heavy hole band of a hole-doped semiconductor thin film through proximity contact with an \textit{s}-wave superconductor. The chirality of the pairing originates from the $3\pi$ Berry phase accumulated for a heavy hole moving along a close path on the Fermi surface. There exist three chiral gapless Majorana edge states, in consistence with the chiral $f+if$% -wave pairing. We show the existence of zero energy Majorana fermions in vortices in the semiconductor-superconductor heterostructure by solving the Bogoliubov-de-Gennes equations numerically as well as analytically in the strong confinement limit.Comment: 5 pages, 4 figure