Anharmonic quantum contribution to vibrational dephasing

Based on a quantum Langevin equation and its corresponding Hamiltonian within a c-number formalism we calculate the vibrational dephasing rate of a cubic oscillator. It is shown that leading order quantum correction due to anharmonicity of the potential makes a significant contribution to the rate and the frequency shift. We compare our theoretical estimates with those obtained from experiments for small diatomics $N_2$, $O_2$ and $CO$.Comment: 21 pages, 1 figure and 1 tabl

Binary isotonic regression procedures, with application to cancer biomarkers

There is a lot of interest in the development and characterization of new biomarkers for screening large populations for disease. In much of the literature on diagnostic testing, increased levels of a biomarker correlate with increased disease risk. However, parametric forms are typically used to associate these quantities. In this article, we specify a monotonic relationship between biomarker levels with disease risk. This leads to consideration of a nonparametric regression model for a single biomarker. Estimation results using isotonic regression-type estimators and asymptotic results are given. We also discuss confidence set estimation in this setting and propose three procedures for computing confidence intervals. Methods for estimating the receiver operating characteristic (ROC) curve are also described. The finite-sample properties of the proposed methods are assessed using simulation studies and applied to data from a pancreatic cancer biomarker study

Semiparametric binary regression under monotonicity constraints

Summary: We study a binary regression model where the response variable $\Delta$ is the indicator of an event of interest (for example, the incidence of cancer) and the set of covariates can be partitioned as $(X,Z)$ where $Z$ (real valued) is the covariate of primary interest and $X$ (vector valued) denotes a set of control variables. For any fixed $X$, the conditional probability of the event of interest is assumed to be a monotonic function of $Z$. The effect of the control variables is captured by a regression parameter $\beta$. We show that the baseline conditional probability function (corresponding to $X=0$) can be estimated by isotonic regression procedures and develop a likelihood ratio based method for constructing confidence intervals for this function that obviates the need to estimate nuisance parameters from the data. We also show how confidence intervals for the regression parameter can be constructed using asymptotically $\chi^2$ likelihood ratio statistics. The confidence sets for the regression parameter and those for the conditional probability function are combined using Bonferroni\u27s inequality to construct conservative confidence intervals for the conditional probability of the event of interest at different fixed values of $X$ and $Z$. We present simulation results to illustrate the theory and apply our results to a prostate cancer data set

Quantum state-dependent diffusion and multiplicative noise: a microscopic approach

The state-dependent diffusion, which concerns the Brownian motion of a particle in inhomogeneous media has been described phenomenologically in a number of ways. Based on a system-reservoir nonlinear coupling model we present a microscopic approach to quantum state-dependent diffusion and multiplicative noise in terms of a quantum Markovian Langevin description and an associated Fokker-Planck equation in position space in the overdamped limit. We examine the thermodynamic consistency and explore the possibility of observing a quantum current, a generic quantum effect, as a consequence of this state-dependent diffusion similar to one proposed by B\"{u}ttiker [Z. Phys. B {\bf 68}, 161 (1987)] in a classical context several years ago.Comment: To be published in Journal of Statistical Physics 28 pages, 3 figure

Inhomogeneous quantum diffusion and decay of a meta-stable state

We consider the quantum stochastic dynamics of a system whose interaction with the reservoir is considered to be linear in bath co-ordinates but nonlinear in system co-ordinates. The role of the space-dependent friction and diffusion has been examined in the decay rate of a particle from a meta-stable well. We show how the decay rate can be hindered by inhomogeneous dissipation due nonlinear system-bath coupling strength.Comment: To be published in Phys. Lett.