DYNAMICAL BEHAVIOR OF A STOCHASTIC HBV INFECTION MODEL WITH LOGISTIC HEPATOCYTE GROWTH

This paper is concerned with a stochastic HBV infection model with logistic growth. First, by constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of ergodic stationary distribution of the solution to the HBV infection model. Then we obtain sufficient conditions for extinction of the disease. The stationary distribution shows that the disease can become persistent in vivo.

QUALITATIVE ANALYSIS OF A STOCHASTIC RATIO-DEPENDENT HOLLING-TANNER SYSTEM

This article addresses a stochastic ratio-dependent predator-prey system with Leslie-Gower and Holling type II schemes. Firstly, the existence of the global positive solution is shown by the comparison theorem of stochastic differential equations. Secondly, in the case of persistence, we prove that there exists a ergodic stationary distribution. Finally, numerical simulations for a hypothetical set of parameter values are presented to illustrate the analytical findings.

Limiting spectral distribution of high-dimensional noncentral Fisher matrices and its analysis

Fisher matrix is one of the most important statistics in multivariate statistical analysis.Its eigenvalues are of primary importance for many applications,such as testing the equality of mean vectors,testing the equality of covariance matrices and signal detection problems.In this paper,we establish the limiting spectral distribution of high-dimensional noncentral Fisher matrices and investigate its analytic behavior.In particular,we show the determination criterion for the support of the limiting spectral distribution of the noncentral Fisher matrices,which is the base of investigating the high-dimensional problems concerned with noncentral Fisher matrices.

Regression Analysis of Misclassified Current Status Data with Informative Observation Times

Misclassified current status data arises if each study subject can only be observed once and the observation status is determined by a diagnostic test with imperfect sensitivity and specificity.For the situation,another issue that may occur is that the observation time may be correlated with the interested failure time,which is often referred to as informative censoring or observation times.It is well-known that in the presence of informative censoring,the analysis that ignores it could yield biased or even misleading results.In this paper,the authors consider such data and propose a frailty-based inference procedure.In particular,an EM algorithm based on Poisson latent variables is developed and the asymptotic properties of the resulting estimators are established.The numerical results show that the proposed method works well in practice and an application to a set of real data is provided.

Dynamics of stochastic predator-prey models with distributed delay and stage structure for prey

In this paper,we analyze two stochastic predator-prey models with distributed delay and stage structure for prey.For the nonautonomous periodic case of the model,by using Khasminskii’s theory of periodic solution,we show that the system has at least one positive T-periodic solution.For the model which is disturbed by both white and telegraph noises,we obtain sufficient criteria for positive recurrence of the solutions to the model by constructing a suitable stochastic Lyapunov function with regime switching.The positive recurrence implies that both prey and predator populations will be persistent in the long term.

Nonparametric Estimation of Interval-censored Failure Time Data in the Presence of Informative Censoring

Nonparametric estimation of a survival function is one of the most commonly asked questions in the analysis of failure time data and for this, a number of procedures have been developed under various types of censoring structures （Kalbfleisch and Prentice, 2002）. In particular, several algorithms are available for interval-censored failure time data with independent censoring mechanism （Sun, 2006; Turnbull, 1976）. In this paper, we consider the interval-censored data where the censoring mechanism may be related to the failure time of interest, for which there does not seem to exist a nonparametric estimation procedure. It is well-known that with informative censoring, the estimation is possible only under some assumptions. To attack the problem, we take a copula model approach to model the relationship between the failure time of interest and censoring variables and present a simple nonparametric estimation procedure. The method allows one to conduct a sensitivity analysis among others.

Dynamical behavior of a stochastic multigroup staged-progression HIV model with saturated incidence rate and higher-order perturbations

In this paper,we analyze a higher-order stochastically perturbed multigroup staged-progression model for the transmission of HlV with saturated incidence rate.We obtainsufficient conditions for the existence and uniqueness of an ergodic stationary distribu-tion of positive solutions to the system by establishing a suitable stochastic Lyapunovfunction.In addition,we make up adequate conditions for complete eradication and wip-ing out the infectious disease.In a biological interpretation,the existence of a stationarydistribution implies that the disease will prevail and persist in the long term.Finally,examples and numerical simulations are introduced to validate our theoretical results.

An improved master-apprentice evolutionary algorithm for minimum independent dominating set problem

The minimum independent dominance set(MIDS)problem is an important version of the dominating set with some other applications.In this work,we present an improved master-apprentice evolutionary algorithm for solving the MIDS problem based on a path-breaking strategy called MAE-PB.The proposed MAE-PB algorithm combines a construction function for the initial solution generation and candidate solution restarting.It is a multiple neighborhood-based local search algorithm that improves the quality of the solution using a path-breaking strategy for solution recombination based on master and apprentice solutions and a perturbation strategy for disturbing the solution when the algorithm cannot improve the solution quality within a certain number of steps.We show the competitiveness of the MAE-PB algorithm by presenting the computational results on classical benchmarks from the literature and a suite of massive graphs from real-world applications.The results show that the MAE-PB algorithm achieves high performance.In particular,for the classical benchmarks,the MAE-PB algorithm obtains the best-known results for seven instances,whereas for several massive graphs,it improves the best-known results for 62 instances.We investigate the proposed key ingredients to determine their impact on the performance of the proposed algorithm.

Proportional Mean Residual Life Model with Varying Coefficients for Length-Biased and Right-Censored Data

Length-biased data are encountered in many fields,including economics,engineering and epidemiological cohort studies.There are two main challenges in the analysis of such data:the assumption of independent censoring is violated and the assumed model for the underlying population is no longer satisfied for the observed data.In this paper,a proportional mean residual life varyingcoefficient model for length-biased data is considered and a local pseudo likelihood method is proposed for estimating the coefficient functions in the model.Asymptotic properties are investigated for the proposed estimators.The finite sample performance of the proposed methodology is demonstrated by simulation studies.Finally,the method is applied to a real data set concerning the Academy Awards.

A Patch-Based Low-Rank Minimization Approach for Speckle Noise Reduction in Ultrasound Images

Ultrasound is a low-cost,non-invasive and real-time imaging modality that has proved popular for many medical applications.Unfortunately,the acquired ultrasound images are often corrupted by speckle noise from scatterers smaller than ultrasound beam wavelength.The signal-dependent speckle noise makes visual observation difficult.In this paper,we propose a patch-based low-rank approach for reducing the speckle noise in ultrasound images.After constructing the patch group of the ultrasound images by the block-matching scheme,we establish a variational model using the weighted nuclear norm as a regularizer for the patch group.The alternating direction method of multipliers(ADMM)is applied for solving the established nonconvex model.We return all the approximate patches to their original locations and get the final restored ultrasound images.Experimental results are given to demonstrate that the proposed method outperforms some existing state-of-the-art methods in terms of visual quality and quantitative measures.