Estimation of constant and time-varying dynamic parameters of HIV infection in a nonlinear differential equation model

Modeling viral dynamics in HIV/AIDS studies has resulted in a deep understanding of pathogenesis of HIV infection from which novel antiviral treatment guidance and strategies have been derived. Viral dynamics models based on nonlinear differential equations have been proposed and well developed over the past few decades. However, it is quite challenging to use experimental or clinical data to estimate the unknown parameters (both constant and time-varying parameters) in complex nonlinear differential equation models. Therefore, investigators usually fix some parameter values, from the literature or by experience, to obtain only parameter estimates of interest from clinical or experimental data. However, when such prior information is not available, it is desirable to determine all the parameter estimates from data. In this paper we intend to combine the newly developed approaches, a multi-stage smoothing-based (MSSB) method and the spline-enhanced nonlinear least squares (SNLS) approach, to estimate all HIV viral dynamic parameters in a nonlinear differential equation model. In particular, to the best of our knowledge, this is the first attempt to propose a comparatively thorough procedure, accounting for both efficiency and accuracy, to rigorously estimate all key kinetic parameters in a nonlinear differential equation model of HIV dynamics from clinical data. These parameters include the proliferation rate and death rate of uninfected HIV-targeted cells, the average number of virions produced by an infected cell, and the infection rate which is related to the antiviral treatment effect and is time-varying. To validate the estimation methods, we verified the identifiability of the HIV viral dynamic model and performed simulation studies.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS290 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Nuclear geometry effect and transport coefficient in semi-inclusive lepton-production of hadrons off nuclei

Hadron production in semi-inclusive deep-inelastic scattering of leptons from nuclei is an ideal tool to determine and constrain the transport coefficient in cold nuclear matter. The leading-order computations for hadron multiplicity ratios are performed by means of the SW quenching weights and the analytic parameterizations of quenching weights based on BDMPS formalism. The theoretical results are compared to the HERMES positively charged pions production data with the quarks hadronization occurring outside the nucleus. With considering the nuclear geometry effect on hadron production, our predictions are in good agreement with the experimental measurements. The extracted transport parameter from the global fit is shown to be $\hat{q} = 0.74\pm0.03 GeV^2/fm$ for the SW quenching weight without the finite energy corrections. As for the analytic parameterization of BDMPS quenching weight without the quark energy E dependence, the computed transport coefficient is $\hat{q} = 0.20\pm0.02 GeV^2/fm$. It is found that the nuclear geometry effect has a significant impact on the transport coefficient in cold nuclear matter. It is necessary to consider the detailed nuclear geometry in studying the semi-inclusive hadron production in deep inelastic scattering on nuclear targets.Comment: 14 pages, 3 figures. arXiv admin note: text overlap with arXiv:1310.569

Truncated unscented particle filter for dealing with non-linear and inequality constraints

This paper presents an elegant state estimation method which considers the available non-linear and inequality constraint information. A truncated unscented particle filter method is proposed in this paper.This method applies the particle filtering to cope with non-linear models and non-Gaussian state distribution. Different from other particle filtering schemes, a truncated unscented Kalman filter is applied as the importance function for sampling new particles, in order to incorporate both the measurement and constraint information. Therefore, more effective particles are generated and a better state estimation result is then obtained. The advantages of the proposed truncated unscented particle filter algorithm over the state-of-the-art ones are presented by multiple Monte-Carlo simulations

CUR Algorithm for Partially Observed Matrices

CUR matrix decomposition computes the low rank approximation of a given matrix by using the actual rows and columns of the matrix. It has been a very useful tool for handling large matrices. One limitation with the existing algorithms for CUR matrix decomposition is that they need an access to the {\it full} matrix, a requirement that can be difficult to fulfill in many real world applications. In this work, we alleviate this limitation by developing a CUR decomposition algorithm for partially observed matrices. In particular, the proposed algorithm computes the low rank approximation of the target matrix based on (i) the randomly sampled rows and columns, and (ii) a subset of observed entries that are randomly sampled from the matrix. Our analysis shows the relative error bound, measured by spectral norm, for the proposed algorithm when the target matrix is of full rank. We also show that only $O(n r\ln r)$ observed entries are needed by the proposed algorithm to perfectly recover a rank $r$ matrix of size $n\times n$, which improves the sample complexity of the existing algorithms for matrix completion. Empirical studies on both synthetic and real-world datasets verify our theoretical claims and demonstrate the effectiveness of the proposed algorithm

Comparative analysis of binocular summation of pattern visual evoked potential before and after the surgery of concomitant strabismus

AIM: To investigate the opportunity of the concomitant strabismus operation and the function in the treatment of strabismic amblyopia through analyzing the changes of binocular summation of pattern visual evoked potential(P-VEP)before and after the surgery of concomitant strabismus. <p>METHODS: In this retrospective study we investigated 67 cases admitted in our hospital. All patients were less than 18a and the postoperation squint angle was less than ±10^△. Patients were divided into three groups according to the strabismus type, age, and amblyopia degree. P-VEP binocular summation response was recorded in all cases, to observe the changes of the binocular summation response of P-VEP before strabismus surgery and 1mo, 3mo after surgery. The P-VEP response of binocular /monocular(B/M)ratio was taken as an evaluation index. <p>RESULTS: B/M value of three groups all improved obviously 1mo after surgery, which the difference showed statistical significant(<i>P</i><0.01). 1)After 3mo surgery, B/M value in esotropia group was higher than that in exotropia group(<i>P</i><0.05). 2)After 3mo surgery, B/M value in ≤6a group was higher than that in >12a group(<i>P</i><0.05). 3)After 1mo surgery, B/M value in severe amblyopia group was higher than that in mild group(<i>P</i><0.05). After 3mo surgery, B/M value in severe amblyopia group was higher than that in mild group significantly(<i>P</i><0.01). <p>CONCLUSION: Concomitant strabismus surgery is suggested to be performed before 6 years old when the patients are difficult to improve the vision after amblyopia treatment, especially with the severe amblyopia and esotropia(accommodative esotropia must be excluded). The early operation is better to amblyopia treatment and binocular vision recovery

Protecting Effects of Dexamethasone on Thymus of Rats with Severe Acute Pancreatitis

Purpose. To study the protecting effects of dexamethasone on thymus of rats with severe acute pancreatitis (SAP). Methods. The SAP rats were randomly assigned to the model group and dexamethasone-treated group, the other normal healthy rats were assigned to the sham operation group. The rat survival, thymus pathological changes, apoptotic index, as well as expression levels of NF-κB, P-selectin, Bax, Bcl-2, and Caspase-3 protein of all groups were observed, respectively, at 3 hours, 6 hours, and 12 hours. The contents of amylase and endotoxin in plasma as well as the contents of TNF-α, PLA2, and NO in serum were determined. Results. There was no marked difference between the model group and treated group in survival. The contents of different indexes in blood of treated group were lower than those of the model group to various degrees at different time points. The thymus pathological score was lower in treated group than in model group at 12 hours.The treated group in Caspase-3 protein expression of thymus significantly exceeded the model group at 12 hours. The apoptotic index was significantly higher in treated group than in model group. Conclusion. Dexamethasone has protecting effects on thymus of SAP rats