1,448 research outputs found
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
Sources of uncertainties and artefacts in back-projection results
Back-projecting high-frequency (HF) waves is a common procedure for imaging rupture processes of large earthquakes (i.e. M_w > 7.0). However, obtained back-projection (BP) results could suffer from large uncertainties since high-frequency seismic waveforms are strongly affected by factors like source depth, focal mechanisms, and the Earth's 3-D velocity structures. So far, these uncertainties have not been thoroughly investigated. Here, we use synthetic tests to investigate the influencing factors for which scenarios with various source and/or velocity set-ups are designed, using either Tohoku-Oki (Japan), Kaikoura (New Zealand), Java/Wharton Basin (Indonesia) as test areas. For the scenarios, we generate either 1-D or 3-D teleseismic synthetic data, which are then back-projected using a representative BP method, MUltiple SIgnal Classification (MUSIC). We also analyse corresponding real cases to verify the synthetic test results. The Tohoku-Oki scenario shows that depth phases of a point source can be back-projected as artefacts at their bounce points on the earth's surface, with these artefacts located far away from the epicentre if earthquakes occur at large depths, which could significantly contaminate BP images of large intermediate-depth earthquakes. The Kaikoura scenario shows that for complicated earthquakes, composed of multiple subevents with varying focal mechanisms, BP tends to image subevents emanating large amplitude coherent waveforms, while missing subevents whose P nodal directions point to the arrays, leading to discrepancies either between BP images from different arrays, or between BP images and other source models. Using the Java event, we investigate the impact of 3-D source-side velocity structures. The 3-D bathymetry together with a water layer can generate strong and long-lasting coda waves, which are mirrored as artefacts far from the true source location. Finally, we use a Wharton Basin outer-rise event to show that the wavefields generated by 3-D near trench structures contain frequency-dependent coda waves, leading to frequency-dependent BP results. In summary, our analyses indicate that depth phases, focal mechanism variations and 3-D source-side structures can affect various aspects of BP results. Thus, we suggest that target-oriented synthetic tests, for example, synthetic tests for subduction earthquakes using more realistic 3-D source-side velocity structures, should be conducted to understand the uncertainties and artefacts before we interpret detailed BP images to infer earthquake rupture kinematics and dynamics
Sieve estimation of constant and time-varying coefficients in nonlinear ordinary differential equation models by considering both numerical error and measurement error
This article considers estimation of constant and time-varying coefficients
in nonlinear ordinary differential equation (ODE) models where analytic
closed-form solutions are not available. The numerical solution-based nonlinear
least squares (NLS) estimator is investigated in this study. A numerical
algorithm such as the Runge--Kutta method is used to approximate the ODE
solution. The asymptotic properties are established for the proposed estimators
considering both numerical error and measurement error. The B-spline is used to
approximate the time-varying coefficients, and the corresponding asymptotic
theories in this case are investigated under the framework of the sieve
approach. Our results show that if the maximum step size of the -order
numerical algorithm goes to zero at a rate faster than , the
numerical error is negligible compared to the measurement error. This result
provides a theoretical guidance in selection of the step size for numerical
evaluations of ODEs. Moreover, we have shown that the numerical solution-based
NLS estimator and the sieve NLS estimator are strongly consistent. The sieve
estimator of constant parameters is asymptotically normal with the same
asymptotic co-variance as that of the case where the true ODE solution is
exactly known, while the estimator of the time-varying parameter has the
optimal convergence rate under some regularity conditions. The theoretical
results are also developed for the case when the step size of the ODE numerical
solver does not go to zero fast enough or the numerical error is comparable to
the measurement error. We illustrate our approach with both simulation studies
and clinical data on HIV viral dynamics.Comment: Published in at http://dx.doi.org/10.1214/09-AOS784 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Effects of ultrasound on milk homogenization and fermentation with yogurt starter
Yogurt production was selected to study the effects of ultrasound on milk homogenization and fermentation. A microscope was used to check the size distribution of fat globules to evaluate ultrasound homogenization. The pH change during fermentation and the water holding capacity, viscosity and syneresis for finished yogurt were evaluated. It was found that ultrasound has a very good homogenization effect at high amplitude levels compared with conventional homogenization. Longer exposure times improved the ultrasound homogenization effect. If enough exposure time and amplitude level are provided, extremely small fat globules can be produced. The fermentation results showed that the method of sonicating bacteria had a significant effect on the pH change. Sonication after inoculation could reduce the total fermentation time by 0.5 hours. Ultrasound also significantly affected the water holding capacity, viscosity and syneresis. In general, increasing the ultrasound amplitude level improved the water holding capacity, and viscosity and reduced syneresis. However, sonication after inoculation did not decrease the syneresis effect. This may have been due to the lower pH of those samples
Vitamin D Intake and Status in a Sample of Healthy Young Adults of Different Ethnicity Living in Canada
Vitamin D plays an important role in over-all health. Few data exist on vitamin D deficiency related with intake for a Canadian population. The purpose of this study is to assess vitamin D intake and status in healthy young adults of diverse ancestry during the wintertime.
One hundred and seven young healthy adults living in Southern Ontario were recruited during the late winter of 2007. Their serum 25-hydroxyvitamin D [25(OH)D], skin melanin and anthropometric measures were determined. They completed a food frequency questionnaire (FFQ) (twice) and a 7-day food diary. Correlation analyses and t-test were used to validate the FFQ against the 7-day diary and 25(OH)D; one way ANOVA was used to determine ethnic group differences in vitamin D intake and status.
The results indicated that the FFQ used in this study was valid. Vitamin D deficiency [25(OH)
Robust Matrix Completion State Estimation in Distribution Systems
Due to the insufficient measurements in the distribution system state
estimation (DSSE), full observability and redundant measurements are difficult
to achieve without using the pseudo measurements. The matrix completion state
estimation (MCSE) combines the matrix completion and power system model to
estimate voltage by exploring the low-rank characteristics of the matrix. This
paper proposes a robust matrix completion state estimation (RMCSE) to estimate
the voltage in a distribution system under a low-observability condition.
Tradition state estimation weighted least squares (WLS) method requires full
observability to calculate the states and needs redundant measurements to
proceed a bad data detection. The proposed method improves the robustness of
the MCSE to bad data by minimizing the rank of the matrix and measurements
residual with different weights. It can estimate the system state in a
low-observability system and has robust estimates without the bad data
detection process in the face of multiple bad data. The method is numerically
evaluated on the IEEE 33-node radial distribution system. The estimation
performance and robustness of RMCSE are compared with the WLS with the largest
normalized residual bad data identification (WLS-LNR), and the MCSE
- …