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Linear Term (linear + term)
Selected AbstractsComputational methods for optical molecular imagingINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2009Duan Chen Abstract A new computational technique, the matched interface and boundary (MIB) method, is presented to model the photon propagation in biological tissue for the optical molecular imaging. Optical properties have significant differences in different organs of small animals, resulting in discontinuous coefficients in the diffusion equation model. Complex organ shape of small animal induces singularities of the geometric model as well. The MIB method is designed as a dimension splitting approach to decompose a multidimensional interface problem into one-dimensional ones. The methodology simplifies the topological relation near an interface and is able to handle discontinuous coefficients and complex interfaces with geometric singularities. In the present MIB method, both the interface jump condition and the photon flux jump conditions are rigorously enforced at the interface location by using only the lowest-order jump conditions. This solution near the interface is smoothly extended across the interface so that central finite difference schemes can be employed without the loss of accuracy. A wide range of numerical experiments are carried out to validate the proposed MIB method. The second-order convergence is maintained in all benchmark problems. The fourth-order convergence is also demonstrated for some three-dimensional problems. The robustness of the proposed method over the variable strength of the linear term of the diffusion equation is also examined. The performance of the present approach is compared with that of the standard finite element method. The numerical study indicates that the proposed method is a potentially efficient and robust approach for the optical molecular imaging. Copyright © 2008 John Wiley & Sons, Ltd. [source] Numerical implementation of the Crank,Nicolson/Adams,Bashforth scheme for the time-dependent Navier,Stokes equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2010Yinnian He Abstract This article considers numerical implementation of the Crank,Nicolson/Adams,Bashforth scheme for the two-dimensional non-stationary Navier,Stokes equations. A finite element method is applied for the spatial approximation of the velocity and pressure. The time discretization is based on the Crank,Nicolson scheme for the linear term and the explicit Adams,Bashforth scheme for the nonlinear term. Comparison with other methods, through a series of numerical experiments, shows that this method is almost unconditionally stable and convergent, i.e. stable and convergent when the time step is smaller than a given constant. Copyright © 2009 John Wiley & Sons, Ltd. [source] Gaussian Process Based Bayesian Semiparametric Quantitative Trait Loci Interval MappingBIOMETRICS, Issue 1 2010Hanwen Huang Summary In linkage analysis, it is often necessary to include covariates such as age or weight to increase power or avoid spurious false positive findings. However, if a covariate term in the model is specified incorrectly (e.g., a quadratic term misspecified as a linear term), then the inclusion of the covariate may adversely affect power and accuracy of the identification of quantitative trait loci (QTL). Furthermore, some covariates may interact with each other in a complicated fashion. We implement semiparametric models for single and multiple QTL mapping. Both mapping methods include an unspecified function of any covariate found or suspected to have a more complex than linear but unknown relationship with the response variable. They also allow for interactions among different covariates. This analysis is performed in a Bayesian inference framework using Markov chain Monte Carlo. The advantages of our methods are demonstrated via extensive simulations and real data analysis. [source] Fungistatic Activity of Heat-Treated Flaxseed Determined by Response Surface MethodologyJOURNAL OF FOOD SCIENCE, Issue 6 2008Y. Xu ABSTRACT:, The objective of this study was to evaluate the effect of heat treatment on the fungistatic activity of flaxseed (Linum usitatissimum) in potato dextrose agar (PDA) medium and a fresh noodle system. The radial growth of Penicillium chrysogenum, Aspergillus flavus, and a Penicillium sp. isolated from moldy noodles, as well as the mold count of fresh noodle enriched with heat treated flaxseed, were used to assess antifungal activity. A central composite design in the response surface methodology was used to predict the effect of heating temperature and time on antifungal activity of flaxseed flour (FF). Statistical analysis determined that the linear terms of both variables (that is, heating temperature and time) and the quadratic terms of the heating temperature had significant (P < 0.05) effects on the radial growth of all 3 test fungi and the mold count log-cycle reduction of fresh noodle. The interactions between the temperature and time were significant for all dependent variables (P < 0.05). Significant reductions in antifungal activities were found when FF was subjected to high temperatures, regardless of heating time. In contrast, prolonging the heating time did not substantially affect the antifungal activities of FF at low temperature. However, 60% of the antifungal activity was retained after FF was heated at 100 °C for 15 min, which suggests a potential use of FF as an antifungal additive in food products subjected to low to mild heat treatments. [source] Antifungal Activity Stability of Flaxseed Protein Extract Using Response Surface MethodologyJOURNAL OF FOOD SCIENCE, Issue 1 2008Y. Xu ABSTRACT:, The stability of the antifungal activity of flaxseed (Linum usitatissimum) protein extract was evaluated in this study. Response surface methodology (RSM) using Box,Behnken factorial design was used to evaluate the effects of treatment variables, that is, temperature (50 to 90 °C), time (1 to 29 min), and pH (2 to 8), on the residual antifungal activity (RAA) against Penicillium chrysogenum, Fusarium graminearum, Aspergillus flavus, and a Penicillium sp. isolated from moldy noodles. Regression analyses suggested that the linear terms of the temperature and time had significant (P < 0.05) negative effects on the RAA against all test fungi, whereas that of pH had a significant (P < 0.1) positive role on the RAA of all 3 fungi. In addition, the RAA was significantly (P < 0.05) affected by the quadratic terms of time for all fungi, and the quadratic term of temperature played a significant (P < 0.1) role on RAA against F. graminearum. One interaction term (temperature-pH) was found to significantly (P < 0.1) affect the RAA against both Penicillium strains tested. The results indicated that , 90% antifungal activity was lost after the protein extracts were heated at 90 °C for 8 min except for F. graminearum. At pasteurization condition, , 50% activity was retained except for P. chrysogenum. The results also suggested that neutral and alkaline pH favored the antifungal activity stability of the protein extracts. Thus, flaxseed protein might be promising if used as a preservative in foods with neutral or alkaline pH requiring mild heat treatments. [source] | ||||||||||