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Order Model (order + model)
Selected AbstractsMeasuring and partitioning the high-order linkage disequilibrium by multiple order Markov chainsGENETIC EPIDEMIOLOGY, Issue 4 2008Yunjung Kim Abstract A map of the background levels of disequilibrium between nearby markers can be useful for association mapping studies. In order to assess the background levels of linkage disequilibrium (LD), multilocus LD measures are more advantageous than pairwise LD measures because the combined analysis of pairwise LD measures is not adequate to detect simultaneous allele associations among multiple markers. Various multilocus LD measures based on haplotypes have been proposed. However, most of these measures provide a single index of association among multiple markers and does not reveal the complex patterns and different levels of LD structure. In this paper, we employ non-homogeneous, multiple order Markov Chain models as a statistical framework to measure and partition the LD among multiple markers into components due to different orders of marker associations. Using a sliding window of multiple markers on phased haplotype data, we compute corresponding likelihoods for different Markov Chain (MC) orders in each window. The log-likelihood difference between the lowest MC order model (MC0) and the highest MC order model in each window is used as a measure of the total LD or the overall deviation from the gametic equilibrium for the window. Then, we partition the total LD into lower order disequilibria and estimate the effects from two-, three-, and higher order disequilibria. The relationship between different orders of LD and the log-likelihood difference involving two different orders of MC models are explored. By applying our method to the phased haplotype data in the ENCODE regions of the HapMap project, we are able to identify high/low multilocus LD regions. Our results reveal that the most LD in the HapMap data is attributed to the LD between adjacent pairs of markers across the whole region. LD between adjacent pairs of markers appears to be more significant in high multilocus LD regions than in low multilocus LD regions. We also find that as the multilocus total LD increases, the effects of high-order LD tends to get weaker due to the lack of observed multilocus haplotypes. The overall estimates of first, second, third, and fourth order LD across the ENCODE regions are 64, 23, 9, and 3%. Genet. Epidemiol. 2008. © 2008 Wiley-Liss, Inc. [source] On the stability and convergence of a Galerkin reduced order model (ROM) of compressible flow with solid wall and far-field boundary treatment,INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2010I. Kalashnikova Abstract A reduced order model (ROM) based on the proper orthogonal decomposition (POD)/Galerkin projection method is proposed as an alternative discretization of the linearized compressible Euler equations. It is shown that the numerical stability of the ROM is intimately tied to the choice of inner product used to define the Galerkin projection. For the linearized compressible Euler equations, a symmetry transformation motivates the construction of a weighted L2 inner product that guarantees certain stability bounds satisfied by the ROM. Sufficient conditions for well-posedness and stability of the present Galerkin projection method applied to a general linear hyperbolic initial boundary value problem (IBVP) are stated and proven. Well-posed and stable far-field and solid wall boundary conditions are formulated for the linearized compressible Euler ROM using these more general results. A convergence analysis employing a stable penalty-like formulation of the boundary conditions reveals that the ROM solution converges to the exact solution with refinement of both the numerical solution used to generate the ROM and of the POD basis. An a priori error estimate for the computed ROM solution is derived, and examined using a numerical test case. Published in 2010 by John Wiley & Sons, Ltd. [source] Reduced order state-space models from the pulse responses of a linearized CFD schemeINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2003Ann L. Gaitonde This paper describes a method for obtaining a time continuous reduced order model (ROM) from a system of time continuous linear differential equations. These equations are first put into a time discrete form using a finite difference approximation. The unit sample responses of the discrete system are calculated for each system input and these provide the Markov parameters of the system. An eigenvalue realization algorithm (ERA) is used to construct a discrete ROM. This ROM is then used to obtain a continuous ROM of the original continuous system. The focus of this paper is on the application of this method to the calculation of unsteady flows using the linearized Euler equations on moving meshes for aerofoils undergoing heave or linearized pitch motions. Applying a standard cell-centre spatial discretization and taking account of mesh movement a continuous system of differential equations is obtained which are continuous in time. These are put into discrete time form using an implicit finite difference approximation. Results are presented demonstrating the efficiency of the system reduction method for this system. Copyright © 2003 John Wiley & Sons, Ltd. [source] SUPERCRITICAL CO2/ETHANOL EXTRACTION OF ASTAXANTHIN FROM BLUE CRAB (CALLINECTES SAPIDUS) SHELL WASTEJOURNAL OF FOOD PROCESS ENGINEERING, Issue 2 2001LETICIA FÉLIX-VALENZUELA ABSTRACT Astaxanthin (AX) is the major naturally occurring carotenoid pigment in marine crustaceans and the flesh of salmonids. These organisms are unable to synthesize AX de novo and when farmed commercially, require it in their feed. The high cost of synthetic AX has promoted research into new natural sources of ihe pigment, such as crustacean wastes. In this work, AX from demineralized crab (Callinectes sapidusj shell waste was extracted with a mixture of supercritical C2 and ethanol as a cosolvent. The effect of total solids load, pressure and temperature was assessed by response surface methodology (RSM). Extracted AX was determined by HPLC. The experimental data were fined to a second order model whereby the conditions for maximum extraction yield were defined (, 34 MPa, 45C and solids load of 25 g). Pressure and solids load were the most important factors affecting AX extraction yields. [source] Monitoring the reaction progress of a high-performance phenylethynyl-terminated poly(etherimide).POLYMER ENGINEERING & SCIENCE, Issue 5 2002Part I: Cure kinetics modeling The cure kinetics of a phenylethynyl-terminated poly(etherimide) are examined via differential scanning calorimetry (DSC) measurements. Isothermal holds at temperatures ranging from 325°C to 360°C provided the necessary information to develop reaction kinetics models using both first-order reaction kinetics and combination reaction kinetics. The first-order reaction kinetics model works well for quick estimates of degree of cure versus time over the experimental temperature range. However, significantly more accurate predictions of degree of cure versus time were provided by the combination reaction kinetics model. The lack of accuracy in the first order model is due to the fact that the reaction cannot be described by a simple order. The experimental procedures followed to obtain the cure kinetics data and the construction of the models from this data are described; the predictions of these models are compared with the experimental results. [source] A new approach for modelling simultaneous storage and growth processes for activated sludge systems under aerobic conditionsBIOTECHNOLOGY & BIOENGINEERING, Issue 5 2005Gürkan Sin Abstract By critically evaluating previous models, a new mechanistic model is developed to describe simultaneous storage and growth processes occurring in activated sludge systems under aerobic conditions. Identifiability was considered an important criterion during the model development since it among others helps to increase the realiability and applicability of models to full-scale WWTPs. A second order model was proposed for description of the degradation of the storage products under famine conditions. The model is successfully calibrated by only using OUR data obtained from batch experiments. Calibrations were performed with biomass from full-scale WWTPs in Belgium and Spain. Predictions of the calibrated model were successfully confirmed using off-line PHB measurements, supporting the validity of the model. An iterative experimental design procedure was successfully applied and found to remarkably improve the parameter estimation accuracy for the growth on storage parameters K1 and K2, which used to have large confidence intervals when using standard experiments. The estimated biomass growth yield on substrate (0.58 mgCOD/mgCOD) is quite close to the theoretically expected range for heterotrophic growth. This became possible by properly accounting for the storage process. Moreover, the maximum growth rate was predicted in the range 0.7,1.3 per day. This range, albeit quite lower than the values reported for the growth-based ASM models, is believed to be more realistic. Finally, the new model is expected to better and more mechanistically describe simultaneous storage and growth activities of activated sludge systems and as such could contribute to improved design, operation and control of those systems. © 2005 Wiley Periodicals, inc. [source] A hybrid model of anaerobic E. coli GJT001: Combination of elementary flux modes and cybernetic variablesBIOTECHNOLOGY PROGRESS, Issue 5 2008Jin Il Kim Flux balance analysis (FBA) in combination with the decomposition of metabolic networks into elementary modes has provided a route to modeling cellular metabolism. It is dependent, however, on the availability of external fluxes such as substrate uptake or growth rate before estimates can become available of intracellular fluxes. The framework classically does not allow modeling of metabolic regulation or the formulation of dynamic models except through dynamic measurement of external fluxes. The cybernetic modeling approach of Ramkrishna and coworkers provides a dynamic framework for modeling metabolic systems because of its focus on describing regulatory processes based on cybernetic arguments and hence has the capacity to describe both external and internal fluxes. In this article, we explore the alternative of developing hybrid models combining cybernetic models for the external fluxes with the flux balance approach for estimation of the internal fluxes. The approach has the merit of the simplicity of the early cybernetic models and hence computationally facile while also providing detailed information on intracellular fluxes. The hybrid model of this article is based on elementary mode decomposition of the metabolic network. The uptake rates for the various elementary modes are combined using global cybernetic variables based on maximizing substrate uptake rates. Estimation of intracellular metabolism is based on its stoichiometric coupling with the external fluxes under the assumption of (pseudo-) steady state conditions. The set of parameters of the hybrid model was estimated with the aid of nonlinear optimization routine, by fitting simulations with dynamic experimental data on concentrations of biomass, substrate, and fermentation products. The hybrid model estimations were tested with FBA (based on measured substrate uptake rate) for two different metabolic networks (one is a reduced network which fixes ATP contribution to the biomass and maintenance requirement of ATP, and the other network is a more complex network which has a separate reaction for maintenance.) for the same experiment involving anaerobic growth of E. coli GJT001. The hybrid model estimated glucose consumption and all fermentation byproducts to better than 10%. The FBA makes similar estimations of fermentation products, however, with the exception of succinate. The simulation results show that the global cybernetic variables alone can regulate the metabolic reactions obtaining a very satisfactory fit to the measured fermentation byproducts. In view of the hybrid model's ability to predict biomass growth and fermentation byproducts of anaerobic E. coli GJT001, this reduced order model offers a computationally efficient alternative to more detailed models of metabolism and hence useful for the simulation of bioreactors. [source] | |||||||||||||