Model Reformulation Research Articles

Estimation and inference in pharmacokinetic models: The effectiveness of model reformulation and resampling methods for functions of parameters

It is well known that high parameter estimate correlations and asymptotic variance estimates can cause estimation and inference problems in the analysis of pharmacokinetic models. In this paper we show that analysis of three important functions of pharmacokinetic parameters, the half-life, mean residence time, and the area under the curve, can sometimes be greatly improved by reformulating the model to address collinearity and by using the bootstrap to form confidence intervals. The resultant estimators can be more accurate than the original ones, and resultant confidence intervals can be narrower. Of the three measures, the half-life estimator is much better behaved than the estimators of mean residence time and area under the curve under collinearity, suggesting that it (or measures like it) should be used more often.

A novel approach to speed control of hydro power stations

Digital control systems of hydro stations implementing translations of analog PID controllers have recently been applied to improve governor performance. This paper presents a novel approach to the power and speed control of hydro stations based on a special discrete-time model of the distributed penstock elasticity. Thanks to the discrete-time model reformulation, the control design allows the following two basic properties to be achieved: the penstock impedance matching, which avoids pressure oscillations being excited, and the active damping of the elastic oscillations at low loads, when they are excited by possible disturbances.

Linear, Integer, Separable and Fuzzy Programming Problems: A Unified Approach Towards Reformulation

For mathematical programming (MP) to have greater impact as a decision tool, MP software systems must offer suitable support in terms of model communication and modelling techniques. In this paper, modelling techniques that allow logical restrictions to be modelled in integer programming terms are described, and their implications discussed. In addition, it is illustrated that many classes of non-linearities which are not variable separable may be, after suitable algebraic manipulation, put in a variable separable form. The methods of reformulating the fuzzy linear programming problem as a max-min problem is also introduced. It is shown that analysis of bounds plays a key role in the following four important contexts: model reduction, reformulation of logical restrictions as 0-1 mixed integer programmes, reformulation of non-linear programmes as variable separable programmes and reformulation of fuzzy linear programmes. It is observed that, as well as incorporating an interface between the modeller and the optimizer, there is a need to make available to the modeller software facilities which support the model reformulation techniques described here.

Linear, Integer, Separable and Fuzzy Programming Problems: A Unified Approach towards Reformulation

For mathematical programming (MP) to have greater impact as a decision tool, MP software systems must offer suitable support in terms of model communication and modelling techniques. In this paper, modelling techniques that allow logical restrictions to be modelled in integer programming terms are described, and their implications discussed. In addition, it is illustrated that many classes of non-linearities which are not variable separable may be, after suitable algebraic manipulation, put in a variable separable form. The methods of reformulating the fuzzy linear programming problem as a max-min problem is also introduced. It is shown that analysis of bounds plays a key role in the following four important contexts: model reduction, reformulation of logical restrictions as 0-1 mixed integer programmes, reformulation of non-linear programmes as variable separable programmes and reformulation of fuzzy linear programmes. It is observed that, as well as incorporating an interface between the modeller and the optimizer, there is a need to make available to the modeller software facilities which support the model reformulation techniques described here.

Post-Instability Behavior of Solids

The necessity of model reformulation in elasticity results from the failure of hyperbolicity of the governing equations of motion for classical models. The reformulation is based upon the introduction of additional kinematical microstructures in the form of multivalued displacement and velocity field (or fractal functions) which arc generated by the mechanism of the instability. The small scale motions describing this microstructure interact with the original large scale motion and restore the hyperbolicity of new governing equations of motion. The applications of the reformulated models to the problem of vibrational control and impact energy absorption are discussed.

The Demand for Home‐Produced Food by Rural Families

consumption in 1965 was only $66 for the 33% of the households engaged in this activity (USDA, p. 7). However, interest in home food production has increased sharply in recent years. Some 44% of all households had a vegetable or fruit garden in 1976 (Kaitz, p. 20). Home production has remained an important source of food for many rural families and is for some the dominant food source. A survey of rural families in 1971 found the average family produced $124 of food at home per year at retail value. Some 60% of the families surveyed produced at least some food for home consumption with an average value of $206 per year for producing families. The value of home-produced food was as high as $1,868 for one family. The role of home food production in satisfying rural family food needs has definite policy implications. The widely used Orshansky poverty index, which is based upon the minimum income a family needs to obtain an adequate diet, takes account of the amount of food households raise for themselves. The poverty threshold for farm families was set at 70% before 1969 and is currently set at 85% of the nonfarm threshold for each family type. This differential is based on the assumed cost savings from home-produced food. A federal technical committee in 1973 recommended that the farm-nonfarm distinction be dropped, however, arguing the questionable appropriateness of singling out income differences in this single factor alone (HEW, p. 90). Most welfare programs take no account of home food production. Even the food stamp program ignores the implications of homeproduced food. Program participation is significantly lower in rural areas, though, and home food production may be a partial cause. The traditional theory of consumer behavior is inadequate for the present analysis since home-produced food is a nonmarket commodity that has no explicit price and requires a large time input on the part of the household. For the latter reason, the opportunity cost of time of the family members and the productive efficiency of the household are important factors. Becker's household production model reformulation of conventional demand theory offers an appropriate analytical framework under these circumstances. Within the household production approach, this study estimates three specifications of the demand function for home-produced food using a 1971 cross-sectional data set for rural families. The equations are estimated with ordinary least squares, weighted least squares, and, finally, with Tobit analysis.