Logistic scaling

FIGURE 11.13 A collection of 10 responses (ordinates) to a compound resulting from exposure of a biological preparation to 10 concentrations of the compound (abscissae, log scale). The dotted line indicates the mean total response of all of the concentrations. The sigmoidal curve indicates the best fit of a four-parameter logistic function to the data points. The data were fit to Emax = 5.2, n = 1, EC5o = 0.4 pM, and basal = 0.3. The value for F is 9.1, df=6, 10. This shows that the fit to the complex model is statistically preferred (the fit to the sigmoidal curve is indicated). 

Sigmoid, the characteristic S-shaped curves defined by functions such as the Langmuir isotherm and logistic function (when plotted on a logarithmic abscissal scale). 

Details are given of processes currently under development in Europe and the US for recycling plastics waste into feedstocks. In particular, the efforts of BP Chemicals and Shell are reported who have plans to form consortia of chemical companies. Problems associated with costs and logistics are discussed, which are preventing full-scale commercialisation. 

Specific predictive factors for outcome after surgical intervention have not been well defined in the literature. In one prospective, multicenter observational study of 95 patients, the state of consciousness was the only predictive factor retained in a logistic regression analysis." In this study, there was a 2.8-fold increased risk for poor outcome for each increase on a three-step scale (awake/drowsy, somnolent/ stuporous, and comatose), and good outcomes (modified Rankin Scale score <2) were achieved in 86%, 76%, and 47% of patients within each group, respectively. 

The simulation module simulates the basic operation(s) which are processed by a combination of a vessel and a station using a discrete event simulator. All necessary data (basic operation(s), equipment parameters, recipe scaling percentage, etc.) is provided by the scheduling-module. The simulator calculates the processing times and the state changes of the contents of the vessels (mass, temperature, concentrations, etc.) that are relevant for logistic considerations. 

If an approximate Km value for the enzyme-substrate combination of interest is known, a full-scale kinetic assay may be done immediately. However, often an approximate value is not known and it is necessary first to do a range finding or suck and see preliminary assay. For such an assay, a concentrated substrate solution is prepared and tenfold serial dilutions of the substrate are made so that a range of substrate concentrations is available within which the experimenter is confident the Km value lies. Initial velocities are determined at each substrate concentration, and data may he plotted either hyperholically (as V versus [S]) or with [S] values expressed as logio values. In the latter case, a sigmoidal curve is fitted to data with a three parameter logistic equation (O Eq. 4) ... 

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