Space response

The location of a point on the response surface must be specified by (1) stating the level of the factor, and (2) stating the level of the response. Stating only the coordinate of the point with respect to the factor locates the point in factor space stating only the coordinate of the point with respect to the response locates the point in response space and stating both coordinates locates the point in experiment space. If the seventh experimental observation gave the third point from the left in Figure 2.3, the location of this point in experiment space would by x,7 = 3.00, y = 4.76 (the first subscript on x and y refers to the factor or response number the second subscript refers to the experiment number). 

Sketch the factor space, response space, and experiment space for Problem 2.1. 

Each response yj, may be viewed as a distance in response space (see Section 2.1). Statisticians find it useful to travel from the origin to each response in a number of discrete steps as illustrated in Figure 9.1. Each journey can be broken up as follows. 

Design of experiments (DOE) tools are widely considered to be some of the most important tools in the development of calibration models for PAT [22]. In cases where snfflciently relevant calibration samples can be synthetically prepared, DOE can be nsed to specify an efficient and effective set of calibration mixture standards for calibration development. Even in those PAT problems where synthetic standards cannot be prepared, the concepts behind DOE are nseful for understanding the importance of covering the needed composition and instrnment response space for a given problem. 

Revisit variable selection A profound expansion or shift in the relevant analyzer response space, or in the measurement objectives, could result in the need to reconsider the optimal set of variables to use for the calibration model. This action is usually considered when new or additional calibration data are obtained. 

The use of and Q prediction outlier metrics as described above is an example of a model-specific health monitor , in that the metrics refer to the specific analyzer response space that was used to develop a PLS, PCR or PCA prediction model. However, many PAT applications involve the deployment of multiple prediction models on a single analyzer. In such cases, one can also develop an analyzer-specific health monitor, where the and Q outlier metrics refer to a wider response space that covers all normal analyzer operation. This would typically be done by building a separate PCA model using a set of data that covers all normal analyzer responses. Of course, one could extend this concept further, and deploy multiple PCA health monitor models that are designed to detect different specific abnormal conditions. 

Do your best to cover the relevant analyzer response space in your calibration data. If this cannot be achieved, then at least know the limitations in your calibration data. 

Establishing a design space (factor s responses spaces)... 

Movement to optimum along the gradient is in steps from the starting point to optimum. Due to the necessary number of steps for reaching optimum, we differentiate several gradient methods that are in use nowadays. Efficiency of gradient methods depends on the complexity of the studied response space, on magnitude of the selected step, on size of experiment error and on other factors. 

FIGURE 16.5 The shaded region satisfies the three flammability criteria for the program and represents 5% of the response space. 

Brown VJ, Robbins TW (1989) Deficits in response space following unilateral striatal dopamine depletion in the rat. J Neurosci 9 983-989. 

The observed result of an experimental called the response. The yield of the desired product is often the most important response and is sometimes used as a single criterion of success. It is, however, common that several responses are of interest, e.g. yields of byproduct, selectivity, cost for producing a given quantify of product. When several responses are considered we will also have to consider variations in a multidimensional response space, see Fig. 1. 

Fig. 1. V ariations of synthetic reactions are illustrated by the reaction space, the experimental space, and the response space...

Quantitative Relations Between the Response Space, the Experimental Space, and the Reaction Space... 

In the above sections it was discussed how different perturbations which can be made when a synthetic reaction is run could be regarded as variations in two different spaces which span different kinds of possible variations of a reaction theme . As there are often more than one response of interest, it is also necessary to consider the response space. In this section is discussed how these spaces can be connected by quantitatie models so that it will be possible to evaluate how perturbations in one space are related to variations in another space. 

Principle 3 defines an applicability domain that refers to the response and chemical structure space in which the model makes predictions with a given reliability. Ideally the applicability domain should express the structural, physicochemical, and response space of the model. The chemical structure space can be expressed by information on physicochemical properties and/or structural fragments. The response can be any physicochemical, biological, or environmental effect that is being predicted. 

PLS is a flexible tool which can be used to describe interdependencies of variables in many situations encountered when synthetic reactions are explored. In the examples given below, it is shown how PLS can be used for linking together the reaction space, the experimental space and the response space. The following examples are discussed ... 

The experimental space linked to the response space, illustrated by a study on the suppression of a by-product in the synthesis of an enamine. 

The reaction space linked to the experimental space and the response space, illustrated by prediction of optimum conditions for new substrates in the Willgerodt-Kindler reaction. 

In the general case, the PLS method is the preferred choice. It can be used to link the variations in the experimental space, the reaction space, and the response space. As the PLS method does not involve any assumptions as to cause-effect relations, it is in that respect a method for unprejudiced analysis. 

The problems in synthesis are truly multidimensional. We have introduced the concepts of the experimental space, and the reaction space to describe different types of variation of the conditions of a synthetic reaction. As there are often more than one response to consider, we also have introduced a response space. The tools for exploring these spaces will be different and dependent on the questions posed to the chemical system. 

Another technique for evaluating several responses is to determine quantitative relations between the experimental space and the response space by means of a PLS model. This technique is especially helpful when there are many response variables to consider and when one wants to know how the variations in the experimental space is coupled to the variation of all responses. 

It is important in any prediction to know whether the query compounds fall within the AD of the model. Ideally, the AD should cover the structural, physicochemical and response space (e.g. mode of action) of the model. The distance-to-model measure can be used as a measure for the AD (see Section III.B.4.). " ... 

In addition to descriptors calculation, some explorative tools are also available that allow one to calculate descriptor values and their univariate statistics, to project and visualize molecules in the descriptor/response space, to calculate descriptor pair correlations, and to identify the most and the least correlated descriptors with a selected one. 

The hermetic dose response can be tested because its low-dose response starts immediately to the left (in the dose-response space) of any hypothetical threshold. Recollecting that the threshold model is the linearized form of the S-shaped toxicological cumulative distribution of responses, this response is generally not within the observations (it is an extrapolation via a probit transformation from the experimental results to a dose intercept). On the other hand, the hormetic dose-response can be either validated or rejected with normal testing protocols, provided that a sufficient number of experimental results are available (five or more). 

Comments PPARa activation is a summary of trans-activation data as well as response of markers such as ACO and CYP4A gene, along with protein and enzymatic activity, which are indicators of PPARa activation and are dependent on level of PPARa expression. The endpoint examined in these studies is indicated below. + indicates a strong response, (+) indicates a weak response, and - indicates no response. Spaces left blank indicate no data available. It should be noted that the table does not include PCO data from monkey species otho- than Cynomolgus monkeys other monkey data (which is almost universally negative) are summarized in Klaunig et al. (2003). PCO, palmitoyl-CoA oxidase. 

We can imagine the response space in terms of the response parameters and the experimental variables as a scalar field function. The experiential variables themselves form a vector and the components of the vector are the experiential variables. 

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