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Redundancy observations

This definition of makes the relative contributions of the terms t in Eq. (30a) independent of At, and therefore equalizes the data sets with different numbers of observation. Relationship (73) assumes that for data set with redundant observations increases as. Such an increase can be caused by the fact that the number of sources of random errors may increase proportionally to the number of simultaneous measurements. For example, increasing spectral and/or angular resolution in remote-sensing measurements likely results in a decrease of the quality of a single measurement due to increased complexity of the instrumentation and calibration. However, the assumption given by Eq. (73) is of intuitive character since it is not based on... [Pg.99]

The apparent contradiction between inflammatory chemokine and chemokine receptor redundancy observed in vitro and specific phenotypes revealed from gene-targeted animals can be resolved if one considers that these chemokines and their receptors function as a cooperative network in vivo to generate a complete immune response. Cooperation exists by coordinating the temporal expression of chemokine receptors on different cell types, the same cell type, or even the same cell. [Pg.25]

We are aware that the examined control networks have different shapes, and also different number of redundant observations. The last parameter has essential influence not only on the results of accuracy analysis, but first of all on reliability of these results, as well as on reliability of computed coordinates. So in order to draw final conclusions from the analysis of control networks with widely diversified numbers of redundant observations, one has to perform statistical analysis of results, based, for example, on the interval estimation. Confidence intervals for true values of the vector of unknowns X can be determined with the known formula... [Pg.368]

The simplicity of the final result is the mincut representation (sum of products Section 2.2) depicted as a fault tree in Figure 3.4.4-9. If the single double, and so on to higher redundancy components had been identified, the complex and awkward tree of Figure 3.4.4-S would have been avoided. Some systems are so complex that this cannot be done by observation, but computer analv. is will show simplicities if they exist. [Pg.110]

Also, for this option, several levels can be observed concerning the integration of the airflow model. The lowest level of integration still requires separate input for the thermal and the airflow model respectively with a high degree of redundancy in the input parameters (e.g., zones must be input for both models), and the connectivity of the airflows and the zones in the thermal model must be established manually by the user. More sophisticated levels have reduced redundancy and automatic establishment of the link connectivity. [Pg.1096]

In spite of this redundancy of results, discrepancies among different data sets obtained from different laboratories on antimicrobial activity of these 0-heterocycles against both prokaryotic and eukaryotic microorganisms have been sometimes observed. This fact is probably due to various causes. [Pg.258]

To reduce intensity effects, the data were normalized by reducing the area under each spectrum to a value of 1 [42]. Principal component analysis (PCA) was applied to the normalized data. This method is well suited to optimize the description of the fluorescence data sets by extracting the most useful data and rejecting the redundant ones [43]. From a data set, PCA assesses principal components and their corresponding spectral pattern. The principal components are used to draw maps that describe the physical and chemical variations observed between the samples. Software for PCA has been written by D. Bertrand (INRA Nantes) and is described elsewhere [44]. [Pg.283]

Microbial communities can respond to disturbances, such as contamination, in many different ways any of these responses may result in perceived stability or the continuation of essential soil functions [80]. The key species may show resistance to perturbation, meaning that the pollutants have no negative (or positive) effect on them. If the initial reaction is negative but the key species are able to regain their numbers and functionality, the community is said to be resilient. If the key species are irreversibly affected but are replaced by other indigenous species that are able to perform the same task under the new conditions, we see redundancy. Only if all these backup strategies fail will the deleterious effects of contamination on soil functions be observed. [Pg.12]

Crowe, C. M. (1989). Observability and redundancy of process data for steady state reconciliation. Chem. Eng. Sci. 44, 2909-2917. [Pg.27]

Kretsovalis, A., and Mah, R. S. H. (1988a). Observability and redundancy classification in generalised process networks. I Theorems. Comput. Chem. Eng. 12, 671-687. [Pg.27]

Since the data are usually obtained from observations (measurements) that are subject to probabilistic fluctuations, redundant data are usually inconsistent in the sense that each sufficient subset yields different results from other subsets. To obtain a unique solution, an additional criterion is necessary. If the least square principle is applied, among all the solutions that are consistent with the measurement model, the estimations that are as close as possible to the measurements are considered to be the solution of the estimation problem. We define a least squares estimation problem as follows ... [Pg.30]

The preceding section discusses the mathematical formulation of the problem under consideration and the general conditions for redundancy and estimability. Now, we are ready to analyze the decomposition of the general estimation problem. The division of linear dynamic systems into their observable and unobservable parts was first suggested by Kalman (1960). The same type of arguments can be extended here to decompose a system considered to be at steady-state conditions. [Pg.33]

In this chapter, similar arguments to that of dynamic observability were extended to establish the conditions for estimability in steady-state processes when the redundancy condition is satisfied. This concept allows decomposition of the general estimation... [Pg.38]

Steady-state process variables are related by mass and energy conservation laws. Although, for reasons of cost, convenience, or technical feasibility, not every variable is measured, some of them can be estimated using other measurements through balance calculations. Unmeasured variable estimation depends on the structure of the process flowsheet and on the instrument placement. Typically, there is an incomplete set of instruments thus, unmeasured variables are divided into determinable or estimable and indeterminable or inestimable. An unmeasured variable is determinable, or estimable, if its value can be calculated using measurements. Measurements are classified into redundant and nonredundant. A measurement is redundant if it remains determinable when the observation is deleted. [Pg.44]


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