Functional redundancy principle

The functional redundancy principle presupposes that, for sustainable functioning of an ecosystem, a decrease in biodiversity can be tolerated, as long as key(stone) species and their functions are not impacted (see Table 1.2). This is because of the redundancy in roles and functions provided by the surviving species in the community (Lawton 1994). Functional redundancy is well known in ecology and has been demonstrated experimentally such as in the work of Tilman et al. (Tilman 1996 Tilman et al. 1996). 

When adopting the functional redundancy principle, the emphasis is on ecosystem processes impacts are considered acceptable when functional attributes are not changed, despite possible effects on community structure. Functional endpoints are rarely more sensitive than structural ones (Ellis 1989 Kersting 1994 Klepper et al. 1999) however, an exception is found in the photosynthesis inhibitors such as the triazines and urea classes of herbicides. Effects on functional endpoints indicate the limit of functional redundancy within the stressed community. Once ecosystem processes have changed due to contamination, this is usually an indication of severe effects on structural endpoints. 

The functional redundancy principle is most appropriate for intensively used environments such as those impacted by urbanization, industrial, agricultural, and forestry activities. When adopting the functional redundancy principle, however, an important... 

Evidence from recent studies in ecology suggest that functional redundancy exists within some natural communities, but the relative contribution of different species to specific functions is far from equal, and the disappearance of certain species (i.e., dominants and keystone species) can have disproportionately large effects on overall system function and the occurrence of other species. For this reason, the precautionary principle advises that species loss be considered at least as a cause of incremental damage. Landscape-level models offer the possibility to improve our interpretation of local phenomena (e.g., species disappearance) in a wider spatial context. 

The fundamental idea is to utilize additional relevant process information for assessing the correctness of information generated by a sensor. This approach is known as the functional redundancy and it is more attractive than physical redundancy by duplicating sensors and using a voting logic to select the correct information. Several techniques based on statistics and system theory have been developed for validation of sensor information by functional redundancy. In most of these techniques, it is assumed that detailed process information is available a priori. Often, this knowledge is in the form of an accurate state-space model [39, 230]. In many cases, this type of accurate representation of a chemical process based on first principles is not available. 

Therefore, a safe-hfe architecture has been established using the redundancy principle, i.e. establishing a sufficient degree of redundant sub-systems to ensure correct function. 

Proposed functional safety requirements on EPB item are listed in Table 2, which meet the level of detail required by the example, but they will not reflect the complete set of functional safety requirements. It adheres to the principle that at least one functional safety requirement shall be specified for each safety goal. In a complete set, consideration has to be taken to operating modes, fault tolerant time interval, safe states, emergency operation interval, and functional redundancies (e.g. fault tolerance). A warning and degradation concept should also be specified. 

For a safe close-loop-controller there are more than just one requirement or more than one permitted operation mode, input condition, possible erroneous environmental influence factor, in many cases it is an array of modes and possible parameter. Safeguarding by a monitoring or by functional redundancy lead to the same complexity or heterogeneous implementation, than the close-loop-control itself. If the monitoring or the functional redundancy based on the same principles the same systematic errors lead to dependent failure and consequently the systematic-errors could not be controlled and consequently not avoided. 

Finally, in order to achieve high levels of safety, the principles of diversified hardware and functional redundancy will be used on a larger scale and will be optimized (see Figures 9.19 to 9.24). 

The concept of hardware and functional redundancy can be optimized. Let us start off from the basic safety principle, which is to make the function fiiUy redundant and to compare the results of these functions in order to determine their proper implementation. The optimization process is described in the context of Figure 9.20 taken from PUF 05]. 

Having examined the parametrization of the Hartree-Fock model in Section 10.1, we now turn our attention to the Hartree-Fock wave function itself, obtained by applying the variation principle to the energy expression E(k) in (10.1.20). In the present section, the emphasis is on the structure and characterization of the Hartree-Fock state rather than on its optimization. We shall examine the Hartree-Fock variational conditions, the gradient and Hessian of the optimized wave function, redundant orbital rotations, the Brillouin theorem and size-extensivity. For optimization techniques, see Sections 10.6-10.9. 

The principles of organization of elementary molecular components of living beings - the formation of networks and machines, pleiotropy and redundancy - are not independent but are closely interlinked. Pleiotropy results from the involvement of the same networks, or at least of the same functional modules (Hartwell et al., 1999) of these networks, in different functional processes. Redundancy makes the functioning of these networks stable. 

The conclusions from this rather elementary survey of the symmetry constraint problem all point in the same general direction. The imposition of symmetry constraints (other than the Pauli principle) on a variationally-based model is either unnecessary or harmful. Far from being necessary to ensure the physical reality of the wave function, these constraints often lead to absurd results or numerical instabilities in the implementation. The spin eigenfunction constraint is only realistic when the electrons are in close proximity and in such cases comes out of the UHF calculation automatically. The imposition of molecular spatial symmetry on the AO basis is not necessary if that basis has been chosen carefully — i.e. is near optimum. Further, any breakdowns in the spatial symmetry of the AO basis are a useful indication that the basis has been chosen badly or is redundant. 

At the risk of being redundant, we may state here the salient features of the TD-functional formalism. The first requirement is a variational principle, and for a time-dependent quantum description only a stationary action principle is available. With this a mapping theorem is established which turns the action functional into a functional of relevant physical quantities (which are the expectation values), and the condition of stationarity is now in terms of these variables instead of the entire density matrix. Thus the stationary property with respect to the density matrix now becomes one with respect to all the variables... 

When this is done these sums of signed products form a non-redundant set for the expansion of any function of the coordinates of n electrons which satisfies the Pauli (antisymmetry) principle. 

Protection System Independence. The protection system shall be designed to ensure that the effects of normal operations, AOEs, maintenance, testing, and DBAs on redundant channels do not result in loss of the protection function. Design techniques, such as redundancy, physical separation, functional diversity, or diversity in component design and principles of operation, shall be used to prevent loss of the protection function. The protection shall be sufficient to ensure no single failure results in loss of protection and capability exists to test channels independently to determine failures and loss of redundancy. 

The network reliabUity is represented as a logical OR of all the paths acting in an active redundancy. A passive redundancy with imperfect switching would have been more realistic but more complicated to evaluate. There exist different techniques for computing Ax y(t) such as the inclusion-exclusion principle (Ru-bino, 1998) or the binary decision diagram (Rauzy, 1993) (Liudong, 2008). Here, the present paper takes into account the behavior of each sensor of WSN. For this reason, each boolean function of each monitored point... 

The safety systems and their elements embody redundancy and diversity, through the use of different operating principles in different systems, to provide functional and physical in-depth protection of the reactor. Complete passivity of the safety systems is attained through the wide use of self-actuated devices for the initiation of the systems at deviation of the most important process parameters beyond the set limits. 

Performance of the safety system functions is provided in the scope required considering external natural and human-induced events and internal events caused by accident conditions. Functioning of the safety systems is provided considering potential failures such as a single failure or a common cause failure resulting from a single failure, or an impact of a personnel error. To ensure reliability of safety systems, the principles of redundancy, diversity and physical separation are applied, as well as certain measures such as ... 

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