Causal

In the case of our linear, stationary and causal device, input and output are linked by the convolution integral ... 

The result is (causality dictates the upper limit of time integration to t)... 

In the same section, we also see that the source of the appropriate analytic behavior of the wave function is outside its defining equation (the Schibdinger equation), and is in general the consequence of either some very basic consideration or of the way that experiments are conducted. The analytic behavior in question can be in the frequency or in the time domain and leads in either case to a Kramers-Kronig type of reciprocal relations. We propose that behind these relations there may be an equation of restriction, but while in the former case (where the variable is the frequency) the equation of resh iction expresses causality (no effect before cause), for the latter case (when the variable is the time), the restriction is in several instances the basic requirement of lower boundedness of energies in (no-relativistic) spectra [39,40]. In a previous work, it has been shown that analyticity plays further roles in these reciprocal relations, in that it ensures that time causality is not violated in the conjugate relations and that (ordinary) gauge invariance is observed [40]. 

Contrary to what appears at a first sight, the integral relations in Eqs. (9) and (10) are not based on causality. However, they can be related to another principle [39]. This approach of expressing a general principle by mathematical formulas can be traced to von Neumann [242] and leads in the present instance to an equation of restriction, to be derived below. According to von Neumann complete description of physical systems must contain ... 

A set of properties of states (causality, resh ictions on the spectra of self-energies, existence or absence of certain isolated energy bands, etc.). 

The equation of restriction can embody causality, lower boundedness of energies in the spectrum, positive wavenumber in the outgoing wave (all these in nonrelativistic physics) and interactions inside the light cone only, conditions of mass speciality, and so on in relativistic physics. In the case of interest in this... 

M. Floissart, in Dispersion Relations and their Connection with Causality, E. P. Wiguer, ed., Academie Press, New York, 1964, p, 1. 

Epidemiological studies of nickel-producing and nickel-using workers seldom indicate excess mortaUty from nonmalignant respiratory disease. Evidence for such effects exists mainly as a few reports of isolated incidents of asthma, pulmonary fibrosis, chronic bronchitis, and emphysema in nickel workers. Nickel may or may not play a causal role in these incidents (131). 

If possible, there should be measurement of the toxic effect in order quantitatively to relate the observations made to the degree of exposure (exposure dose). Ideally, there is a need to determine quantitatively the toxic response to several differing exposure doses, in order to determine the relationship, if any, between exposure dose and the nature and magnitude of any effect. Such dose—response relationship studies are of considerable value in determining whether an effect is causally related to the exposure material, in assessing the possible practical (in-use) relevance of the exposure conditions, and to allow the most reasonable estimates of hazard. 

Dose—response relationships are useful for many purposes in particular, the following if a positive dose—response relationship exists, then this is good evidence that exposure to the material under test is causally related to the response the quantitative information obtained gives an indication of the spread of sensitivity of the population at risk, and hence influences ha2ard evaluation the data may allow assessments of no effects and minimum effects doses, and hence may be valuable in assessing ha2ard and by appropriate considerations of the dose—response data, it is possible to make quantitative comparisons and contrasts between materials or between species. 

There should be sufficient dose—response information to allow decisions on causal relationships and relevance. 

The results of the study should allow decisions on whether injury is a direct result of toxicity or secondary to other events. In addition to confirming a causal relationship between exposure to the test material and development of an injury, the study should be reviewed in order to assess whether information is available to determine if the effect is traceable to parent material or metaboUte. 

Relationships Between Objects, Processes, and Events. Relationships can be causal, eg, if there is water in the reactor feed, then an explosion can take place. Relationships can also be stmctural, eg, a distiUation tower is a vessel containing trays that have sieves in them or relationships can be taxonomic, eg, a boiler is a type of heat exchanger. Knowledge in the form of relationships connects facts and descriptions that are already represented in some way in a system. Relational knowledge is also subject to uncertainty, especiaUy in the case of causal relationships. The representation scheme has to be able to express this uncertainty in some way. 

The relationship set out in Eq. (9-115) can also be viewed via a different chain of causality with (DCFRR) as a given parameter, (PBP) as the independent variable, and n as the variable whose value is being sought. Such an approach is the basis for the lines in Fig. 9-31, each of which shows the number of years of projec t life required to achieve an effective interest rate or a (DCFRR) of 20 percent by projects having various payback periods. The three hues differ from each other with respec t to the matter of inflation. 

Evidence for chemically mediated disruption of thyroid function in wild reptile populations includes the finding of elevated thyroxine levels in male alligators from Lake Apopka, although a causal relationship with specific chemicals has not been established. ... 

S Greenland. Probability logic and probability induction. Epidemiology 9 322-332, 1998. GM Petersen, G Parmigiam, D Thomas. Missense mutations in disease genes A Bayesian approach to evaluate causality. Am J Hum Genet. 62 1516-1524, 1998. 

To establish the required causal effect of production rate on nitrates a year s history was investigated. For various production rate ranges the percentage of nitrate contents of various magnitudes was tabulated as follows ... 

In addition to these formal studies of human error in the CPI, almost all the major accident investigations in recent years, for example, Texas City, Piper Alpha, Phillips 66, Feyzin, Mexico City, have shown human error as a significant causal factors in design, operations, maintenance or the management of the process. Figures 4.4-1 and 4.4-2 show the effects of human error on nuclear plant operation. 

In a cross-sectional study, exposure and effect are studied simultaneously. This approach contains an inherent problem because exposure must precede the effect. However, it can he used to investigate acute effects and also mild chronic effects (which do not force people to leave their jobs) if exposure has remained rather stable for a long time. When the prevalence of the effects studied are compared with the prevalence in other worker groups (controls or references) which correspond otherwise with the study group but are not exposed to the agent investigated, indicative evidence of possible causality may be obtained. For example, cross-sectional studies have been applied successfully to reveal the associations between mild neurotoxic effects and exposure to organic solvents. ... 

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