Threshold distribution

For food allergens, validated animal models for dose-response assessment are not available and human studies (double-blind placebo-controlled food challenges [DBPCFCs]) are the standard way to establish thresholds. It is practically impossible to establish the real population thresholds this way. Such population threshold can be estimated, but this is associated with major statistical and other uncertainties of low dose-extrapolation and patient recruitment and selection. As a matter of fact, uncertainties are of such order of magnitude that a reliable estimate of population thresholds is currently not possible. The result of the dose-response assessment can also be described as a threshold distribution rather than a single population threshold. Such distribution can effectively be used in probabilistic modeling as a tool in quantitative risk assessment (see Section 15.2.5)... 

Both variability and uncertainty in threshold and exposure data can be taken into account by using probability distributions to represent the input variables instead of point estimates. The data are plotted in a cumulative distribution curve. For example, threshold data and intake data can be plotted as probability distributions. By combining the threshold distribution and the intake distribution, the output distribution will describe the probability that a part of the population will be exposed at such levels and under such circumstances that adverse effects may occur. Consequently, an approximation of the percentage of the population likely to experience adverse effects at various exposure levels can be made. 

In well-performed food challenge studies, the individual allergic reactions per dose are documented. Grouping the type of reaction, for instance distinction between subjective and objective allergic reactions, results in different threshold distributions, in this case a distribution for subjective and objective reactions, respectively (Figure 15.3). 

FIGURE 15.3 Distinction of the threshold distribution into type and/or severity. 

To close this section, we mention that this case of disorder was extended to other kinds of threshold distributions, like the Weibull distribution (de Arcangelis 1990). 

Van Noortwijk, J.M., Van der Weide, J.A.M., Kallen, J.M., and Pandey, M.D. 2007. Gamma processes and peaks-over-threshold distributions for time-dependent reliability. gi jlity n ineerin S sterr j 92(12) 1651-1658. 

Among the most interesting of these features are, in particular, a strong dependence of the threshold of the PFT induced in a homeotropic cell by an obliquely incident ordinary (o) wave on the angle of incidence of this wave and the oscillatory time dependence of the above-threshold distribution of the orientation in this geometry. These effects are... 

Pradhan, S. Hansen, A., 2005. Failure properties of fiber bundle model having lower cutoff in fiber threshold distribution. Phys. Rev. E., IT. 026111. 

Therefore an automatic method, which means an objective and reproducible process, is necessary to determine the threshold value. The results of this investigations show that the threshold value can be determined reproducible in the point of intersection of two normal distributed frequency approximations. 

The Superfund Amendments and Reauthorization Act of 1986 (SARA) Tide III requires emergency planning based on threshold planning quantities (TPQ) and release reporting based on RQs in 40 CER part 355 (used for SARA 302, 303, and 304). The TPQ for acrolein is 500 lb (227 kg), and its RQ is 1 lb (0.454 kg). SARA also requires submission of aimual reports of release of toxic chemicals that appear on the Hst in 40 CER 372.65 (for SARA 313). Acrolein appears on that Hst. This information must be included in all MSDSs that are copied and distributed for acrolein. 

The use of molecular and atomic beams is especially useful in studying chemiluminescence because the results of single molecular interactions can be observed without the complications that arise from preceding or subsequent energy-transfer coUisions. Such techniques permit determination of active vibrational states in reactants, the population distributions of electronic, vibrational, and rotational excited products, energy thresholds, reaction probabihties, and scattering angles of the products (181). 

Volume of vessel (free volume V) Shape of vessel (area and aspect ratio) Type of dust cloud distribution (ISO method/pneumatic-loading method) Dust explosihility characteristics Maximum explosion overpressure P ax Maximum explosion constant K ax Minimum ignition temperature MIT Type of explosion suppressant and its suppression efficiency Type of HRD suppressors number and free volume of HRD suppressors and the outlet diameter and valve opening time Suppressant charge and propelling agent pressure Fittings elbow and/or stub pipe and type of nozzle Type of explosion detector(s) dynamic or threshold pressure, UV or IR radiation, effective system activation overpressure Hardware deployment location of HRD suppressor(s) on vessel... 

Data that is not evenly distributed is better represented by a skewed distribution such as the Lognormal or Weibull distribution. The empirically based Weibull distribution is frequently used to model engineering distributions because it is flexible (Rice, 1997). For example, the Weibull distribution can be used to replace the Normal distribution. Like the Lognormal, the 2-parameter Weibull distribution also has a zero threshold. But with increasing numbers of parameters, statistical models are more flexible as to the distributions that they may represent, and so the 3-parameter Weibull, which includes a minimum expected value, is very adaptable in modelling many types of data. A 3-parameter Lognormal is also available as discussed in Bury (1999). 

The value of the eorrelation eoeffieient using the least squares teehnique and the use of goodness-of-fit tests (in the non-linear domain) together probably provide the means to determine whieh distribution is the most appropriate (Keeeeioglu, 1991). However, a more intuitive assessment about the nature of the data must also be made when seleeting the eorreet type of distribution, for example when there is likely to be a zero threshold. 

PSvcHomrsicAL (eye-brain) RESPONSE TOINCOMIN6 LIGHT "THRESHOLDS OF PERCEPTION FOR CONTRAST COLOR CHANGE -SENSITIVITY TO SIZE,PATTERN DISTRIBUTION OF COLOR. -SUBJECTIVE JUDGMENT OF PERCEIVED IMAGES... 

Individuals differ in their sensitivity to odor. Figure 14-7 shows a typical distribution of sensitivities to ethylsulfide vapor (17). There are currently no guidelines on inclusion or exclusion of individuals with abnormally high or low sensitivity. This variability of response complicates the data treatment procedure. In many instances, the goal is to determine some mean value for the threshold representative of the panel as a whole. The small size of panels (generally fewer than 10 people) and the distribution of individual sensitivities require sophisticated statistical procedures to find the threshold from the responses. 

Solutions. Two substances on the list, ammonium nitrate and ammonium sulfate, are qualified by the term solution," which refers to the physical state of these chemicals. Solid, molten, and pelletized forms of these chemicals are exempt from threshold and release determinations. Only facilities that manufacture, process, or otherwise use these chemicals in the form of a solution are required to report. Supplier notification applies only if the chemical is distributed as a solution. 

A chemical manufactured at the facility that does not remain in a product distributed by the facility. A threshold determination must be made on the annual quantity of the chemical manufactured regardless of the concentration. For example, quantities of formaldehyde created as a result of waste treatment must be applied toward the threshold for manufacture of this chemical, regardless of the concentration of this chemical in the wastestream. 

The links between levels of exposure and inconvenience caused by ventilation noise are described in an investigation carried out on office workers.- Technical measurements and analyses of the ventilation noise at 155 typical office workplaces were in this study combined with assessments by the office workers of the level of disturbance that they experienced, the effect on working performance, fatigue, stress-related pain, and headaches. The average noise level was about 40 dB(A) at two of the workplaces, while it was about 35 dB(A) at two others. It emerged from rhe narrow-band analyses that the sound pressure levels of rhe infrasound were not in any event of an order that this type of sound frequencies (below 20 Hz) could contribute to any disturbance effects. Any steps taken to counter the sound frequencies of the ventilation noise under 50 Hz, i.e., the point of btersection between the threshold curve of auditory perception and the spectral level distribution curve of... 

The similarity of velocity and of turbulence intensity is documented in Fig. 12.29. The figure shows a vertical dimensionless velocity profile and a turbulence intensity profile measured by isothermal model experiments at two different Reynolds numbers. It is obvious that the shown dimensionless profiles of both the velocity distribution and the turbulence intensity distribution are similar, which implies that the Reynolds number of 4700 is above the threshold Reynolds number for those two parameters at the given location. 

These properties include (l)a continuous decrease in the average density of turbulent sites as the threshold is approached from above (with exponent /3) (2) divergence of the average transient time (3) algebraic distributions of the sizes and durations of laminar clusters at the threshold (with exponents and < ). Houlrik, Webrnan arid Jensen [houl90] discuss the critical behavior of this map from a mean-field theoretic perspective. 

Figure 10-15 shows the output vs. input energy relation with a clear threshold at a pump pulse energy of approximately 1.5 nJ. This value is an order of magnitude lower than the threshold for the observation of ASE in simple planar waveguides, i.e. without distributed feedback but prepared with the same conjugated polymer. 

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