Continuous measurement data

The first two types of data that we will consider are both concerned with the measurement of some characteristic. Interval scale , or what is commonly called Continuous measurement , data include most of the information that would be generated in a laboratory. These include weights, lengths, timings, concentrations, pressures, etc. Imagine we had a series of objects weighing 1, 2, 3 up to 7 g as in Figure 1.1. 

The structure of this book is based upon the different data types. Chapters 2—14 all deal with the handling of continuous measurement data, with Chapters 15 and 16 focusing on categorical data, and then Chapter 17 covers ordered data. 

With interval scale (continuous measurement) data, there are two aspects to the figures that we should be trying to describe ... 

Figure 5.37 depicts the basic set up of a wireline logging operation. A sonde is lowered downhole after the drill string has been removed. The sonde is connected via an insulated and reinforced electrical cable to a winch unit at the surface. At a speed of about 600m per hour the cable Is spooled upward and the sonde continuously records formation properties like natural gamma ray radiation, formation resistivity or formation density. The measured data is sent through the cable and is recorded and processed in a sophisticated logging unita the surface. Offshore, this unit will be located in a cabin, while on land it is truck mounted. In either situation data can be transmitted in real time via satellite to company headquarters if required. 

Optical devices or optical systems have provided most of the available strong shock data and were the primary tools used in the early shock-compression investigations. They are still the most widely used systems in fundamental studies of high explosives. The earliest systems, the flash gap and mirror systems on samples, provided discrete or continuous measurements of displacement versus time. 

The wavelet interval-tree of scale is constructed fi om log 2 N distinct representations, where N is the number of points in the record of measured data. This is a far more efficient representation than that of scale-space filtering with continuous variation of Gaussian a. 

In summary, for data to be useful in clinical trial analyses they need to be quantifiable. The data must be either a continuous measure or a categorical value. Free text poses a problem for analysis, and if it is a valuable variable for the statistical analyses it really must be coded. Finally, hardcoding should be used only when absolutely necessary, because it is inherently problematic. Organizations that do allow hardcoding should document in their standard operating procedures (SOPs) that it is an approved business practice and how it is to be used. 

There are different ways to classify clinical trial data. As mentioned earlier, data can be classified by their physical nature into discrete chunks or as a more continuous measurable quantity. In clinical trials there are other important contextual ways of grouping data as well. For instance, clinical trials are primarily focused on determining two things about a drug, biologic, or device Is it efficacious, and is it safe The data that help to answer these questions are broadly classified as efficacy data and safety data, respectively. 

Input Errors. Errors in model input often constitute one of the most significant causes of discrepancies between observed data and model predictions. As shown in Figure 2, the natural system receives the "true" input (usually as a "driving function") whereas the model receives the "observed" input as detected by some measurement method or device. Whenever a measurement is made possible source of error is introduced. System inputs usually vary continuously both in space and time, whereas measurements are usually point values, or averages of multiple point values, and for a particular time or accumulated over a time period. Although continuous measurement devices are in common use, errors are still possible, and essentially all models require transformation of a continuous record into discrete time and space scales acceptable to the model formulation and structure. 

In Section 11.1.3.2 we considered a model of reactor performance in which the actual reactor is simulated by a cascade of equal-sized continuous stirred tank reactors operating in series. We indicated how the residence time distribution function can be used to determine the number of tanks that best model the tracer measurement data. Once this parameter has been determined, the techniques discussed in Section 8.3.2 can be used to determine the effluent conversion level. 

The EPM required some measured data to determine the Fourier coefficients of the pseudopotential. However, the most modem approaches follow the Fermi [5] concept of developing a pseudopotential to yield a wave function without nodes that coincides with the all-electron atomic wave function outside the core and is still normalized. Several methods were developed [16-19] in the 1970s and 1980s, and new methods for constructing useful pseudopotentials continue to appear in the literature. The applications discussed here are mostly based on the pseudopotentials developed using the approach described in Ref. [19]. The important point to empha-... 

Figure 12,19. Temperature tuning of an optical parametric oscillator. The continuous curve is a theoretical prediction and the circles represent measured data. (From Ref. 75.)...

The first step in all this is the capacity to transfer measured data, he continued. "That s the first hurdle that I see you get over for any reasonable number of samples. I certainly feel that 50 samples is a reasonable size of information. It could be 1000 or it could be less. The cost to do these kind of things is a cost more in time than money. Time wise, I think it s... 

Before 1970, most of the data for nitrogen oxides were obtained by continuous measurements with a colorimetric analyzer that was similar in principle to the colorimetric oxidant analyzer shown in Figure 6-8. The scrubbing agent is a mixture of -(l-naphthyl)ethylenediamine, sulfanilic acid, and acetic acid in aqueous solution. The color is produced when both nitrogen dioxide and nitrites react with this reagent to form an azo dye. The color is not affected by nitric oxide in the air sample. 

It is important to separate conceptually, and in practice, the calibration process from the monitoring process. Photochemical oxidants consisting primarily of ozone were firrt continuously measured in southern California by measuring the color change of potassium iodide solutions brought into contact with the ambient air. This measurement continues to yield valid photochemical-oxidant data in California. However, it has yielded questionable data at ambient air monitoring sites elsewhere in... 

In the example we have been using (see Section 3.1), the response from the system was measured nine times. The resulting data is a sample of the conceptually infinite number of results that might be obtained if the system were continuously measured. This conceptually infinite number of responses constitutes what is called the... 

The particle light scattering coefficient has been continuously measured at this location since 1976. Measurements of the particle size distribution have been made daily since 1978, providing the data base necessary to assess the variability of the normalized aerosol volume distribution. 

The mean residence time of carbon in the mixed layer of the sea before transfer into the deep sea is of considerable interest, for as has already been pointed out, the rate of this transfer will eventually govern the levels of excess 14C in the atmosphere. There have been several estimates of this residence time. Craig (29) concluded that it was most probably not more than 10 years, and in one of his calculations he deduced a value of 4 years. Broecker et al. (14) concluded it was 5 years in the Atlantic Ocean and 8 years in the Pacific Ocean. Nydal (45) found that for the North Atlantic it was around 3 years or less. The profiles of Figure 6, and a few others which are not shown, all show a significant penetration of excess 14C below the mixed surface layer, pointing to a short residence time, of the order of 2 years, in the mixed layer of the sea before transfer below the thermocline into the deep sea. Considering the size of the oceans these data are very meager, and no firm conclusions can be drawn from them. However, continued measurements of 14C in the sea should help to establish a firmer estimate of this quantity. 

Figure E5.7 displays the kinetic progress curve of a typical enzyme-catalyzed reaction and illustrates the advantage of a kinetic assay. The rate of product formation decreases with time. This may be due to any combination of factors such as decrease in substrate concentration, denaturation of the enzyme, and product inhibition of the reaction. The solid line in Figure E5.7 represents the continuously measured time course of a reaction (kinetic assay). The true rate of the reaction is determined from the slope of the dashed line drawn tangent to the experimental result. From the data given, the rate is 5 jumoles of product formed per minute. Data from a fixed-time assay are also shown on Figure E5.7. If it is assumed that no product is present at the start of the reaction, then only a single measurement after a fixed period is necessary. This is shown by a circle on the experimental rate curve. The measured rate is now 16 jumoles of product formed every 5 minutes or about 3 /rmoles/minute, considerably lower than the rate derived from the continuous, kinetic assay. Which rate measurement is correct Obviously, the kinetic assay gives the true rate because it corrects for the decline in rate with time. The fixed-time assay can be improved by changing the time of the measurement, in this example, to 2 minutes of reaction time, when the experimental rate is still linear. It is possible to obtain...

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