Derivative spike

Oral immunogenicity of the plant derived spike protein from swine-transmissible gastroenteritis coronavirus. Arch. Virol., 2000 ... 

This form of the equation, however, exhibits a problem known as derivative spike. Consider how the derivative action responds to a change in SP. If, before the change, the process is at steady state and at SP then... 

This derivative-on-PV version will no longer cause a derivative spike when there is a change in SP. But the response of derivative action to process disturbances is unaffected. In many DCS this modification is standard. Others retain both this and the derivative-on-error versions as options. It is also common for this algorithm to include some form of filtering to reduce the impact of the spike but, even with this in place, there is no reason why the engineer should ever use the deiivative-on-error version if the deiivative-on-PV version is available. 

We covered derivative spikes in Chapter 3 and, by switching derivative action to be based on PV rather than error, were able to eliminate them when the SP was changed. However... 

Figure 7.6 Derivatives spikes caused by discontinuous measurement...

Transposing the mixing equation (1.3.4) derived for 87Sr/86Sr and using the subscripts sa, sp, and mix for sample, spike, and mixture, we write the atomic mixing equation as... 

If the x-data of an object are time-series or digitized data from a continuous spectrum (infrared, IR near infrared, NIR) then smoothing and/or transformation to first or second derivative may be appropriate preprocessing techniques. Smoothing tries to reduce random noise and thus removes narrow spikes in a spectrum. Differentiation extracts relevant information (but increases noise). In the first derivative an additive baseline is removed and therefore spectra that are shifted in parallel to other... 

To elucidate the fate of these compounds at sediment-water interfaces, sediment/water mixtures (Lake Macatawa, Holland, MI) were spiked with DCB and incubated at 20 °C for 12 months under anaerobic conditions [72]. Dehalogenation of DCB to benzidine appeared to take place through a transient intermediate, 3-monochlorobenzidine (Fig. 27), which was observed in time-course analyses of the sediment/water mixtures. No metabolites were observed in autoclaved samples, suggesting that dehalogenation of DCB in anaerobic sediment/water systems was mediated by microbial activity. The product of dehalogenation (benzidine, Fig. 27) is more toxic to humans than the parent compound, DCB. From sediment/water distribution experiments, DCB showed greater affinity for the sediment phase than its non-chlorinated derivative,... 

You et al. (1995) studied bulk samples of fluids incorporated in sediments from ODP Site 808, in the Nankai Trough, southwest of Japan. Pore fluids have somewhat variable isotopic compositions (8 Li = +10 to +21), with a spike of light compositions near the basal decollement. These authors interpreted the decollement zone geochemical anomaly to represent influx of waters with Li derived from leaching of sediments at high temperatures. 

This equation says that we have a process whose output x depends on the value of the input and the value of the derivative of the input. Therefore the process must be able to diflerentiate, perfectly, the input signal. But it is impossible for any real system to differentiate perfectly. This would require that a step change in the input produce an infinite spike in the output. This is physically impossible. 

---