Sigmoidal relation

The steady-state component of the glomerular feedback is described by a sigmoidal relation between the muscular activation xjr of the afferent arteriole and the delayed version xj, of the Henle flow ... 

These latex emulsions are ideal systems for studying the drying curves obtained using the impedometer technique (2). The recorded attenuation obeys a sigmoid relation when the film is formed above the MFT. 

This sigmoid relation is analogous to a standard population increase. 

Sometimes the sigmoid relation is not achieved when emulsions are dried at temperatures below their MFT. A catastrophic termination of the rise in attenuation followed by a decrease to a lower level, indicates partial or total loss of adhesion of the film with the substrate. Again, this type of response is analogous to a population which experiences a catastrophe where the host (substrate) cannot tolerate the conditions. 

K2C03 3 H202 contains hydrogen peroxide of crystallization and the solid phase decomposition involves the production of the free radicals OH and HOi, detected by EPR measurements [661]. a—Time curves were sigmoid and E = 138 kJ mole-1 for reactions in the range 333—348 K. The reaction rate was more rapid in vacuum than in nitrogen, possibly through an effect on rate of escape of product water, and was also determined by particle size. From microscopic observations, it was concluded that centres of decomposition were related to the distribution of dislocations in the reactant particles. 

There have been few satisfactory demonstrations that decompositions of hydrides, carbides and nitrides proceed by interface reactions, i.e. either nucleation and growth or contracting volume mechanisms. Kinetic studies have not usually been supplemented by microscopic observations and this approach is not easily applied to carbides, where the product is not volatile. The existence of a sigmoid a—time relation is not, by itself, a proof of the occurrence of a nucleation and growth process since an initial slow, or very slow, process may represent the generation of an active surface, e.g. poison removal, or the production of an equilibrium concentration of adsorbed intermediate. The reactions included below are, therefore, tentative classifications based on kinetic indications of interface-type processes, though in most instances this mechanistic interpretation would benefit from more direct experimental support. 

The transfer function of the hidden units in MLF networks is always a sigmoid or related function. As can be seen in Fig. 44.5b, 0, represents the offset, and has the same function as in the simple perceptron-like networks. P determines the slope of the transfer function. It is often omitted in the transfer function since it can implicitly be adjusted by the weights. The main function of the transfer function is modelling the non-linearities in the data. In Fig. 44.11 it can be seen that there are five different response regions in the sigmoidal function ... 

Figure 7.19 Permeability-lipophilicity relations (a) linear (b) hyperbolic (c) sigmoidal (d) bilinear.

Sigmoidal activation functions generate an output signal that is related uniquely to the size of the input signal, so, unlike both binary and capped linear activation functions, they provide an unambiguous transfer of information from the input side of a node to its output. 

Provided that the time-temperature curve obtained from the calorimetric experiments is wholly of first-order, or comprises a first-order section, usually after the inflection point of sigmoid reaction curves, a conventional analysis yields a first-order rate constant ku which is related to the concentration of monomer, m, and the initial concentration of initiator, c0, by the equations... 

The results obtained with PhViE in the extra dry PhN02 are listed in Table 3 and are plotted in Figures 4-6. All the reaction curves were sigmoid and kx was evaluated by the usual first-order analysis of the reaction curves beyond the inflection point (line A in Figure 4) and also from the relation... 

When the sigmoidal shape of the rate constant/pH profile associated with (1.207) or the simpler derivatives (1.208) or (1.209) give way to a bell-shape or inverted bell-shape plot, the reactions of at least three acid-base-related species (two equilibria) have to be considered. This may involve acid-base forms of (a) one reactant or (b) two different reactants. 

The quantal dose-response curve is actually a cumulative plot of the normal frequency distribution curve. The frequency distribution curve, in this case relating the minimum protective dose to the frequency with which it occurs in the population, generally is bell shaped. If one graphs the cumulative frequency versus dose, one obtains the sigmoid-shaped curve of Figure 22A. The sigmoid shape is a characteristic of most dose-response curves when the dose is plotted on a geometric, or log, scale. 

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