Activity variable

Excitable media are some of tire most commonly observed reaction-diffusion systems in nature. An excitable system possesses a stable fixed point which responds to perturbations in a characteristic way small perturbations return quickly to tire fixed point, while larger perturbations tliat exceed a certain tlireshold value make a long excursion in concentration phase space before tire system returns to tire stable state. In many physical systems tliis behaviour is captured by tire dynamics of two concentration fields, a fast activator variable u witli cubic nullcline and a slow inhibitor variable u witli linear nullcline [31]. The FitzHugh-Nagumo equation [34], derived as a simple model for nerve impulse propagation but which can also apply to a chemical reaction scheme [35], is one of tire best known equations witli such activator-inlribitor kinetics ... 

In practice, each CSF is a Slater determinant of molecular orbitals, which are divided into three types inactive (doubly occupied), virtual (unoccupied), and active (variable occupancy). The active orbitals are used to build up the various CSFs, and so introduce flexibility into the wave function by including configurations that can describe different situations. Approximate electronic-state wave functions are then provided by the eigenfunctions of the electronic Flamiltonian in the CSF basis. This contrasts to standard FIF theory in which only a single determinant is used, without active orbitals. The use of CSFs, gives the MCSCF wave function a structure that can be interpreted using chemical pictures of electronic configurations [229]. An interpretation in terms of valence bond sti uctures has also been developed, which is very useful for description of a chemical process (see the appendix in [230] and references cited therein). 

Species differences indicate that the AOS is not invariably operational prenatally, even though most peripheral and central neural units are in place and available for activation. Variability in the timing of maturation of the Organ-to-AOB linkage could well provide the necessary flexibility of response consistently associated with higher mammalian, and especially primate, neural systems. The onset of effective accessory... 

Even this patch is not quite enough. Our simple example shows that a condition C on or on and but not on u, is not enough. All the active variables must be tied together for the verification procedure to return a positive answer. But the actual parameters may change in value during a CALL, so we would have to put the added assertions into the verification process for the procedure called. This can multiply itself indefinitely and so is obviously unsatisfactory. 

Thus far, it could be shown that stable liposomes can be prepared by polymerization of lipids. These vesicle systems, however, are still far away from being a real biomembrane model. As of now, they do not show any typical biological behavior such as surface recognition, enzymatic activities, variable lipid distribution, and the ability to undergo fusion. 

Resin oil 0-850-0-950 120-200° Active Variable Complete Almost c 0 m-p1etely attacked... 

Figure 6.1. Schematic drawing of the holeboard apparatus used to record behaviour of rats. The box is 70 70 cm and has 32 holes in the floor (circles). The position of photobeams recording nonspecific behavioural activity (variable x,) are indicated by black triangles. These photobeams also record the two locomotion variables (x2 and x3) indicated by arrows. The frequency and accumulated duration of hole visits, comer visits and raising on the hind-legs (variables x4-x9) are recorded by separate photocells [2J. The 10th variable is the ratio between the activity during the second and the first half...

The strength of the feedback and also whether it is positive or negative depends on the reference value x, or, more precisely, on its distance to the actual disease state x. Scaling parameters are given by the values w with corresponding activation variables... 

If a second variable participates in an additional feedback loop with a negative regulation, oscillations become possible. The mutual dependencies of the two variables, which have been coined activator and inhibitor, are depicted in Fig. 1. A, the autocatalytic species is the activator it activates the production of /, and I is the inhibitor because it slows down or inhibits the growth of A [13, 14]. Oscillations arise in activator-inhibitor systems if characteristic changes of the activator occur on a faster time-scale than the ones of the inhibitor. In other words, the inhibitor must respond to a variation of the activator variable with some delay. In fields as diverse as semiconductor physics, chemistry, biochemistry or astrophysics, and also in electrochemistry, most simple periodic oscillations can be traced back to such an activator-inhibitor scheme. 

In most electrochemical systems displaying nonlinear phenomena, the electrode potential is an essential variable, that is, it participates in one of the above-mentioned feedback loops.1 In the overwhelming number of cases it takes on the role of the activator variable, but occasionally it also acts as the negative feedback variable. Depending on the mechanistic role of the electrode potential, the instabilities that prevail the dynamic properties in these two classes of systems are fundamentally different. 

Compile values of Kdis for the solid phases. Write an algebraic equation for each log Kdis in terms of log [activity] variables for the products and reactants in the corresponding dissolution reaction. Rearrange the equation to have log[(solid phase)/(free ion)]—the log activity ratio—on the left side, with all other log[activity] variables on the right side. 

Choose an independent log[activity] variable against which log[(solid)/ (free ion)] can be plotted for each solid phase. A typical example is pH = -log(H%... 

Select fixed values for all other log [activity] variables, corresponding to an assumed set of soil conditions. Use these values and that of log Kdis to develop a linear relation between log[(solid)/(free ion)] and the independent log [activity] variable for each solid phase considered. Plot all of these equations on the same graph. 

Fig. 1 First factorial plane of MCA of data on crustacean grazing experiment on Phaeocystis. (A) Projections of continuous illustrative variables in the correlation circle (radius 1) and ordination of active variables Phaeocystis species (A), growth (

In equations (1) (2) "s" is the activity variable and is assumed to be separable from the intrinsic kinetics [1]. The active site balance is as follows, where the deactivation kinetics... 

When compounds are selected according to SMD, this necessitates the adequate description of their structures by means of quantitative variables, "structure descriptors". This description can then be used after the compound selection, synthesis, and biological testing to formulate quantitative models between structural variation and activity variation, so called Quantitative Structure Activity Relationships (QSARs). For extensive reviews, see references 3 and 4. With multiple structure descriptors and multiple biological activity variables (responses), these models are necessarily multivariate (M-QSAR) in their nature, making the Partial Least Squares Projections to Latent Structures (PLS) approach suitable for the data analysis. PLS is a statistical method, which relates a multivariate descriptor data set (X) to a multivariate response data set Y. PLS is well described elsewhere and will not be described any further here [42, 43]. 

The PLS multivariate data analysis of the training set was carried out on the descriptors matrix to correlate the complete set of variables with the activity data. From a total of 710 variables, 559 active variables remained after filtering descriptors with no variability by the ALMOND program. The PLS analysis resulted in four latent variables (LVs) with / = 0.76. The cross validation of the model using the leave-one-out (LOO) method yielded values of 0.72. As shown in Table 9.2, the GRIND descriptors 11-36, 44-49, 12-28, 13-42, 14-46, 24-46 and 34-45 were found to correlate with the inhibition activity in terms of high coefficients. 

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