Log Variance Research Articles

A New Temperature Compensating Method for Logarithmic Amplifier

A new method of temperature compensation for a dc logarithmic amplifier is presented. By this method temperature effect on both parallel shift and slope variance of log I vs. VBE curve can be compensated easily by using only one compensating resistor of copper wire wound type. (hereafter called parallel and slope compensations.) An absolute compensation condition can be determined for each type of logarithmic transistors, like silicon NPN, germanium PNP irrespective of current measuring range. The temperature dependence of the logarithmic amplifier is reduced to 0.01 decade for the temperature range from 0°C to 50°C and the current range from 10-11 to 10-3A.

Kinetics of pharmacologic response II: Equation for turnover time of goldfish as a function of concentration of ethanol and a theoretical derivation based on a combination of occupation and rate receptor theories

Turnover time (T) of goldfish in 2-8% v/v ethanol-water (C) was determined in two crossover studies: (a) three body weight groups of six fish each, and (b) six larger fish. Each fish had different treatment schedule. Analyses of variance of log T showed: (a) no residual effects of a treatment, and (b) no significant differences among fish. Log T was linearly related to log C and the variances were homogeneous. For individual fish: T = (a/C)b where a and b are apparently normally distributed with 95% C.I. of 9.31 ± 3.8 and 2.28 ± 1.17, respectively. For all 24 fish, a.b = D, where D is essentially a constant but has a narrow apparently normal distribution with a coefficient of variation of 11.5 %; hence, T = (D/bC)b. This equation was also derived by marrying occupation and rate receptor theories. Basic assumptions are: dT/T = -b(dv/v) and v ≪ Vm, where v is the overall reaction rate of the receptor-ethanol reaction and Vm is the maximum rate. Also note that dv/v = dn/n, where n is the fraction of receptors occupied. Literature data are shown to obey the derived equations. Hence 1/T ∝ C only in those rare instances when b = 1. The theory assumes only a partitioning across the absorbing membranes of the fish. It differs from a previous theory which assumes a first order rate constant for absorption is involved.

Some Considerations in Multivariate Allometry

Generally, multivariate population covariance matrices for measurements xi of parts of organisms will be of the form X = W + A, with W resulting from systematic covariance and A from independent random variance of individual xi . For isometry or allometry (constant equal or differential relative growth or size) W for log x must be of rank one. Then if also the random variance of log x is uniform for all i the vectors of W will be vectors of X and the first principal vector of an observed covariance matrix S will provide an estimate of the underlying population relative growth or size pattern. Alternatively, if the random variance of each log xi is proportional to its systematic variance, the main diagonal elements of A, also estimable from S, will be proportional to those of W and hence when the latter is of rank one to the squares of its vector coefficients. Otherwise allometric coefficients must generally be estimated from factor analysis of S after screening of any variates whose relative growth is size-dependent. Tests of goodness of fit of allometric relations may be affected by non-normality of logarithmic size distributions. From an application of these considerations to illustrative data for nine body parts of rats it was inferred that in this instance liver, heart, spleen, lungs, skin and adrenal weights were consistent with a single allometric pattern, but that interrelations involving kidneys, genitals and brain were size-dependent.