Some conditions for sustained oscillations in chain processes with feedback inhibition and saturable removal

A biochemical chain with feedback inhibition, enzymatic removal and catalyzed input is considered. Some conditions on the parameters are given for which the result is a simple limit cycle behavior or a limit cycle surrounding an unstable limit cycle and a stable point. In the latter case, the system in the steady state can either be at rest or oscillate around the point at rest, depending on the initial conditions. Presented at the May 23–24, 1975 meeting of the Society for Mathematical Biology, Bowling Green State University, Bowling Green, Ohio.     

An approach to a neurobiophysical interpretation of motivational interactions

Some problems of the interaction between two individuals are considered in terms of the theory of neural nets. Among these are: the effect of individual differences on the total output of two individuals who share equally the results of their effort; the problem of stability of the equilibrium effort; the problem of the division of the results of a cooperative effort, and the effect of individual differences in the parameters on the results; the case in which two types of activity are possible—one cooperative, the other solitary; and the effect of certain parameters on the fraction of effort spent in each kind of activity.     

The half-life of a drug in relation to its therapeutic index

A procedure is given for the determination of the effective half-life of a drugin vivo with respect to an arbitrary response. If the half-life of the drug with respect to toxicity is different from that for therapy, the therapeutic index would be expected to depend on the temporal spacing of the dose. Equations are derived for this variation for a special case. This work was carried out under contract with the Medical Division of the Chemical Warfare Service.     

Mathematical biophysics of color vision II: Theory of color changes induced by the alternation of colors at various frequencies.

A model previously introduced to account for a number of phenomena of color vision is studied for the conditions in which the alternation of colors is periodic. The case of three primary receptors having no differences in their time constants is considered for the situations such as the temporal alternation of two primaries, a primary and a neighboring binary, a primary and white, a binary and white, etc. Using the same mathematical model which was used to account for the enhancement effect of interrupted illumination, it is found possible to account for observed changes in hue in a qualitative manner. A method is suggested for measuring the color changes quantitatively. This method is readily adapted for demonstration purposes. The model shows that there should be differences between “primaries” and “binaries” with respect to change in hue. In principle, therefore, comparison between theory and experiment should yield information regarding the physiological primaries. This research was supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command under contract No. AF 18 (600) 1454.     

Note on a mechanism of the distribution of wealth

A population of individuals is considered to be characterized by a distribution of wealth which is the result of gain and loss from the outside as well as a result of exchange. The population is assumed to be uniform except for the variation in a parameter determining the manner of partition during exchange. The parameter is assumed to be normally distributed over the population. The resulting distribution of wealth is calculated for some special cases and it is found to be very asymmetric.     

A note on the units of membrane permeability to water

In the usual experimental technique, the membrane permeability to water in the units of cm/sec is not measured directly. The quantity which is usually obtained may be considered to be a measure of a coefficient of penetrability having the dimensions time/length. The purpose of this paper is to show that by introducing the bulk modulus of water, an expression is obtained from which it is possible to calculate the water permeability in the units of cm/sec from the values in conventional units.     

Influence of the Season and of Preservation Methods on Wet- and Dry Weights of Larvae of Chironomus plumosus L

Preservation in 70% ethanol or 4% formaldehyde solution resulted in the leaching of ca. 30% arid ca. 10% dry matter, respectively. Subsequent soaking in water considerably increased leaching. The percent ratio of dry weight to live weight decreased during the summer from ca. 15% in June to ca. 11 % in September for the fourth instar larvae. The results indicate that formaldehyde can chemically react with the larvae, thereby increasing their dry weight. The dry weight of the gut content was ca. 4% of the total dry weight.     

A three stage population model with cannibalism

A simple population model consisting of one adult and two larval stages with cannibalism or competition among the larval stages is presented. The solutions are found to be either periodic or of a steady state nature depending on the ratios of fertility and cannibalism among the larvae. Two similar cannibalism pressure functions are compared and the conditions that lead to steady or periodic solutions, or to extinction, are examined.