A note on the derivation of the stevens power law

Previous derivations of the Stevens Power Law relating loudness to intensity assume, in addition to level invariance, that the relation must be analytic or at least differentiable. This last condition is replaced here by the weaker one of requiring only continuity.     

A note on the diffusion approximation for single neuron firing problems

Summary This paper presents a well-known stochastic model used to describe the firing or discharge pattern of a single neuron in terms of various input processes, and shows how the potential level of the neuron can be given by means of a diffusion equation approximation. There is a discussion of the adequacy of this approximation, and the paper concludes with a brief discussion of first passage time problems.Supported in part by a grant from the Alfred P. Sloan Foundation to the Committee on Mathematical Biology and by a grant of the Statistical Branch, Office of Naval Research to the Department of Statistics, University of Chicago.     

A note on the “sixth power law” of carcinogenesis

A simple model for carcinogenesis based on single cell origin is presented. It is shown that this model is capable of displaying the phenomenon known as the “sixth power law”.     

A mathematical note on the fahraeuslindqvist effect in power law fluid

An axisymmetric flow of a power law fluid through circular tubes under constant pressure gradient with the flow parameters varying radially is analyzed theoretically. The main finding is that for the Fahraeus-Lindqvist (F-L) effect to occur, it is necessary to have at least one of the parametersK (consistency) andn (index) as a discontinuous function ofr in the absence of wall slip; and with slip condition the parameters could be continuous functions ofr under specific conditions. In both the cases the existence of more than one discontinuity cannot be ruled out. The results obtained are consistent with experimental findings of blood flow through narrow tubes.     

A note on craniofacial sutural growth

The paper presents and discusses some features of sutural structures. Fibre orientation in sutures seems to be quite variable and associated with minute local growth phenomena. Trabecular patterns in bones, reflecting growth, appear to support the idea of the outside determination of growth. The bevelled and interdigitated structures seen in many sutures may be interpreted as an expedient solution to the problem of fast growth.     

A note on pH gradient plates for fungal growth studies

A pH gradient agar plate with surface pH ranging from about 3.2 to 7.1 was easily prepared. The gradient was sufficiently stable to permit different growth characteristics among various fungal species at different pH values to be distinguished. The pH effects on growth rate, conidiogenesis, pigment and toxin formation were consistent with the results obtained by other workers who used more laborious methods.     

A technical note on seasonal growth models

The growth of many organisms is seasonal, with a dependence on variation in temperature, light, and food availability. A growth model proposed by Somers (Fishbyte 6:8?C11, 1988) is one of the most widely used models to describe seasonal growth. We point out that three different formulae (beyond numerous typographical errors) have been used in the literature referring to Somers (Fishbyte 6:8?C11, 1988). These formulae correspond to different curves and yield different parameter estimates with different biological interpretations. These inconsistencies have led to the wrong identification of the period of lowest growth rate (winter point) in some papers of the literature. We urge authors to carefully edit their formulae to assure use of the original definition in Somers (Fishbyte 6:8?C11, 1988).     

A note on a single tube technique for the Hugh and Leifson's oxidation-fermentation test

A method of conducting the oxidation-fermentation (O/F) test in a single tube containing two layers of Hugh & Leifson's medium separated by a layer of vaspar is described.     

A note on correlations in single ion channel records

General expressions are derived for the correlation coefficients between the length of an opening and that of the nth subsequent opening for a single ion channel. Analogous results are given for the correlation between shut times, and between an open time and subsequent shut times. An alternative derivation of the results of Fredkin et al. (in Proc. Berkeley Conf. in honor of Neyman & Kiefer, vol. 1, pp. 269-289 (1985] is given, and their results are extended to the case where openings occur in bursts. Expressions are given for the correlation between the first and nth opening in a burst, between the lengths of bursts, and between the number of openings per burst. Each of these sorts of correlation can give information about the connections that exist between the various states of the system; interpretations of the correlations are discussed. Expressions are derived for the distributions of the nth open time, shut time, burst length, etc. following the application of a perturbation (e.g. a voltage jump or a concentration jump). It is shown that these distributions will all be the same (namely the equilibrium distribution) only in the case where the openings, burst lengths, etc. are not correlated. Certain reaction schemes predict a component in the distribution of the number of openings per burst that has a unit mean (i.e. a component of isolated single openings). For some schemes this component is predicted to have zero amplitude, in principle, whereas in others it may be quite prominent. The presence or absence of this component can give information about the way in which the various states of the system are connected. The interpretation in terms of mechanism is discussed.     

A note on yeast growth in media used for the cultivation of lactobacilli

Yeast species found in mayonnaise-based salads are capable of growth in media used for the isolation of lactobacilli. Many counts of lactobacilli from such products may, therefore, inadvertently include counts of yeasts. A method is presented whereby the use of media with and without chloramphenicol makes it possible to deduce a differential count of bacteria. It was not possible to prevent yeast growth in de Man, Rogosa and Sharpe agar by the addition of cycloheximide since many isolates were resistant to it.     

A note on population growth under random dispersal

An approximation method using a sine function is used to solve the second degree growth equation for the case in which an organism may simultaneously become dispersed throughout a uniform region. The resulting expression for a special case is compared with the expression obtained by R. Barakat (1959,Bull. Math. Biophysics,21, 141–51), giving the first two terms, by an iterative, procedure. The agreement is satisfactory.     

A note on growth processes in random environment

The purpose of this note is to discuss certain features of population growth models carlier proposed and to construct an alternative diffusion model for regulated growth in random environment. This model is shown to be the analogue of the Malthusian one, although it is a generalization of the latter due to the presence of regulation.     

A brief note on growth physiology of plants

The concepts of physiological structure of plant axial organ and its main components are discussed. Their physiological meanings, in particular the role of the surface and the xylem proton pumps are highlighted: the former loosens the cell wall via acidification, and the latter produces the driving force for active uptake of water. Theoretical and experimental examination on the validity of the Lock-hart growth equation is reviewed. Development of a new experimental system, perfusible glycerinated hollow cylinder of cowpea hypocotyl, demonstrates the validity of the Lock-hart type mechanical equation even in such anin vitro system. The pH-dependency of both extensibility and yield threshold offer a strong support for the acid growth theory. A molecular model of cell wall extension is proposed on the basis of these results. The importance of growth regulation via control of the cell wall yield threshold is demonstrated as a very economical way, by an analogy with the performance of electron tube of triode type. Also augmentation of the classic acid growth theory is proposed on the basis of Katou's diagram and the Katou-Furumoto's model of active water uptake.     

A note on the diffusion of electrolytes in cells

A somewhat simpler solution is given to the problem previously discussed by R. R. Williamson relating to the diffusion of a metabolized electrolyte whose ions have different mobilities.     

A note on the growth of Thiothrix in road drainage ditches

Macroscopic growth of Thiothrix -has been observed in ditches which drained a road under which furnace slag and limestone had been used as hard core. Extremely high sulphide concentrations, pH and total ion concentrations in one ditch may have contributed to the absence of Thiothrix spp. at this site.