A reinforcement depletion urn problem—II. Application and generalizationShenton, L. R.
doi: 10.1007/BF02459382pmid: 6850152
Abstract The urn model discussed in part is generalized so that the random depletion of balls from the urn in any cycle is not necessarily the same as the reinforcement in that cycle. This model is applied to an urn containing balls of three colors (white, red, black) for which the black balls always receive reinforcements, whereas there is only one cycle in which red balls are added. Experimental data are considered in which red balls correspond to radioactive iodine atoms, black balls to stable iodine atoms and white balls to empty space, all relating to the thyroid gland. Half-life periods for the radioactive iodine in relation to the time of uptake (ten years, fifteen years, etc.) are considered.
On a simple epidemic model with a heterogeneous infective populationLefevre, Claude
doi: 10.1007/BF02459383pmid: 6850154
Abstract This paper is concerned with a generalization of the simple epidemic model in which the infective population is partitioned intom classes, each of specific infectiousness. Attention is restricted, however, to the case where all the meeting rates between two individuals are equal to each other. Both deterministic and stochastic versions are examined. In either case the development in time of the epidemic process is investigated by exploiting a connection with the standard simple epidemic model. Finally, it is shown that the technique used also applies to a similar model for the spread of information.
Kinetics of deterrence of gompertzian growthTorkington, P.
doi: 10.1007/BF02459384pmid: 6850158
Abstract Kinetic equations for the action of a reagent on a population which is increasing by Gompertzian growth are solved by a combination of analytical and numerical methods for both dilute distributions and cellular aggregates. For the aggregates an empirical function controlling extent of diffusion is used with external reagent concentration held constant, and the effective diminution of reagent activity caused by aggregation is related to the extent of penetration by diffusion. Diffusion from the centre is considered. Solutions with time-dependent reagent concentration are obtained for a distribution, and the effect of successive inputs of reagent studied.
Numbering binary trees with labeled terminal verticesRohlf, F. James
doi: 10.1007/BF02459385pmid: 6850159
Abstract For each rooted binary tree witht labeled terminal vertices (leaves) a natural number can be assigned uniquely. Unrooted trees witht labeled terminal vertices andt-2 unlabeled internal vertices of degree 3 can also be numbered uniquely using the same convention. Rooted trees in which the hights of the internal vertices are rank ordered are also considered. Applications to problems in taxonomy are discussed.
Hematocrit reduction in bifurcations due to plasma skimmingPerkkiö, J.;Keskinen, R.
doi: 10.1007/BF02459386pmid: 6850160
Abstract Expressions and numerical values for hematocrit reduction are calculated as blood flows from a cylindrical feeding tube into a cylindrical capillary at a right-angle branch. Blood is considered to consist of two Newtonian fluids, plasma and red cell suspension, which have equal densities but different viscosities. The concentration profile of the red cells is concluded to depend on the size of the feeding tube. An estimate for the thickness of the plasma layer adjacent to the wall is obtained.
A simple competition model involving selectionMosqueira, F. G.
doi: 10.1007/BF02459387pmid: N/A
Abstract Asimple model system of two self-reproducing objects is considered. A set of equations, similar to Eigen's equation, describing competition of these objects is derived and analyzed under the effect of an ‘ecological constraint’. The relation with other constraints used in the literature is discussed.
Electric field dependence of phase transitions in bilayer lipid membranes and possible biological implicationsBhaumik, Debajyoti;Dutta-Roy, Binaryak;Chaki, Tarun Kumar;Lahiri, Avijit
doi: 10.1007/BF02459389pmid: 6850162
Abstract Bilayer lipid membranes consist of an inner hydrocarbon tail region with the hydrophilic polar heads on either side. The order-disorder transition in the hydrocarbon tail reigon, from liquid crystalline (fluid) to gel state, is characterised in terms of a Landau-de Gennes description, in which the effect of an external electric field is incorporated through its description, in which the effect of an external electric field is incorporated through its interaction with the surface charges on the bilayer (placed as it is in an ionic medium) or with the polar heads. Biological implications of such a phase transition, for excitable membranes, resides in a model wherein ion channels (taken to be composed of protein bundles) are postulated to be surrounded by lipid molecules in the fluid phase when the membrane is in its resting state, while surface charges and/or the polar heads of the lipid molecules responding to an electric stimulus, if of adequate magnitude, induces a transition in the hydrocarbon tail region of the (boundary) lipid surrounding the ion channels from the liquid crystalline (fluid) to the crystalline (gel) phase which, in turn, through coupling with the relevant modes of the protein bundles, results in the opening of the ion channels, provinding thereby a mechanism for the desired response.
Non-linear growth mechanics—I. Volterrahamilton systemsAntonelli, P. L.;Voorhees, B. H.
doi: 10.1007/BF02459390pmid: 6850153
Abstract In this, the first of a series of papers on stochastic and deterministic non-linear allometric growth models, a deterministic model is proposed which generalizes the widely applicable classical linear model of Huxley and Needham. There aren types of producers, each type depositing a product which accumulates monotonically in the environment. Producers interact via a mass action law satisfying an optimality condition. Coefficients may be interpreted as competition between the various producer types in the usual Volterra sense. An ideal coral reef is studied in which then species of coral polyps lay down aragonite calcium carbonate in building the reef framework. This deterministic model predicts that younger reefs are strongly unstable relative to initial species abundance, while older reefs grow in the classical sense of Huxley and Needham, asymptotically, as time goes to infinity.
The uniqueness of protein sequences. o -Uniqueness and infrequent peptidesSaroff, H. A.;Pretorius, H. T.
doi: 10.1007/BF02459391pmid: 6850155
Abstract Concepts of the uniqueness of the amino acid sequences of proteins were defined in a prior report (Saroff, H. A. and F. A. Kutyna. 1981. “The Uniqueness of Protein Sequences: A Monte Carlo Analysis.”Bull. math. Biol. 43, 619–639), which presented a detailed discussion ofi-uniqueness, i.e. the tendency of small peptides to be repeated within an amino acid sequence of a protein. We now report on the quantitative analysis ofo-uniqueness, which evaluates the tendency of small peptides to be repeated amongst different proteins, usually of a single species. A detailed analysis of theo-uniqueness of several proteins is presented to illustrate the method and the range of values encountered. Uniqueness data on sequences of human proteins in a data bank of sequences containing about 32,500 amino acids are made available in the form of a microfiche. Analysis of biologically active subsequences such as the angiotensins and the enkephalins suggest a tendency of the subsequences contributing to the property ofo-uniqueness to cluster in portions of the parent protein sequence which are biologically active. This property may provide a general method for predicting biologically active areas of proteins. Current data may already be adequate to permit useful predictions, and the rapidly accumulating and interrelated new data on nucleic acid and protein sequences will further enhance the power ofo-uniqueness analysis.