Note on a combinatorial problem in topological biology

In connection with a previous paper, an expression is derived for the number of possibilities in whichn distinguishable elements can be distributed intom≤n classes, so that each class contains at least one element.     

Note on a problem in probit analysis

The statistical treatment of dosage-mortality data when the number of survivors is counted but not the total number of organisms in each sample, the latter being estimated from an untreated sample, has been discussed by Wadley (1949), on the assumption of Poisson variation in the number of organisms per sample. The procedure to be followed when a wider hypothesis is made that the number of organisms has a negative binomial distribution is described here; both the arithmetical analysis of the results and the optimum arrangement of the samples are considered.     

A combinatorial problem in pharmacology

A novel coding scheme is used to enumerate configurations in a combinatorial problem arising in research on effects of drugs or radiation on DNA.     

Solving a combinatorial problem via self-organizing process: An application of the Kohonen algorithm to the traveling salesman problem

We present an application of the Kohonen algorithm to the traveling salesman problem: Using only this algorithm, without energy function nor any parameter choosen ad hoc, we found good suboptimal tours. We give a neural model version of this algorithm, closer to classical neural networks. This is illustrated with various numerical examples.     

Reconstructing pedigrees: a combinatorial perspective

A pedigree is a directed graph that displays the relationship between individuals according to their parentage. We derive a combinatorial result that shows how any pedigree-up to individuals who have no extant (present-day) ancestors-can be reconstructed from (sex-labelled) pedigrees that describe the ancestry of single extant individuals and pairs of extant individuals. Furthermore, this reconstruction can be done in polynomial time. We also provide an example to show that the corresponding reconstruction result does not hold for pedigrees that are not sex-labelled. We then show how any pedigree can also be reconstructed from two functions that just describe certain circuits in the pedigree. Finally, we obtain an enumeration result for pedigrees that is relevant to the question of how many segregating sites are needed to reconstruct pedigrees.     

Note on a case of nonlinear diffusion

When the functionQ in the equation ∇²c +Q(c) = 0 is positive and is of a specified kind, the equation admits of a centrally spherical solution such thatc is positive everywhere, tending to zero at infinity anddc/dr=0 atr=0. Physically this corresponds to a local concentration of the solute in an infinite medium without any membranes present. This result would indicate the possibility of the formation of spontaneous concentrations and non-uniformities in non-linear diffusion fields. Possible biological implications are mentioned. *** DIRECT SUPPORT *** A01E2041 00002     

The death factors: a combinatorial analysis

This paper presents theoretical and computational tools to understand how a small group of proteins, the death factors, are involved in widely different behavior of the cell. Experiments were done using a virtual laboratory that can simulate cellular response to different external stimuli. WARNING: It is not certain which of the theoretical protein clusters described here really occur in nature. In addition, the rules of cluster assembly are combinatorial, and thus an oversimplification to describe the real situation.     

Note on a method for analyzing stage-frequency data

A new method for analyzing stage-frequency data is proposed which is based on the estimation of rates of transition between one stage and the next highest stage in one unit of time, and a unit time survival rate that is assumed to be constant. Once these estimates are calculated it becomes possible to also estimate the mean durations of stages, stage-specific survival rates, and numbers entering stages. An advantage of the method is that it can be applied with any distribution of entry times to stage 1, and any distribution of numbers in stages when sampling begins. Use of the method is illustrated on data from a copepod population in a Canadian lake.