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L E Trainor

Publications and source records attributed to L E Trainor.

12 recordsLinked to original sources
PubMed2001

Two-category model of task allocation with application to ant societies.

In many network models of interacting units such as cells or insects, the coupling coefficients between units are independent of the state of the units. Here we analyze the temporal behavior of units that can switch between two 'category' states according to rules that involve category-dependent coupling coefficients. The behaviors of the category populations resulting from the asynchronous random updating of units are first classified according to the signs of the coupling coefficients using numerical simulations. They range from isolated fixed points to lines of fixed points and stochastic attractors. These behaviors are then explained analytically using iterated function systems and birth-death jump processes. The main inspiration for our work comes from studies of non-hierarchical task allocation in, e.g., harvester ant colonies where temporal fluctuations in the numbers of ants engaged in various tasks occur as circumstances require and depend on interactions between ants. We identify interaction types that produce quick recovery from perturbations to an asymptotic behavior whose characteristics are function of the coupling coefficients between ants as well as between ants and their environment. We also compute analytically the probability density of the population numbers, and show that perturbations in our model decay twice as fast as in a model with random switching dynamics. A subset of the interaction types between ants yields intrinsic stochastic asymptotic behaviors which could account for some of the experimentally observed fluctuations. Such noisy trajectories are shown to be random walks with state-dependent biases in the 'category population' phase space. With an external stimulus, the parameters of the category-switching rules become time-dependent. Depending on the growth rate of the stimulus in comparison to its population-dependent decay rate, the dynamics may qualitatively differ from the case without stimulus. Our simple two-category model provides a framework for understanding the rich variety of behaviors in network dynamics with state-dependent coupling coefficients, and especially in task allocation processes with many tasks.

Animals↗
PubMed1992

A stochastic evolutionary model of molecular sequences.

A stochastic evolutionary model of molecular sequences is proposed. The basic forces in evolution are supposed to be mutation and selection. The concept is somewhat similar to Kauffman-Levin's concept of adaptive walks and corresponding analytical expressions have been developed. The selective force is divided into two parts: a slowly-varying part and a rapidly-changing fluctuation. The latter influences the distribution of sequences and results in an equation of motion along the flow line. The former plays a more important role in the emergence of evolutionary order. It is demonstrated that the asymmetry of selective forces would lead to a definite order of the system.

Animals↗
PubMed1989

Geometrical aspects of surface morphogenesis.

This paper is concerned with the morphogenesis of structures which form thin deformable sheets. A general formalism is presented for the deformation of a sheet in the presence of an isotropic local body stress. This formalism leads to a set of equations, based on the theory of shells, in which corrections are made in the geometry due to large deformations. Under certain conditions the equations may be solved to give the surface metric tensor as a function of the local tension. A numerical example based on a simple "threshold" model is also presented.

Elasticity↗
PubMed1989

Diffusion effects in calcium-regulated strain fields.

The Goodwin-Trainor equations for cellular morphogenesis, based on calcium ion regulation of the visco-elastic properties of the cellular cortex, are generalized to the situation where the concentration of calcium ions (free plus bound) is allowed to change locally. A stability analysis is presented which shows that the generalized equations are also stable against perturbations at low and high wave lengths and may, for certain parameter values, develop instabilities at intermediate wave lengths.

Animals↗
PubMed1985

A two vector field model of limb regeneration and transplant phenomena.

We propose a new field description of limb regeneration in developmental biology. Central to our approach is the recognition of the importance of vector fields as descriptors in problems involving polarities or a sense of direction. In limb regeneration these vector fields represent the organisms sense of the distal direction, and its sense of the circumferential ordering of structures. Essentially all experimental results obtained to date are consistent with or explained by the model.

Ambystoma↗
PubMed1984

Cluster analysis of genes in codon space.

We construct a "codon space" in which a given DNA sequence can be plotted as a function of its base composition in each of the three codon positions. We demonstrate that the base composition is very highly nonrandom, with sequences from more primitive organisms having the least random compositions. By using cluster analysis on the points plotted in codon space we show that there is a strong correlation between base composition and type of organism, with the most primitive organisms having the highest A or T content in the second and third codon positions. A smooth transition toward lower A + T and higher G + C content is observed in the second and third codon positions as the evolutionary complexity of the organism increases. Besides this general trend, more detailed structure can be observed in the clustering that will become clearer as the data base is increased.

Bacteriophages↗
PubMed1983

On the informational content of viral DNA.

This paper is concerned primarily with how information is stored in viral DNA. The general problem of defining information content is discussed and a procedure for analysis extended from that of Gatlin (1972) is developed. Long range correlations in base sequences are analyzed for several viral genomes. The relationship of these correlations to the existence of strong codon biases is examined and the consequences discussed.

Base Sequence↗
PubMed1983

A thermodynamic theory of codon bias in viral genes.

The relationship between degeneracy in the genetic code and the occurrence of a strong codon bias is examined, with particular reference to a group of viral genomes. The present paper shows how codon bias may have been imposed by thermodynamic considerations at the time the primitive DNA first formed in the primordial soup. Using a four-state Ising-like model with stacking interactions between successive base pairs, we show how primeval periodic DNA polymers could have arisen the remnants of which are still observed in codon biases today.

Base Composition↗