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J K Percus

Publications and source records attributed to J K Percus.

4 recordsLinked to original sources
PubMed1988

On the stationary state analysis of reaction-diffusion mechanisms for biological pattern formation.

We present a biologically plausible two-variable reaction-diffusion model for the developing vertebrate limb, for which we postulate the existence of a stationary solution. A consequence of this assumption is that the stationary state depends on only a single concentration-variable. Under these circumstances, features of potential biological significance, such as the dependence of the steady-state concentration profile of this variable on parameters such as tissue size and shape, can be studied without detailed information about the rate functions. As the existence and stability of stationary solutions, which must be assumed for any biochemical system governing morphogenesis, cannot be investigated without such information, an analysis is made of the minimal requirements for stable, stationary non-uniform solutions in a general class of reaction-diffusion systems. We discuss the strategy of studying stationary-state properties of systems that are incompletely specified. Where abrupt transitions between successive compartment-sizes occur, as in the developing limb, we argue that it is reasonable to model pattern reorganization as a sequence of independent stationary states.

Animals↗
PubMed1984

A model of cell sorting.

Voronoi polygons are introduced as a suitable representation for a two-dimensional cell sheet. These polygons are defined in terms of a finite number of points, making numerical simulations tractable and yet allowing cells to change neighbors and their shape in response to deforming forces without leaving gaps in the tissue. Using this geometry and an extension of the equilibrium theory proposed by Steinberg to drive the motion, simulations of rounding of uneven tissue and engulfment of two intact tissues are carried out.

Amphibians↗
PubMed1984

Modified Bayes technique in sequential clinical trials.

We consider the problem of optimizing the treatment of a population by two drugs of unknown efficacy. The success or failure of each treatment is assumed to be known before the next patient arrives to be treated, and the objective is to use the developing information both to select optimally for a given patient and to asymptotically restrict treatment to the better of the two drugs. A straightforward Bayes estimator is first assumed. It is shown by computer simulation, and to some extent algebraically , that this leads to the possibility of "trapping" into treatment by the poorer drug, due to early anomalously poor performance by the better drug. The difficulty is ameliorated by imposing a bias towards success on the input (a priori) distribution of the unknown success probabilities. In fact, the resulting protocol, which is ethical from the point of view of the individual patient, is also superior for the full treated population to a few sampling-plus-stopping-rule techniques against which it is compared.

Clinical Trials as Topic↗