Examples of the failure of the local-global principle for similarity of matrices

A cohomological method for computing the set of similarity classes of endomorphisms locally similar to a given endomorphism is presented and several calculations are made.     

COAST: Controllable approximative stochastic reaction algorithm

We present an approximative algorithm for stochastic simulations of chemical reaction systems, called COAST, based on three different modeling levels: for small numbers of particles an exact stochastic model; for intermediate numbers an approximative, but computationally more efficient stochastic model based on discrete Gaussian distributions; and for large numbers the deterministic reaction kinetics. In every simulation time step, the subdivision of the reaction channels into the three different modeling levels is done automatically, where all approximations applied can be controlled by a single error parameter for which an appropriate value can easily be found. Test simulations show that the results of COAST simulations agree well with the outcomes of exact algorithms; however, the asymptotic run times of COAST are asymptotically proportional to smaller powers of the particle numbers than exact algorithms.     

Nonlinear dynamics in pulsatile secretion of parathyroid hormone in normal human subjects

In many biological systems, information is transferred by hormonal ligands, and it is assumed that these hormonal signals encode developmental and regulatory programs in mammalian organisms. In contrast to the dogma of endocrine homeostasis, it could be shown that the biological information in hormonal networks is not only present as a constant hormone concentration in the circulation pool. Recently, it has become apparent that hormone pulses contribute to this hormonal pool, which modulates the responsiveness of receptors within the cell membrane by regulation of the receptor synthesis, movement within the membrane layer, coupling to signal transduction proteins and internalization. Phase space analysis of dynamic parathyroid hormone (PTH) secretion allowed the definition of a (in comparison to normal subjects) relatively quiet "low dynamic" secretory pattern in osteoporosis, and a "high dynamic" state in hyperparathyroidism. We now investigate whether this pulsatile secretion of PTH in healthy men exhibits characteristics of nonlinear determinism. Our findings suggest that this is conceivable, although on the basis of presently available data and techniques, no proof can be established. Nevertheless, pulsatile secretion of PTH might be a first example of nonlinear deterministic dynamics in an apparently irregular hormonal rhythm in human physiology. (c) 1995 American Institute of Physics.