A weakly stable algorithm for general Toeplitz systems

We show that a fast algorithm for the QR factorization of a Toeplitz or Hankel matrix A is weakly stable in the sense that R^T.R is close to A^T.A. Thus, when the algorithm is used to solve the semi-normal equations R^T.Rx = A^Tb, we obtain a weakly stable method for the solution of a nonsingular Toeplitz or Hankel linear system Ax = b. The algorithm also applies to the solution of the full-rank Toeplitz or Hankel least squares problem.Comment: 17 pages. An old Technical Report with postscript added. For further details, see http://wwwmaths.anu.edu.au/~brent/pub/pub143.htm

Encoding and retrieval in a CA1 microcircuit model of the hippocampus

Recent years have witnessed a dramatic accumulation of knowledge about the morphological, physiological and molecular characteristics, as well as connectivity and synaptic properties of neurons in the mammalian hippocampus. Despite these advances, very little insight has been gained into the computational function of the different neuronal classes; in particular, the role of the various inhibitory interneurons in encoding and retrieval of information remains elusive. Mathematical and computational models of microcircuits play an instrumental role in exploring microcircuit functions and facilitate the dissection of operations performed by diverse inhibitory interneurons. A model of the CA1 microcircuitry is presented using biophysical representations of its major cell types: pyramidal, basket, axo-axonic, bistratified and oriens lacunosummoleculare cells. Computer simulations explore the biophysical mechanisms by which encoding and retrieval of spatio-temporal input patterns are achieved by the CA1 microcircuitry. The model proposes functional roles for the different classes of inhibitory interneurons in the encoding and retrieval cycles

Oxidation of water to hydrogen peroxide at the rock–water interface due to stress-activated electric currents in rocks

Common igneous and high-grade metamorphic rocks contain dormant defects, which release electronic charge carriers when stressed. Rocks thereby behave like a battery. The charge carriers of interest are defect electrons h•, e.g. electronic states associated with O− in a matrix of O2−. Known as “positive holes” or pholes for short, the h• travel along stress gradients over distances on the order of meters in the laboratory and kilometers in the field. At rock–water interfaces the h• turn into •O radicals, e.g. highly reactive oxygen species, which oxidize H2O to H2O2. For every two h• charge carriers one H2O2 molecule is formed. In the laboratory the battery circuit is closed by running a Cu wire from the stressed to the unstressed rock. In the field closure of the circuit may be provided through the electrolytical conductivity of water. The discovery of h• charge carriers, their stress-activation, and their effect on Earth's surface environment may help better understand the oxidation of the early Earth and the evolution of early life.

Prokaryotic transport in electrohydrodynamic structures

When a high-voltage direct-current is applied to two beakers filled with water, a horizontal electrohydrodynamic (EHD) bridge forms between the two beakers. In this work we study the transport and behavior of bacterial cells added to an EHD bridge set-up. Organisms were added to one or to both beakers, and the transport of the cells through the bridge was monitored using optical and microbiological techniques. It is shown that Escherichia coli top10 (Invitrogen, Carlsbad, CA, USA) and bioluminescent E. coli YMC10 with a plasmid (pJE202) containing Vibrio fischeri genes can survive the exposure to an EHD liquid bridge set-up and the cells are drawn toward the anode due to their negative surface charge. Dielectrophoresis and hydrostatic forces are likely to be the cause for their transport in the opposite direction which was observed as well, but to a much lesser extent. Most E. coli YMC10 bacteria which passed the EHD bridge exhibited increased luminescent activity after 24 h. This can be explained by two likely mechanisms: nutrient limitation in the heavier inoculated vials and a 'survival of the strongest' mechanism