Extended GCD and Hermite normal form algorithms via lattice basis reduction

Extended gcd calculation has a long history and plays an important role in computational number theory and linear algebra. Recent results have shown that finding optimal multipliers in extended gcd calculations is difficult. We present an algorithm which uses lattice basis reduction to produce small integer multipliers x(1), ..., x(m) for the equation s = gcd (s(1), ..., s(m)) = x(1)s(1) + ... + x(m)s(m), where s1, ... , s(m) are given integers. The method generalises to produce small unimodular transformation matrices for computing the Hermite normal form of an integer matrix.

Thermal diffusion in molecular dynamics simulations of thin film diamond deposition

Molecular dynamics simulations of carbon atom depositions are used to investigate energy diffusion from the impact zone. A modified Stillinger-Weber potential models the carbon interactions for both sp2 and sp3 bonding. Simulations were performed on 50 eV carbon atom depositions onto the (111) surface of a 3.8 x 3.4 x 1.0 nm diamond slab containing 2816 atoms in 11 layers of 256 atoms each. The bottom layer was thermostated to 300 K. At every 100th simulation time step (27 fs), the average local kinetic energy, and hence local temperature, is calculated. To do this the substrate is divided into a set of 15 concentric hemispherical zones, each of thickness one atomic diameter (0.14 nm) and centered on the impact point. A 50-eV incident atom heats the local impact zone above 10 000 K. After the initial large transient (200 fs) the impact zone has cooled below 3000 K, then near 1000 K by 1 ps. Thereafter the temperature profile decays approximately as described by diffusion theory, perturbed by atomic scale fluctuations. A continuum model of classical energy transfer is provided by the traditional thermal diffusion equation. The results show that continuum diffusion theory describes well energy diffusion in low energy atomic deposition processes, at distance and time scales larger than 1.5 nm and 1-2 ps, beyond which the energy decays essentially exponentially. (C) 1998 Published by Elsevier Science S.A. All rights reserved.

Ultrastructure and small-subunit ribosomal DNA sequence of Henneguya lesteri n. sp (Myxosporea), a parasite of sand whiting Sillago analis (Sillaginidae) from the coast of Queensland, Australia

Henneguya lesteri n. sp, (Myxosporea) is described from sand whiting, Sillago analis, from the southern Queensland coast of Australia. H. lesteri displays a preference for the pseudobranchs and is typically positioned along the afferent blood vessels, displacing the adjoining lamellae and disrupting their normal array, The plasmodia appeared as whitish-hyaline, elliptical cysts (mean dimensions 230 x 410 mum) attached to the oral mucosa lining of the hyoid arch on the inner surface of the operculum. Infections of the gills were also found, in which the plasmodia were spherical, averaged 240 x 240 mum in size and were located on the inner hemibranch margin. The parasites lodged in the gill filament crypts and generated a mild hyperplastic response of the branchial epithelium, In histological sections, the plasmodium wall and adjoining ectoplasm appeared as a finely granulated, weakly eosinophilic layer, Ultrastructurally, this section of the host-parasite interface contained an intricate complex of pinocytotic channels. H. lesteri is polysporic, disporoblastic and pansporoblast forming. Sporogenesis is asynchronous, with the earliest developmental stages aligned predominantly along the plasmodium periphery, and maturing sporoblasts and spores toward the center. Ultrastructural details of sporoblast and spore development are in agreement with previously described myxosporeans. The mature spore is drop-shaped, length (mean) 9.1 mum, width 4.7 mum, thickness 2.5 mum, and comprises 2 polar capsules positioned closely together, a binucleated sporoplasm and a caudal process of 12.6 mum. The polar capsules are elongated, 3.2 x 1.6 mum, with 4 turns of the polar filament. Mean length of the everted filament is 23.2 mum, Few studies have analyzed the 18S gene-of marine Myxosporea. In fact, H. lesteri is the first marine species of Henneguya to be characterized at the molecular level: we determined 1966 bp of the small-subunit (18S) rDNA, The results indicated that differences between this and the hitherto studied freshwater Henneguya species are greater than differences among the freshwater Henneguya species.