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.

Dysregulated hematopoiesis and a progressive neurological disorder induced by expression of an activated form of the human common beta chain in transgenic mice

Previously we described activating mutations of h beta(c), the common signaling subunit of the receptors for the hematopoietic and inflammatory cytokines, GM-CSF, IL-3, and IL-5. The activated mutant, h beta(c)FI Delta, is able to confer growth factor-independent proliferation on the murine myeloid cell line FDC-P1, and on primary committed myeloid progenitors. We have used this activating mutation to study the effects of chronic cytokine receptor stimulation. Transgenic mice were produced carrying the h beta(c)FI Delta cDNA linked to the constitutive promoter derived from the phosphoglycerate kinase gene, PGK-1. Transgene expression was demonstrated in several tissues and functional activity of the mutant receptor was confirmed in hematopoietic tissues by the presence of granulocyte macrophage and macrophage colony-forming cells (CFU-GM and CFU-M) in the absence of added cytokines. All transgenic mice display a myeloproliferative disorder characterized by splenomegaly, erythrocytosis, and granulocytic and megakaryocytic hyperplasia. This disorder resembles the human disease polycythemia vera, suggesting that activating mutations in h beta(c) may play a role in the pathogenesis of this myeloproliferative disorder. In addition, these transgenic mice develop a sporadic, progressive neurological disease and display bilateral, symmetrical foci of necrosis in the white matter of brain stem associated with an accumulation of macrophages. Thus, chronic h beta(c) activation has the potential to contribute to pathological events in the central nervous system.

Net uptake of dissolved free amino acids by the giant clam, Tridacna maxima: alternative sources of energy and nitrogen?

The role of dissolved free amino acids (DFAA) in nitrogen and energy budgets was investigated for the giant clam, Tridacna maxima, growing under field conditions at One Tree Island, at the southern end of the Great Barrier Reef, Australia. Giant clams (121.5-143.7 mm in shell length) took up neutral, acidic and basic amino acids. The rates of net uptake of DFAA did not differ between light and dark, nor for clams growing under normal or slightly enriched ammonium concentrations. Calculations based on the net uptake concentrations typical of the maximum concentrations of DFAA found in coral reef waters (similar to 0.1 mu M)revealed that DFAA could only contribute 0.1% and 1% of the energy and nitrogen demands of giant clams, respectively. These results suggest that DFAA does not supply significant amounts of energy or nitrogen for giant clams or their symbionts.

Numerical and experimental study of seepage in unconfined aquifers with a periodic boundary condition

The assessment of groundwater conditions within an unconfined aquifer with a periodic boundary condition is of interest in many hydrological and environmental problems. A two-dimensional numerical model for density dependent variably saturated groundwater flow, SUTRA (Voss, C.I., 1984. SUTRA: a finite element simulation model for saturated-unsaturated, fluid-density dependent ground-water flow with energy transport or chemically reactive single species solute transport. US Geological Survey, National Center, Reston, VA) is modified in order to be able to simulate the groundwater flow in unconfined aquifers affected by a periodic boundary condition. The basic flow equation is changed from pressure-form to mixed-form. The model is also adjusted to handle a seepage-face boundary condition. Experiments are conducted to provide data for the groundwater response to the periodic boundary condition for aquifers with both vertical and sloping faces. The performance of the numerical model is assessed using those data. The results of pressure- and mixed-form approximations are compared and the improvement achieved through the mixed-form of the equation is demonstrated. The ability of the numerical model to simulate the water table and seepage-face is tested by modelling some published experimental data. Finally the numerical model is successfully verified against present experimental results to confirm its ability to simulate complex boundary conditions like the periodic head and the seepage-face boundary condition on the sloping face. (C) 1999 Elsevier Science B.V. All rights reserved.

Metal-centred versus ligand-centred luminescence quenching of a macrocyclic copper(II) complex

The new macrocyclic ligand trans-6-(9-anthracenylmethylamino)-6,13-dimethyl-1,4,8,11-tetraazacyclotetradecan-13-amine has been synthesized and characterised as its copper(II) complex and the crystal structure of this complex has been determined. Fluorescence of the anthracenyl group of the macrocycle is quenched in its free base form and when complexed with Cu-II. Fluorescence returns when Lewis acids such as H+ and Zn-II are added to solutions of the ligand, indicating that photoinduced electron transfer from the amine lone pairs is responsible for fluorescence quenching in the free base form. By contrast, fluorescence of the complex is quenched by intramolecular electronic energy transfer.

Assessment of limb muscle and adipose tissue by dual-energy X-ray absorptiometry using magnetic resonance imaging for comparison

OBJECTIVE: To use magnetic resonance imaging (MRI) to validate estimates of muscle and adipose tissue (AT) in lower limb sections obtained by dual-energy X-ray absorptiometry (DXA) modelling. DESIGN: MRI measurements were used as reference for validating limb muscle and AT estimates obtained by DXA models that assume fat-free soft tissue (FFST) comprised mainly muscle: model A accounted for bone hydration only; model B also applied constants for FFST in bone and skin and fat in muscle and AT; model C was as model B but allowing for variable fat in muscle and AT. SUBJECTS: Healthy men (n = 8) and women (n = 8), ages 41 - 62 y; mean (s.d.) body mass indices (BMIs) of 28.6 (5.4) kg/m(2) and 25.1 (5.4) kg/m2, respectively. MEASUREMENTS: MRI scans of the legs and whole body DXA scans were analysed for muscle and AT content of thigh (20 cm) and lower leg (10 cm) sections; 24 h creatinine excretion was measured. RESULTS: Model A overestimated thigh muscle volume (MRI mean, 2.3 l) substantially (bias 0.36 l), whereas model B underestimated it by only 2% (bias 0.045 l). Lower leg muscle (MRI mean, 0.6 l) was better predicted using model A (bias 0.04 l, 7% overestimate) than model B (bias 0.1 l, 17% underestimate). The 95% limits of agreement were high for these models (thigh,+/- 20%; lower leg,+/- 47%). Model C predictions were more discrepant than those of model B. There was generally less agreement between MRI and all DXA models for AT. Measurement variability was generally less for DXA measurements of FFST (coefficient of variation 0.7 - 1.8%) and fat (0.8 - 3.3%) than model B estimates of muscle (0.5-2.6%) and AT (3.3 - 6.8%), respectively. Despite strong relationships between them, muscle mass was overestimated by creatinine excretion with highly variable predictability. CONCLUSION: This study has shown the value of DXA models for assessment of muscle and AT in leg sections, but suggests the need to re-evaluate some of the assumptions upon which they are based.

Bonding effects and the crystal structures of (NH4)(2)[Cu(H2O)(6)](SO4)(2) and its (H2O)-O-18 substituted form at 9.5 K

The crystal structures of the Tutton salts (NH4)(2)[Cu(H2O)(6)](SO4)(2), diammonium hexaaquacopper disulfate, formed with normal water and isotopically substituted (H2O)-O-18, have been determined by X-ray diffraction at 9.5 K and are very similar, with Cu-O(7) the longest of the Cu-O bonds of the Jahn-Teller distorted octahedral [Cu(H2O)(6)](2+) complex. It is known that structural differences accompany deuteration of (NH4)(2)[Cu(H2O)(6)](SO4)(2), the most dramatic of which is a switch to Cu-O(8) as the longest such bond. The present result suggests that the structural differences are associated with hydrogen-bonding effects rather than with increased mass of the water ligands affecting the Jahn-Teller coupling. The Jahn-Teller distortions and hydrogen-bonding contacts in the compounds are compared with those reported for other Tutton salts at ambient and high pressure.

Feed intake and liveweight responses to nitrogen and/or protein supplements by steers of Bos taurus, Bos indicus and Bos taurus x Bos indicus breed types offered a low quality grass hay

Thirty steers were used in two pen experiments (Expts 1 and 2). and 27 of these in a third (Expt 3), to quantify their responses of hay intake, rumen ammonia nitrogen (RAN) concentrations, and liveweight to inputs of rumen soluble nitrogen (urea) and rumen undegradable protein (formaldehyde-treated casein; F-casein) when added to a basal diet of low quality hays. The hays were made From unimproved native pastures typical of those grazed by cattle in the subtropics of Australia and contained 7.8 g N/kg dry matter (DM) with coefficient of organic matter digestibility of 0.503 in Expts 1 and 2, and 5.2 g N/kg DM with a digestibility range from 0.385 to 0.448 in Expt 3. The steers (15 months old) were either Brahman (B), Hereford (H) or the F-1 Brahman x Hereford (BH) cross. Steers were offered supplementary minerals with the hays in each experiment. In Expt 1 (35 days) urea was sprayed on part of the hay, allowing for daily urea intakes (g/steer) of either 0, 5, 11, 16 or 26. In Expt 2 (42 days), F-casein was offered daily (g/steer) at either 0, 75, 150, 225 or 300 and in Expt 3 (56 days) discrete offerings were made of soluble casein (225 g/day), of urea (18 g/day) + F-casein (225 g/day) or of nil. There were significant linear effects of urea intake upon hay intake and liveweight change of steers. However, B steers had smaller increases in intake and liveweight change than did H steers, and B steers did not have a linear increase in RAN concentrations with increasing urea intake as did H and SH steers. In Expt 2 there were significant linear effects of F-casein supplements on hay intake and liveweight change of steers and a significant improvement in their feed conversion ratio (i.e. DM intake:liveweight change). The B steers did not differ from H and BH steers in liveweight change but had significantly lower hay intakes and non-significantly smaller increases in RAN with increasing F-casein intake. In Expt 3, hay intake of the steers increased with soluble casein (by 16.8 %) and with urea + F-casein (24.5 %). Only steers given urea + F-casein had a high RAN concentration (94 mg/l) and a high liveweight gain. The B steers had a liveweight loss and a lower hay intake than H or BH steers in Expt 3 but a higher RAN concentration. These studies have indicated the importance of the form and quantity of additional N required by cattle of differing breed types to optimize their feed intake and liveweight gain when offered low-N, low-digestible hays.

Determination of activation energy distributions for chemisorption of oxygen on carbon: an improved approach

The present paper proposes an approach to obtaining the activation energy distribution for chemisorption of oxygen onto carbon surfaces, while simultaneously allowing for the activation energy dependence of the pre-exponential factor of the rate constant. Prior studies in this area have considered this factor to be uniform, thereby biasing estimated distributions. The results show that the derived activation energy distribution is not sensitive to the chemisorption mechanism because of the step function like property of the coverage. The activation energy distribution is essentially uniform for some carbons, and has two or possibly more discrete stages, suggestive of at least two types of sites, each with its own uniform distribution. The pre-exponential factors of the reactions are determined directly from the experimental data, and are found not to be constant as assumed in earlier work, but correlated with the activation energy. The latter results empirically follow an exponential function, supporting some earlier statistical and experimental work. The activation energy distribution obtained in the present paper permits improved correlation of chemisorption data in comparison to earlier studies. (C) 2000 Elsevier Science Ltd. All rights reserved.

Accelerating seismic energy release and evolution of event time and size statistics: Results from two heterogeneous cellular automaton models

The evolution of event time and size statistics in two heterogeneous cellular automaton models of earthquake behavior are studied and compared to the evolution of these quantities during observed periods of accelerating seismic energy release Drier to large earthquakes. The two automata have different nearest neighbor laws, one of which produces self-organized critical (SOC) behavior (PSD model) and the other which produces quasi-periodic large events (crack model). In the PSD model periods of accelerating energy release before large events are rare. In the crack model, many large events are preceded by periods of accelerating energy release. When compared to randomized event catalogs, accelerating energy release before large events occurs more often than random in the crack model but less often than random in the PSD model; it is easier to tell the crack and PSD model results apart from each other than to tell either model apart from a random catalog. The evolution of event sizes during the accelerating energy release sequences in all models is compared to that of observed sequences. The accelerating energy release sequences in the crack model consist of an increase in the rate of events of all sizes, consistent with observations from a small number of natural cases, however inconsistent with a larger number of cases in which there is an increase in the rate of only moderate-sized events. On average, no increase in the rate of events of any size is seen before large events in the PSD model.

Free energy approximations in simple lattice proteins

This work addresses the question of whether it is possible to define simple pairwise interaction terms to approximate free energies of proteins or polymers. Rather than ask how reliable a potential of mean force is, one can ask how reliable it could possibly be. In a two-dimensional, infinite lattice model system one can calculate exact free energies by exhaustive enumeration. A series of approximations were fitted to exact results to assess the feasibility and utility of pairwise free energy terms. Approximating the true free energy with pairwise interactions gives a poor fit with little transferability between systems of different size. Adding extra artificial terms to the approximation yields better fits, but does not improve the ability to generalize from one system size to another. Furthermore, one cannot distinguish folding from nonfolding sequences via the approximated free energies. Most usefully, the methodology shows how one can assess the utility of various terms in lattice protein/polymer models. (C) 2001 American Institute of Physics.

Energy and averages in the mechanics of granular materials

We derive a general thermo-mechanical theory for particulate materials consisting of granules of arbitrary whose material points possess three translational and three independent rotational degrees of freedom. Additional field variables are the translational and rotational granular temperatures, the kinetic energies shape and size. The kinematics of granulate is described within the framework of a polar continuum theory of the velocity and spin fluctuations respectively and the usual thermodynamic temperature. We distinguish between averages over particle categories (averages in mass/velocity and moment of inertia/spin space, respectively) and particle phases where the average extends over distinct subsets of particle categories (multi phase flows). The relationship between the thermal energy in the granular system and phonon energy in a molecular system is briefly discussed in the main body of the paper and discussed in detail in the Appendix A. (C) 2001 Elsevier Science B.V. All rights reserved.

The spectra of red quasars

We measure the spectral properties of a representative sub-sample of 187 quasars, drawn from the Parkes Half-Jansky, Flat-radio-spectrum Sample (PHFS). Quasars with a wide range of rest-frame optical/UV continuum slopes are included in the analysis: their colours range over 2 < B-K < 7. We present composite spectra of red and blue sub-samples of the PHFS quasars. and tabulate their emission line properties. The median Hbeta and [0 111] emission line equivalent widths of the red quasar sub-sample are a factor of ten weaker than those of the blue quasar sub-sample. No significant differences are seen between the equivalent width distributions of the C IV, C III] and Mg 11 lines. Both the colours and the emission line equivalent widths of the red quasars can be explained by the addition of a featureless red synchrotron continuum component to an otherwise normal blue quasar spectrum. The red synchrotron component must have a spectrum at least as red as a power-law of the form F-nu proportional to nu(-2.8). The relative strengths of the blue and red components span two orders of magnitude at rest-frame 500 nm. The blue component is weaker relative to the red component in low optical luminosity sources. This suggests that the fraction of accretion energy going into optical emission from the jet is greater in low luminosity quasars. This correlation between colour and luminosity may be of use in cosmological distance scale work. This synchrotron model does not, however, fit similar to10% of the quasars, which have both red colours and high equivalent width emission lines. We hypothesise that these red, strong-lined quasars have intrinsically weak Big Blue Bumps. There is no discontinuity in spectral properties between the BL Lac objects in our sample and the other quasars. BL Lac objects appear to be the red, low equivalent width tail of a continuous distribution. The synchrotron emission component only dominates the spectrum at longer wavelengths, so existing BL Lac surveys will be biased against high redshift objects. This will affect measurements of BL Lac evolution. The blue PHFS quasars have significantly higher equivalent width C IV, Hbeta and [0 111] emission than a matched sample of optically selected QSOs.