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.

Agri-food restructuring: A synthesis of recent Australian research

Globalizing tendencies within capitalism are leading to important alterations in the structure of agricultural production and the ways food companies are involving themselves in processing and marketing. Increasingly, finance capital and transnational agribusiness have sought ways to influence, and in some cases redirect, farming activities in Australia. The penetration of farming structures by corporate capital has been hastened by state deregulation. Rather than providing detailed empirical evidence, this paper presents a broad synthesis of recent Australian research with the aim of informing readers otherwise unaware of events in the Antipodes of the forms and impacts of agri-food change in Australia.

The conserved quantity theory of causation and chance raising

In this paper I offer an 'integrating account' of singular causation, where the term 'integrating' refers to the following program for analysing causation. There are two intuitions about causation, both of which face serious counterexamples when used as the basis for an analysis of causation. The 'process' intuition, which says that causes and effects are linked by concrete processes, runs into trouble with cases of misconnections', where an event which serves to prevent another fails to do so on a particular occasion and yet the two events are linked by causal processes. The chance raising intuition, according to which causes raise the chance of their effects, easily accounts for misconnections but faces the problem of chance lowering causes, a problem easily accounted for by the process approach. The integrating program attempts to provide an analysis of singular causation by synthesising the two insights, so as to solve both problems. In this paper I show that extant versions of the integrating program due to Eells, Lewis, and Menzies fail to account for the chance-lowering counterexample. I offer a new diagnosis of the chance lowering case, and use that as a basis for an integrating account of causation which does solve both cases. In doing so, I accept various assumptions of the integrating program, in particular that there are no other problems with these two approaches. As an example of the process account, I focus on the recent CQ theory of Wesley Salmon (1997).

Life-history consequences of divergent selection on egg size in Drosophila melanogaster

Life histories are generally assumed to evolve via antagonistic pleiotropy (negative genetic correlations) among traits, and trade-offs between life-history traits are typically studied using either phenotypic manipulations or selection experiments. We investigated the trade-off between egg size and fecundity in Drosophila melanogaster by examining both the phenotypic and genetic relationships between these traits after artificial selection for large and small eggs, relative to female body size. Egg size responded strongly to selection in both directions, increasing in the large-egg selected lines and decreasing in the small-egg selected lines. Phenotypic correlations between egg size and fecundity in the large-egg selected lines were negative, but no relationship between these traits occurred in either the control or small-egg selected lines. There was no negative genetic correlation between egg size and fecundity. Total reproductive allocation decreased in the small-egg selected lines but did not increase in the large-egg lines. Our results have three implications. First, our selection procedure may have forced females selected for large eggs into a physiological trade-off not reflected in a negative genetic correlation between these traits. Second, the lack of a negative genetic correlation between egg size and number suggests that the phenotypic trade-off frequently observed between egg size and number in other organisms may not evolve over the short term via a direct genetic trade-off whereby increases in egg size are automatically accompanied by decreased fecundity. Finally, total reproductive allocation may not evolve independently of egg size as commonly assumed.

Pursuing the popular in Australian history

No abstract

Seeing is believing: Recent trends in the measurement of Ca2+ in subcellular domains and intracellular organelles

The role of Ca2+ in the regulation of the cell cycle has been investigated mostly in studies assessing global cytosolic free Ca2+. Recent studies, however, have used unique techniques to assess Ca2+ in subcellular organelles, such as mitochondria, and in discrete regions of the cytoplasm. These studies have used advanced fluorescence digital imaging techniques and Ca2+-sensitive fluorescence probes, and/or targeting of Ca2+-sensitive proteins to intracellular organelles. The present review describes the results of some of these studies and the techniques used. The novel techniques used to measure Ca2+ in microdomains and intracellular organelles are likely to be of great use in future investigations assessing Ca2+ homeostasis during the cell cycle.

Absolute risk of breast cancer for Australian women with a family history

Background: The purpose of the present paper was to estimate the absolute risk of breast cancer over the remainder of a lifetime in Australian women with different categories of family history. Methods: Age-specific breast cancer incidence rates were adjusted for screening effects, and rates in those with no family history were estimated using the attributable fraction (AF). Relative risks from a published meta-analysis were applied to obtain incidence rates for different categories of family history, and age-specific incidence was converted to cumulative risk of breast cancer. The risk estimates were based upon Australian population statistics and published relative risks. Breast cancer incidence was from New South Wales women for 1996. The AF was calculated using prevalence of a family history of breast cancer from data on Queensland women. The cumulative absolute risk of breast cancer was calculated from decade and mid-decade ages to age 79 years, not adjusted for competing causes of death. Results: Lifetime risk is approximately 8.6% (1 in 12) for the general population and 7.8% (1 in 13) for those without a family history. Women with one relative affected have lifetime risks of 1 in 6-8 and those with two relatives affected have lifetime risks of 1 in 4-6. The cumulative residual lifetime risk decreases with advancing age; by age 60 years all groups with only one relative affected have well above a 90% probability of not developing breast cancer to age 79 years. Conclusions: These Australian risk statistics are useful for public information and in the clinical setting. Risks given here apply to women with average breast cancer risk from other risk factors.

Iron deficiency, general health and fatigue: Results from the Australian Longitudinal Study on Women's Health

Associations between self-reported 'low iron', general health and well-being, vitality and tiredness in women, were examined using physical (PCS) and mental (MCS) component summary and vitality (VT) scores from the MOS short-form survey (SF-36). 14,762 young (18-23 years) and 14,072 mid-age (45-50 years) women, randomly selected from the national health insurance commission (Medicare) database, completed a baseline mailed self-report questionnaire and 12,328 mid-age women completed a follow-up questionnaire 2 years later. Young and mid-age women who reported (ever) having had 'low iron' reported significantly lower mean PCS, MCS and VT scores, and greater prevalence of 'constant tiredness' at baseline than women with no history of iron deficiency [Differences: young PCS = -2.2, MCS = -4.8, VT = -8.7; constant tiredness: 67% vs. 45%; mid-age PCS = -1.4, MCS = -3.1, VT = -5.9; constant tiredness: 63% vs. 48%]. After adjusting for number of children, chronic conditions, symptoms and socio-demographic variables, mean PCS, MCS and VT scores for mid-age women at follow-up were significantly lower for women who reported recent iron deficiency (in the last 2 years) than for women who reported past iron deficiency or no history of iron deficiency [Means: PCS - recent = 46.6, past = 47.8, never = 47.7; MCS - recent = 45.4, past = 46.9, never = 47.4; VT - recent = 54.8, past = 57.6, never = 58.6]. The adjusted mean change in PCS, MCS and VT scores between baseline and follow-up were also significantly lower among mid-age women who reported iron deficiency only in the last 2 years (i.e. recent iron deficiency) [Mean change: PCS = -3.2; MCS = -2.1; VT = -4.2]. The results suggest that iron deficiency is associated with decreased general health and well-being and increased fatigue.