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.

Beyond prejudice as simple antipathy: Hostile and benevolent sexism across cultures

The authors argue that complementary hostile and benevolent components of sexism exist across cultures. Male dominance creates hostile sexism IHS), but men's dependence on women fosters benevolent sexism (BS)-subjectively positive attitudes that put women on a pedestal but reinforce their subordination. Research with 15,000 men and women in 19 nations showed that (a) HS and BS are coherent constructs that correlate positively across nations, but (b) HS predicts the ascription of negative and BS the ascription of positive traits to women, (c) relative to men, women are more likely to reject HS than BS, especially when overall levels of sexism in a culture are high, and (d) national averages on BS and HS predict gender inequality across nations. These results challenge prevailing notions of prejudice as an antipathy in that BS tan affectionate, patronizing ideology) reflects inequality and is a cross-culturally pervasive complement to HS.

Epidural anaesthesia and analgesia and outcome of major surgery: a randomised trial

Background Epidural block is widely used to manage major abdominal surgery and postoperative analgesia, but its risks. and benefits are uncertain. We compared adverse outcomes in high-risk patients managed for major surgery with epidural block or alternative analgesic regimens with general anaesthesia in a multicentre randomised trial. Methods 915 patients undergoing major abdominal surgery with one of nine defined comorbid states to identify high-risk status were randomly assigned intraoperative epidural anaesthesia and postoperative epidural analgesia for 72 h with general anaesthesia (site of epidural selected to provide optimum block) or control. The primary endpoint was death at 30 days or major postsurgical morbidity. Analysis by intention to treat involved 447 patients assigned epidural and 441 control. Findings 255 patients (57.1%) in the epidural group and 268 (60.7%) in the control group had at least one morbidity endpoint or died (p=0.29). Mortality at 30 days was low in both groups (epidural 23 [5.1%], control 19 [4.3%], p=0.67). Only one of eight categories of morbid endpoints in individual systems (respiratory failure) occurred less frequently in patients managed with epidural techniques (23% vs 30%, p=0.02). Postoperative epidural analgesia was associated with lower pain scores during the first 3 postoperative days. There were no major adverse consequences of epidural-catheter insertion. Interpretation Most adverse morbid outcomes in high-risk patients undergoing major abdominal surgery are not reduced by use of combined epidural and general anaesthesia and postoperative epidural analgesia. However, the improvement in analgesia, reduction in respiratory failure, and the low risk of serious adverse consequences suggest that many high-risk patients undergoing major intra-abdominal surgery will receive substantial benefit from combined general and epidural anaesthesia intraoperatively with continuing postoperative epidural analgesia.

Perioperative epidural analgesia and outcome after major abdominal surgery in high-risk patients

In a primary analysis of a large recently completed randomized trial in 915 high-risk patients undergoing major abdominal surgery, we found no difference in outcome between patients receiving perioperative epidural analgesia and those receiving IV opioids, apart from the incidence of respiratory failure. Therefore, we performed a selected number of predetermined subgroup analyses to identify specific types of patients who may have derived benefit from epidural analgesia. We found no difference in outcome between epidural and control groups in subgroups at increased risk of respiratory or cardiac complications or undergoing aortic surgery, nor in a subgroup with failed epidural block (all P > 0.05). There was a small reduction in the duration of postoperative ventilation (geometric mean [SD]: control group, 0.3 [6.5] h, versus epidural group, 0.2 [4.8] h, P = 0.048). No differences were found in length of stay in intensive care or in the hospital. There was no relationship between frequency of use of epidural analgesia in routine practice outside the trial and benefit from epidural analgesia in the trial. We found no evidence that perioperative epidural analgesia significantly influences major morbidity or mortality after major abdominal surgery.

A family of perfect hashing methods

Minimal perfect hash functions are used for memory efficient storage and fast retrieval of items from static sets. We present an infinite family of efficient and practical algorithms for generating order preserving minimal perfect hash functions. We show that almost all members of the family construct space and time optimal order preserving minimal perfect hash functions, and we identify the one with minimum constants. Members of the family generate a hash function in two steps. First a special kind of function into an r-graph is computed probabilistically. Then this function is refined deterministically to a minimal perfect hash function. We give strong theoretical evidence that the first step uses linear random time. The second step runs in linear deterministic time. The family not only has theoretical importance, but also offers the fastest known method for generating perfect hash functions.

A low-temperature insulating phase at v=1.5 for 2D holes in high-mobility SiSi1-xGex heterostructures with Landau level degeneracy

Magneto-transport measurements of the 2D hole system (2DHS) in p-type Si-Si1-xGex heterostructures identify the integer quantum Hall effect (IQHE) at dominantly odd-integer filling factors v and two low-temperature insulating phases (IPs) at v = 1.5 and v less than or similar to 0.5, with re-entrance to the quantum Hall effect at v = 1. The temperature dependence, current-voltage characteristics, and tilted field and illumination responses of the IP at v = 1.5 indicate that the important physics is associated with an energy degeneracy of adjacent Landau levels of opposite spin, which provides a basis for consideration of an intrinsic, many-body origin.

Self-organization with traveling waves: A case for a convective torus

A traveling wave of BaSO4 in the chlorite-thiourea reaction has shown concentric precipitation patterns upon being triggered by the autocatalyst HOCl. The precipitation patterns show circular rings of alternate null and full precipitation regions. This self-organization appears to be the result of the formation of a convective torus. The formation of the convective torus can be described as a Benard-Marangoni instability with lateral heating.

Integer matrix diagonalization

We consider algorithms for computing the Smith normal form of integer matrices. A variety of different strategies have been proposed, primarily aimed at avoiding the major obstacle that occurs in such computations-explosive growth in size of intermediate entries. We present a new algorithm with excellent performance. We investigate the complexity of such computations, indicating relationships with NP-complete problems. We also describe new heuristics which perform well in practice. Wie present experimental evidence which shows our algorithm outperforming previous methods. (C) 1997 Academic Press Limited.

Proximal arterial vasoconstriction precedes regression of the hyaloid vasculature

Purpose: To determine whether constriction of proximal arterial vessels precedes involution of the distal hyaloid vasculature in the mouse, under normal conditions, and whether this vasoconstriction is less pronounced when the distal hyaloid network persists, as it does in oxygen-induced retinopathy (OIR). Methods: Photomicrographs of the vasa hyaloidea propria were analysed from pre-term pups (1-2 days prior to birth), and on Days 1-11 post-birth. The OIR model involved exposing pups to similar to 90% O-2 from D1-5, followed by return to ambient air. At sampling times pups were anaesthetised and perfused with india ink. Retinal flatmounts were also incubated with FITC-lectin (BS-1, G. simplicifolia,); this labels all vessels, allowing identification of vessels not patent to the perfusate. Results: Mean diameter of proximal hyaloid vessels in preterm pups was 25.44 +/- 1.98 mum; +/-1 SEM). Within 3-12 hrs of birth, significant vasoconstriction was evident (diameter:12.45 +/- 0.88 mum), and normal hyaloid regression subsequently occurred. Similar vasoconstriction occurred in the O-2-treated group, but this was reversed upon return to room air, with significant dilation of proximal vessels by D7 (diameter: 31.75 +/- 11.99 mum) and distal hyaloid vessels subsequently became enlarged and tortuous. Conclusions: Under normal conditions, vasoconstriction of proximal hyaloid vessels occurs at birth, preceding attenuation of distal hyaloid vessels. Vasoconstriction also occurs in O-2-treated pups during treatment, but upon return to room air, the remaining hyaloid vessels dilate proximally, and the distal vessels become dilated and tortuous. These observations support the contention that regression of the hyaloid network is dependent, in the first instance, on proximal arterial vasoconstriction.

The ratio of messenger RNA levels of receptor activator of nuclear factor kappa B ligand to osteoprotegerin correlates with bone remodeling indices in normal human cancellous bone but not in osteoarthritis

skeletal disease. Bone remodeling is initiated by osteoclastic resorption followed by osteoblastic formation of new bone. Receptor activator of nuclear factor KB ligand (RANKL) is a newly described regulator of osteoclast formation and function, the activity of which appears to be a balance between interaction with its receptor RANK and with an antagonist binding protein osteoprotegerin (OPG). Therefore, we have examined the relationship between the expression of RANKL, RANK, and OPG and indices of bone structure and turnover in human cancellous bone from the proximal femur. Bone samples were obtained from individuals with osteoarthritis (OA) at joint replacement surgery and from autopsy controls. Histomorphometric analysis of these samples showed that eroded surface (ES/BS) and osteoid surface (OS/BS) were positively associated in both control (p < 0.001) and OA (p < 0.02), indicating that the processes of bone resorption and bone formation remain coupled in OA, as they are in controls. RANKL, OPG, and RANK messenger RNA, (mRNA) were abundant in human cancellous bone, with significant differences between control and OA individuals. In coplotting the molecular and histomorphometric data, strong associations were found between the ratio of RANKL/OPG mRNA and the indices of bone turnover (RANKL/OPG vs. ES/BS: r = 0.93, p < 0.001; RANKL/OPG vs. OS/BS: r = 0.80, p < 0.001). These relationships were not evident in trabecular bone from severe OA, suggesting that bone turnover may be regulated differently in this disease. We propose that the effective concentration of RANKL is related causally to bone turnover.

Tungsten isotope evidence from similar to 3.8-Gyr metamorphosed sediments for early meteorite bombardment of the Earth

The 'Late Heavy Bombardment' was a phase in the impact history of the Moon that occurred 3.8-4.0 Gyr ago, when the lunar basins with known dates were formed(1,2). But no record of this event has yet been reported from the few surviving rocks of this age on the Earth. Here we report tungsten isotope anomalies, based on the Hf-182-W-182 system (half-life of 9 Myr), in metamorphosed sedimentary rocks from the 3.7-3.8-Gyr-old Isua greenstone belt of West Greenland and closely related rocks from northern Labrador, Canada. As it is difficult to conceive of a mechanism by which tungsten isotope heterogeneities could have been preserved in the Earth's dynamic crust-mantle environment from a time when short-lived Hf-182 was still present, we conclude that the metamorphosed sediments contain a component derived from meteorites.

New W-isotope evidence for rapid terrestrial accretion and very early core formation

The short-lived Hf-182-W-182-isotope system is an ideal clock to trace core formation and accretion processes of planets. Planetary accretion and metal/silicate fractionation chronologies are calculated relative to the chondritic Hf-182-W-182-isotope evolution. Here, we report new high-precision W-isotope data for the carbonaceous chondrite Allende that are much less radiogenic than previously reported and are in good agreement with published internal Hf-W chronometry of enstatite chondrites. If the W-isotope composition of terrestrial rocks, representing the bulk silicate Earth, is homogeneous and 2.24 epsilon(182W) units more radiogenic than that of the bulk Earth, metal/silicate differentiation of the Earth occurred very early. The new W-isotope data constrain the mean time of terrestrial core formation to 34 million years after the start of solar system accretion. Early terrestrial core formation implies rapid terrestrial accretion, thus permitting formation of the Moon by giant impact while Hf-182 was still alive. This could explain why lunar W-isotopes are more radiogenic than the terrestrial value. Copyright (C) 2002 Elsevier Science Ltd.