Facets of the polytope of the asymmetric travelling salesman problem with replenishment arcs

The Asymmetric Travelling Salesman Problem with Replenishment Arcs (RATSP) is a new class of problems arising from work related to aircraft routing. Given a digraph with cost on the arcs, a solution of the RATSP, like that of the Asymmetric Travelling Salesman Problem, induces a directed tour in the graph which minimises total cost. However the tour must satisfy additional constraints: the arc set is partitioned into replenishment arcs and ordinary arcs, each node has a non-negative weight associated with it, and the tour cannot accumulate more than some weight limit before a replenishment arc must be used. To enforce this requirement, constraints are needed. We refer to these as replenishment constraints.

In this paper, we review previous polyhedral results for the RATSP and related problems, then prove that two classes of constraints developed in V. Mak and N. Boland [Polyhedral results and exact algorithms for the asymmetric travelling salesman problem with replenishment arcs, Technical Report TR M05/03, School of Information Technology, Deakin University, 2005] are, under appropriate conditions, facet-defining for the RATS polytope.

Experimental study on effect of loading rate on mode I delamination of z-pin reinforced laminates

This paper presents an experimental investigation on mode I delamination of z-pinned double-cantilever-beams (DCB) and associate z-pin bridging mechanisms. Tests were performed with three types of samples: big-pin with an areal density of 2%, small-pin with an areal density of 2% and small-pin with an areal density of 0.5%. The loading rates for each type of samples were set at 1 mm/min and 100 mm/min. Comparison of fracture load under different loading rates shows the rate effects on delamination crack opening and delamination growth. Optical micrographs of z-pins after pullout were also presented to identify the bridging mechanisms of z-pins under different loading rates.

Polyhedral results and exact algorithms for the asymmetric travelling salesman problem with replenishment arcs

The asymmetric travelling salesman problem with replenishment arcs (RATSP), arising from work related to aircraft routing, is a generalisation of the well-known ATSP. In this paper, we introduce a polynomial size mixed-integer linear programming (MILP) formulation for the RATSP, and improve an existing exponential size ILP formulation of Zhu [The aircraft rotation problem, Ph.D. Thesis, Georgia Institute of Technology, Atlanta, 1994] by proposing two classes of stronger cuts. We present results that under certain conditions, these two classes of stronger cuts are facet-defining for the RATS polytope, and that ATSP facets can be lifted, to give RATSP facets. We implement our polyhedral findings and develop a Lagrangean relaxation (LR)-based branch-and-bound (BNB) algorithm for the RATSP, and compare this method with solving the polynomial size formulation using ILOG Cplex 9.0, using both randomly generated problems and aircraft routing problems. Finally we compare our methods with the existing method of Boland et al. [The asymmetric traveling salesman problem with replenishment arcs, European J. Oper. Res. 123 (2000) 408–427]. It turns out that both of our methods are much faster than that of Boland et al. [The asymmetric traveling salesman problem with replenishment arcs, European J. Oper. Res. 123 (2000) 408–427], and that the LR-based BNB method is more efficient for problems that resemble the aircraft rotation problems.

Tenocyte responses to mechanical loading in vivo : A role for local insulin-like growth factor 1 signaling in early tendinosis in rats

Objective
To investigate tenocyte regulatory events during the development of overuse supraspinatus tendinosis in rats.

Methods
Supraspinatus tendinosis was induced by running rats downhill at 1 km/hour for 1 hour a day. Tendons were harvested at 4, 8, 12, and 16 weeks and processed for brightfield, polarized light, or transmission electron microscopy. The development of tendinosis was assessed semiquantitatively using a modified Bonar histopathologic scale. Apoptosis and proliferation were examined using antibodies against fragmented DNA or proliferating cell nuclear antigen, respectively. Insulin-like growth factor 1 (IGF-1) expression was determined by computer-assisted quantification of immunohistochemical reaction. Local IGF-1 signaling was probed using antibodies to phosphorylated insulin receptor substrate 1 (IRS-1) and ERK-1/2.

Results
Tendinosis was present after 12 weeks of downhill running and was characterized by tenocyte rounding and proliferation as well as by glycosaminoglycan accumulation and collagen fragmentation. The proliferation index was elevated in CD90+ tenocytes in association with tendinosis and correlated with increased local IGF-1 expression by tenocytes and phosphorylation of IRS-1 and ERK-1/2. Both apoptosis and cellular inflammation were absent at all time points.

Conclusion
In this animal model, early tendinosis was associated with local stimulation of tenocytes rather than with extrinsic inflammation or apoptosis. Our data suggest a role for IGF-1 in the load-induced tenocyte responses during the pathogenesis of overuse tendon disorders.

Heterozygous tx mice have an increased sensitivity to copper loading: implications for Wilson's Disease carriers

Wilson's disease carriers constitute 1% of the human population. It is unknown whether Wilsons disease carriers are at increased susceptibility to copper overload when exposed to chronically high levels of ingested copper. This study investigated the effect of chronic excess copper in drinking water on the heterozygous form of the Wilson’s disease mouse model – the toxic milk (tx) mouse. Mice were provided with drinking water containing 300 mg/l copper for 4–7, 8–11, 12–15 or 16–20 months. At the completion of the study liver, spleen, kidney and brain tissue were analyzed by atomic absorption spectroscopy to determine copper concentration. Plasma ceruloplasmin oxidase activity and liver histology were also assessed. Chronic copper loading resulted in significantly increased liver copper in both tx heterozygous and tx homozygous mice, while wild type mice were resistant to the effects of copper loading. Copper loading effects were greatest in tx homozygous mice, with increased extrahepatic copper deposition in spleen and kidney – an effect absent in heterozygote and wild type mice. Although liver histology in homozygous mice was markedly abnormal, no histological differences were noted between heterozygous and wild type mice with copper loading. Tx heterozygous mice have a reduced ability to excrete excess copper, indicating that half of the normal liver Atp7b copper transporter activity is insufficient to deal with large copper intakes. Our results suggest that Wilsons disease carriers in the human population may be at increased risk of copper loading if chronically exposed to elevated copper in food or drinking water.

New insights in asymmetric tetraorganodistannoxane ladder formation. A NMR-spectroscopic and crystallographic study

The syntheses of the asymmetrically substituted tetraorganodistannoxanes [t-Bu₂(X)SnOSn(Y)(CH₂SiMe₃)₂1₂ (1, X = Y = OH; 2, X = Cl, Y = OH; 3, X = Y = Cl) are reported and their structures in solution and in the solid state are characterized by multinuclear NMR spectroscopy and single crystal X-ray analyses. In toluene, the tetrahydroxy-substituted derivative 1 is in equilibrium with the organotin oxides cyclo-[t-Bu₂Sn{OSn(CH₂SiMe₃)₂}₂O] (4), cyclo[(Me₃SiCH₂)₂Sn(OSnt-Bu₂)₂O] (5), and cyclo-(t-Bu₂SnO)₃, and some additional, undefined species containing pentacoordinated tin atoms. In contrast, the dihydroxydichloro-substituted derivative 2 is inert in solution.

Effects of creatine loading and prolonged creatine supplementation of body composition, fuel selection, sprint and endurance performance in humans

Most research on creatine has focused on short-term creatine loading and its effect on high-intensity performance capacity. Some studies have investigated the effect of prolonged creatine use during strength training. However, studies on the effects of prolonged creatine supplementation are lacking. In the present study, we have assessed the effects of both creatine loading and prolonged supplementation on muscle creatine content, body composition, muscle and whole-body oxidative capacity, substrate utilization during submaximal exercise, and on repeated supramaximal sprint, as well as endurance-type time-trial performance on a cycle ergometer. Twenty subjects ingested creatine or a placebo during a 5-day loading period (20g·day^-1) after which supplementation was continued for up to 6 weeks (2g·day^-1). Creatine loading increased muscle free creatine, creatine phosphate (CrP) and total creatine content (P<0.05). The subsequent use of a 2g·day^-1 maintenance dose, as suggested by an American College of Sports Medicine Roundtable, resulted in a decline in both the elevated CrP and total creatine content and maintenance of the free creatine concentration. Both short- and long-term creatine supplementation improved performance during repeated supramaximal sprints on a cycle ergometer. However, whole-body and muscle oxidative capacity, substrate utilization and time-trial performance were not affected. The increase in body mass following creatine loading was maintained after 6 weeks of continued supplementation and accounted for by a corresponding increase in fat-free mass. This study provides definite evidence that prolonged creatine supplementation in humans does not increase muscle or whole-body oxidative capacity and, as such, does not influence substrate utilization or performance during endurance cycling exercise. In addition, our findings suggest that prolonged creatine ingestion induces an increase in fat-free mass.

Chronological changes in tissue copper, zinc and iron in the toxic milk mouse and effects of copper loading

The toxic milk (tx) mouse is a rodent model for Wilson disease, an inherited disorder of copper overload. Here we assessed the effect of copper accumulation in the tx mouse on zinc and iron metabolism. Copper, zinc and iron concentrations were determined in the liver, kidney, spleen and brain of control and copper-loaded animals by atomic absorption spectroscopy. Copper concentration increased dramatically in the liver, and was also significantly higher in the spleen, kidney and brain of control tx mice in the first few months of life compared with normal DL mice. Hepatic zinc was increased with age in the tx mouse, but zinc concentrations in the other organs were normal. Liver and kidney iron concentrations were significantly lower at birth in tx mice, but increased quickly to be comparable with control mice by 2 months of age. Iron concentration in the spleen was significantly higher in tx mice, but was lower in 5 day old tx pups. Copper-loading studies showed that normal DL mice ingesting 300 mg/l copper in their diet for 3 months maintained normal liver, kidney and brain copper, zinc and iron levels. Copper-loading of tx mice did not increase the already high liver copper concentrations, but spleen and brain copper concentrations were increased. Despite a significant elevation of copper in the brain of the copper-loaded tx mice no behavioural changes were observed. The livers of copper-loaded tx mice had a lower zinc concentration than control tx mice, whilst the kidney had double the concentration of iron suggesting that there was increased erythrocyte hemolysis in the copper-loaded mutants.

Sequential technology adoption with asymmetric firms

We analyse the incentives and welfare implications of costly technology adoption in a two-period duopoly model where firms have different amounts of capital. We also extend our framework to an open economy set-up and examine the relationship between trade and technology adoption. Our findings are as follows. First, no monotone relationship exists between the threshold cost of adoption and capital shares. Second, an unequal distribution of capital, despite lessening competition, can increase total surplus. Third, trade generally encourages adoption of modern technology unless the share of capital for the adopters is too low.

High strain mechanical loading rapidly induces tendon apoptosis : an ex vivo rat tibialis anterior model

Background: The role of apoptosis, or programmed cell death, has only recently been explored in tendon.

Objective: To investigate the development of apoptosis after high strain loading of rat tendon.

Methods: The right tibialis anterior tendons of three rats were prepared for mechanical loading, and left tendons were prepared identically as non-loaded controls. Tendon was loaded with 20% strain for six hours using a 1 Hz longitudinal sine wave signal. The following were used to assess apoptosis: (a) a monoclonal mouse antibody (F7-26) to label single stranded DNA breaks; (b) a rabbit polyclonal antibody that specifically recognises the cleaved form of caspase-3.

Results: Light microscopy confirmed that the high strain protocol induced a stretch overload injury. Control tendons showed little or no staining with the F7-26 antibody, but the loaded tendons displayed numerous apoptotic cells. The percentage of apoptotic cells (20%) in the loaded tendon was significantly greater than in the control tendon (1%) (p = 0.000). The labelled cells colocalised with abnormal nuclear morphology, including nuclear fragmentation. The staining against cleaved caspase-3 was positive in loaded tendons only, and localised both to nucleus and cytoplasm.

Conclusion: This experiment extends knowledge of human tendon apoptosis by showing that apoptosis can occur in response to short term, high strain mechanical loading. This is the first report of mechanical loading of intact tendon causing excessive apoptosis.

Discriminative ability of functional loading tests for adolescent jumper

Objective: To investigate the reliability and validity of five squat-based loading tests that are clinically appropriate for jumper's knee. The loading tests were step up, double leg squat, double leg squat on a 25-degree decline (decline squat), single leg decline squat, and decline hop. Design: Cross-sectional controlled cohort. Subjects without knee pain comprised controls, those with extensor tendon pain comprised the jumper's knee group. Setting: Institutional athlete study group in Australia. Participants: Fifty-six elite adolescent basketball players participated in this study, thirteen comprised the jumper's knee group, fifteen athletes formed a control group. Intervention: Each subject performed each loading test for baseline and reliability data on the first testing day. Subjects then performed three days of intensive (6 h daily) basketball training, after which each loading test was reexamined. Main outcome measures: Eleven point interval scale for pain. Results: The tests that best detected a change in pain due to intensive workload were the single leg decline squat and single leg decline hop. This study found that decline tests have better discriminative ability than the standard squat to detect change in jumper's knee pain due to intensive training. The typical error for these tests ranged from 0.3 to 0.5, however, caution should be exercised in the interpretation of these reliability figures due to relatively low scores. Conclusions: The single leg decline squat is recommended in the physical assessment of adolescent jumper's knee. The decline squat was selected as the best clinical test over the decline hop because it was easier to standardise performance.