Relaxations and Duality for Multiobjective Integer Programming

Multiobjective integer programs (MOIPs) simultaneously optimize multiple objective functions over a set of linear constraints and integer variables. In this paper, we present continuous, convex hull and Lagrangian relaxations for MOIPs and examine the relationship among them. The convex hull relaxation is tight at supported solutions, i.e., those that can be derived via a weighted-sum scalarization of the MOIP. At unsupported solutions, the convex hull relaxation is not tight and a Lagrangian relaxation may provide a tighter bound. Using the Lagrangian relaxation, we define a Lagrangian dual of an MOIP that satisfies weak duality and is strong at supported solutions under certain conditions on the primal feasible region. We include a numerical experiment to illustrate that bound sets obtained via Lagrangian duality may yield tighter bounds than those from a convex hull relaxation. Subsequently, we generalize the integer programming value function to MOIPs and use its properties to motivate a set-valued superadditive dual that is strong at supported solutions. We also define a simpler vector-valued superadditive dual that exhibits weak duality but is strongly dual if and only if the primal has a unique nondominated point

Rural smokers : a prevention opportunity

Background: Smoking is the largest single cause of preventable death and disease in Australia. This study describes smoking prevalence and the characteristics of rural smokers to guide general practitioners in targeting particular groups.Methods: Cross sectional surveys in the Greater Green Triangle region of southeast Australia using a random population sample (n=1563, participation rate 48.7%) aged 25&ndash;74 years. Smoking information was assessed by a self administered questionnaire.Results: Complete smoking data were available for 1494 participants. Overall age adjusted current smoking prevalence was 14.9% (95% CI: 13.1&ndash;16.7). In both genders, current smoking prevalence decreased with age. Those aged 25&ndash;44 years were more likely to want to stop smoking and to have attempted cessation, but less likely to have received cessation advice than older smokers.Discussion: This study provides baseline smoking data for rural health monitoring and identifies intervention opportunities. General practice is suited to implement interventions for smoking prevention and cessation at every patient encounter, particularly in younger individuals.<br /

Eucalypts as a genus for short rotation forestry in Great Britain

The study focused on four research objectives: 1. To identify the species and provenances of eucalypts most suitable for biomass production in Great Britain. 2. To compare growth of eucalypts with other promising short rotation forestry genera. 3. To develop volume and biomass functions for E. gunnii. 4. To estimate yields and patterns of growth for E. gunnii. Searches on CAB abstracts and World of Science showed that there was limited research conducted on eucalypts in the UK. This research provides an original contribution to knowledge through; a long term assessment of the performance of species of cold tolerant eucalypts across a range of sites, identification of the basis for the rapid growth of eucalypts in comparison with trees from other genera, identification of the best fit function to describe stem form in E.gunnii and a characterisation of the pattern of growth in this species. The thesis provides an account of the long history of eucalypts in the UK, the first record of a eucalypt being planted in Britain probably being Eucalyptus obliqua in the late 1700s (Aiton 1789). A review is then provided of the experience and constraints to growing nine eucalypt species in the UK and their potential for short rotation forestry are described. The rapid growth of eucalypts makes them well suited to short rotation forestry, but there are considerable risks from frosts and extreme winters. Results from a trial established in Cumbria, north west England are described. Survival and growth was compared between E.gunnii, E. nitens and native or naturalised species, identified by Hardcastle (2006) as having potential for short rotation forestry. The rapid rate of growth of E. gunnii was attributed to a combination of large leaf area, a long period of growth during the year and a high specific leaf area. There was 99% mortality of E. nitens at the trial over winter, preventing comparison with other species. At the same trial and assessment was made of frost damage during the winter of 2009-2010, which proved to be the coldest for thirty years (Met Office 2010). E. gunnii was found to be more cold-tolerant than E. nitens, with 35% of the former surviving the winter and less than 1% of the latter. Larger trees were damaged more so than smaller trees reinforcing the argument for good silviculture to promote rapid, early growth. The study on stem form and growth of E. gunnii represents the first in the UK. Volume, height and dbh of a total of 636 trees, measured by felling, optical dendrometer and terrestrial laser scanner were used to test the goodness of fit of a volume function developed in France by AFOCEL and is South America by Shell Oil. The AFOCEL function was found to predict volume with less bias and be suitable for all but the smallest trees. Characterisation of growth curves using mined historic data indicated yields of 16 m3 ha-1 y-1 or approximately 8 t ha-1 y-1 at 20 years old. In contrast, growth curves derived from stem analysis of nine trees from Chiddingfold (south east England) and Glenbranter (central western Scotland) indicated lower yields at 7 m3 ha-1 y-1 at age 28 years and 4.5 m3 ha-1 y-1 at age 30 years respectively. Evidence from plantings elsewhere in the UK show that higher rates of growth are possible, but also that yields are often compromised by high mortality

Calibration and Uncertainty Quantification of Convective Parameters in an Idealized GCM

Parameters in climate models are usually calibrated manually, exploiting only small subsets of the available data. This precludes both optimal calibration and quantification of uncertainties. Traditional Bayesian calibration methods that allow uncertainty quantification are too expensive for climate models; they are also not robust in the presence of internal climate variability. For example, Markov chain Monte Carlo (MCMC) methods typically require $O(10^5)$ model runs and are sensitive to internal variability noise, rendering them infeasible for climate models. Here we demonstrate an approach to model calibration and uncertainty quantification that requires only $O(10^2)$ model runs and can accommodate internal climate variability. The approach consists of three stages: (i) a calibration stage uses variants of ensemble Kalman inversion to calibrate a model by minimizing mismatches between model and data statistics; (ii) an emulation stage emulates the parameter-to-data map with Gaussian processes (GP), using the model runs in the calibration stage for training; (iii) a sampling stage approximates the Bayesian posterior distributions by sampling the GP emulator with MCMC. We demonstrate the feasibility and computational efficiency of this calibrate-emulate-sample (CES) approach in a perfect-model setting. Using an idealized general circulation model, we estimate parameters in a simple convection scheme from synthetic data generated with the model. The CES approach generates probability distributions of the parameters that are good approximations of the Bayesian posteriors, at a fraction of the computational cost usually required to obtain them. Sampling from this approximate posterior allows the generation of climate predictions with quantified parametric uncertainties

The effect of expectation on satisfaction in total knee replacements : a systematic review

Total knee replacement has reliably been shown to have a beneficial effect in knee osteoarthritis; however, around 17 % of patients are dissatisfied with the result. A commonly proposed mechanism driving the dissatisfaction rate is a discrepancy between expected and actual/perceived outcome. Our aim was to conduct a systematic review examining any association between pre-operative expectations and satisfaction. A comprehensive electronic search strategy was used to identify studies from MEDLINE, EMBASE, and the Cochrane Library from inception until May 2015. Data was extracted according to PRISMA guidelines and an online, published protocol. Four studies are included in this review. One study found an association between expectations and satisfaction. Different measures of expectation and satisfaction were used in all studies. To date, there is no consensus on how expectations or satisfaction should be measured, and a large number of studies that have the available information failed to conduct the relevant sub-group analysis. Further elucidation and consensus of how to measure expectations and satisfaction around joint replacement would aid this area of study greatly. On the basis of the current evidence it appears expectations have a small effect, if any, on satisfaction after knee replacement

Provenance and Paleogeography of the 25-17 Ma Rainbow Gardens Formation: Evidence for Tectonic Activity at Ca. 19 Ma and Internal Drainage rather than Throughgoing Paleorivers on the Southwestern Colorado Plateau

The paleogeographic evolution of the Lake Mead region of southern Nevada and northwest Arizona is crucial to understanding the geologic history of the U.S. Southwest, including the evolution of the Colorado Plateau and formation of the Grand Canyon. The ca. 25–17 Ma Rainbow Gardens Formation in the Lake Mead region, the informally named, roughly coeval Jean Conglomerate, and the ca. 24–19 Ma Buck and Doe Conglomerate southeast of Lake Mead hold the only stratigraphic evidence for the Cenozoic pre-extensional geology and paleogeography of this area. Building on prior work, we present new sedimentologic and stratigraphic data, including sandstone provenance and detrital zircon data, to create a more detailed paleogeographic picture of the Lake Mead, Grand Wash Trough, and Hualapai Plateau region from 25 to 18 Ma. These data confirm that sediment was sourced primarily from Paleozoic strata exposed in surrounding Sevier and Laramide uplifts and active volcanic fields to the north. In addition, a distinctive signal of coarse sediment derived from Proterozoic crystalline basement first appeared in the southwestern corner of the basin ca. 25 Ma at the beginning of Rainbow Gardens Formation deposition and then prograded north and east ca. 19 Ma across the southern half of the basin. Regional thermochronologic data suggest that Cretaceous deposits likely blanketed the Lake Mead region by the end of Sevier thrusting. Post-Laramide northward cliff retreat off the Kingman/Mogollon uplifts left a stepped erosion surface with progressively younger strata preserved northward, on which Rainbow Gardens Formation strata were deposited. Deposition of the Rainbow Gardens Formation in general and the 19 Ma progradational pulse in particular may reflect tectonic uplift events just prior to onset of rapid extension at 17 Ma, as supported by both thermochronology and sedimentary data. Data presented here negate the California and Arizona River hypotheses for an “old” Grand Canyon and also negate models wherein the Rainbow Gardens Formation was the depocenter for a 25–18 Ma Little Colorado paleoriver flowing west through East Kaibab paleocanyons. Instead, provenance and paleocurrent data suggest local to regional sources for deposition of the Rainbow Gardens Formation atop a stripped low-relief western Colorado Plateau surface and preclude any significant input from a regional throughgoing paleoriver entering the basin from the east or northeast

A calcium and calmodulin-dependent protein kinase present in differentiating Dictyostelium discoideum

Abstract.&quot; A protein kinase from Dictyostelium discoideum which phosphorylates the synthetic peptide, calmodulin-dependent protein kinase substrate (CDPKS, amino acid sequence: PLRRTLSVAA) and is stimulated by Ca2+/calmodulin is described. This is the first report of a protein kinase with these characteristics in D. discoideum. The enzyme was partially purified by Q-Sepharose chromatography. The protein kinase is very labile, and rapidly loses Ca2+/calmodulin-dependence upon standing at 4°C, even in the presence of protease inhibitors, making further purification and characterisation difficult. In the active fractions, a 55 kDa polypeptide is labelled with [y-32p]ATP in vitro under conditions in which intramolecular rather than intermolecular reactions are favoured. The phosphorylation of this peptide is stimulated in the presence of Ca 2+ and calmodulin but not Ca 2+ alone. Ca2+/calmodulin-dependent stimulation is inhibited in the presence of the calmodulin antagonist, trifluoperazine (TFP). It is proposed that the 55 kDa polypeptide may represent the autophosphorylated form of the enzyme

Scaling up Type 2 Diabetes Prevention Programs: National and State Interventions in Australia

Australia has one of the world's largest systematic, government-funded diabetes prevention programs. This chapter describes a federally-funded national program, a state-funded program in Victoria and an implementation trial in New South Wales. A coincidence of events, influential individuals and policy directions has led to these initiatives

Combined aerobic and resistance exercise program improves task performance in patients with heart failure

OBJECTIVES: To assess the effects of a home-based aerobic and resistance training program on the physical function of adults with New York Heart Association (NYHA) class II and III patients and systolic heart failure (HF). DESIGN: Randomized controlled trial. SETTING: Home based. PARTICIPANTS: Stable patients (N=24; mean age, 60±10y; left ventricular ejection fraction, 25%±9%; 50% white; 50% women) with New York Heart Association (NYHA) classes II and III (NYHA class III, 58%) systolic heart failure (HF). INTERVENTION: A 12-week progressive home-based program of moderate-intensity aerobic and resistance exercise. Attention control wait list participants performed light stretching and flexibility exercises. MAIN OUTCOME MEASURES: A 10-item performance-based physical function measure, the Continuous Scale Physical Functional Performance test (CS-PFP10), was the major outcome variable and included specific physical activities measured in time to complete a task, weight carried during a task, and distance walked. Other measures included muscle strength, HRQOL (Minnesota Living With Heart Failure Questionnaire, Epworth Sleepiness Scale), functional capacity (Duke Activity Status Index), and disease severity (brain natriuretic peptide) levels. RESULTS: After the exercise intervention, 9 of 10 specific task activities were performed more rapidly, with increased weight carried by exercise participants compared with the attention control wait list group. Exercise participants also showed significant improvements in CS-PFP10 total score (P<.025), upper and lower muscle strength, and HRQOL (P<.001) compared with the attention control wait list group. Adherence rates were 83% and 99% for the aerobic and resistance training, respectively. CONCLUSIONS: Patients with stable HF who participate in a moderate-intensity combined aerobic and resistance exercise program may improve performance of routine physical activities of daily living by using a home-based exercise approach. Performance-based measures such as the CS-PFP10 may provide additional insights into physical function in patients with HF that more commonly used exercise tests may not identify. Early detection of subtle changes that may signal declining physical function that are amenable to intervention potentially may slow further loss of function in this patient population