On the Cubicity of Interval Graphs

A k-cube (or ``a unit cube in k dimensions'') is defined as the Cartesian product R-1 x . . . x R-k where R-i (for 1 <= i <= k) is an interval of the form [a(i), a(i) + 1] on the real line. The k-cube representation of a graph G is a mapping of the vertices of G to k-cubes such that the k-cubes corresponding to two vertices in G have a non-empty intersection if and only if the vertices are adjacent. The cubicity of a graph G, denoted as cub(G), is defined as the minimum dimension k such that G has a k-cube representation. An interval graph is a graph that can be represented as the intersection of intervals on the real line - i. e., the vertices of an interval graph can be mapped to intervals on the real line such that two vertices are adjacent if and only if their corresponding intervals overlap. We show that for any interval graph G with maximum degree Delta, cub(G) <= inverted right perpendicular log(2) Delta inverted left perpendicular + 4. This upper bound is shown to be tight up to an additive constant of 4 by demonstrating interval graphs for which cubicity is equal to inverted right perpendicular log(2) Delta inverted left perpendicular.

Effect of defoliation interval and height on the growth and quality of Arachis pintoi cv. Amarillo

The effect of defoliation on Amarillo (Arachis pintoi cv. Amarillo) was studied in a glasshouse and in mixed swards with 2 tropical grasses. In the glasshouse, Amarillo plants grown in pots were subjected to a 30/20°C or 25/15°C temperature regime and to defoliation at 10-, 20- or 30-day intervals for 60 days. Two field plot studies were conducted on Amarillo with either irrigated kikuyu (Pennisetum clandestinum) in autumn and spring or dryland Pioneer rhodes grass (Chloris gayana) over summer and autumn. Treatments imposed were 3 defoliation intervals (7, 14 and 28 days) and 2 residual heights (5 and 10 cm for kikuyu; 3 and 10 cm for rhodes grass) with extra treatments (56 days to 3 cm for both grasses and 21 days to 5 cm for kikuyu). Defoliation interval had no significant effect on accumulated Amarillo leaf dry matter (DM) at either temperature regime. At the higher temperature, frequent defoliation reduced root dry weight (DW) and increased crude protein (CP) but had no effect on stolon DW or in vitro organic matter digestibility (OMD). On the other hand, at the lower temperature, frequent defoliation reduced stolon DW and increased OMD but had no effect on root DW or CP. Irrespective of temperaure and defoliation, water-soluble carbohydrate levels were higher in stolons than in roots (4.70 vs 3.65%), whereas for starch the reverse occured (5.37 vs 9.44%). Defoliating the Amarillo-kikuyu sward once at 56 days to 3 cm produced the highest DM yield in autumn and sprong (582 and 7121 kg/ha DM, respectively), although the Amarillo component and OMD were substantially reduced. Highest DM yields (1726 kg/ha) were also achieved in the Amarillo-rhodes grass sward when defoliated every 56 days to 3 cm, although the Amarillo component was unaffected. In a mixed sward with either kikuyu or rhodes grass, the Amarillo component in the sward was maintained up to a 28-day defoliation interval and was higher when more severely defoliated. The results show that Amarillo can tolerate frequent defoliation and that it can co-exist with tropical grasses of differing growth habits, provided the Amarillo-tropical grass sward is subject to frequent and severe defoliation.

Modeling dynamic demand response using Monte Carlo simulation and interval mathematics for boundary estimation

With the rapid development of various technologies and applications in smart grid implementation, demand response has attracted growing research interests because of its potentials in enhancing power grid reliability with reduced system operation costs. This paper presents a new demand response model with elastic economic dispatch in a locational marginal pricing market. It models system economic dispatch as a feedback control process, and introduces a flexible and adjustable load cost as a controlled signal to adjust demand response. Compared with the conventional “one time use” static load dispatch model, this dynamic feedback demand response model may adjust the load to a desired level in a finite number of time steps and a proof of convergence is provided. In addition, Monte Carlo simulation and boundary calculation using interval mathematics are applied for describing uncertainty of end-user's response to an independent system operator's expected dispatch. A numerical analysis based on the modified Pennsylvania-Jersey-Maryland power pool five-bus system is introduced for simulation and the results verify the effectiveness of the proposed model. System operators may use the proposed model to obtain insights in demand response processes for their decision-making regarding system load levels and operation conditions.

Wet season resting - economic insights from scenario modelling

Pasture degradation, particularly that attributable to overgrazing, is a significant problem across the northern Australian rangelands. Although grazing studies have identified the scope for wet season resting strategies to be used to rehabilitate degraded pastures, the economic outcome of these strategies has not been extensively demonstrated. An exploratory study of the prospective economic value of wet season resting is presented using an economic simulation model of a 28000 ha beef enterprise located in the Charters Towers region of north-eastern Australia to explore seven hypothetical scenarios centred on the projected performance of a wet season resting strategy. A series of 20-year simulations for a range of pasture recovery profiles, stocking capacity, animal productivity responses, beef prices and agistment options are compared with a baseline scenario of taking no action. Estimates of the net present value of the 20-year difference in total enterprise gross margins between the various resting options and the 'do nothing' option identify that wet season resting can offer a positive economic return for the range of scenarios examined, although this is contingent on the assumptions that are made concerning the trajectories of change in carrying capacity and animal productivity. Some implications for management and policy making to support the practical implementation of wet season resting strategies are discussed.

Interval Data Classification under Partial Information: A Chance-Constraint Approach

This paper presents a Chance-constraint Programming approach for constructing maximum-margin classifiers which are robust to interval-valued uncertainty in training examples. The methodology ensures that uncertain examples are classified correctly with high probability by employing chance-constraints. The main contribution of the paper is to pose the resultant optimization problem as a Second Order Cone Program by using large deviation inequalities, due to Bernstein. Apart from support and mean of the uncertain examples these Bernstein based relaxations make no further assumptions on the underlying uncertainty. Classifiers built using the proposed approach are less conservative, yield higher margins and hence are expected to generalize better than existing methods. Experimental results on synthetic and real-world datasets show that the proposed classifiers are better equipped to handle interval-valued uncertainty than state-of-the-art.

Burning, then resting, reduces wiregrass (Aristida spp.) in black speargrass pastures

Wiregrasses (Aristida spp.) are becoming more prevalent, causing reduced productivity, in the black speargrass (Heterpogon contortus) pastures of south-east Queensland. Burning a native pasture of poor botanical composition (with a high proportion of wiregrass) in spring, and resting a heavily-grazed pasture also of poor composition, both improved the condition of these pastures. However, burning in late summer did not. Three months after burning in spring, relative density of wiregrass had decreased and that of a desirable species, black speargrass, had increased. However, this effect did not persist under continuous and heavy grazing. Resting increased threefold both the yield of pasture and the proportion of black speargrass, and decreased the proportion of wiregrass by two-thirds. Burning in late summer had no effect on the relative density of black speargrass but relative density of wiregrass increased. Selective grazing after burning in late summer kept this pasture in very poor condition for 14 months. These results suggest that the best way to increase the proportion of black speargrass and reduce the proportion of wiregrass in a pasture would be to burn in spring and then rest the pasture

Resting sites, edge effects and dispersion of a polyphagous Bactrocera fruit fly within crops of different architecture

The spot or strip application of poisoned protein bait is a lure-and-kill technique used for the management of fruit flies. Knowledge of where flies occur in the crop environment is an important part of maximizing the efficacy of this tool. Bactrocera tryoni is a polyphagous pest of horticulture for which very little is known about its distribution within crops. With particular reference to edge effects, we monitored the abundance of B. tryoni in two crops of different architecture; strawberry and apple. In strawberries, we found more flies on the crop edge early in the fruiting season, which lessened gradually and eventually disappeared as the season progressed. In apple orchards, no such edge effect was observed and flies were found equally throughout the orchard. We postulated these differences may be due to differences in crop height (high vs. short) and/or crop canopy architecture (opened and branched in apple, dense and closed in strawberry). In a field cage trial, we tested these predictions using artificial plants of different height and canopy condition. Height and canopy structure type had no significant effects on fly oviposition and protein feeding, but the ‘apple’ type canopy significantly influenced resting. We thus postulate that there was an edge effect in strawberry because the crop was not providing resting sites and flies were doing so in vegetation around the field margins. The finding that B. tryoni shows different resting site preferences based on plant architecture offers the potential for strategic manipulation of the fly through specific border or inter-row plantings.

Principles and guidelines for managing cattle grazing in the grazing lands of northern Australia: stocking rates, pasture resting, prescribed fire, paddock size and water points - a review

Beef cattle grazing is the dominant land use in the extensive tropical and sub-tropical rangelands of northern Australia. Despite the considerable knowledge on land and herd management gained from both research and practical experience, the adoption of improved management is limited by an inability to predict how changes in practices and combinations of practices will affect cattle production, economic returns and resource condition. To address these issues, past Australian and international research relating to four management factors that affect productivity and resource condition was reviewed in order to identify key management principles. The four management factors considered were stocking rates, pasture resting, prescribed fire, and fencing and water point development for managing grazing distribution. Four management principles for sound grazing management in northern Australia were formulated as follows: (1) manage stocking rates to meet goals for livestock production and land condition; (2) rest pastures to maintain them in good condition or to restore them from poor condition to increase pasture productivity; (3) devise and apply fire regimes that enhance the condition of grazing land and livestock productivity while minimising undesirable impacts; and (4) use fencing and water points to manipulate grazing distribution. Each principle is supported by several more specific guidelines. These principles and guidelines, and the supporting research on which they are based, are presented.

Assessing the effectiveness of High Intensity Interval Training (HIIT) for smoking cessation in women: HIIT to quit study protocol

Background: Smoking and physical inactivity are major risk factors for heart disease. Linking strategies that promote improvements in fitness and assist quitting smoking has potential to address both these risk factors simultaneously. The objective of this study is to compare the effects of two exercise interventions (high intensity interval training (HIIT) and lifestyle physical activity) on smoking cessation in female smokers. Method/design: This study will use a randomised controlled trial design. Participants: Women aged 18–55 years who smoke ≥ 5 cigarettes/day, and want to quit smoking. Intervention: all participants will receive usual care for quitting smoking. Group 1 - will complete two gym-based supervised HIIT sessions/week and one home-based HIIT session/week. At each training session participants will be asked to complete four 4-min (4 × 4 min) intervals at approximately 90 % of maximum heart rate interspersed with 3- min recovery periods. Group 2 - participants will receive a resource pack and pedometer, and will be asked to use the 10,000 steps log book to record steps and other physical activities. The aim will be to increase daily steps to 10,000 steps/day. Analysis will be intention to treat and measures will include smoking cessation, withdrawal and cravings, fitness, physical activity, and well-being. Discussion: The study builds on previous research suggesting that exercise intensity may influence the efficacy of exercise as a smoking cessation intervention. The hypothesis is that HIIT will improve fitness and assist women to quit smoking.

Resting pastures to improve land condition in northern Australia: guidelines based on the literature and simulation modelling

Pasture rest is a possible strategy for improving land condition in the extensive grazing lands of northern Australia. If pastures currently in poor condition could be improved, then overall animal productivity and the sustainability of grazing could be increased. The scientific literature is examined to assess the strength of the experimental information to support and guide the use of pasture rest, and simulation modelling is undertaken to extend this information to a broader range of resting practices, growing conditions and initial pasture condition. From this, guidelines are developed that can be applied in the management of northern Australia’s grazing lands and also serve as hypotheses for further field experiments. The literature on pasture rest is diverse but there is a paucity of data from much of northern Australia as most experiments have been conducted in southern and central parts of Queensland. Despite this, the limited experimental information and the results from modelling were used to formulate the following guidelines. Rest during the growing season gives the most rapid improvement in the proportion of perennial grasses in pastures; rest during the dormant winter period is ineffective in increasing perennial grasses in a pasture but may have other benefits. Appropriate stocking rates are essential to gain the greatest benefit from rest: if stocking rates are too high, then pasture rest will not lead to improvement; if stocking rates are low, pastures will tend to improve without rest. The lower the initial percentage of perennial grasses, the more frequent the rests should be to give a major improvement within a reasonable management timeframe. Conditions during the growing season also have an impact on responses with the greatest improvement likely to be in years of good growing conditions. The duration and frequency of rest periods can be combined into a single value expressed as the proportion of time during which resting occurs; when this is done the modelling suggests the greater the proportion of time that a pasture is rested, the greater is the improvement but this needs to be tested experimentally. These guidelines should assist land managers to use pasture resting but the challenge remains to integrate pasture rest with other pasture and animal management practices at the whole-property scale.

Resting sites, edge effects and dispersion of a polyphagous Bactrocera fruit fly within crops of different architecture

The spot or strip application of poisoned protein bait is a lure-and-kill technique used for the management of fruit flies. Knowledge of where flies occur in the crop environment is an important part of maximizing the efficacy of this tool. Bactrocera tryoni is a polyphagous pest of horticulture for which very little is known about its distribution within crops. With particular reference to edge effects, we monitored the abundance of B. tryoni in two crops of different architecture; strawberry and apple. In strawberries, we found more flies on the crop edge early in the fruiting season, which lessened gradually and eventually disappeared as the season progressed. In apple orchards, no such edge effect was observed and flies were found equally throughout the orchard. We postulated these differences may be due to differences in crop height (high vs. short) and/or crop canopy architecture (opened and branched in apple, dense and closed in strawberry). In a field cage trial, we tested these predictions using artificial plants of different height and canopy condition. Height and canopy structure type had no significant effects on fly oviposition and protein feeding, but the 'apple' type canopy significantly influenced resting. We thus postulate that there was an edge effect in strawberry because the crop was not providing resting sites and flies were doing so in vegetation around the field margins. The finding that B. tryoni shows different resting site preferences based on plant architecture offers the potential for strategic manipulation of the fly through specific border or inter-row plantings. © 2013 Blackwell Verlag GmbH.

Finite field computation technique for exact solution of systems of linear equations and interval linear programming problems

An error-free computational approach is employed for finding the integer solution to a system of linear equations, using finite-field arithmetic. This approach is also extended to find the optimum solution for linear inequalities such as those arising in interval linear programming probloms.

Ion channel gene variants predisposing to severe human ventricular arrhythmias

Congenital long QT syndrome (LQTS) with an estimated prevalence of 1:2000-1:10 000 manifests with prolonged QT interval on electrocardiogram and risk for ventricular arrhythmias and sudden death. Several ion channel genes and hundreds of mutations in these genes have been identified to underlie the disorder. In Finland, four LQTS founder mutations of potassium channel genes account for up to 40-70% of genetic spectrum of LQTS. Acquired LQTS has similar clinical manifestations, but often arises from usage of QT-prolonging medication or electrolyte disturbances. A prolonged QT interval is associated with increased morbidity and mortality not only in clinical LQTS but also in patients with ischemic heart disease and in the general population. The principal aim of this study was to estimate the actual prevalence of LQTS founder mutations in Finland and to calculate their effect on QT interval in the Finnish background population. Using a large population-based sample of over 6000 Finnish individuals from the Health 2000 Survey, we identified LQTS founder mutations KCNQ1 G589D (n=8), KCNQ1 IVS7-2A>G (n=1), KCNH2 L552S (n=2), and KCNH2 R176W (n=16) in 27 study participants. This resulted in a weighted prevalence estimate of 0.4% for LQTS in Finland. Using a linear regression model, the founder mutations resulted in a 22- to 50-ms prolongation of the age-, sex-, and heart rate-adjusted QT interval. Collectively, these data suggest that one of 250 individuals in Finland may be genetically predisposed to ventricular arrhythmias arising from the four LQTS founder mutations. A KCNE1 D85N minor allele with a frequency of 1.4% was associated with a 10-ms prolongation in adjusted QT interval and could thus identify individuals at increased risk of ventricular arrhythmias at the population level. In addition, the previously reported associations of KCNH2 K897T, KCNH2 rs3807375, and NOS1AP rs2880058 with QT interval duration were confirmed in the present study. In a separate study, LQTS founder mutations were identified in a subgroup of acquired LQTS, providing further evidence that congenital LQTS gene mutations may underlie acquired LQTS. Catecholaminergic polymorphic ventricular tachycardia (CPVT) is characterized by exercise-induced ventricular arrhythmias in a structurally normal heart and results from defects in the cardiac Ca2+ signaling proteins, mainly ryanodine receptor type 2 (RyR2). In a patient population of typical CPVT, RyR2 mutations were identifiable in 25% (4/16) of patients, implying that noncoding variants or other genes are involved in CPVT pathogenesis. A 1.1 kb RyR2 exon 3 deletion was identified in two patients independently, suggesting that this region may provide a new target for RyR2-related molecular genetic studies. Two novel RyR2 mutations showing a gain-of-function defect in vitro were identified in three victims of sudden cardiac death. Extended pedigree analyses revealed some surviving mutation carriers with mild structural abnormalities of the heart and resting ventricular arrhythmias suggesting that not all RyR2 mutations lead to a typical CPVT phenotype, underscoring the relevance of tailored risk stratification of a RyR2 mutation carrier.