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.

A class of exact solutions for the flow of a micropolar fluid

The flow of a micropolar fluid in an orthogonal rheometer is considered. It is shown that an infinite number of exact solutions characterizing asymmetric motions are possible. The expressions for pressure in the fluid, the components of the forces and couples acting on the plates are obtained. The effect of microrotation on the flow is brought out by considering numerical results for the case of coaxially rotating disks.

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.

Embedding sustainability in a real-world context: Developing a world class early learning centre

This symposium describes what is possible when early childhood professionals work with designers to develop a vision for an exemplary early childhood centre with a focus on Education for Sustainability (EfS). The symposium provides insights into cross-disciplinary initiatives between QUT Early childhood and Design staff and students, who have worked together with the iconic Lone Pine Koala Sanctuary in Brisbane, to explore imperatives around EfS, including leadership and professionalism. This practical, real world project has seen all stakeholders engage in a focus on sustainability which has opened new ways of thinking about early childhood centre design. Cross-disciplinarity has created space to re-think the potential of the disciplines to interweave, and in so doing opened different ways for thinking about early childhood centres – their operation and their function. For the first time in Queensland, this project creates strategic alliances between EfS, childcare, business and sustainable design. EfS is essential for addressing local and global environmental issues and early childhood EfS research has been gaining international momentum, with governments nominating this area as having significant capacity to empower communities and promote change. While models for collaboration exist in the early childhood programs in Reggio Emilia, we offer sustainability as a unique and contemporary focus with immense potential to generate international and national interest. To date Early Childhood degree students enrolled in a leadership and management unit/subject have worked collaboratively with Design students to explore the sustainable design of the proposed Lone Pine early childhood centre. Providing students with a ‘real world’ project sees them re-positioned from ‘novice’ to ‘professional’, where their knowledge, expertise and perspectives are simultaneously validated and challenged. These learning experiences are enabling students to practice a new model of early childhood leadership, one that is vital for leading in an increasingly complex world. The symposium will be comprised of three discrete, though interconnected presentations, that work together to tell the story of this project. Three key facets of the project will be explored during the 90 minute session, as the perspectives of key stakeholders are shared. The first presentation (A/Prof Julie Davis, Dr Lyndal O’Gorman& Dr Megan Gibson) will outline the role of QUT School of Early Childhood staff and students, with attention to the ways in which the project was embedded in students’ work in the final year of their degree program of study. The second presentation (Ms Lindy Osborne) will provide insights into the Design students’ collaborative work in the project. Finally, the key role of the Lone Pine Koala Sanctuary and their commitment for EfS (Ms Peta Wilson & Dr Sue Elliott) will map out the philosophy that underpins the project. Together, the authors will conclude key project outcomes that have been achieved through this real-world, cross-disciplinary work.

D-MG Tradeoff and Optimal Codes for a Class of AF and DF Cooperative Communication Protocols

Cooperative relay communication in a fading channel environment under the orthogonal amplify-and-forward (OAF), nonorthogonal and orthogonal selection decode-and-forward (NSDF and OSDF) protocols is considered here. The diversity-multiplexing gain tradeoff (DMT) of the three protocols is determined and DMT-optimal distributed space-time (ST) code constructions are provided. The codes constructed are sphere decodable and in some instances incur minimum possible delay. Included in our results is the perhaps surprising finding that the orthogonal and the nonorthogonal amplify-and-forward (NAF) protocols have identical DMT when the time durations of the broadcast and cooperative phases are optimally chosen to suit the respective protocol. Moreover our code construction for the OAF protocol incurs less delay. Two variants of the NSDF protocol are considered: fixed-NSDF and variable-NSDF protocol. In the variable-NSDF protocol, the fraction of time occupied by the broadcast phase is allowed to vary with multiplexing gain. The variable-NSDF protocol is shown to improve on the DMT of the best previously known static protocol when the number of relays is greater than two. Also included is a DMT optimal code construction for the NAF protocol.

Representing the epistemic nature of teachers’ practical knowledge : The case of class teachers’ general pedagogy

The present study addressed the epistemology of teachers’ practical knowledge. Drawing from the literature, teachers’ practical knowledge is defined as all teachers’ cognitions (e.g., beliefs, values, motives, procedural knowing, and declarative knowledge) that guide their practice of teaching. The teachers’ reasoning that lies behind their practical knowledge is addressed to gain insight into its epistemic nature. I studied six class teachers’ practical knowledge; they teach in the metropolitan region of Helsinki. Relying on the assumptions of the phenomenographic inquiry, I collected and analyzed the data. I analyzed the data in two stages where the first stage involved an abductive procedure, and the second stage an inductive procedure for interpretation, and thus developed the system of categories. In the end, a quantitative analysis nested into the qualitative findings to study the patterns of the teachers’’ reasoning. The results indicated that teachers justified their practical knowledge based on morality and efficiency of action; efficiency of action was found to be presented in two different ways: authentic efficiency and naïve efficiency. The epistemic weight of morality was embedded in what I call “moral care”. The core intention of teachers in the moral care was the commitment that they felt about the “whole character” of students. From this perspective the “dignity” and the moral character of the students should not replaced for any other “instrumental price”. “Caring pedagogy” was the epistemic value of teachers’ reasoning in the authentic efficiency. The central idea in the caring pedagogy was teachers’ intentions to improve the “intellectual properties” of “all or most” of the students using “flexible” and “diverse” pedagogies. However, “regulating pedagogy” was the epistemic condition of practice in the cases corresponding to naïve efficiency. Teachers argued that an effective practical knowledge should regulate and manage the classroom activities, but the targets of the practical knowledge were mainly other “issues “or a certain percentage of the students. In these cases, the teachers’ arguments were mainly based on the notion of “what worked” regardless of reflecting on “what did not work”. Drawing from the theoretical background and the data, teachers’ practical knowledge calls for “praxial knowledge” when they used the epistemic conditions of “caring pedagogy” and “moral care”. It however calls for “practicable” epistemic status when teachers use the epistemic condition of regulating pedagogy. As such, praxial knowledge with the dimensions of caring pedagogy and moral care represents the “normative” perspective on teachers’ practical knowledge, and thus reflects a higher epistemic status in comparison to “practicable” knowledge, which represents a “descriptive” perception toward teachers’ practical knowledge and teaching.

The politics of race, class and special education: The selected works of Sally Tomlinson

Upon reading this esteemed collection of Sally Tomlinson’s works, published in Routledge’s prestigious World Library of Educationalists series, I was struck by three things. First, Sally is one of only three women among the 26 scholars whose collections have been published in this series to date, and the only scholar researching questions relating to disability and special education. Second, her early work on the sociology of special education Tomlinson, 1982) is just as pertinent today as her most recent research on the political scapegoating of low-attainers in a global knowledge economy (Tomlinson, 2012). Third, I was reminded of the extent to which her research has both inspired and guided me as I now grapple with the same research problems, albeit in a different country and at a different time, but always from a similar sociological standpoint (Graham & Jahnukainen, 2011; Graham & Sweller, 2011; Graham, 2012; Graham, 2014; Graham, Van Bergen & Sweller, 2014). Not surprisingly, the phrase that kept echoing through my head as I read through the 11 chapters chronicling a rich and immensely productive academic career was: ‘history repeats’. And, throughout the book are numerous examples and observations as to why it does. To paraphrase, the answer is power, status and politics.

Tripartite Entanglement versus Tripartite Nonlocality in Three-Qubit Greenberger-Horne-Zeilinger-Class States

We analyze the relationship between tripartite entanglement and genuine tripartite nonlocality for three-qubit pure states in the Greenberger-Horne-Zeilinger class. We consider a family of states known as the generalized Greenberger-Horne-Zeilinger states and derive an analytical expression relating the three-tangle, which quantifies tripartite entanglement, to the Svetlichny inequality, which is a Bell-type inequality that is violated only when all three qubits are nonlocally correlated. We show that states with three-tangle less than 1/2 do not violate the Svetlichny inequality. On the other hand, a set of states known as the maximal slice states does violate the Svetlichny inequality, and exactly analogous to the two-qubit case, the amount of violation is directly related to the degree of tripartite entanglement. We discuss further interesting properties of the generalized Greenberger-Horne-Zeilinger and maximal slice states.

Universality class of the reversible-irreversible transition in sheared suspensions

Collections of non-Brownian particles suspended in a viscous fluid and subjected to oscillatory shear at very low Reynolds number have recently been shown to exhibit a remarkable dynamical phase transition separating reversible from irreversible behavior as the strain amplitude or volume fraction are increased. We present a simple model for this phenomenon, based on which we argue that this transition lies in the universality class of the conserved directed percolation models. This leads to predictions for the scaling behavior of a large number of experimental observables. Non-Brownian suspensions under oscillatory shear may thus constitute the first experimental realization of an inactive-active phase transition which is not in the universality class of conventional directed percolation.

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.

Unidentified girls class seated at desks in classroom Institutions; Educational; Schools; Portraits; Groups

"Chanukah" written on blackboard at rear left of classroom

Unidentified girls class Institutions; Educational; Schools; Portraits; Groups

Digital Image

Predicting the cost of eradication for 41 Class 1 declared weeds in Queensland

The feasibility of state-wide eradication of 41 invasive plant taxa currently listed as ‘Class 1 declared pests’ under the Queensland Land Protection (Pest and Stock Route Management) Act 2002 was assessed using the predictive model ‘WeedSearch’. Results indicated that all but one species (Alternanthera philoxeroides) could be eradicated, provided sufficient funding and labour were available. Slightly less than one quarter (24.4%) (n = 10) of Class 1 weed taxa could be eradicated for less than $100 000 per taxon. An additional 43.9% (n = 18) could be eradicated for between $100 000 and $1M per taxon. Hence, 68.3% of Class 1 weed taxa (n = 28) could be eradicated for less than $1M per taxon. Eradication of 29.3% (n = 12) is predicted to cost more than $1M per taxon. Comparison of these WeedSearch outputs with either empirical analysis or results from a previous application of the model suggests that these costs may, in fact, be underestimates. Considering the likelihood that each weed will cost the state many millions of dollars in long-term losses (e.g. losses to primary production, environmental impacts and control costs), eradication seems a wise investment. Even where predicted costs are over $1M, eradication can still offer highly favourable benefit:cost ratios. The total (cumulative) cost of eradication of all 41 weed taxa is substantial; for all taxa, the estimated cost of eradication in the first year alone is $8 618 000. This study provides important information for policy makers, who must decide where to invest public funding.

Cervical headgear in Class II division 1 correction in children : Academic Dissertation

Class II division 1 malocclusion occurs in 3.5 to 13 percent of 7 12 year-old children. It is the most common reason for orthodontic treatment in Finland. Correction is most commonly performed using headgear treatment. The aim of this study was to investigate the effects of cervical headgear treatment on dentition, facial skeletal and soft tissue growth, and upper airway structure, in children. 65 schoolchildren, 36 boys and 29 girls were studied. At the onset of treatment a mean age was 9.3 (range 6.6 12.4) years. All the children were consequently referred to an orthodontist because of Class II division 1 malocclusion. The included children had protrusive maxilla and an overjet of more than 2mm (3 to 11 mm). The children were treated with a Kloehn-type cervical headgear as the only appliance until Class I first molar relationships were achieved. The essential features of the headgear were cervical strong pulling forces, a long upward bent outer bow, and an expanded inner bow. Dental casts and lateral and posteroanterior cephalograms were taken before and after the treatment. The results were compared to a historical, cross-sectional Finnish cohort or to historical, age- and sex-matched normal Class I controls. The Class I first molar relationships were achieved in all the treated children. The mean treatment time was 1.7 (range 0.3-3.1) years. Phase 2 treatments were needed in 52% of the children, most often because of excess overjet or overbite. The treatment decreased maxillary protrusion by inhibiting alveolar forward growth, while the rest of the maxilla and mandible followed normal growth. The palate rotated anteriorly downward. The expansion of the inner bow of the headgear induced widening of the maxilla, nasal cavity, and the upper and lower dental arches. Class II malocclusion was associated with narrower oro- and hypopharyngeal space than in the Class I normal controls. The treatment increased the retropalatal airway space, while the rest of the airway remained unaffected. The facial profile improved esthetically, while the facial convexity decreased. Facial soft tissues masked the facial skeletal convexity, and the soft tissue changes were smaller than skeletal changes. In conclusion, the headgear treatment with the expanded inner bow may be used as an easy and simple method for Class II correction in growing children.