A lower bound of the surviving rate of a planar graph with girth at least seven

Let G be a connected graph with n≥2 vertices. Suppose that a fire breaks out at a vertex v of G. A firefighter starts to protect vertices. At each time interval, the firefighter protects one vertex not yet on fire. At the end of each time interval, the fire spreads to all the unprotected vertices that have a neighbor on fire. Let sn(v) denote the maximum number of vertices in G that the firefighter can save when a fire breaks out at vertex v. The surviving rate ρ(G) of G is defined to be ∑ _v∈V(G)sn(v)/n ², which is the average proportion of saved vertices. In this paper, we show that if G is a planar graph with n≥2 vertices and having girth at least 7, then $\rho(G)>\frac{1}{301}$ .     

Task partitioning in new product development teams: A knowledge and learning perspective

R&D alliances and outsourcing elements of the new product development process are now commonplace practices among many firms. However, little previous work has examined how these organizational choices influence project knowledge and learning. Based on a comparison of three new product development projects in the software industry, this paper examines how task partitioning in the project influences learning and knowledge development within the firm. The paper suggests that internal development projects encourage synthetic learning and development of architectural and tacit knowledge; in contrast, outsourcing and joint ventures encourage analytic learning and development of component and explicit knowledge.     

When bubbles burst: Mimetic insights into minimising confidentiality breaches

This paper presents a theoretical model to help managers visualise and manage confidential situations more effectively. The model metaphorically likens a confidential setting to the properties of a soap bubble, e.g. elastic expansion or contraction, minimal surface area to contain a given volume, fragility, surface tension, pressure, stress, strain and the potential for bursting thereby releasing the contents to the external environment. We explore the conceptual developments in two phases. Firstly, looking at how a bubble and confidential scenario form and grow. Secondly, we consider how a bubble may burst and map these forces to ways in which confidentiality may be breached. Many attributes are mapped, the key ones being: the embedded value within the system, the criticality of maintaining confidentiality, increasing pressure, the corresponding stress/strain dynamics and the levels of trust between stakeholders. Key research propositions are derived from the model which aims to minimise the risk of a confidentiality breach.     

The nature, extent and determinants of violence against psychiatric personnel

Violence against psychiatric staff seems to be on the increase. Such abuse can lead to mental health consequences for the staff and a reluctance to be closely involved with patients. Few Swedish investigations have examined violence against mental nurses and psychiatrists, or undertaken comparative studies between them. In this study we examined the extent, nature and determinants (i.e. risk factors) of violence against psychiatric nurses (n = 731) and psychiatrists (n = 320) working in the eight health care districts of Stockholm. These caregivers were assessed cross-sectionally by means of a questionnaire covering various areas (e.g. violence and work environment). The majority of the participants (85%) reported having been exposed to violence during their careers, with 57% being victimized in the past 12 months. Physical violence was common, and factors such as negative attitudes to work and diminished sense of autonomy were associated with an increased vulnerability to violence. Nurses and psychiatrists did not differ in violence variables. In spite of the weaknesses of the design (cross-sectional self-selecting sample), this study corroborates previous findings and identifies personal factors associated with violence that have received little attention in the literature (e.g. lack of respect for the organization of care).     

Two-stage evaluation of bank branch efficiency using data envelopment analysis

There are two key motivations for this paper: (1) the need to respond to the often observed rejections of efficiency studies’ results by management as they claim that a single-perspective evaluation cannot fully reflect the operating units’ multi-function nature; and (2) a detailed bank branch performance assessment that is acceptable to both line managers and senior executives is still needed. In this context, a two-stage Data Envelopment Analysis approach is developed for simultaneously benchmarking the performance of operating units along different dimensions (for line managers) and a modified Slacks-Based Measure model is applied for the first time to aggregate the obtained efficiency scores from stage one and generate a composite performance index for each unit. This approach is illustrated by using the data from a major Canadian bank with 816 branches operating across the nation. Three important branch performance dimensions are evaluated: Production, Profitability, and Intermediation. This approach improves the reality of the performance assessment method and enables branch managers to clearly identify the strengths and weaknesses in their operations. Branch scale efficiency and the impacts of geographic location and market size on branch performance are also investigated. This multi-dimensional performance evaluation approach may improve management acceptance of the practical applications of DEA in real businesses.     

Enterprising Education: Doing Away with the Public School System

We critically examine the accepted notion that primary education is a legitimate and necessary function of the state. The notion is based upon three tenets: 1) public education is a necessary condition for democracy, 2) the market will not provide equal access and quality of education to all, and 3) education represents an external economy. Each tenet is addressed and evaluated according to its merits. In doing so, we also contrast the fulfillment of the ends implicit in the tenets under state and market provisions. We conclude that the state provision of primary education cannot be justified by these goals, and that market provision is a preferable alternative. This revised version was published online in July 2006 with corrections to the Cover Date.     

Compliance Versus Risk in Assessing Occupational Exposures

Assessments of occupational exposures to chemicals are generally based upon the practice of compliance testing in which the probability of compliance is related to the exceedance [γ, the likelihood that any measurement would exceed an occupational exposure limit (OEL)] and the number of measurements obtained. On the other hand, workers’ chronic health risks generally depend upon cumulative lifetime exposures which are not directly related to the probability of compliance. In this paper we define the probability of “overexposure” (θ) as the likelihood that individual risk (a function of cumulative exposure) exceeds the risk inherent in the OEL (a function of the OEL and duration of exposure). We regard θ as a relevant measure of individual risk for chemicals, such as carcinogens, which produce chronic effects after long-term exposures but not necessarily for acutely-toxic substances which can produce effects relatively quickly. We apply a random-effects model to data from 179 groups of workers, exposed to a variety of chemical agents, and obtain parameter estimates for the group mean exposure and the within- and between-worker components of variance. These estimates are then combined with OELs to generate estimates of γ and θ. We show that compliance testing can significantly underestimate the health risk when sample sizes are small. That is, there can be large probabilities of compliance with typical sample sizes, despite the fact that large proportions of the working population have individual risks greater than the risk inherent in the OEL. We demonstrate further that, because the relationship between θ and γ depends upon the within- and between-worker components of variance, it cannot be assumed a priori that exceedance is a conservative surrogate for overexposure. Thus, we conclude that assessment practices which focus upon either compliance or exceedance are problematic and recommend that employers evaluate exposures relative to the probabilities of overexposure.     

A generalisation of T‐optimality for discriminating between competing models with an application to pharmacokinetic studies

The T‐optimality criterion is used in optimal design to derive designs for model selection. To set up the method, it is required that one of the models is considered to be true. We term this local T‐optimality. In this work, we propose a generalisation of T‐optimality (termed robust T‐optimality) that relaxes the requirement that one of the candidate models is set as true. We then show an application to a nonlinear mixed effects model with two candidate non‐nested models and combine robust T‐optimality with robust D‐optimality. Optimal design under local T‐optimality was found to provide adequate power when the a priori assumed true model was the true model but poor power if the a priori assumed true model was not the true model. The robust T‐optimality method provided adequate power irrespective of which model was true. The robust T‐optimality method appears to have useful properties for nonlinear models, where both the parameter values and model structure are required to be known a priori, and the most likely model that would be applied to any new experiment is not known with certainty. Copyright © 2012 John Wiley & Sons, Ltd.