Co-2-plex polynomials

This paper offers a generalization of the independence polynomial, the co-k-plex polynomial. The resulting family of polynomials carries combinatorial information on a class of independence systems defined over the vertex set of a finite graph. Specifically, we offer a recursion formula and examples of the co-2-plex polynomial on certain graphs. In addition, we characterize the class of graphs whose co-2-plex polynomial will have all real roots.     

Meta-Analysis of Food Safety Information Based on a Combination of a Relational Database and a Predictive Modeling Tool

The management of microbial risk in food products requires the ability to predict growth kinetics of pathogenic microorganisms in the event of contamination and growth initiation. Useful data for assessing these issues may be found in the literature or from experimental results. However, the large number and variety of data make further development difficult. Statistical techniques, such as meta-analysis, are then useful to realize synthesis of a set of distinct but similar experiences. Moreover, predictive modeling tools can be employed to complete the analysis and help the food safety manager to interpret the data. In this article, a protocol to perform a meta-analysis of the outcome of a relational database, associated with quantitative microbiology models, is presented. The methodology is illustrated with the effect of temperature on pathogenic Escherichia coli and Listeria monocytogenes, growing in culture medium, beef meat, and milk products. Using a database and predictive models, simulations of growth in a given product subjected to various temperature scenarios can be produced. It is then possible to compare food products for a given microorganism, according to its growth ability in these products, and to compare the behavior of bacteria in a given foodstuff. These results can assist decisions for a variety of questions on food safety.     

Risk-Based Approaches to Deal with Uncertainty in a Data-Poor System: Stakeholder Involvement in Hazard Identification for Marine National Parks and Marine Sanctuaries in Victoria, Australia

Management responsibilities for the system of marine national parks and sanctuaries declared in Victoria, Australia in 2002 have created imperatives for robust, scientifically defendable approaches to identifying threats to valued ecological attributes of the parks, setting management priorities, and developing monitoring systems. We are developing a protocol for ecological risk assessment in the parks that has due regard for the perception of risks by individuals, and ensures that stakeholder values are an intrinsic part of decision making. The inclusive and transparent protocol provides an opportunity for stakeholder involvement in the identification of valued attributes, as well as in the assessment of associated risks. Our approach brings together ideas about how science enters the community engagement domain in ways that promote collaboration and transparency in decision making. A series of stakeholder workshops across the state drew on the expertise of agency staff, community groups, fishers, industry representatives, academics, and knowledgeable park neighbors to identify hazards of major concern in the parks. Many hazards involved predictable, tangible threats like pollution and exotic species, but the approach also identified a number of less obvious threats related to governance issues and the knowledge-base for the parks. Importantly, the workshops with their broad range of stakeholders identified threats not previously considered by the management agency in its internal assessments, and several of these "new" threats are already the subject of action by the agency. The deliberate incorporation of local knowledge and local networks in the risk assessment process also provided opportunities for greater engagement of stakeholders with the management agency.     

Exordium for DNA Codes

We describe how deletion-correcting codes may be enhanced to yield codes with double-strand DNA-sequence codewords. This enhancement involves abstractions of the pertinent aspects of DNA; it nevertheless ensures specificity of binding for all pairs of single strands derived from its codewords—the key desideratum of DNA codes– i.e. with binding feasible only between reverse complementary strands. We defer discussing the combinatorial-optimization superincumbencies of code construction. Generalization of deletion similarity to an optimal sequence-alignment score could readily effect advantageous improvements (Kaderali, Master's Thesis, Informatics, U. Köln, 2001) but would render the combinatorics opaque. We mention motivating applications of DNA codes.     

Why Reduced-Form Regression Models of Health Effects Versus Exposures Should Not Replace QRA: Livestock Production and Infant Mortality as an Example

Do pollution emissions from livestock operations increase infant mortality rate (IMR)? A recent regression analysis of changes in IMR against changes in aggregate “animal units” (a weighted sum of cattle, pig, and poultry numbers) over time, for counties throughout the United States, suggested the provocative conclusion that they do: “[A] doubling of production leads to a 7.4% increase in infant mortality.” Yet, we find that regressing IMR changes against changes in specific components of “animal units” (cattle, pigs, and broilers) at the state level reveals statistically significant negative associations between changes in livestock production (especially, cattle production) and changes in IMR. We conclude that statistical associations between livestock variables and IMR variables are very sensitive to modeling choices (e.g., selection of explanatory variables, and use of specific animal types vs. aggregate “animal units). Such associations, whether positive or negative, do not warrant causal interpretation. We suggest that standard methods of quantitative risk assessment (QRA), including emissions release (source) models, fate and transport modeling, exposure assessment, and dose-response modeling, really are important—and indeed, perhaps, essential—for drawing valid causal inferences about health effects of exposures to guide sound, well-informed public health risk management policy. Reduced-form regression models, which skip most or all of these steps, can only quantify statistical associations (which may be due to model specification, variable selection, residual confounding, or other noncausal factors). Sound risk management requires the extra work needed to identify and model valid causal relations.     

Game Theory and Risk Analysis

Risk analysts often analyze adversarial risks from terrorists or other intelligent attackers without mentioning game theory. Why? One reason is that many adversarial situations—those that can be represented as attacker‐defender games, in which the defender first chooses an allocation of defensive resources to protect potential targets, and the attacker, knowing what the defender has done, then decides which targets to attack—can be modeled and analyzed successfully without using most of the concepts and terminology of game theory. However, risk analysis and game theory are also deeply complementary. Game‐theoretic analyses of conflicts require modeling the probable consequences of each choice of strategies by the players and assessing the expected utilities of these probable consequences. Decision and risk analysis methods are well suited to accomplish these tasks. Conversely, game‐theoretic formulations of attack‐defense conflicts (and other adversarial risks) can greatly improve upon some current risk analyses that attempt to model attacker decisions as random variables or uncertain attributes of targets (“threats”) and that seek to elicit their values from the defender's own experts. Game theory models that clarify the nature of the interacting decisions made by attackers and defenders and that distinguish clearly between strategic choices (decision nodes in a game tree) and random variables (chance nodes, not controlled by either attacker or defender) can produce more sensible and effective risk management recommendations for allocating defensive resources than current risk scoring models. Thus, risk analysis and game theory are (or should be) mutually reinforcing.     

Unity is strength: staff college and the British officer corps

Utilizing Bourdieu's concept of the habitus, Keith Macdonald has recently examined the elite social origins of the British officer corps. His analysis is valid as far at it goes but it ignores the professional practices of British officers. This article examines Britain's Joint Services Command and Staff College to assess the unification of the three services around common forms of military practice. It argues that while the new staff college has been effective in disseminating new forms of professional expertise among British officers, various practices have been institutionalized which actively undermine the unity of the officer corps.     

Stability of Approximations of Average Run Length of Risk-Adjusted CUSUM Schemes Using the Markov Approach: Comparing Two Methods of Calculating Transition Probabilities

Risk-adjusted CUSUM schemes are designed to monitor the number of adverse outcomes following a medical procedure. An approximation of the average run length (ARL), which is the usual performance measure for a risk-adjusted CUSUM, may be found using its Markov property. We compare two methods of computing transition probability matrices where the risk model classifies patient populations into discrete, finite levels of risk. For the first method, a process of scaling and rounding off concentrates probability in the center of the Markov states, which are non overlapping sub-intervals of the CUSUM decision interval, and, for the second, a smoothing process spreads probability uniformly across the Markov states. Examples of risk-adjusted CUSUM schemes are used to show, if rounding is used to calculate transition probabilities, the values of ARLs estimated using the Markov property vary erratically as the number of Markov states vary and, on occasion, fail to converge for mesh sizes up to 3,000. On the other hand, if smoothing is used, the approximate ARL values remain stable as the number of Markov states vary. The smoothing technique gave good estimates of the ARL where there were less than 1,000 Markov states.     

Asymptotic properties of bivariate k-means clusters

A bounded region in R² with a uniform density function defined over it is partitioned into k sub-regions such that the within cluster sum of squares is minimized. An asymptotic (k+∞) lower bound for the within cluster sum of squares of this optimal k-means partition is obtained. This lower bound is useful in suggesting that the graph-configuration of the optimal k-partition would consist of regular hexagons of equal size when k is large enough. An empirical study illustrating these asymptotic properties of blvariate k-means cluster is also presented.