Similar Markov chains

enin et al. (2000) recently introduced the idea of similarity in the context of birth-death processes. This paper examines the extent to which their results can be extended to arbitrary Markov chains. It is proved that, under a variety of conditions, similar chains are strongly similar in a sense which is described, and it is shown that minimal chains are strongly similar if and only if the corresponding transition-rate matrices are strongly similar. A general framework is given for constructing families of strongly similar chains; it permits the construction of all such chains in the irreducible case.

PCDDs in the water/sediment-seagrass-dugong (Dugong dugon) food chain on the Great Barrier Reef (Australia)

Polychlorinated dibenzo-p-dioxin (PCDD) and dibenzofuran (PCDF) concentrations were measured in sediment and seagrass from five locations in or adjacent to the Great Barrier Reef Marine Park. A full spectrum of Cl(5-8)DDs were present in all samples and, in particular, elevated levels of Cl8DD were found. PCDFs could not be quantified in any samples. The PCDD concentrations ranged over two orders of magnitude between sites, and there was a good correlation between sediment and seagrass levels. There were large quantities of sediment present on the seagrass (20-62% on a dry wt. basis), and it was concluded that this was a primary source of the PCDDs in the seagrass samples. The PCDD levels in the seagrass samples were compared with the levels in the tissue of three dugongs stranded in the same region. The relative accumulation of the 2,3,7,8-substituted PCDD congeners in the dugongs decreased by over two orders of magnitude with increasing degree of chlorination. This was attributed to the reduced absorption of the higher chlorinated congeners in the digestive tract, a behaviour that has been observed in other mammals such as domestic cows. (C) 2001 Elsevier Science Ltd. All rights reserved.

Begging and food distribution in crimson rosella (Platycercus elegans) broods: why don't hungry chicks beg more?

Altricial nestlings solicit food by begging and engaging in scramble competition. Solicitation displays can thus signal both hunger and competitive ability. I examined nestling solicitation and parental responses in crimson rosellas (Platycercus elegans), a species in which parents engage in complex patterns of food allocation and appear to control the distribution of food. By manipulating the hunger of individual chicks and entire broods, I assessed how chick behaviours and parental food allocation varied with hatching rank, level of hunger, and intensity of nestling competition. Last-hatched chicks begged more than first-hatched chicks irrespective of individual hunger levels. The two parents combined fed individually hungry chicks more, but mothers and fathers varied in their responses to begging chicks: fathers fed last-hatched chicks in proportion to their begging intensity, whereas mothers fed chicks equally. Since fathers generally allocate more food to first-hatched chicks, fathers appear to use begging rates to adjust food allocation to non-preferred chicks within the brood. When I manipulated brood hunger levels, begging rates increased for first- and last-hatched chicks suggesting that chick begging rates are sensitive to the level of competition. This study shows that begging by rosella chicks does not correlate with hunger in a straightforward way and that the primary patterns of food allocation by parents art: not influenced by chick begging. Thus the benefits of increased begging may be limited for nestlings in this species.

Path integrals for continuous-time Markov chains

This note presents a method of evaluating the distribution of a path integral for Markov chains on a countable state space.

Set-valued Markov chains and negative semitrajectories of discretized dynamical systems

Computer simulation of dynamical systems involves a phase space which is the finite set of machine arithmetic. Rounding state values of the continuous system to this grid yields a spatially discrete dynamical system, often with different dynamical behaviour. Discretization of an invertible smooth system gives a system with set-valued negative semitrajectories. As the grid is refined, asymptotic behaviour of the semitrajectories follows probabilistic laws which correspond to a set-valued Markov chain, whose transition probabilities can be explicitly calculated. The results are illustrated for two-dimensional dynamical systems obtained by discretization of fractional linear transformations of the unit disc in the complex plane.

Relationship of high energy expenditure and variation in dietary intake with reporting accuracy on 7 day food records and diet histories in a group of healthy adult volunteers

Objectives: To assess the accuracy of reporting from both a diet history and food record and identify some of the characteristics of more accurate reporters in a group of healthy adult volunteers for an energy balance study. Design: Prospective measurements in free-living people. Setting: Wollongong, Australia. Subjects: Fifteen healthy volunteers (seven male, eight female; aged 22 -59 y; body mass index (BMI) 19 - 33 kg/m(2)) from the local community in the city of Wollongong, Australia. Interventions: Measurement of energy intake via diet history interview and 7 day food records, total energy expenditure by the doubly labelled water technique over 14 days, physical activity by questionnaire, and body fat by dual-energy X-ray absorptiometry. Results: Increased misreporting of energy intake was associated with increased energy expenditure (r = 0.90, P < 0.0001, diet history; r(s)=0.79, P=0.0005, food records) but was not associated with age, sex, BMI or body fat. Range in number of recorded dinner foods correlated positively with energy expenditure (r(s)=0.63, P=0.01) and degree of misreporting (r(s)=0.71, P=0.003, diet history; r(s)=0.63, P=0.01, food records). Variation in energy intake at dinner and over the whole day identified by the food records correlated positively with energy expenditure (r=0.58, P = 0.02) and misreporting on the diet history (r=0.62, P=0.01). Conclusions: Subjects who are highly active or who have variable dietary and exercise behaviour may be less accurate in reporting dietary intake. Our findings indicate that it may be necessary to screen for these characteristics in studies where accuracy of reporting at an individual level is critical. Sponsorship: The study was supported in part by Australian Research Council funds made available through the University of Wollongong.

Integrals for continuous-time Markov chains

This paper presents a method of evaluating the expected value of a path integral for a general Markov chain on a countable state space. We illustrate the method with reference to several models, including birth-death processes and the birth, death and catastrophe process. (C) 2002 Elsevier Science Inc. All rights reserved.

Lexicographic decomposition of chains and the concept of a planar chain

In an earlier paper [Journal of Mathematical Economics, 37 (2002) 17-38], we proved that if a preference relation on a commodity space is non-representable by a real-valued function then that chain is necessarily a long chain, a planar chain, an Aronszajn-like chain or a Souslin chain. In this paper, we study the class of planar chains, the simplest example of which is the Debreu chain (R-2, <(l)). (C) 2002 Elsevier Science B.V. All rights reserved.

Eating 'Green': Motivations behind organic food consumption in Australia

Central to the development of green lifestyles is the consumption of foods that by dint of their status as chemical-free, locally produced and/or free of genetically modified ingredients, reduce the environmental impact of food provision. Yet there are many other factors, such as health concerns, that may also encourage the consumption of 'green' foods. This paper explores the ways in which Australian consumers construct organic food-a sector of the food industry that is currently growing at between 20 and 50 percent per annum but is struggling to keep up with rising consumer demand. In order to examine the significance of 'green' signifiers in the consumption practices of Australian consumers a series of focus group interviews and a national consumer survey were conducted. These examined both those characteristics of food that were valued in general, and those meanings that were associated with organic food in particular. In very general terms, analysis reveals that while consumers believed organic foods to be healthy and environmentally sound-both of which were considered desirable-these characteristics were subsumed by an overarching concern with convenience. This does not mean that consumers did not hold genuinely positive environmental attitudes. Rather, it reflects a range of contradictory beliefs and practices that appeared to derive from the discursive conflict between conventional and organic food industries over environmental, health and safety claims. The paper concludes by identifying the barriers and opportunities for expanding the organic industry in Australia in the context of the ways organics is constructed by consumers.