A multifractal zeta function for Gibbs measures supported on cookie-cutter sets

Starting with the work of Lapidus and van Frankenhuysen a number of papers have introduced zeta functions as a way of capturing multifractal information. In this paper we propose a new multifractal zeta function and show that under certain conditions the abscissa of convergence yields the Hausdorff multifractal spectrum for a class of measures.

Realizability of Point Processes

There are various situations in which it is natural to ask whether a given collection of k functions, ρ j (r 1,…,r j ), j=1,…,k, defined on a set X, are the first k correlation functions of a point process on X. Here we describe some necessary and sufficient conditions on the ρ j ’s for this to be true. Our primary examples are X=ℝ d , X=ℤ d , and X an arbitrary finite set. In particular, we extend a result by Ambartzumian and Sukiasian showing realizability at sufficiently small densities ρ 1(r). Typically if any realizing process exists there will be many (even an uncountable number); in this case we prove, when X is a finite set, the existence of a realizing Gibbs measure with k body potentials which maximizes the entropy among all realizing measures. We also investigate in detail a simple example in which a uniform density ρ and translation invariant ρ 2 are specified on ℤ; there is a gap between our best upper bound on possible values of ρ and the largest ρ for which realizability can be established.

Dichotomous-choice contingent valuation with 'don't know' responses and misreporting

A new approach is presented that simultaneously deals with Misreporting and Don't Know (DK) responses within a dichotomous-choice contingent valuation framework. Utilising a modification of the standard Bayesian Probit framework, a Gibbs with Metropolis-Hastings algorithm is used to estimate the posterior densities for the parameters of interest. Several model specifications are applied to two contingent valuation datasets: one on wolf management plans, and one on the US Fee Demonstration Program. We find that DKs are more likely to be from people who would be predicted to have positive utility for the bid. Therefore, a DK is more likely to be a YES than a NO. We also find evidence of misreporting, primarily in favour of the NO option. The inclusion of DK responses has an unpredictable impact on willingness-to-pay estimates, since it impacts differently on the results for the two datasets we examine. Copyright (C) 2009 John Wiley & Sons, Ltd.

Very long chain n-3 polyunsaturated fatty acids in the food chain in the UK and the potential of animal-derived foods to increase intake

The very long chain (VLC) n-3 polyunsaturated fatty acids (PUFA), particularly eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA), are widely recognised to have beneficial effects on human health. However, recommended intakes of VLC n-3 PUFA (450 mg/day) are not being met by the diet in the majority of the population mainly because of low consumption of oil-rich fish. Current mean intake of VLC n-3 PUFA by adults is estimated to be about 282 mg/day with EPA and DHA contributing about 244 mg/day. Furthermore, the fact that only about 27% of adults eat any oil-rich fish (excluding canned tuna) and knowledge of the poor conversion of α-linolenic acid to EPA and DHA in vivo, particularly in men, leads to the need to review current dietary sources of these fatty acids. Animal-derived foods are likely to have an important function in increasing intake and studies have shown that feeding fish oils to animals can increase the EPA and DHA content of the resulting food products. This paper highlights the importance of examining current and projected consumption trends of meat and other animal products when exploring the potential impact of enriched foods by means of altering animal diets. When related to current food consumption data, potential dietary intakes of EPA+DHA from foods derived from animals fed enriched diets are calculated to be about 231 mg/day. If widely consumed, such foods could have a significant impact on progression of conditions such as cardiovascular disease. Consideration is also given to the sources of VLC n-3 PUFA in animal diets, with the sustainability of fish oil being questioned and the need to investigate the use of alternative dietary sources such as those of algal origin.

Current intakes of EPA and DHA in European populations and the potential of animal-derived foods to increase them

The beneficial effects of long-chain (C chain >= 20) n-3 PUFA are well documented and, overall, increased intake reduces risk of CVD. Recent evidence also points to a role in reducing, age-related decline in cognitive function. The two key fatty acids are EPA (20:5) and DHA (22:6), with current UK recommendation for adults being 450 mg EPA + DHA/d. Whilst some EPA and DHA can be synthesised in vivo from alpha-linolenic acid, recent data indicate this source to be very limited, Suggesting that EPA and DHA should be classified as dietary essentials. In many parts of Europe the daily intake of EPA + DHA by adults and especially young adults (18-24 years) is < 100 mg/d, since many never eat oily fish. Poultry meat contributes small but worthwhile amounts of EPA+DHA. Studies to enrich the EPA+DHA content of animal-derived foods mainly use fish oil in the diet of the animal. Recent work has shown that such enrichment has the potential to provide to the UK adult diet a daily intake of EPA+DHA of about 230 mg, with poultry meat providing the largest amount (74 mg). There are. however. concerns that the Continued and possibly increased use of fish oils in animals diets is not Sustainable and alternative approaches are being examined, including the genetic modification of certain plants to allow them to synthesise EPA and DHA from shorter-chain precursors.

Current intakes of EPA and DHA in European populations and the potential of animal-derived foods to increase them

The beneficial effects of long-chain (C chain >= 20) n-3 PUFA are well documented and, overall, increased intake reduces risk of CVD. Recent evidence also points to a role in reducing, age-related decline in cognitive function. The two key fatty acids are EPA (20:5) and DHA (22:6), with current UK recommendation for adults being 450 mg EPA + DHA/d. Whilst some EPA and DHA can be synthesised in vivo from alpha-linolenic acid, recent data indicate this source to be very limited, Suggesting that EPA and DHA should be classified as dietary essentials. In many parts of Europe the daily intake of EPA + DHA by adults and especially young adults (18-24 years) is < 100 mg/d, since many never eat oily fish. Poultry meat contributes small but worthwhile amounts of EPA+DHA. Studies to enrich the EPA+DHA content of animal-derived foods mainly use fish oil in the diet of the animal. Recent work has shown that such enrichment has the potential to provide to the UK adult diet a daily intake of EPA+DHA of about 230 mg, with poultry meat providing the largest amount (74 mg). There are. however. concerns that the Continued and possibly increased use of fish oils in animals diets is not Sustainable and alternative approaches are being examined, including the genetic modification of certain plants to allow them to synthesise EPA and DHA from shorter-chain precursors.

The role of meat as a source of n-3 polyunsaturated fatty acids in the human diet

It is considered that consumption of very long chain (VLC, carbon chain length >= 20) n - 3 PUFAs in most Western populations is sub-optimal and benefits in relation to chronic disease would be gained from increased consumption. This review examines the current contribution that meat makes to dietary intake of VLC n - 3 PUFA and given its current low contribution, how ruminant meat may be enriched. Enrichment both directly with VLC n - 3 fatty acids and indirectly by increasing intake by the animals of alpha-linolenic acid (ALNA; C 18:3 n - 3) are considered. Since it now appears that dietary ALNA is a very limited source of VLC n - 3 PUFA in humans, the indirect route is controversial but since some forages-are rich sources of ALNA this route has many sustainability and environmental attractions. Consideration is also given to the increased concentrations of trans and conjugated fatty acids that will arise from enriching ruminant meat with PUFA.

The role of meat as a source of n-3 polyunsaturated fatty acids in the human diet

It is considered that consumption of very long chain (VLC, carbon chain length >= 20) n - 3 PUFAs in most Western populations is sub-optimal and benefits in relation to chronic disease would be gained from increased consumption. This review examines the current contribution that meat makes to dietary intake of VLC n - 3 PUFA and given its current low contribution, how ruminant meat may be enriched. Enrichment both directly with VLC n - 3 fatty acids and indirectly by increasing intake by the animals of alpha-linolenic acid (ALNA; C 18:3 n - 3) are considered. Since it now appears that dietary ALNA is a very limited source of VLC n - 3 PUFA in humans, the indirect route is controversial but since some forages-are rich sources of ALNA this route has many sustainability and environmental attractions. Consideration is also given to the increased concentrations of trans and conjugated fatty acids that will arise from enriching ruminant meat with PUFA.

An old problem revisited - and solved: Upton and Dalton's linear production response: A note

This note presents a robust method for estimating response surfaces that consist of linear response regimes and a linear plateau. The linear response-and-plateau model has fascinated production scientists since von Liebig (1855) and, as Upton and Dalton indicated, some years ago in this Journal, the response-and-plateau model seems to fit the data in many empirical studies. The estimation algorithm evolves from Bayesian implementation of a switching-regression (finite mixtures) model and demonstrates routine application of Gibbs sampling and data augmentation-techniques that are now in widespread application in other disciplines.

Bayesian ranking and selection of fishing boat efficiencies

The steadily accumulating literature on technical efficiency in fisheries attests to the importance of efficiency as an indicator of fleet condition and as an object of management concern. In this paper, we extend previous work by presenting a Bayesian hierarchical approach that yields both efficiency estimates and, as a byproduct of the estimation algorithm, probabilistic rankings of the relative technical efficiencies of fishing boats. The estimation algorithm is based on recent advances in Markov Chain Monte Carlo (MCMC) methods—Gibbs sampling, in particular—which have not been widely used in fisheries economics. We apply the method to a sample of 10,865 boat trips in the US Pacific hake (or whiting) fishery during 1987–2003. We uncover systematic differences between efficiency rankings based on sample mean efficiency estimates and those that exploit the full posterior distributions of boat efficiencies to estimate the probability that a given boat has the highest true mean efficiency.

Detecting recombination in 4-taxa DNA sequence alignments with Bayesian hidden Markov models and Markov chain Monte Carlo

This article presents a statistical method for detecting recombination in DNA sequence alignments, which is based on combining two probabilistic graphical models: (1) a taxon graph (phylogenetic tree) representing the relationship between the taxa, and (2) a site graph (hidden Markov model) representing interactions between different sites in the DNA sequence alignments. We adopt a Bayesian approach and sample the parameters of the model from the posterior distribution with Markov chain Monte Carlo, using a Metropolis-Hastings and Gibbs-within-Gibbs scheme. The proposed method is tested on various synthetic and real-world DNA sequence alignments, and we compare its performance with the established detection methods RECPARS, PLATO, and TOPAL, as well as with two alternative parameter estimation schemes.