Uniquely determined uniform probability on the natural numbers

In this paper, we address the problem of constructing a uniform probability measure on $\mathbb{N}$. Of course, this is not possible within the bounds of the Kolmogorov axioms and we have to violate at least one axiom. We define a probability measure as a finitely additive measure assigning probability $1$ to the whole space, on a domain which is closed under complements and finite disjoint unions. We introduce and motivate a notion of uniformity which we call weak thinnability, which is strictly stronger than extension of natural density. We construct a weakly thinnable probability measure and we show that on its domain, which contains sets without natural density, probability is uniquely determined by weak thinnability. In this sense, we can assign uniform probabilities in a canonical way. We generalize this result to uniform probability measures on other metric spaces, including $\mathbb{R}^n$.Comment: We added a discussion of coherent probability measures and some explanation regarding the operator we study. We changed the title to a more descriptive one. Further, we tidied up the proofs and corrected and simplified some minor issue

Assessing forensic evidence by computing belief functions

We first discuss certain problems with the classical probabilistic approach for assessing forensic evidence, in particular its inability to distinguish between lack of belief and disbelief, and its inability to model complete ignorance within a given population. We then discuss Shafer belief functions, a generalization of probability distributions, which can deal with both these objections. We use a calculus of belief functions which does not use the much criticized Dempster rule of combination, but only the very natural Dempster-Shafer conditioning. We then apply this calculus to some classical forensic problems like the various island problems and the problem of parental identification. If we impose no prior knowledge apart from assuming that the culprit or parent belongs to a given population (something which is possible in our setting), then our answers differ from the classical ones when uniform or other priors are imposed. We can actually retrieve the classical answers by imposing the relevant priors, so our setup can and should be interpreted as a generalization of the classical methodology, allowing more flexibility. We show how our calculus can be used to develop an analogue of Bayes' rule, with belief functions instead of classical probabilities. We also discuss consequences of our theory for legal practice.Comment: arXiv admin note: text overlap with arXiv:1512.01249. Accepted for publication in Law, Probability and Ris

Fire analysis of timber composite beams with interlayer slip

The purpose of this paper is to model the behaviour of timber composite beams with interlayer slip, when simultaneously exposed to static loading and fire. A transient moisture-thermal state of a timber beam is analysed by the Luikov equations, and mechanical behaviour of timber composite beam is modelled by Reissner's kinematic equations. The model can handle layers of different materials. Material properties are functions of temperature. The thermal model is validated against the experimental data presented in the literature. Generally, the model provides excellent agreement with the experimental data. It is shown that the material properties of timber play an important role in the fire resistance analysis of timber structures when exposed to fire

Inventory analysis of the timber industry in Ghana

Background, aim, and scope The timber sector, i.e., forestry and timber industry, plays an important role in the socioeconomic development of Ghana through timber products export. Timber production in this sector is associated with increasing environmental burdens in terms of use of materials and energy, production of emissions and waste, and land use changes. The purpose of this study was to compile a comprehensive life cycle inventory (LCI) to identify the most dominant environmental pressures for five major production lines in the timber industry, and to evaluate the influence of the choice of the functional unit on the results (1 m3, 1 kg, and 1 euro). LCA’s of wood typically base their functional unit on volume, but mass or money may be more appropriate for the rather different products considered in this study. Materials and methods The LCI covers five timber production lines, namely, air-dried lumber, kiln-dried lumber, plywood, veneer, and furniture parts. Three functional units were used for this study to identify the most appropriate basis for a fair comparison of the different timber products (functional units were 1 m3, 1 kg and 1 euro). Questionnaires were administered to thirty selected companies in Ghana. These companies provided data about their material uses, energy requirements, and waste production for their operations from 2000 to 2007. The collected data were first converted into total annual average values, and next extrapolated to reflect the national average data for all 104 active companies. Finally, these data were expressed per functional unit for each of the five product lines on the basis of their production outputs (in volume, mass or money according to functional unit applied). Forest land used changes data was taken from the Ghana Timber Industry Development Division. Emissions for the several activities were taken from literature. Results and discussion Land use change for timber production in Ghana between the estimated periods turned out to be 34.0¿×¿103 ha per year, which will lead to complete deforestation in the year 2023 if continued. The total energy consumed by the timber sector per year was estimated at 1.9¿×¿109 MJ per year. The results showed that CO2 emissions by the timber sector activities per year accounted for 745k tons per year and dominate overall greenhouse gases emissions in the timber sector (changes in carbons storage related to land use changes not included). Wood waste by the timber sector accounted for 0.8 million m3 per year. The enormous wastage of wood contributes enormously to the rapid depletion of the country’s timber resources. The choice of the functional unit influences inventory results. The money-based functional unit, which also seems more appropriate for the different products considered, favors the value-added. Value-added products with strict sustainable forest management policy hold a promising future in terms of sustainability for the timber industry in Ghana. Conclusions This study has yielded good quality primary data unique for LCA research in Africa. This will enhance LCA approaches in Ghana, and allows here identification of the main environmental pressures and their dominantly contributing processes in the timber sector. Land use changes due to forestry form a critical issue and require urgent attention. The chosen functional units’ plays a crucial role in the environmental comparison of production line in the timber sector in Ghana. Recommendations and perspectives A comprehensive and transparent inventory for the timber industry provides the industry with an overview of areas in which material and thus economic savings can be made for the good of both environment and the industry finances. Good data keeping in the Ghanaian timber industry will help to build the required research capacity to develop local familiarity and competence in LCA techniques and applying these techniques will help to further certify tropical timber international markets

Is there a commercial case for tropical timber certification?

The authors estimate the potential commercial benefits that tropical timber producing countries could enjoy by adopting timber certification schemes. Such benefits are crucial for encouraging the supply of certified timber. Timber certification is a reality: various countries and organizations have launched initiatives for it. The initial response among producing countries was less than positive, but some have come to realize its potential benefits and have begun to adopt timber certification schemes. Tropical timber trade accounts for only a small fraction of tropical timber production, and most of that trade is concentrated among developing countries in Asia and Japan - markets where demand for certified timber is currently weak. Only a small part of the trade reaches the eco-sensitive markets of Europe and the United States, where there is demand for certified timber. Developing countries can benefit commercially from timber certification in two ways: through the"green premium"(consumers'willingness to pay a premium for certified timber"and by averting losses of market share in the tropical timber market from not having timber certified. Based on surveys, on discussions with nongovernmental organizations, on market participants and analysts, and on estimates of price elasticity, the authors develop a scenario for estimating the potential commercial benefits from adopting timber certification. Under this scenario, benefits would not exceed US$500 million a year (roughly 4 percent of all tropical-timber-related revenues earned by developing countries). Timber certification is not expected to provide significant commercial benefits to developing countries in the near future. But timber certification could provide significant rents to individual firms that develop market niche strategies. And producing countries that pursue certification may enjoy longer-term social, economic, and environmental benefits by adopting the better forest management practices required for timber certification.Environmental Economics&Policies,Silviculture,Agribusiness&Markets,Roads&Highways,Forests and Forestry,Environmental Economics&Policies,Forestry,Silviculture,Agribusiness&Markets,Roads&Highways

A Socio-economic Analysis of French Public Timber Sales

This socio-economic study aims to better understand the functioning and the evolution of timber sales held by the French public forest service. The auction mechanism is the historical institution which has been used in France for centuries. The recent will to develop supply contracts through private agreements is a major change in the French timber industry. It accurately raises questions about the timber prices issue.Timber sales, timber auctions, timber prices, French public forests, French wood industry, institution