Optimal strategies for a game on amenable semigroups

The semigroup game is a two-person zero-sum game defined on a semigroup S as follows: Players 1 and 2 choose elements x and y in S, respectively, and player 1 receives a payoff f(xy) defined by a function f from S to [-1,1]. If the semigroup is amenable in the sense of Day and von Neumann, one can extend the set of classical strategies, namely countably additive probability measures on S, to include some finitely additive measures in a natural way. This extended game has a value and the players have optimal strategies. This theorem extends previous results for the multiplication game on a compact group or on the positive integers with a specific payoff. We also prove that the procedure of extending the set of allowed strategies preserves classical solutions: if a semigroup game has a classical solution, this solution solves also the extended game.Comment: 17 pages. To appear in International Journal of Game Theor

Against the Tide. A Critical Review by Scientists of How Physics and Astronomy Get Done

Nobody should have a monopoly of the truth in this universe. The censorship and suppression of challenging ideas against the tide of mainstream research, the blacklisting of scientists, for instance, is neither the best way to do and filter science, nor to promote progress in the human knowledge. The removal of good and novel ideas from the scientific stage is very detrimental to the pursuit of the truth. There are instances in which a mere unqualified belief can occasionally be converted into a generally accepted scientific theory through the screening action of refereed literature and meetings planned by the scientific organizing committees and through the distribution of funds controlled by "club opinions". It leads to unitary paradigms and unitary thinking not necessarily associated to the unique truth. This is the topic of this book: to critically analyze the problems of the official (and sometimes illicit) mechanisms under which current science (physics and astronomy in particular) is being administered and filtered today, along with the onerous consequences these mechanisms have on all of us.\ud \ud The authors, all of them professional researchers, reveal a pessimistic view of the miseries of the actual system, while a glimmer of hope remains in the "leitmotiv" claim towards the freedom in doing research and attaining an acceptable level of ethics in science

Planar projections of graphs

We introduce and study a new graph representation where vertices are embedded in three or more dimensions, and in which the edges are drawn on the projections onto the axis-parallel planes. We show that the complete graph on $n$ vertices has a representation in $\lceil \sqrt{n/2}+1 \rceil$ planes. In 3 dimensions, we show that there exist graphs with $6n-15$ edges that can be projected onto two orthogonal planes, and that this is best possible. Finally, we obtain bounds in terms of parameters such as geometric thickness and linear arboricity. Using such a bound, we show that every graph of maximum degree 5 has a plane-projectable representation in 3 dimensions.Comment: Accepted at CALDAM 202

Bayesian D-Optimal Choice Designs for Mixtures

__Abstract__ \n \nConsumer products and services can often be described as mixtures of ingredients. Examples are the mixture of ingredients in a cocktail and the mixture of different components of waiting time (e.g., in-vehicle and out-of-vehicle travel time) in a transportation setting. Choice experiments may help to determine how the respondents\' choice of a product or service is affected by the combination of ingredients. In such studies, individuals are confronted with sets of hypothetical products or services and they are asked to choose the most preferred product or service from each set. \n \nHowever, there are no studies on the optimal design of choice experiments involving mixtures. We propose a method for generating an optimal design for such choice experiments. To this end, we first introduce mixture models in the choice context and next present an algorithm to construct optimal experimental designs, assuming the multinomial logit model is used to analyze the choice data. To overcome the problem that the optimal designs depend on the unknown parameter values, we adopt a Bayesian D-optimal design approach. We also consider locally D-optimal designs and compare the performance of the resulting designs to those produced by a utility-neutral (UN) approach in which designs are based on the assumption that individuals are indifferent between all choice alternatives. We demonstrate that our designs are quite different and in general perform better than the UN designs

Costs and Cost-Effectiveness of Training Traditional Birth Attendants to Reduce Neonatal Mortality in the Lufwanyama Neonatal Survival Study (LUNESP)

The Lufwanyama Neonatal Survival Project (“LUNESP”) was a cluster randomized, controlled trial that showed that training traditional birth attendants (TBAs) to perform interventions targeting birth asphyxia, hypothermia, and neonatal sepsis reduced all-cause neonatal mortality by 45%. This companion analysis was undertaken to analyze intervention costs and cost-effectiveness, and factors that might improve cost-effectiveness.We calculated LUNESP's financial and economic costs and the economic cost of implementation for a forecasted ten-year program (2011–2020). In each case, we calculated the incremental cost per death avoided and disability-adjusted life years (DALYs) averted in real 2011 US dollars. The forecasted 10-year program analysis included a base case as well as ‘conservative’ and ‘optimistic’ scenarios. Uncertainty was characterized using one-way sensitivity analyses and a multivariate probabilistic sensitivity analysis. The estimated financial and economic costs of LUNESP were $118,574 and$127,756, respectively, or $49,469 and$53,550 per year. Fixed costs accounted for nearly 90% of total costs. For the 10-year program, discounted total and annual program costs were $256,455 and$26,834 respectively; for the base case, optimistic, and conservative scenarios, the estimated cost per death avoided was $1,866,$591, and $3,024, and cost per DALY averted was$74, $24, and$120, respectively. Outcomes were robust to variations in local costs, but sensitive to variations in intervention effect size, number of births attended by TBAs, and the extent of foreign consultants' participation.Based on established guidelines, the strategy of using trained TBAs to reduce neonatal mortality was ‘highly cost effective’. We strongly recommend consideration of this approach for other remote rural populations with limited access to health care

Reducing Calorie Intake May Not Help You Lose Body Weight

Background Previously a meta-analysis found that multi-vitamin/mineral supplementation reduced mild psychiatric symptoms. To establish mechanisms, and to pin-point the individuals most likely to benefit, the role of various polymorphisms were examined. Supplementation was found to influence mild-psychiatric symptoms depending on the form of particular genes: genes that are risk factors for psychiatric disease and influence mechanisms by which drugs act. Methods In a double-blind trial young healthy males rated psychiatric symptoms, before and after taking vitamin/mineral supplements for three months, and the response was related to single nucleotide polymorphisms associated with catecholamines and serotonin. Outcomes With rs1800497 (Taq1A; dopamine D2 receptor), those with the CT allele benefitted from a vitamin/mineral supplement. Similarly with rs1800955 (DRD4 – dopamine D4 receptor), the mood of those with the CC allele benefitted selectively. With rs6296 (HTR1B) only those with the GC alleles responded, and with rs6311 (HTR2A) supplementation produced a beneficial response in those with the GG allele. With rs1050565 (5HTT gene - Human Serotonin Transporter gene) supplementation increased the mental health of those with the AA allele. Interpretation In a situation where a substantial proportion of patients do not benefit from drug therapy, and there is an element of trial and error when prescribing, it was proposed that future work should consider distinguishing patients depending on various polymorphisms and micro-nutrient status. In those with particular alleles, we should consider if drug administration and vitamin / mineral status interact synergistically to influence the therapeutic outcom

Food Composition of the Diet in Relation to Changes in Waist Circumference Adjusted for Body Mass Index

Dietary factors such as low energy density and low glycemic index were associated with a lower gain in abdominal adiposity. A better understanding of which food groups/items contribute to these associations is necessary.To ascertain the association of food groups/items consumption on prospective annual changes in "waist circumference for a given BMI" (WC(BMI)), a proxy for abdominal adiposity.We analyzed data from 48,631 men and women from 5 countries participating in the European Prospective Investigation into Cancer and Nutrition (EPIC) study. Anthropometric measurements were obtained at baseline and after a median follow-up time of 5.5 years. WC(BMI) was defined as the residuals of waist circumference regressed on BMI, and annual change in WC(BMI) (ΔWC(BMI), cm/y) was defined as the difference between residuals at follow-up and baseline, divided by follow-up time. The association between food groups/items and ΔWC(BMI) was modelled using centre-specific adjusted linear regression, and random-effects meta-analyses to obtain pooled estimates.Higher fruit and dairy products consumption was associated with a lower gain in WC(BMI) whereas the consumption of white bread, processed meat, margarine, and soft drinks was positively associated with ΔWC(BMI). When these six food groups/items were analyzed in combination using a summary score, those in the highest quartile of the score--indicating a more favourable dietary pattern--showed a ΔWC(BMI) of -0.11 (95% CI -0.09 to -0.14) cm/y compared to those in the lowest quartile.A dietary pattern high in fruit and dairy and low in white bread, processed meat, margarine, and soft drinks may help to prevent abdominal fat accumulation

Analysis of Sample Correlations for Monte Carlo Rendering

Modern physically based rendering techniques critically depend on approximating integrals of high dimensional functions representing radiant light energy. Monte Carlo based integrators are the choice for complex scenes and effects. These integrators work by sampling the integrand at sample point locations. The distribution of these sample points determines convergence rates and noise in the final renderings. The characteristics of such distributions can be uniquely represented in terms of correlations of sampling point locations. Hence, it is essential to study these correlations to understand and adapt sample distributions for low error in integral approximation. In this work, we aim at providing a comprehensive and accessible overview of the techniques developed over the last decades to analyze such correlations, relate them to error in integrators, and understand when and how to use existing sampling algorithms for effective rendering workflows.publishe