Abstract
We consider a Bertrand duopoly model with unknown costs. The firms' aim is to choose the price of its product according to the well-known concept of Bayesian Nash equilibrium. The chooses are made simultaneously by both firms. In this paper, we suppose that each firm has two different technologies, and uses one of them according to a certain probability distribution. The use of either one or the other technology affects the unitary production cost. We show that this game has exactly one Bayesian Nash equilibrium. We analyse the advantages, for firms and for consumers, of using the technology with highest production cost versus the one with cheapest production cost. We prove that the expected profit of each firm increases with the variance of its production costs. We also show that the expected price of each good increases with both expected production costs, being the effect of the expected production costs of the rival dominated by the effect of the own expected production costs.

Abstract
The consequences of regulatory T cell (Treg) inhibition of interleukine 2 secretion are examined by mathematical modelling. We demonstrate that cytokine dependent growth exhibits quorum T cell population thresholds that determine whether immune responses develop on activation and whether the immune system returns to a control state. We study the effects in the quorum T cell population thresholds, by the T cell maximum growth rate, by the growth rate ratio between Tregs and T cells, by the value of the secretion rate of cytokines, and by the effectiveness of T cell secretion inhibition by Tregs.

Abstract
In this paper, we consider a Stackelberg duopoly competition with differentiated goods and with unknown costs. The firms' aim is to choose the output levels of their products according to the well-known concept of perfect Bayesian equilibrium. There is a firm (F(1)) that chooses first the quantity q(1) of its good; the other firm (F(2)) observes q(1) and then chooses the quantity g(2) of its good. We suppose that each firm has two different technologies, and uses one of them following a probability distribution. The use of either one or the other technology affects the unitary production cost. We show that there is exactly one perfect Bayesian equilibrium for this game. We analyse the advantages, for firms and for consumers, of using the technology with the highest production cost versus the one with the cheapest cost.

Abstract
The Watson distribution is frequently used for modeling axial data. We propose the two-way analysis of variance for a concentrated Watson distribution defined on the hypersphere in the girdle or bipolar form. We illustrate this technique with spherical data.

Abstract
Part of the reason for rejecting aquatic environments as possible vectors for the transmission of Helicobacter pylori has been the preference of this microorganism to inhabit the human stomach and hence use a direct oral-oral route for transmission. On the other hand, most enteric bacterial pathogens are well known for being able to use water as an environmental reservoir. In this work, we have exposed 13 strains of seven different Helicobacter spp. (both gastric and enterohepatic) to water and tracked their survival by standard plating methods and membrane integrity assessment. The influence of different plating media and temperatures and the presence of light on recovery was also assessed. There was good correlation between cultivability and membrane integrity results (Pearson's correlation coefficient = 0.916), confirming that the culture method could reliably estimate differences in survival among different Helicobacter spp. The species that survived the longest in water was H. pylori (> 96 It in the dark at 25 degrees C), whereas H. felis appeared to be the most sensitive to water (<6 h). A hierarchical cluster analysis demonstrated that there was no relationship between the enterohepatic nature of Helicobacter spp. and an increased time of survival in water. This work assesses for the first time the survival of multiple Helicobacter spp., such has H. mustelae, H. muridarum, H. felis, H. canadensis, H. pullorum, and H. canis, in water under several conditions and concludes that the roles of water in transmission between hosts are likely to be similar for all these species, whether enterohepatic or not.

Abstract
In this paper, we consider the single machine scheduling problem with linear earliness and quadratic tardiness costs, and no machine idle time. We propose a lower bounding procedure based on the relaxation of the jobs' completion times. Optimal branch-and-bound algorithms are then presented. These algorithms incorporate the proposed lower bound, as well as an insertion-based dominance test. The branch-and-bound procedures are tested on a wide set of randomly generated problems. The computational results show that the branch-and-bound algorithms are capable of optimally solving, within reasonable computation times, instances with up to 20 jobs.