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.

Abstract
In this paper, we consider the single machine scheduling problem with quadratic earliness and tardiness costs, and no machine idle time. We propose several dispatching heuristics, and analyse their performance on a wide range of instances. The heuristics include simple and widely used scheduling rules, as well as adaptations of those rules to a quadratic objective function. We also propose heuristic procedures that specifically address both the earliness and the tardiness penalties, as well as the quadratic cost function. Several improvement procedures were also analysed. These procedures are applied as an improvement step, once the heuristics have generated a schedule. The computational experiments show that the best results are provided by the heuristics that explicitly consider both early and tardy costs, and the quadratic objective function. Therefore, it is indeed important to specifically address the quadratic feature of the cost function, instead of simply using procedures originally developed for a linear objective function. The heuristics are quite fast, and are capable of quickly solving even very large instances. The use of an improvement step is recommended, since it usually improves the solution quality with little additional computational effort.