A mathematical excursion: From the three-door problem to a Cantor-type perfect set

We start with a generalization of the well-known three-door problem:the n-door problem. The solution of this new problem leads us toa beautiful representation system for real numbers in (0,1] as alternated series, known in the literature as Pierce expansions. A closer look to Pierce expansions will take us to some metrical properties of sets defined through the Pierce expansions of its elements. Finally, these metrical properties will enable us to present 'strange' sets, similar to the classical Cantor set.

Locating emergency services with priority rules: The priority queuing covering location problem

One of the assumptions of the Capacitated Facility Location Problem (CFLP) is thatdemand is known and fixed. Most often, this is not the case when managers take somestrategic decisions such as locating facilities and assigning demand points to thosefacilities. In this paper we consider demand as stochastic and we model each of thefacilities as an independent queue. Stochastic models of manufacturing systems anddeterministic location models are put together in order to obtain a formula for thebacklogging probability at a potential facility location.Several solution techniques have been proposed to solve the CFLP. One of the mostrecently proposed heuristics, a Reactive Greedy Adaptive Search Procedure, isimplemented in order to solve the model formulated. We present some computationalexperiments in order to evaluate the heuristics performance and to illustrate the use ofthis new formulation for the CFLP. The paper finishes with a simple simulationexercise.

A multi-objective model for a multi-period distribution management problem

The problems arising in commercial distribution are complex and involve several players and decision levels. One important decision is relatedwith the design of the routes to distribute the products, in an efficient and inexpensive way.This article deals with a complex vehicle routing problem that can beseen as a new extension of the basic vehicle routing problem. The proposed model is a multi-objective combinatorial optimization problemthat considers three objectives and multiple periods, which models in a closer way the real distribution problems. The first objective is costminimization, the second is balancing work levels and the third is amarketing objective. An application of the model on a small example, with5 clients and 3 days, is presented. The results of the model show the complexity of solving multi-objective combinatorial optimization problems and the contradiction between the several distribution management objective.

Clinical outcome following combination of cutting balloon angioplasty and coronary β-radiation for in-stent restenosis : a report from the RENO registry

RESUME : Actuellement la brachythérapie endovasculaire reste le seul traitement efficace pour la resténose intrastent. Malgré ceci, la limitation majeure de cette technique est la resténose aux extrémités du stent (effet de bord) due à une couverture incomplète par la source radioactive (geographical miss). Le ballon coupant et qui ne glisse pas pourrait limiter le barotraumatisme engendré par la dilatation et qui avec la diminution de la radiation aux extrémités de la source radioactive, est à la base du geographical miss. Cette étude prospective a pour but d'examiner l'efficacité du traitement de la resténose intrastent par la combinaison d'angioplastie avec cutting ballon et β - irradiation. Le registre « Radiation in Europe NOvoste » (RENO) inclut tous les patients traités par β - irradiation coronaire avec le système Beta-CathTM System (Novoste Corporation, Brussels, Belgium) n'ayant pas été inclus dans une autre étude randomisée. Un premier sous-groupe de ces patients (groupe 1, n=166), représente les patients traités par cutting ballon et β - irradiation intra coronaire. Ce groupe a été défini d'une manière prospective et les résultats cliniques à 6 mois ont été comparés par rapport aux autres patients qui ont reçu un traitement par dilatation coronaire conventionnelle et β - irradiation (groupe 2, n=712). A 6 mois de suivi, on a retrouvé une différence significative entre les 2 groupes par rapport à la nécessité d'une nouvelle revascularisation du vaisseau préalablement traité (10,2% de récidive dans le groupe 1 contre 16,6 % dans le groupe 2 , p=0,04). Le nombre d'événements cardiaques majeurs (mortalité, infarctus du myocarde et revascularisation) a également été diminué de manière significative (10,8% contre 19,2% ; />=0,01). Cette observation a été confirmée par une analyse multivariée qui indique un risque diminué pour les événements cardiaques majeurs à 6 mois, (rapport de côtes : 0,49 ; intervalle de confiance 0,27-0,88 ; p=0,02). Comparé à l'angioplastie coronarienne avec ballon conventionnel, l'utilisation de cutting ballon avant la β - irradiation dans le traitement de la resténose intrastent démontre une meilleure évolution clinique à 6 mois. ABSTRACT: At present, vascular brachytherapy is the only efficient therapy for in-stent restenosis. Nevertheless edge restenosis often relat¬ed to geographical miss has been identified as a major limitation of the technique. The non-slippery cutting balloon has the potential to limit vascular barotraumas which, together with low-dose irradiation at both ends of the radioactive source, are the prerequisite for geographical miss. This prospective study aimed to examine the efficacy of combining cut¬ting balloon angioplasty and brachytherapy for in-stent restenosis. The Radiation in Europe NOvoste (RENO) registry prospectively tracked all patients who had been treated by coronary β-radiation with the Beta-CathTM System (Novoste Corporation. Brussels, Belgium) but were not included in a randomized radiation trial, A subgroup of patients with in-stent restenosis treated by cutting balloon angioplasty and coronary β-radiation (group 1, n = 166) was prospectively defined, and clinical outcomes of patients at 6 months were compared with those of patients treated by conventional angioplasty and coronary β -radiation (group 2, n = 712). At 6-month follow-up, there was a significant difference between groups 1 and 2 in- target vessel revascularization (10.2% versus 16.6% respectively; p = 0.04) and in the incidence of major adverse clinical events (MACE) including, death, myocardial infarction, and revascularization (10.8% versus 19.2%; p= 0.01). This observation was confirmed by a multivariate analysis indicating a. lower risk for MACE at 6 months (odds ratio: 0.49; confidence intervals: 0.27-0.88; p = 0.02). Compared to conventional angioplasty, cutting balloon angio¬plasty prior to coronary beta-radiation with the Beta-CathTM System seems to improve the 6-month clinical outcome in patients with in-stent restenosis.

Minimax lower bounds for the two-armed bandit problem

We obtain minimax lower bounds on the regret for the classicaltwo--armed bandit problem. We provide a finite--sample minimax version of the well--known log $n$ asymptotic lower bound of Lai and Robbins. Also, in contrast to the log $n$ asymptotic results on the regret, we show that the minimax regret is achieved by mere random guessing under fairly mild conditions on the set of allowable configurations of the two arms. That is, we show that for {\sl every} allocation rule and for {\sl every} $n$, there is a configuration such that the regret at time $n$ is at least 1 -- $\epsilon$ times the regret of random guessing, where $\epsilon$ is any small positive constant.

Modeling the forensic two-trace problem with Bayesian networks

The forensic two-trace problem is a perplexing inference problem introduced by Evett (J Forensic Sci Soc 27:375-381, 1987). Different possible ways of wording the competing pair of propositions (i.e., one proposition advanced by the prosecution and one proposition advanced by the defence) led to different quantifications of the value of the evidence (Meester and Sjerps in Biometrics 59:727-732, 2003). Here, we re-examine this scenario with the aim of clarifying the interrelationships that exist between the different solutions, and in this way, produce a global vision of the problem. We propose to investigate the different expressions for evaluating the value of the evidence by using a graphical approach, i.e. Bayesian networks, to model the rationale behind each of the proposed solutions and the assumptions made on the unknown parameters in this problem.

Mutualism with sea anemones triggered the adaptive radiation of clownfishes.

ABSTRACT: BACKGROUND: Adaptive radiation is the process by which a single ancestral species diversifies into many descendants adapted to exploit a wide range of habitats. The appearance of ecological opportunities, or the colonisation or adaptation to novel ecological resources, has been documented to promote adaptive radiation in many classic examples. Mutualistic interactions allow species to access resources untapped by competitors, but evidence shows that the effect of mutualism on species diversification can greatly vary among mutualistic systems. Here, we test whether the development of obligate mutualism with sea anemones allowed the clownfishes to radiate adaptively across the Indian and western Pacific oceans reef habitats. RESULTS: We show that clownfishes morphological characters are linked with ecological niches associated with the sea anemones. This pattern is consistent with the ecological speciation hypothesis. Furthermore, the clownfishes show an increase in the rate of species diversification as well as rate of morphological evolution compared to their closest relatives without anemone mutualistic associations. CONCLUSIONS: The effect of mutualism on species diversification has only been studied in a limited number of groups. We present a case of adaptive radiation where mutualistic interaction is the likely key innovation, providing new insights into the mechanisms involved in the buildup of biodiversity. Due to a lack of barriers to dispersal, ecological speciation is rare in marine environments. Particular life-history characteristics of clownfishes likely reinforced reproductive isolation between populations, allowing rapid species diversification.

Characterization of the effects of radiation therapy on the tumour microenvironment and their consequences on cancer progression

RESUME La radiothérapie est utilisée avec succès pour le traitement d'un grand nombre de pathologies tumorales (1). Cependant, les récidives post-actiniques sont associées à un risque accru de développer des métastases régionales et à distance (2, 3). La prise en charge de ce type de patients demeure insatisfaisante à l'heure actuelle, principalement parce que les mécanismes physio-pathologiques sous- sous-jacents restent mal compris. Etant donné le rôle primordial du stroma dans la progression tumorale (4) et l'importance des effets de la radiothérapie sur le micro-environnement des tumeurs (5), nous avons émis l'hypothèse que la radiothérapie pouvait engendrer des modifications stromales susceptibles de contribuer à l'émergence d'un phénotype tumoral plus agressif. Nous avons observé que l'exposition préalable d'un environnement tumoral à des radiations ionisantes engendre une inhibition locale et à long terme de l'angiogenèse. Cette inhibition conduit à la création d'un environnement tumoral hypoxique favorisant l'invasion et la métastatisation tumorale. Les mécanismes sous-jacents impliquent l'activation de gènes prométastatiques sous le contrôle du facteur de transcription HIF-1, ainsi que la sélection hypoxique de cellules hautement invasives et métastatiques. Par des analyses de profile d'expression génétique ainsi que par des analyses fonctionnelles, nous avons identifié la protéine matri-cellulaire CYR61 ainsi que ses partenaires d'interaction, les intégrines aVb5/aVb3, comme médiateurs importants de ces effets. De plus, une corrélation significative a également été trouvée entre le niveau d'expression de CYR61 et le taux d'hypoxie dans un grand nombre de carcinomes mammaires chez l'humain. Une association a aussi été observée entre le niveau d'expression de CYR61 et le pronostic de patientes souffrant d'un cancer du sein traité par chimiothérapie adjuvante. Globalement ces résultats identifient l'interaction entre la protéine CYR61 et ses récepteurs aVb5/aVb3 comme un mécanisme important du processus de métastatisation et en font une cible thérapeutique potentielle pour le traitement de patients souffrant d'une récidive tumorale après un traitement de radiothérapie. Finalement, bien que l'inhibition de l'angiogenèse soit locale dans ce cas particulier, nos résultats justifient une surveillance particulière des patients souffrant d'une pathologie tumorale et étant au bénéfice d'un traitement inhibiteur de l'angiogenèse. SUMMARY Radiotherapy is successfully used to treat a large variety of tumours (1 ). However, cancer patients experiencing local recurrent disease after radiation therapy are at increased risk of developing regional and distant metastasis (2, 3). The clinical management of this condition represents a difficult and challenging issue, mainly because the underlying physio-pathological mechanisms remain poorly understood. Given the well established role of the tumour stroma in promoting cancer progression (4) and since radiotherapy is known to persistently alter the tumour microenvironment (5), we hypothesized that ionising radiations may generate stromal modifications contributing to the metastatic spread of relapsing tumours. Here, we report that irradiation of the prospective tumour microenvironment promotes tumour invasion and metastasis through a mechanism of local and sustained impairment of angiogenesis leading to both HIF-1 dependent activation of pro-metastatic genes and hypoxia-mediated selection of highly metastatic tumour cell variants. Through gene expression profiling and functional experiments, we identified the matricellular signalling protein CYR61 and its interaction partners aVb5/ aVb3 integrins as critical mediators of these effects. Furthermore, we found a significant correlation between CYR61 expression and the hypoxic status of a large number of human mammary carcinomas. A positive correlation between increased levels of CYR61 expression and shorter relapse free survival was also identified in breast cancer patients treated with adjuvant chemotherapy. Together, these results identify CYR61 and aVb5/aVb3 integrins as critical mediators of metastasis and potential therapeutic targets to improve outcome in patients with post-radiation tumour recurrences. Finally, although inhibition of angiogenesis is local in this setting, our data warrant close monitoring of tumour progression in patients under anti-angiogenic therapy.

Strategies for an integrated distribution problem

The problems arising in the logistics of commercial distribution are complexand involve several players and decision levels. One important decision isrelated with the design of the routes to distribute the products, in anefficient and inexpensive way.This article explores three different distribution strategies: the firststrategy corresponds to the classical vehicle routing problem; the second isa master route strategy with daily adaptations and the third is a strategythat takes into account the cross-functional planning through amulti-objective model with two objectives. All strategies are analyzed ina multi-period scenario. A metaheuristic based on the Iteratetd Local Search,is used to solve the models related with each strategy. A computationalexperiment is performed to evaluate the three strategies with respect to thetwo objectives. The cross functional planning strategy leads to solutions thatput in practice the coordination between functional areas and better meetbusiness objectives.