Generalized Colonel Blotto Game

Competitive resource allocation between adversarial decision makers arises in a wide spectrum of real-world applications such as in communication systems, cyber-physical systems security, as well as financial, political, and electoral competition. As such, developing analytical tools to model and analyze competitive resource allocation is crucial for devising optimal allocation strategies and anticipating the potential outcomes of the competition. To this end, the Colonel Blotto game is one of the most popular game-theoretic frameworks for modeling and analyzing such competitive resource allocation problems. However, in many real-world competitive situations, the Colonel Blotto game does not admit solutions in deterministic strategies and, hence, one must rely on analytically complex mixed-strategies with their associated tractability, applicability, and practicality challenges. In this paper, a generalization of the Colonel Blotto game which enables the derivation of deterministic, practical, and implementable equilibrium strategies is proposed while accounting for the heterogeneity of the battlefields. In addition, the proposed generalized game enables accounting for the consumed resources in each battlefield, a feature that is not considered in the classical Blotto game. For the generalized game, the existence of a Nash equilibrium in pure-strategies is shown. Then, closed-form analytical expressions of the equilibrium strategies, are derived and the outcome of the game is characterized; based on the number of resources of each player as well as the valuation of each battlefield. The generated results provide invaluable insights on the outcome of the competition. For example, the results show that, when both players are fully rational, the more resourceful player can achieve a better total payoff at the Nash equilibrium, a result that is not mimicked in the classical Blotto game.Comment: 8 pages, 5 figure

Effects of processing methods on nutritive values of Ekuru from two cultivars of beans (Vigna unguiculata and Vigna angustifoliata)

Beans contain substantial amount of protein, dietary fibre, B-vitamins, minerals, and anti-nutrients which limit their utilisation. Processing reduce the level of antinutrients in plant products but little information exist on effects of processing methods on nutrient and antinutrient composition of bean products. This study was undertaken to determine the effects of processing methods on nutrient and antinutrient composition, and micronutrient potential of bean paste (Ekuru) from two cultivars of beans, white (Vigna unguiculata) and red (Vigna angustifoliata) species of beans which were processed into white and brown Ekuru using standardised traditional methods. 100 g of raw V. unguiculata and V. angustifoliata contained 22.83 and 23.94 g protein, 1.94 and 2.11 g crude lipid, 30 and 29 mg sodium, 1.110 and 1.124 mg potassium, 390 and 130 mg phosphorus, 10.65 and 10.95 mg iron and 5.87 and 5.95 mg zinc, respectively. Ekuru products contained between 18.76 and 21.90 g protein, 0.81 and 1.38 g crude lipid, 20.00 and 90.00 mg sodium, 870 and 1124 mg potassium, 8.16 and 8.36 mg iron and 4.87 and 5.21 mg zinc, respectively. Processing decreased the nutrient content of the products compared with raw samples, the red bean product was higher in crude protein, crude lipid and ash; while the white bean product was higher in crude fibre and moisture content. The bean products were very low in antinutrients, with no trypsin inhibitors. Ekuru samples can be good sources of plant protein, nonhaeme iron and zinc, and their consumption should be encouraged.Key words: Processing methods, nutritive value, antinutrients, Ekuru, Vigna unguiculata, Vigna angustifoliata

Interpolation de données manquantes dans des séquences multi-modales d'images géophysiques satellitaires

Session "Articles"National audienceCet article étudie l'estimation conjointe de données manquantes et de champs de déplacements dans des séquences multimodales d'observations satellitaires géophysiques. La complexité de la tâche est liée au taux élevé de données manquantes (entre 20% et 90%) pour des observations journalières de haute résolution et la reconstruction de structures fines en accord avec la dynamique sous jacente. Nous avons développé une méthode basée sur l'assimilation variationnelle de données pour des séries multimodales et multi-résolutions. A l'aide de données synthétiques et de données réelles de la surface océanique, une évaluation numérique et qualitative démontre l'apport de deux composantes clés du modèle proposé: la fusion d'informations multimodales à partir d'une contrainte géométrique basée sur les structures frontales, et la méthode d'assimilation variationnelle utilisant comme à priori dynamique un modèle d'advection-diffusion. Les expérimentations conduites montrent que de bonnes performances de reconstruction sont obtenues pour les observations hautes résolutions en dépit du pourcentage élevé de données manquante

Importance of organic phosphate hydrolyzed in stalks of the lotic diatom Didymosphenia geminata and the possible impact of atmospheric and climatic changes

The aquatic colonial stalked diatom, Didymosphenia geminata, has acquired notoriety in recent years because of huge increases in many rivers of temperate regions. However, in some streams in northern England it has probably or, in the case of the R. Coquet (Northumberland), certainly been abundant for many decades. The paper describes the nutrient environment and phosphatase activities of Didymosphenia in Stony Gill (N. Yorkshire), a fast-flowing stream draining an upland catchment with peaty soils overlying limestone. Organic phosphate formed 85% of the filtrable phosphate in the water during the study (January–August 2000), with a maximum in April. Colonies were most abundant in June, but had disappeared by August. Surface phosphomonoesterase (PMEase) and phosphodiesterase activities assayed from March to July showed low PMEase activity in early March, but otherwise both were high throughout the period and especially so in June and July. Use of BCIP-NBT staining procedure showed that PMEase activity occurred in the stalks. A more detailed study of colony structure and staining with material from the R. Coquet in June 2006 also showed marked PMEase activity, with staining localized in the upper part of the stalks and the cells remaining unstained. It is suggested that organic phosphate is hydrolyzed in the stalk and the inorganic phosphate passes to the cell via a central tube in the stalk. It seems likely that organic phosphate as a major P source is a key factor favouring the success of Didymosphenia. The possible impact of environmental changes in the catchment such as climatic warming, C loss from peat and atmospheric N deposition is discussed

Biology of the freshwater diatom Didymosphenia : a review

Features of the colonial diatom Didymosphenia are reviewed, especially D. geminata. Although there is a long record of its occurrence in north temperate regions, mass growths have been reported much more widely in recent years. Contrary to some statements in the literature, there are also reliable older records for the southern hemisphere, though the first report of mass growth was in New Zealand in 2004. The annual cycle of morphological changes in D. geminata in northern England, and probably elsewhere, includes a winter period when motile cells are attached to the substratum followed by spring when stalks start to develop. These raise cells into the water column and provide a site for phosphatase activity. Environmental factors associated with success include absence of extreme floods, high light, pH above neutral and nutrient chemistry. D. geminata often, but not always, occurs in waters where the N:P ratio is high for much of the year, but the key factor is the ratio of organic to inorganic phosphate. D. geminata thrives where organic P is predominant and the overall P concentration is low enough for organic P to be an important P source. It is unknown whether organic N can be used. Environmental changes increasing the relative importance of organic P are likely to favour D. geminata. Likely examples are increased N:P due to atmospheric N deposition and changes in form and seasonality of P release from organic-rich soils due to climatic warming. The nutrient chemistry of deep water released from dams to rivers also needs investigation. To what extent are genetic changes occurring in response to environmental changes and are new ecotypes spreading round the world? In spite of many adverse reports about D. geminata, such as detached mats blocking water pipes, there is still doubt about the extent to which it causes problems, particularly for fish. There have been few adverse effects on migratory salmonids in Europe and North America, but at least one report of harm to a brown trout population in USA. In New Zealand, it has caused serious problems for water sports, although it remains open to question how much adverse effect it has had on fish populations. If the presence of microcystins in or associated with D. geminata, as indicated recently for two populations, proves to be widespread and at sufficiently high concentration, their possible accumulation in fish requires study. Where control is required, this could be achieved by enhancing the ratio of inorganic to organic phosphate in the water early in the growth season. Practical ways to achieve this are suggested

Determining the date of diagnosis – is it a simple matter? The impact of different approaches to dating diagnosis on estimates of delayed care for ovarian cancer in UK primary care

Background Studies of cancer incidence and early management will increasingly draw on routine electronic patient records. However, data may be incomplete or inaccurate. We developed a generalisable strategy for investigating presenting symptoms and delays in diagnosis using ovarian cancer as an example. Methods The General Practice Research Database was used to investigate the time between first report of symptom and diagnosis of 344 women diagnosed with ovarian cancer between 01/06/2002 and 31/05/2008. Effects of possible inaccuracies in dating of diagnosis on the frequencies and timing of the most commonly reported symptoms were investigated using four increasingly inclusive definitions of first diagnosis/suspicion: 1. "Definite diagnosis" 2. "Ambiguous diagnosis" 3. "First treatment or complication suggesting pre-existing diagnosis", 4 "First relevant test or referral". Results The most commonly coded symptoms before a definite diagnosis of ovarian cancer, were abdominal pain (41%), urogenital problems(25%), abdominal distension (24%), constipation/change in bowel habits (23%) with 70% of cases reporting at least one of these. The median time between first reporting each of these symptoms and diagnosis was 13, 21, 9.5 and 8.5 weeks respectively. 19% had a code for definitions 2 or 3 prior to definite diagnosis and 73% a code for 4. However, the proportion with symptoms and the delays were similar for all four definitions except 4, where the median delay was 8, 8, 3, 10 and 0 weeks respectively. Conclusion Symptoms recorded in the General Practice Research Database are similar to those reported in the literature, although their frequency is lower than in studies based on self-report. Generalisable strategies for exploring the impact of recording practice on date of diagnosis in electronic patient records are recommended, and studies which date diagnoses in GP records need to present sensitivity analyses based on investigation, referral and diagnosis data. Free text information may be essential in obtaining accurate estimates of incidence, and for accurate dating of diagnoses