The extreme core allocations of the assignment game

Although assignment games are hardly ever convex, in this paper a characterization of their set or extreme points of the core is provided, which is also valid for the class of convex games. For each ordering in the player set, a payoff vector is defined where each player receives his marginal contribution to a certain reduced game played by his predecessors. We prove that the whole set of reduced marginal worth vectors, which for convex games coincide with the usual marginal worth vectors, is the set of extreme points of the core of the assignment game

All assignment games with the same core have the same nucleolus

There exist coalitional games with transferable utility which have the same core but different nucleoli. We show that this cannot happen in the case of assignment games. Whenever two assignment games have the same core, their nucleoli also coincide. To show this, we prove that the nucleolus of an assignment game coincides with that of its buyer-seller exact representative

On the monotonic core

The monotonic core of a cooperative game with transferable utility (T.U.-game) is the set formed by all its Population Monotonic Allocation Schemes. In this paper we show that this set always coincides with the core of a certain game associated to the initial game.

On the dimension of the core of the assignment game

The set of optimal matchings in the assignment matrix allows to define a reflexive and symmetric binary relation on each side of the market, the equal-partner binary relation. The number of equivalence classes of the transitive closure of the equal-partner binary relation determines the dimension of the core of the assignment game. This result provides an easy procedure to determine the dimension of the core directly from the entries of the assignment matrix and shows that the dimension of the core is not as much determined by the number of optimal matchings as by their relative position in the assignment matrix.

The relationship of capitalization period length with market portfolio composition and betas

Beta coefficients are not stable if we modify the observation periods of the returns. The market portfolio composition also varies, whereas changes in the betas are the same, whether they are calculated as regression coefficients or as a ratio of the risk premiums. The instantaneous beta, obtained when the capitalization frequency approaches infinity, may be a useful tool in portfolio selection.

Multi-sided Böhm-Bawerk assignment markets: the nucleolus and the core-center

En aquest treball mostrem que, a diferència del cas bilateral, per als mercats multilaterals d'assignació coneguts amb el nom de Böhm-Bawerk assignment games, el nucleolus i el core-center, i. e. el centre de masses del core, no coincideixen en general. Per demostrar-ho provem que donant un m-sided Böhm-Bawerk assignment game les dues solucions anteriors poden obtenir-se respectivament del nucleolus i el core-center d'un joc convex definit en el conjunt format pels m sectors. Encara més, provem que per calcular el nucleolus d'aquest últim joc només les coalicions formades per un jugador o m-1 jugadors són importants. Aquests resultats simplifiquen el càlcul del nucleolus d'un multi-sided ¿¿ohm-Bawerk assignment market amb un número molt elevat d'agents.

The Lorenz-maximal core allocations and the kernel in some classes of assignment games

En aquest treball demostrem que en la classe de jocs d'assignació amb diagonal dominant (Solymosi i Raghavan, 2001), el repartiment de Thompson (que coincideix amb el valor tau) és l'únic punt del core que és maximal respecte de la relació de dominància de Lorenz, i a més coincideix amb la solucié de Dutta i Ray (1989), també coneguda com solució igualitària. En segon lloc, mitjançant una condició més forta que la de diagonal dominant, introduïm una nova classe de jocs d'assignació on cada agent obté amb la seva parella òptima almenys el doble que amb qualsevol altra parella. Per aquests jocs d'assignació amb diagonal 2-dominant, el repartiment de Thompson és l'únic punt del kernel, i per tant el nucleolo.

On the coincidence between the Shimomura's bargaining sets and the core

[cat] En l'article es dona una condició necessària per a que els conjunts de negociació definits per Shimomura (1997) i el nucli d'un joc cooperatiu amb utilitat transferible coincideixin. A tal efecte, s'introdueix el concepte de vectors de màxim pagament. La condició necessària consiteix a verificar que aquests vectors pertanyen al nucli del joc.

The assignment game: core bounds for mixed-pair coalitions

In the assignment game framework, we try to identify those assignment matrices in which no entry can be increased without changing the coreof the game. These games will be called buyer¿seller exact games and satisfy the condition that each mixed¿pair coalition attains the corresponding matrix entry in the core of the game. For a given assignment game, a unique buyerseller exact assignment game with the same core is proved to exist. In order to identify this matrix and to provide a characterization of those assignment games which are buyer¿seller exact in terms of the assignment matrix, attainable upper and lower core bounds for the mixed¿pair coalitions are found. As a consequence, an open question posed in Quint (1991) regarding a canonical representation of a ¿45o¿lattice¿ by means of the core of an assignment game can now be answered

Optimal perfusion computed tomographic thresholds for ischemic core and penumbra are not time dependent in the clinically relevant time window.

BACKGROUND AND PURPOSE: This study aims to determine whether perfusion computed tomographic (PCT) thresholds for delineating the ischemic core and penumbra are time dependent or time independent in patients presenting with symptoms of acute stroke. METHODS: Two hundred seventeen patients were evaluated in a retrospective, multicenter study. Patients were divided into those with either persistent occlusion or recanalization. All patients received admission PCT and follow-up imaging to determine the final ischemic core, which was then retrospectively matched to the PCT images to identify optimal thresholds for the different PCT parameters. These thresholds were assessed for significant variation over time since symptom onset. RESULTS: In the persistent occlusion group, optimal PCT parameters that did not significantly change with time included absolute mean transit time, relative mean transit time, relative cerebral blood flow, and relative cerebral blood volume when time was restricted to 15 hours after symptom onset. Conversely, the recanalization group showed no significant time variation for any PCT parameter at any time interval. In the persistent occlusion group, the optimal threshold to delineate the total ischemic area was the relative mean transit time at a threshold of 180%. In patients with recanalization, the optimal parameter to predict the ischemic core was relative cerebral blood volume at a threshold of 66%. CONCLUSIONS: Time does not influence the optimal PCT thresholds to delineate the ischemic core and penumbra in the first 15 hours after symptom onset for relative mean transit time and relative cerebral blood volume, the optimal parameters to delineate ischemic core and penumbra.

Assessment of physical activity with a pedometer and its relationship with VO2max among adolescents in Switzerland.

OBJECTIVES: In the absence of a gold standard, the assessment of physical activity in children remains difficult. To record physical activity with a pedometer and to examine to what extent it is correlated with VO2max. METHODS: Survey on physical activity and fitness; 233 Swiss adolescents aged 11 to 15 carried a pedometer (Pedoboy) during seven consecutive days. VO2max was estimated through an endurance shuttle run test. RESULTS: The physical activity recorded by the pedometer did not vary from one day to the other (p > 0.05). The physical activity was higher among boys than among girls (p < 0.001) and higher among younger adolescents (6th versus 8th grade; p < 0.001). The correlation between physical activity and estimated VO2max was 0.30 (p < 0.01). CONCLUSIONS: The use of a pedometer to assess physical activity over one entire week is feasible among adolescents. The record provided by the pedometer gives an objective measure of the usual physical activity and, as such, is relatively well correlated with aerobic capacity.

Relationship between cigarette smoking and abdominal obesity

BACKGROUND: Although smokers tend to have a lower body-mass index (BMI) than non-smokers, smoking may affect body fat (BF) distribution. Some studies have assessed the association between smoking, BMI and waist circumference (WC), but, to our knowledge, no population-based studies assessed the relation between smoking and BF composition. We assessed the association between amount of cigarette smoking, BMI, WC and BF composition. METHODS: Data was analysed from a cross-sectional population-based study including 6187 Caucasians aged 32-76 and living in Switzerland. Height, weight and WC were measured. BF, expressed in percent of total body weight, was measured by electrical bioimpedance. Obesity was defined as a BMI>=30 kg/m2 and normal weight as a BMI<25 kg/m2. Abdominal obesity was defined as a WC>=102 cm for men and >=88 cm for women and normal WC as <94 cm for men and <80 cm for women. In men, excess BF was defined as %BF >=28.1, 28.7, 30.6 and 32.6 for age groups 32-44, 45-54, 55-64 and 65-76, respectively; the corresponding values for women were 35.9, 36.5, 40.5 and 44.4. Cigarette smoking was assessed using a self-reported questionnaire. RESULTS: 29.3% of men and 25.0% of women were smokers. Prevalence of obesity, abdominal obesity, and excess of BF was 16.9% and 26.6% and 14.2% in men and 15.0%, 33.0% and 27.5% in women, respectively. Smokers had lower age-adjusted mean BMI, WC and percent of BF compared to non-smokers. However, among smokers,mean age-adjusted BMI,WC and BF increased with the number of cigarettes smoked per day: among light (1-10 cig/day), moderate (11-20) and heavy smokers (>20), mean +/-SE %BF was 22.4 +/−0.3, 23.1+/−0.3 and 23.5+/−0.4 for men, and 31.9+/−0.3, 32.6+/−0.3 and 32.9+/−0.4 for women, respectively. Mean WC was 92.9+/−0.6, 94.0+/−0.5 and 96.0+/−0.6 cm for men, and 80.2+/−0.5, 81.3+/−0.5 and 83.3+/−0.7 for women, respectively. Mean BMI was 25.7+/−0.2, 26.0+/−0.2, and 26.1+/−0.2 kg/m2 for men; and 23.6+/−0.2, 24.0+/−0.2 and 24.1+/−0.3 for women, respectively. Compared with light smokers, the age-adjusted odds ratio (95% Confidence Interval) for excess of BF was 1.04 (0.58 to 1.85) formoderatesmokers and 1.06 (0.57 to 1.99) for heavy smokers in men (p-trend = 0.9), and 1.35 (0.92 to 1.99) and 2.26 (1.38 to 3.72), respectively, in women (p-trend = 0.04). Odds ratio for abdominal obesity vs. normal WC was 1.32 (0.81 to 2.15) for moderate smokers and 1.95 (1.16 to 3.27) for heavy smokers in men (p-trend < 0.01), and 1.15 (0.79 to 1.69) and 2.36 (1.41 to 3.93) in women (p-trend = 0.03). Odds ratio for obesity vs. normal weight was 1.35 (0.76 to 2.41) for moderate smokers and 1.33 (0.71 to 2.49) for heavy smokers in men (p-trend = 0.9) and 0.78 (0.45 to 1.35) and 1.44 (0.73 to 2.85), in women (p-trend = 0.08). CONCLUSIONS: WC and BF were positively and dose-dependently associated with the number of cigarettes smoked per day in women, whereas onlyWC was dose dependently and significantly associated with the amount of cigarettes smoked per day in men. This suggests that heavy smokers, especially women, are more likely to have an excess of BF and to accumulate BF in the abdomen compared to lighter smokers.

A Mendelian randomization approach to assess the causal relationship of gamma-glutamyl transferase with blood pressure and insulin

Background: Elevated levels of g-glutamyl transferase (GGT) have been associated with subsequent risk of elevated blood pressure (BP), hypertension and diabetes. However, the causality of these relationships has not been addressed. Mendelian randomization refers to the random allocation of alleles at the time of gamete formation. Such allocation is expected to be independent of any behavioural and environmental factors (known or unknown), allowing the analysis of largely unconfounded risk associations that are not due to reverse causation. Methods: We performed a cross-sectional analysis among 4361 participants to the population based CoLaus study. Associations of sex-specific GGT quartiles with systolic BP, diastolic BP and insulin levels were assessed using multivariable linear regression analyses. The rs2017869 GGT1 variant, which explained 1.6% of the variance in GGT levels, was used as an instrument to perform a Mendelian randomization analysis. Results: Median age of the study population was 53 years. After age and sex adjustment, GGT quartiles were strongly associated with systolic and diastolic BP (all p for linear trend <0.0001). After multivariable adjustment, these relationships were significantly attenuated, but remained significant for systolic (b(95%CI)¼1.30 (0.32;2.03), p¼0.007) and diastolic BP (b (95%CI)¼0.57 (0.02;1.13), p¼0.04). Using Mendelian randomization, we observed no positive association of GGT with either systolic BP (b (95%CI)¼-5.68 (-11.51-0.16), p¼0.06) or diastolic BP (b (95%CI)¼ -2.24 (-5.98;1.49) p¼0.24). The association of GGT with insulin was also attenuated after multivariable adjustment. Nevertheless, a strong linear trend persisted in the fully adjusted model (b (95%CI)¼0.07 (0.04;0.09), p<0.0001). Using Mendelian randomization, we observed a similar positive association of GGT with insulin (b (95%CI)¼0.19 (0.01-0.37), p¼0.04). Conclusion: In this study, we found evidence for a direct causal relationship between GGT and insulin, suggesting that oxidative stress may be causally implicated in the pathogenesis of type 2 diabetes mellitus.