Integral representation with convex capacities that are squeeze of (additive) probability measures

In this paper I will investigate the conditions under which a convex capacity (or a non-additive probability which exhibts uncertainty aversion) can be represented as a squeeze of a(n) (additive) probability measure associate to an uncertainty aversion function. Then I will present two alternatives forrnulations of the Choquet integral (and I will extend these forrnulations to the Choquet expected utility) in a parametric approach that will enable me to do comparative static exercises over the uncertainty aversion function in an easy way.

Laws of large numbers for non-additive probabilities

We apply the concept of exchangeable random variables to the case of non-additive robability distributions exhibiting ncertainty aversion, and in the lass generated bya convex core convex non-additive probabilities, ith a convex core). We are able to rove two versions of the law of arge numbers (de Finetti's heorems). By making use of two efinitions. of independence we rove two versions of the strong law f large numbers. It turns out that e cannot assure the convergence of he sample averages to a constant. e then modal the case there is a true" probability distribution ehind the successive realizations of the uncertain random variable. In this case convergence occurs. This result is important because it renders true the intuition that it is possible "to learn" the "true" additive distribution behind an uncertain event if one repeatedly observes it (a sufficiently large number of times). We also provide a conjecture regarding the "Iearning" (or updating) process above, and prove a partia I result for the case of Dempster-Shafer updating rule and binomial trials.

Non-additive genetic effects on weights and performance of a Brazilian Bos taurus x Bos indicus beef composite

The aim of the present study was to evaluate the heterosis effects on weaning weight at 205 days (WW, N = 146,464), yearling weight at 390 days (YW, N = 69,315) and weight gain from weaning to yearling (WG, N = 59,307) in composite beef cattle. The fixed models were: RM, which included contemporary groups, class of age of dam, outcrossing percentages for direct and maternal effects, and additive direct and maternal ( AM) breed effects; R, RM model, minus AM breed effects, and H, RM model, minus additive breed effects. The estimates for W205 were in general positive (P < 0.01). The R and H models resulted in similar estimates, but they were very different from the ones estimated by the RM model. For W390, the R and H models resulted in general positive estimates (P < 0.05). For WG, the RM model resulted in general significant heterosis effects (P < 0.05). It can be concluded that the RM model seems to supply estimates of better quality (P < 0.01).

Toward a rational-choice foundation of non-additive theories

A classical argument of de Finetti holds that Rationality implies Subjective Expected Utility (SEU). In contrast, the Knightian distinction between Risk and Ambiguity suggests that a rational decision maker would obey the SEU paradigm when the information available is in some sense good, and would depart from it when the information available is not good. Unlike de Finetti's, however, this view does not rely on a formal argument. In this paper, we study the set of all information structures that might be availabe to a decision maker, and show that they are of two types: those compatible with SEU theory and those for which SEU theory must fail. We also show that the former correspond to "good" information, while the latter correspond to information that is not good. Thus, our results provide a formalization of the distinction between Risk and Ambiguity. As a consequence of our main theorem (Theorem 2, Section 8), behavior not-conforming to SEU theory is bound to emerge in the presence of Ambiguity. We give two examples of situations of Ambiguity. One concerns the uncertainty on the class of measure zero events, the other is a variation on Ellberg's three-color urn experiment. We also briefly link our results to two other strands of literature: the study of ambiguous events and the problem of unforeseen contingencies. We conclude the paper by re-considering de Finetti's argument in light of our findings.

Non-additive genetic effects on weights and performance of a Brazilian Bos taurus x Bos indicus beef composite

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Evidences of non-additive effects of multiple parasitoids on Diatraea saccharalis Fabr. (Lep., Crambidae) populations in sugarcane fields in Brazil

Biological control is a relatively benign method of pest control. However, considerable debate exists over whether multiple natural enemies often interact to produce additive or non-additive effects on their prey or host populations. Based on the large data set stored in the Sao Joao and Barra sugarcane mills (state of São Paulo, Brazil) regarding the programme of biological control of Diatraea saccharalis using the parasitoids Cotesia flavipes and tachinid flies, in the present study the author investigated whether the parasitoids released into sugarcane fields interfered significantly with the rate of parasitized D. saccharalis hosts. The author also observed whether there was an additive effect of releasing C. flavipes and tachinids on the rate of parasitized hosts, and looked for evidence of possible negative effects of the use of multiple parasitoid species in this biological control programme. Results showed that C. flavipes and the tachinids were concomitantly released in the Barra Mill, but not in the Sao Jao Mill. Furthermore, in the Barra Mill there was evidence that the parasitoids interacted because the percentage of parasitism did not increase after the release of either C. flavipes or tachinids. In the Sao Joao Mill, when both parasitoid species were released out of synchrony, both the percentage of parasitism by C. flavipes as well as that of the tachinids increased. When large numbers of tachinids were released in the Barra Mill, they caused a significant lower percentage of parasitism imposed by C. flavipes. The implications of the results as evidence of non-additive effects of C. flavipes plus tachinids on D. saccharalis populations are discussed.

Estimation methods of non-additive effects for characteristics of weight and scrotal circumference in crossbred beef cattle

The objective of this study was to investigate, in a population of crossbred cattle, the obtainment of the non-additive genetic effects for the characteristics weight at 205 and 390 days and scrotal circumference, and to evaluate the consideration of these effects in the prediction of breeding values of sires using different estimation methodologies. In method 1, the data were pre-adjusted for the non-additive effects obtained by least squares means method in a model that considered the direct additive, maternal and non-additive fixed genetic effects, the direct and total maternal heterozygosities, and epistasis. In method 2, the non-additive effects were considered covariates in genetic model. Genetic values for adjusted and non-adjusted data were predicted considering additive direct and maternal effects, and for weight at 205 days, also the permanent environmental effect, as random effects in the model. The breeding values of the categories of sires considered for the weight characteristic at 205 days were organized in files, in order to verify alterations in the magnitude of the predictions and ranking of animals in the two methods of correction data for the non-additives effects. The non-additive effects were not similar in magnitude and direction in the two estimation methods used, nor for the characteristics evaluated. Pearson and Spearman correlations between breeding values were higher than 0.94, and the use of different methods does not imply changes in the selection of animals.

Continuous positive airway pressure increases inspiratory capacity of COPD patients

Background and objective: Hyperinflation with a decrease in inspiratory capacity (IC) is a common presentation for both unstable and stable COPD patients. As CPAP can reduce inspiratory load, possibly secondary to a reduction in hyperinflation, this study examined whether CPAP would increase IC in stable COPD patients. Methods: Twenty-one stable COPD patients (nine emphysema, 12 chronic bronchitis) received a trial of CPAP for 5 min at 4, 7 and 11 cmH(2)O. Fast and slow VC (SVC) were measured before and after each CPAP trial. In patients in whom all three CPAP levels resulted in a decreased IC, an additional trial of CPAP at 2 cmH(2)O was conducted. For each patient, a `best CPAP` level was defined as the one associated with the greatest IC. This pressure was then applied for an additional 10 min followed by spirometry. Results: Following application of the `best CPAP`, the IC and SVC increased in 15 patients (nine emphysema, six chronic bronchitis). The mean change in IC was 159 mL (95% CI: 80-237 mL) and the mean change in SVC was 240 mL (95% CI: 97-386 mL). Among these patients, those with emphysema demonstrated a mean increase in IC of 216 mL (95% CI: 94-337 mL). Six patients (all with chronic bronchitis) did not demonstrate any improvement in IC. Conclusions: The best individualized CPAP can increase inspiratory capacity in patients with stable COPD, especially in those with emphysema.

Co-evolution between sociality and dispersal: The role of synergistic cooperative benefits.

Explaining the evolution of sociality is challenging because social individuals face disadvantages that must be balanced by intrinsic benefits of living in a group. One potential route towards the evolution of sociality may emerge from the avoidance of dispersal, which can be risky in some environments. Although early studies found that local competition may cancel the benefits of cooperation in viscous populations, subsequent studies have identified conditions, such as the presence of kin recognition or specific demographic conditions, under which altruism will still spread. Most of these studies assume that the costs of cooperating outweigh the direct benefits (strong altruism). In nature, however, many organisms gain synergistic benefits from group living, which may counterbalance even costly altruistic behaviours. Here, we use an individual based model to investigate how dispersal and social behaviour co-evolve when social behaviours result in synergistic benefits that counterbalance the relative cost of altruism to a greater extent than assumed in previous models. When the cost of cooperation is high, selection for sociality responds strongly to the cost of dispersal. In particular, cooperation can begin to spread in a population when higher cooperation levels become correlated with lower dispersal tendencies within individuals. In contrast, less costly social behaviours are less sensitive to the cost of dispersal. In line with previous studies, we find that mechanisms of global population control also affect this relationship: when whole patches (groups) go extinct each generation, selection favours a relatively high dispersal propensity, and social behaviours evolve only when they are not very costly. If random individuals within groups experience mortality each generation to maintain a global carrying capacity, on the other hand, social behaviours spread and dispersal is reduced, even when the latter is not costly.

Degree of multicollinearity and variables involved in linear dependence in additive-dominant models

The objective of this work was to assess the degree of multicollinearity and to identify the variables involved in linear dependence relations in additive-dominant models. Data of birth weight (n=141,567), yearling weight (n=58,124), and scrotal circumference (n=20,371) of Montana Tropical composite cattle were used. Diagnosis of multicollinearity was based on the variance inflation factor (VIF) and on the evaluation of the condition indexes and eigenvalues from the correlation matrix among explanatory variables. The first model studied (RM) included the fixed effect of dam age class at calving and the covariates associated to the direct and maternal additive and non-additive effects. The second model (R) included all the effects of the RM model except the maternal additive effects. Multicollinearity was detected in both models for all traits considered, with VIF values of 1.03 - 70.20 for RM and 1.03 - 60.70 for R. Collinearity increased with the increase of variables in the model and the decrease in the number of observations, and it was classified as weak, with condition index values between 10.00 and 26.77. In general, the variables associated with additive and non-additive effects were involved in multicollinearity, partially due to the natural connection between these covariables as fractions of the biological types in breed composition.

Dynamical control of the mesosphere by orographic and non-orographic gravity wave drag during the extended northern winters of 2006 and 2009

A version of the Canadian Middle Atmosphere Model (CMAM) that is nudged toward reanalysis data up to 1 hPa is used to examine the impacts of parameterized orographic and non-orographic gravity wave drag (OGWD and NGWD) on the zonal-mean circulation of the mesosphere during the extended northern winters of 2006 and 2009 when there were two large stratospheric sudden warmings. The simulations are compared to Aura Microwave Limb Sounder (MLS) observations of mesospheric temperature, carbon monoxide (CO) and derived zonal winds. The control simulation, which uses both OGWD and NGWD, is shown to be in good agreement with MLS. The impacts of OGWD and NGWD are assessed using simulations in which those sources of wave drag are removed. In the absence of OGWD the mesospheric zonal winds in the months preceding the warmings are too strong, causing increased mesospheric NGWD, which drives excessive downwelling, resulting in overly large lower mesospheric values of CO prior to the warming. NGWD is found to be most important following the warmings when the underlying westerlies are too weak to allow much vertical propagation of the orographic gravity waves to the mesosphere. NGWD is primarily responsible for driving the circulation that results in the descent of CO from the thermosphere following the warmings. Zonal mean mesospheric winds and temperatures in all simulations are shown to be strongly constrained by (i.e. slaved to) the stratosphere. Finally, it is demonstrated that the responses to OGWD and NGWD are non-additive due to their dependence and influence on the background winds and temperatures.

The ex-Ante non-optimality of the Dempster-Schafer updating rule for ambiguous beliefs

The most widely used updating rule for non-additive probalities is the Dempster-Schafer rule. Schmeidles and Gilboa have developed a model of decision making under uncertainty based on non-additive probabilities, and in their paper “Updating Ambiguos Beliefs” they justify the Dempster-Schafer rule based on a maximum likelihood procedure. This note shows in the context of Schmeidler-Gilboa preferences under uncertainty, that the Dempster-Schafer rule is in general not ex-ante optimal. This contrasts with Brown’s result that Bayes’ rule is ex-ante optimal for standard Savage preferences with additive probabilities.

Heterose e capacidade combinatória em melão rendilhado

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Degree of multicollinearity and variables involved in linear dependence in additive-dominant models

The objective of this work was to assess the degree of multicollinearity and to identify the variables involved in linear dependence relations in additive-dominant models. Data of birth weight (n=141,567), yearling weight (n=58,124), and scrotal circumference (n=20,371) of Montana Tropical composite cattle were used. Diagnosis of multicollinearity was based on the variance inflation factor (VIF) and on the evaluation of the condition indexes and eigenvalues from the correlation matrix among explanatory variables. The first model studied (RM) included the fixed effect of dam age class at calving and the covariates associated to the direct and maternal additive and non-additive effects. The second model (R) included all the effects of the RM model except the maternal additive effects. Multicollinearity was detected in both models for all traits considered, with VIF values of 1.03 - 70.20 for RM and 1.03 - 60.70 for R. Collinearity increased with the increase of variables in the model and the decrease in the number of observations, and it was classified as weak, with condition index values between 10.00 and 26.77. In general, the variables associated with additive and non-additive effects were involved in multicollinearity, partially due to the natural connection between these covariables as fractions of the biological types in breed composition.