Optimal Transport, Convection, Magnetic Relaxation and Generalized Boussinesq equations

We establish a connection between Optimal Transport Theory and classical Convection Theory for geophysical flows. Our starting point is the model designed few years ago by Angenent, Haker and Tannenbaum to solve some Optimal Transport problems. This model can be seen as a generalization of the Darcy-Boussinesq equations, which is a degenerate version of the Navier-Stokes-Boussinesq (NSB) equations. In a unified framework, we relate different variants of the NSB equations (in particular what we call the generalized Hydrostatic-Boussinesq equations) to various models involving Optimal Transport (and the related Monge-Ampere equation. This includes the 2D semi-geostrophic equations and some fully non-linear versions of the so-called high-field limit of the Vlasov-Poisson system and of the Keller-Segel for Chemotaxis. Finally, we show how a ``stringy'' generalization of the AHT model can be related to the magnetic relaxation model studied by Arnold and Moffatt to obtain stationary solutions of the Euler equations with prescribed topology

Cooperation, Norms, and Revolutions: A Unified Game-Theoretical Approach

Cooperation is of utmost importance to society as a whole, but is often challenged by individual self-interests. While game theory has studied this problem extensively, there is little work on interactions within and across groups with different preferences or beliefs. Yet, people from different social or cultural backgrounds often meet and interact. This can yield conflict, since behavior that is considered cooperative by one population might be perceived as non-cooperative from the viewpoint of another. To understand the dynamics and outcome of the competitive interactions within and between groups, we study game-dynamical replicator equations for multiple populations with incompatible interests and different power (be this due to different population sizes, material resources, social capital, or other factors). These equations allow us to address various important questions: For example, can cooperation in the prisoner's dilemma be promoted, when two interacting groups have different preferences? Under what conditions can costly punishment, or other mechanisms, foster the evolution of norms? When does cooperation fail, leading to antagonistic behavior, conflict, or even revolutions? And what incentives are needed to reach peaceful agreements between groups with conflicting interests? Our detailed quantitative analysis reveals a large variety of interesting results, which are relevant for society, law and economics, and have implications for the evolution of language and culture as well

From Local to Global Dilemmas in Social Networks

Social networks affect in such a fundamental way the dynamics of the population they support that the global, population-wide behavior that one observes often bears no relation to the individual processes it stems from. Up to now, linking the global networked dynamics to such individual mechanisms has remained elusive. Here we study the evolution of cooperation in networked populations and let individuals interact via a 2-person Prisoner's Dilemma – a characteristic defection dominant social dilemma of cooperation. We show how homogeneous networks transform a Prisoner's Dilemma into a population-wide evolutionary dynamics that promotes the coexistence between cooperators and defectors, while heterogeneous networks promote their coordination. To this end, we define a dynamic variable that allows us to track the self-organization of cooperators when co-evolving with defectors in networked populations. Using the same variable, we show how the global dynamics — and effective dilemma — co-evolves with the motifs of cooperators in the population, the overall emergence of cooperation depending sensitively on this co-evolution

Analytical Results for Individual and Group Selection of Any Intensity

The idea of evolutionary game theory is to relate the payoff of a game to reproductive success (= fitness). An underlying assumption in most models is that fitness is a linear function of the payoff. For stochastic evolutionary dynamics in finite populations, this leads to analytical results in the limit of weak selection, where the game has a small effect on overall fitness. But this linear function makes the analysis of strong selection difficult. Here, we show that analytical results can be obtained for any intensity of selection, if fitness is defined as an exponential function of payoff. This approach also works for group selection (= multi-level selection). We discuss the difference between our approach and that of inclusive fitness theory

Functional Dentition in Brazilian Adults: An Investigation of Social Determinants of Health (SDH) Using a Multilevel Approach.

OBJECTIVES:Estimate the prevalence of functional dentition among Brazilian adults using four different definitions and identify associated factors. METHODS:A cross-sectional study was conducted involving 9564 Brazilian adults aged 35-44 years who participated in the 2010 National Oral Health Survey. Data collection involved oral examinations and the administration of questionnaires. The following definitions were used: 1-WHO Functional Dentition (FDWHO: ≥ 20 teeth present); 2-well-distributed teeth (WDT: ≥ 10 teeth in each arch); 3 -Functional dentition classified by esthetics and occlusion (FDClass5: dentitions that sequentially exhibit at least one tooth in each arch, at least 10 teeth in each arch, all maxillary and mandibular anterior teeth, three or four premolar posterior occluding pairs [POPs], and at least one molar POP bilaterally); 4-Functional dentition classified by esthetics, occlusion and periodontal status (FDClass6: corresponds to FDClass5 with the addition of periodontal status of all sextants in the oral cavity with, at most, shallow pockets and/or clinical attachment level of 5 mm (CPI ≤ 3 and/or CAL ≤ 1). The independent variables were individual factors (gender, self-declared skin color, schooling, monthly household income, age group, self-rated treatment need, dental pain, dental appointment in the previous 12 months and dental services) and contextual factors (Municipal Human Development Index [MHDI]), Gini coefficient, fluoridated water supply and oral health coverage). Multilevel mixed-effect Poisson regression analyses were performed. RESULTS:The prevalence of functional dentition based on the FDWHO, WDT, FDClass5 and FDClass6 definitions was 77.9%, 72.9%, 42.6% and 40.3%, respectively. Adults with ≥12 years of schooling and monthly household income from US$ 853 to 2557 had higher prevalence rates of FDWHO (PR: 1.41 and 1.10, respectively), WDT (PR: 1.58 and 1.14, respectively), FDClass5 (PR: 2.03 and 1.27, respectively) and FDClass6 (PR: 2.15 and 1.35, respectively). These values in the final models were adjusted for gender, self-declared skin color (FDClass5), age group, self-rated treatment need (FDWHO, FDClass5 and FDClass6), dental appointment in the previous 12 months (FDWHO and WDT), dental services (FDWHO and WDT) and contextual factors. A very high MHDI and presence of fluoridated water supply were associated with higher prevalence rates of the four outcomes. CONCLUSIONS:The incorporation of the criteria of new definitions of functional dentition led to a lower prevalence rate among Brazilian adults. Striking individual and contextual inequalities were identified with regard to the four definitions analyzed, which need to be addressed through inter-sector efforts