The Master Equation for Large Population Equilibriums

We use a simple N-player stochastic game with idiosyncratic and common noises to introduce the concept of Master Equation originally proposed by Lions in his lectures at the Coll\`ege de France. Controlling the limit N tends to the infinity of the explicit solution of the N-player game, we highlight the stochastic nature of the limit distributions of the states of the players due to the fact that the random environment does not average out in the limit, and we recast the Mean Field Game (MFG) paradigm in a set of coupled Stochastic Partial Differential Equations (SPDEs). The first one is a forward stochastic Kolmogorov equation giving the evolution of the conditional distributions of the states of the players given the common noise. The second is a form of stochastic Hamilton Jacobi Bellman (HJB) equation providing the solution of the optimization problem when the flow of conditional distributions is given. Being highly coupled, the system reads as an infinite dimensional Forward Backward Stochastic Differential Equation (FBSDE). Uniqueness of a solution and its Markov property lead to the representation of the solution of the backward equation (i.e. the value function of the stochastic HJB equation) as a deterministic function of the solution of the forward Kolmogorov equation, function which is usually called the decoupling field of the FBSDE. The (infinite dimensional) PDE satisfied by this decoupling field is identified with the \textit{master equation}. We also show that this equation can be derived for other large populations equilibriums like those given by the optimal control of McKean-Vlasov stochastic differential equations. The paper is written more in the style of a review than a technical paper, and we spend more time and energy motivating and explaining the probabilistic interpretation of the Master Equation, than identifying the most general set of assumptions under which our claims are true

Evolutionary game of coalition building under external pressure

We study the fragmentation-coagulation (or merging and splitting) evolutionary control model as introduced recently by one of the authors, where $N$ small players can form coalitions to resist to the pressure exerted by the principal. It is a Markov chain in continuous time and the players have a common reward to optimize. We study the behavior as $N$ grows and show that the problem converges to a (one player) deterministic optimization problem in continuous time, in the infinite dimensional state space

A Semi-Lagrangian scheme for a modified version of the Hughes model for pedestrian flow

In this paper we present a Semi-Lagrangian scheme for a regularized version of the Hughes model for pedestrian flow. Hughes originally proposed a coupled nonlinear PDE system describing the evolution of a large pedestrian group trying to exit a domain as fast as possible. The original model corresponds to a system of a conservation law for the pedestrian density and an Eikonal equation to determine the weighted distance to the exit. We consider this model in presence of small diffusion and discuss the numerical analysis of the proposed Semi-Lagrangian scheme. Furthermore we illustrate the effect of small diffusion on the exit time with various numerical experiments

Recommendations for increasing the use of HIV/AIDS resource allocation models

The article of record as published may be found at: http://dx.doi.org/10.1186/1471-2458-9-S1-S8Background: Resource allocation models have not had a substantial impact on HIV/AIDS resource allocation decisions in spite of the important, additional insights they may provide. In this paper, we highlight six difficulties often encountered in attempts to implement such models in policy settings; these are: model complexity, data requirements, multiple stakeholders, funding issues, and political and ethical considerations. We then make recommendations as to how each of these difficulties may be overcome. Results: To ensure that models can inform the actual decision, modellers should understand the environment in which decision-makers operate, including full knowledge of the stakeholders' key issues and requirements. HIV/AIDS resource allocation model formulations should be contextualized and sensitive to societal concerns and decision-makers' realities. Modellers should provide the required education and training materials in order for decision-makers to be reasonably well versed in understanding the capabilities, power and limitations of the model. Conclusion: This paper addresses the issue of knowledge translation from the established resource allocation modelling expertise in the academic realm to that of policymaking

Body image disturbance and surgical decision making in egyptian post menopausal breast cancer patients

<p>Abstract</p> <p>Background</p> <p>In most developing countries, as in Egypt; postmenopausal breast cancer cases are offered a radical form of surgery relying on their unawareness of the subsequent body image disturbance. This study aimed at evaluating the effect of breast cancer surgical choice; Breast Conservative Therapy (BCT) versus Modified Radical Mastectomy (MRM); on body image perception among Egyptian postmenopausal cases.</p> <p>Methods</p> <p>One hundred postmenopausal women with breast cancer were divided into 2 groups, one group underwent BCT and the other underwent MRM. Pre- and post-operative assessments of body image distress were done using four scales; Breast Impact of Treatment Scale (BITS), Impact of Event Scale (IES), Situational Discomfort Scale (SDS), and Body Satisfaction Scale (BSS).</p> <p>Results</p> <p>Preoperative assessment showed no statistical significant difference regarding cognitive, affective, behavioral and evaluative components of body image between both studied groups. While in postoperative assessment, women in MRM group showed higher levels of body image distress among cognitive, affective and behavioral aspects.</p> <p>Conclusion</p> <p>Body image is an important factor for postmenopausal women with breast cancer in developing countries where that concept is widely ignored. We should not deprive those cases from their right of less mutilating option of treatment as BCT.</p

How to achieve synergy between medical education and cognitive neuroscience? An exercise on prior knowledge in understanding

A major challenge in contemporary research is how to connect medical education and cognitive neuroscience and achieve synergy between these domains. Based on this starting point we discuss how this may result in a common language about learning, more educationally focused scientific inquiry, and multidisciplinary research projects. As the topic of prior knowledge in understanding plays a strategic role in both medical education and cognitive neuroscience it is used as a central element in our discussion. A critical condition for the acquisition of new knowledge is the existence of prior knowledge, which can be built in a mental model or schema. Formation of schemas is a central event in student-centered active learning, by which mental models are constructed and reconstructed. These theoretical considerations from cognitive psychology foster scientific discussions that may lead to salient issues and questions for research with cognitive neuroscience. Cognitive neuroscience attempts to understand how knowledge, insight and experience are established in the brain and to clarify their neural correlates. Recently, evidence has been obtained that new information processed by the hippocampus can be consolidated into a stable, neocortical network more rapidly if this new information fits readily into a schema. Opportunities for medical education and medical education research can be created in a fruitful dialogue within an educational multidisciplinary platform. In this synergetic setting many questions can be raised by educational scholars interested in evidence-based education that may be highly relevant for integrative research and the further development of medical education