Blacks had poorer HTN control compared with whites and Hispanics. Significant discrepancies in BP control between hypertensive patients with and without diabetes may be related to a lack of provider adherence to JNC 7 guidelines that define BP control in this population as <130/80. Further research is needed to understand racial disparities in BP control as well as factors influencing clinician's management of BP among patients with diabetes.

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We consider an n-player symmetric stochastic game with weak interactions between the players. Time is continuous and the horizon and the number of states are finite. We show that the value function of each of the players can be approximated by the solution of a partial differential equation called the master equation. Moreover, we analyze the fluctuations of the empirical measure of the states of the players in the game and show that it is governed by a solution to a stochastic differential equation. Finally, we prove the regularity of the master equation, which is required for the above results. , web: https://sites.google.com/site/asafcohentau/ 1 During the review of this paper it was brought to our attention that Cecchin and Pelino [10] also independently analyzed the finite-state MFG using the master equation approach. The n-player game in that paper is formulated using the formulation in [9] while we follow the formulation given in [18]. We prove our main result, the fluctuations, using a probabilistic approach which relies on coupling, whereas [10] uses an analytical approach relying on the convergence of the generators. It also happens that our assumptions for the convergence results (in Section 2) are slightly weaker. In obtaining sufficient conditions, Section 3.4 of this paper, both papers adapt the approach of [5] to discrete state space.

In this paper, we present a simpler and more restricted variant of the universally composable security (UC) framework that is suitable for "standard" two-party and multiparty computation tasks. Many of the complications of the UC framework exist in order to enable more general tasks than classic secure computation. This generality may be a barrier to entry for those who are used to the stand-alone model of secure computation and wish to work with universally composable security but are overwhelmed by the differences. The variant presented here (called simplified universally composable security, or just SUC) is closer to the definition of security for multiparty computation in the stand-alone setting. The main difference is that a protocol in the SUC framework runs with a fixed set of parties who know each other's identities ahead of time, and machines cannot be added dynamically to the execution. As a result, the definitions of polynomial time and protocol composition are much simpler. In addition, the SUC framework has authenticated channels built in, as is standard in previous definitions of security, and all communication is done via the adversary in order to enable arbitrary scheduling of messages. Due to these differences, not all cryptographic tasks can be expressed in the SUC framework. Nevertheless, standard secure computation tasks (like secure function evaluation) can be expressed. Importantly, we show a natural security-preserving transformation from protocols in the SUC model to protocols in the full-fledged UC model. Consequently, the UC composition theorem holds in the SUC model, and any protocol that is proven secure under SUC can be transformed to a protocol that is secure in the UC model.

Bandit problems model the trade-off between exploration and exploitation in various decision problems. We study two-armed bandit problems in continuous time, where the risky arm can have two types: High or Low; both types yield stochastic payoffs generated by a Lévy process. We show that the optimal strategy is a cut-off strategy and we provide an explicit expression for the cut-off and for the optimal payoff. web: www.math.tau.ac.il/∼eilons. 1 2 ASAF COHEN AND EILON SOLAN an index, which is a real number, based on past rewards of that arm, and chooses the arm with the highest index. It turns out that to calculate the index of an arm it is sufficient to consider an auxiliary problem with two arms: an arm for which the index is calculated and an arm that yields a constant payoff. The former arm is termed the risky arm, because its payoff distribution is not known, while the latter is termed the safe arm. The literature therefore focuses on such problems, called two-armed bandit problems. 1 Once the optimality of the index strategy is guaranteed, one looks for the relation between the data of the problems and the index. Explicit formulas for the index when the payoff is one of two distributions that have a simple form have been established in the literature. Berry and Friestedt (1985) [3] provide the solution to the problem in several cases, e.g., in discrete time when the payoff distribution is one of two Bernoulli distributions, and in continuous time when the payoff distribution is one of two Brownian motions. By studying the dynamic programming equation that describes the problem in continuous time, Keller, Rady, and Cripps (2005) [14] and Keller and Rady (2010) [13] provided an explicit form for the index when time is continuous and the payoff's distribution is Poisson. 2 In the present paper we study two-armed bandit problems in continuous time and provide an explicit solution when the payoff distribution of the risky arm is one of two Lévy processes. We assume that one distribution, called High, dominates the other, called Low, in a strong sense (see Assumption 2.6 below). To eliminate trivial cases, we assume that the expected payoff generated by the safe arm is lower than the expected payoff generated by the High distribution, and higher than the expected payoff generated by the Low distribution.In discrete time, under these assumptions the optimal strategy is a cut-off strategy: the DM keeps experimenting as long as the posterior belief that the distribution is High is higher than some cut-off point, and, once the posterior probability that the distribution is High falls below the cut-off point, the DM switches to the safe arm forever. We extend this result to our setup, and prove that when the two payoff distributions are Lévy processes that satisfy several requirements, the optimal strategy is a cut-off strategy. Moreover, we provide an explicit expression for the cut-off point in terms of the data of the problem. When particularized to the models studied by Bolton and Harris (1999) [6], Keller, Rady...

We study a differential game that governs the moderate-deviation heavy-traffic asymptotics of a multiclass single-server queueing control problem with a risk-sensitive cost. We consider a cost set on a finite but sufficiently large time horizon, and show that this formulation leads to stationary feedback policies for the game. Several aspects of the game are explored, including its characterization via a (one-dimensional) free boundary problem, the semi-explicit solution of an optimal strategy, and the specification of a saddle point. We emphasize the analogy to the well-known Harrison-Taksar free boundary problem which plays a similar role in the diffusion-scale heavy-traffic literature.

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