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We study the experimental design problem of selecting a most informative subset, having prespecified size, from a set of correlated random variables. The problem arises in many applied domains, such as meteorology, environmental statistics, and statistical geology. In these applications, observations can be collected at different locations, and possibly, at different times. Information is measured by “entropy.” In the Gaussian case, the problem is recast as that of maximizing the determinant of the covariance matrix of the chosen subset. We demonstrate that this problem is NP-hard. We establish an upper bound for the entropy, based on the eigenvalue interlacing property, and we incorporate this bound in a branch-and-bound algorithm for the exact solution of the problem. We present computational results for estimated covariance matrices that correspond to sets of environmental monitoring stations in the United States.

Submodular function maximization is a central problem in combinatorial optimization, generalizing many important problems including Max Cut in directed/undirected graphs and in hypergraphs, certain constraint satisfaction problems, maximum entropy sampling, and maximum facility location problems. Unlike submodular minimization, submodular maximization is NP-hard.In this paper, we give the first constant-factor approximation algorithm for maximizing any non-negative submodular function subject to multiple matroid or knapsack constraints. We emphasize that our results are for non-monotone submodular functions. In particular, for any constant k, we present a " 1 k+2+ 1 k + " -approximation for the submodular maximization problem under k matroid constraints, and a`1 5 − ´-approximation algorithm for this problem subject to k knapsack constraints ( > 0 is any constant). We improve the approximation guarantee of our algorithm to 1 k+1+ 1 k−1 + for k ≥ 2 partition matroid constraints. This idea also gives a " 1 k+ "-approximation for maximizing a monotone submodular function subject to k ≥ 2 partition matroids, which improves over the previously best known guarantee of 1 k+1 .

Ceftaroline fosamil demonstrated high clinical cure and microbiological response rates in hospitalized patients with CAP of PORT risk class III or IV. Ceftaroline fosamil was well tolerated, with a safety profile similar to that of ceftriaxone and consistent with the cephalosporin class. In this study, ceftaroline fosamil was an effective and well-tolerated treatment option for CAP.

Ceftaroline fosamil achieved high clinical cure and microbiological response rates in patients hospitalized with CAP of PORT risk class III or IV. Ceftaroline fosamil was well tolerated, with a safety profile that is similar to that of ceftriaxone and other cephalosporins. Ceftaroline fosamil is a promising agent for the treatment of CAP.

Submodular function maximization is a central problem in combinatorial optimization, generalizing many important problems including Max Cut in directed/undirected graphs and in hypergraphs, certain constraint satisfaction problems, maximum entropy sampling, and maximum facility location problems. Unlike submodular minimization, submodular maximization is NP-hard. In this paper, we give the first constant-factor approximation algorithm for maximizing any non-negative submodular function subject to multiple matroid or knapsack constraints. We emphasize that our results are for non-monotone submodular functions. In particular, for any constant k, we present a

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