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In this paper, we study nonzero-sum separable games, which are continuous games whose payoffs take a sum-of-products form. Included in this subclass are all finite games and polynomial games. We investigate the structure of equilibria in separable games. We show that these games admit finitely supported Nash equilibria. Motivated by the bounds on the supports of mixed equilibria in two-player finite games in terms of the ranks of the payoff matrices, we define the notion of the rank of an n-player continuous game and use this to provide bounds on the cardinality of the support of equilibrium strategies. We present a general characterization theorem that states that a continuous game has finite rank if and only if it is separable. Using our rank results, we present an efficient algorithm for computing approximate equilibria of two-player separable games with fixed strategy spaces in time polynomial in the rank of the game.

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A whole-body single-photon emission computed tomography system (SPECT) consisting of two large-field-of-view scintillation cameras mounted on a rotatable gantry, a minicomputer and a display station has been designed, constructed and evaluated. In its usual mode of operation, eleven contiguous transverse sections, each 12.5 or 25 mm thick, are reconstructed from projection data acquired during a single, continuous 360 degree rotation lasting from 2 to 22 min. A generalised filtered and weighted backprojection algorithm is used to reconstruct data obtained with conventional parallel-hole collimators in the case of body scanning, or with specially designed fan beam collimators in the case of centrally positioned organs. A simple, yet effective, correction is used to compensate for the effects of gamma ray attenuation within the patient. In addition to providing transverse section images, the system is capable of simultaneous acquisition of opposed conventional scintigrams, the reconstruction of longitudinal section images, and the acquisition of gated cardiac transverse sections. Resolutions in the reconstructed images are typically 15 mm for body scans and 11 mm for brain scans, with only slight variations in sensitivity and resolution within the image. Phantoms and clinical data demonstrate that the SPECT system generates high quality section images while maintaining most of the flexibility of normal scintillation cameras, with the added advantage of dual heads.