Biolog phenotype microarrays (PMs) enable simultaneous, high throughput analysis of cell cultures in di®erent environments. The output is high-density time-course data showing redox curves (approximating growth) for each experimental condition. The software provided with the Omnilog incubator/reader summarizes each time-course as a single datum, so most of the information is not used. However, the time courses can be extremely varied and often contain detailed qualitative (shape of curve) and quantitative (values of parameters) information. We present a novel, Bayesian approach to estimating parameters from Phenotype Microarray data, tting growth models using Markov Chain Monte Carlo (MCMC) methods to enable high throughput estimation of important information, including length of lag phase, maximal \growth" rate and maximum output. We¯nd that the Baranyi model for microbial growth is useful for¯tting Biolog data. Moreover, we introduce a new growth model that allows for diauxic growth with a lag phase, which is particularly useful where Phenotype Microarrays have been applied to cells grown in complex mixtures of substrates, for example in industrial or
We study the computational challenge faced by a intermediary who attempts to profit from trade with a small number of buyers and sellers of some item. In the version of the problem that we study, the number of buyers and sellers is constant, but their joint distribution of the item's value may be complicated. We consider discretized distributions, where the complexity parameter is the support size, or number of different prices that may occur. We show that maximizing the expected revenue is computationally tractable (via an LP) if we are allowed to use randomized mechanisms. For the deterministic case, we show how an optimal mechanism can be efficiently computed for the oneseller/one-buyer case, but give a contrasting NP-completeness result for the one-seller/two-buyer case.
We characterise the set of dominant strategy incentive compatible (DSIC), strongly budget balanced (SBB), and ex-post individually rational (IR) mechanisms for the multi-unit bilateral trade setting. In such a setting there is a single buyer and a single seller who holds a finite number k of identical items. The mechanism has to decide how many units of the item are transferred from the seller to the buyer and how much money is transferred from the buyer to the seller. We consider two classes of valuation functions for the buyer and seller: Valuations that are increasing in the number of units in possession, and the more specific class of valuations that are increasing and submodular.Furthermore, we present some approximation results about the performance of certain such mechanisms, in terms of social welfare: For increasing submodular valuation functions, we show the existence of a deterministic 2-approximation mechanism and a randomised e/(1 − e) approximation mechanism, matching the best known bounds for the single-item setting. * Supported by ERC Advanced Grant 321171 (ALGAME) and the EPSRC.
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