We present a search for electroweak production of single top quarks in $\approx 90$ $pb^{-1}$ of data collected with the DZero detector at the Fermilab Tevatron collider. Using arrays of neural networks to separate signals from backgrounds, we set upper limits on the cross sections of 17 pb for the s-channel process $p\bar{p} \to tb + X$, and 22 pb for the t-channel process $p\bar{p} \to tqb + X$, both at the 95% confidence level.
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