1 This is an ongoing draft of a report describing our work on Active Shape Models and Active Appearance Models. Hopefully it will be expanded to become more comprehensive, when I get the time. My apologies for the missing and incomplete sections and the inconsistancies in notation. TFC

We derive a simple relationship between the values and exercise boundaries of American puts and calls. The relationship holds for options with the same \moneyness", although the absolute level of the strike price and underlying may di er. The result holds in both the Black Scholes model and in a more general di usion setting. We thank Neil Chriss, the editor, and two anonymous referees for thei...

This note contains a proof of the exponential separation of depth-d circuits from depth(d + 1) circuits due to Håstad [Has89]. The separating functions are the Sipser functions, denoted fd+1,n. We use a simplified proof of Håstad’s second switching lemma due to Neil Thapen [Tha09].

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