We have developed a method for reconstructing equations of motion for systems where all the necessary variables have not been observed. This technique can be applied to systems with one or several such hidden variables, and can be used to reconstruct maps or differential equations. The effects of experimental noise are discussed through specific examples. The control of nonlinear systems containing hidden variables is also discussed.

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We have developed a procedure for finding optimal representations of experimental data. Criteria for optimality vary according to context; an optimal state space representation will be one that best suits one’s stated goal for reconstruction. We consider an ∞-dimensional set of possible reconstruction coordinate systems that include time delays, derivatives, and many other possible coordinates; and any optimality criterion is specified as a real valued functional on this space. We present a method for finding the optima using a learning algorithm based upon the genetic algorithm and evolutionary programming. The learning algorithm machinery for finding optimal representations is independent of the definition of optimality, and thus provides a general tool useful in a wide variety of contexts.

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In an attempt to expand the understanding of auction-price dynamics for fine wines, an age-period-cohort (APC) algorithm is applied to a database of 1.5 million auction results to quantify key drivers of these price dynamics. APC algorithms are designed to separate price appreciation with the age of the wine from overall wine-market conditions as well as to adjust for the unique value of specific vintages. In this context, the APC modeling provides a kind of Hedonic modeling, with specific controls regarding specification errors.The analysis was segmented by Château Lafite Rothschild, Bordeaux excluding Lafite, and Burgundy so that we could test specific events related to Château Lafite Rothschild. The results show price dynamics versus the ages of the wines and allow for the measurement of long-term price-appreciation potential. Environment functions versus auction dates quantify the “Lafite Bubble” and suggest past correlation to Chinese stock-market indices. An analysis of wine ratings versus price quantifies their nonlinear relationship. An analysis across nine auction houses shows a significant price spread for similar wines. (JEL Classifications: C23, D44, G11, G12, Q11)