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Another presentation of the problem Let 2 :IRK IR be a continuously differentiable, strictly increasing function in each of its arguments. Let Q :R R be a continuously differentiable and strictly increas- ing function. Let W :IRK IR be defined by composition as follows: W (x) == p(2(x)). Let Wk denote the partial derivative of W with respect to xk. For each k = 1, K, and all x, xe RK, let Dk be an order with the following property: X Dk x' - W, (x) (x). Suppose we know 2, the orders Dk and that W is defined by composition as explained above (to be sure, we do not know the derivatives Wk (x) or Wk (x'), only the sign of Wk (x) - W, (x')). The questioni is: do we nevertheless have enough information to uniquely recover Q (up to positive affine transformations)?

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