The Information Level

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The continuation of research on the information level of information based complexity is proposed. The application of information.based complexity to problems in many disciplines and areas is summarized. Six new research directions are proposed: *Optimal Information for multivariate integration in the random and average settings *Randomization and the power of integral information *Applications of random information to eigenvalue problems *Optimal information for solving nonlinear equations in the average case setting *Noisy information *Optimal information in mixed settings. In the first three of these we will explore whether we can break intractability or noncomputability by using randomness or an average case setting. In the fourth we propose the study of nonlinear average equations in the average case setting. The fifth is the study of optimal information and computational complexity when the information is noisy. Finally, we would like to initiate the study of optimal information in a mixed setting.