Suppose we are given a vector f in RN. How many linear measurements do we need to make about f to be able to recover f to within precision ɛ in the Euclidean (ℓ2) metric? Or more exactly, suppose we are interested in a class F of such objects— discrete digital signals, images, etc; how many linear measurements do we need to recover objects from this class to within accuracy ɛ? This paper shows that if the objects of interest are sparse or compressible in the sense that the reordered entries of a signal f ∈ F decay like a power-law (or if the coefficient sequence of f in a fixed basis decays like a power-law), then it is possible to reconstruct f to within very high accuracy from a small number of random measurements. typical result is as follows: we rearrange the entries of f (or its coefficients in a fixed basis) in decreasing order of magnitude |f | (1) ≥ |f | (2) ≥... ≥ |f | (N), and define the weak-ℓp ball as the class F of those elements whose entries obey the power decay law |f | (n) ≤ C · n −1/p. We take measurements 〈f, Xk〉, k = 1,..., K, where the Xk are N-dimensional Gaussian

This paper puts forward two useful methods for self-adaptation of the mutation distribution -- the concepts of derandomization and cumulation. Principle shortcomings of the concept of mutative strategy parameter control and two levels of derandomization are reviewed. Basic demands on the self

) can be applied to other optimization problems like the asymmetric traveling salesman, the quadrat...

outputs and the destination’s channel output. The strategies are applied to wireless channels, and it is shown that decode-and-forward achieves the ergodic capacity with phase fading if phase information is available only locally, and if the relays are near the source node. The ergodic capacity coincides

Model predictive control is a form of control in which the current control action is obtained by solving, at each sampling instant, a finite horizon open-loop optimal control problem, using the current state of the plant as the initial state; the optimization yields an optimal control sequence

incremental optimization, permitting transformations to be triggered by one another and applied only to affected dependences.

This paper presents an approach to automatically optimizing the retrieval quality of search engines using clickthrough data. Intuitively, a good information retrieval system should present relevant documents high in the ranking, with less relevant documents following below. While previous

words in different The effective slope constraint characteristic is qualitatively analyzed, and the optimum slope constraint condition is determined through experiments. The optimized algorithm is then extensively subjected to experimentat comparison with various DP-algorithms, previously applied

(Article begins on next page) The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters. Citation Mumford, David Bryant, and Jayant Shah. 1989. Optimal approximations by piecewise smooth functions and associated variational problems

-deepening algorithm is shown to be asymptotically optimal along all three dimensions for exponential pee searches. The algorithm has been used successfully in chess programs, has been eflectiuely combined with bi-directional search, and has been applied to best-first heuristic search as well. This heuristic depth