2,142 research outputs found

    A note on quantum algorithms and the minimal degree of epsilon-error polynomials for symmetric functions

    Full text link
    The degrees of polynomials representing or approximating Boolean functions are a prominent tool in various branches of complexity theory. Sherstov recently characterized the minimal degree deg_{\eps}(f) among all polynomials (over the reals) that approximate a symmetric function f:{0,1}^n-->{0,1} up to worst-case error \eps: deg_{\eps}(f) = ~\Theta(deg_{1/3}(f) + \sqrt{n\log(1/\eps)}). In this note we show how a tighter version (without the log-factors hidden in the ~\Theta-notation), can be derived quite easily using the close connection between polynomials and quantum algorithms.Comment: 7 pages LaTeX. 2nd version: corrected a few small inaccuracie

    Comparison between Oja's and BCM neural networks models in finding useful projections in high-dimensional spaces

    Get PDF
    This thesis presents the concept of a neural network starting from its corresponding biological model, paying particular attention to the learning algorithms proposed by Oja and Bienenstock Cooper & Munro. A brief introduction to Data Analysis is then performed, with particular reference to the Principal Components Analysis and Singular Value Decomposition. The two previously introduced algorithms are then dealt with more thoroughly, going to study in particular their connections with data analysis. Finally, it is proposed to use the Singular Value Decomposition as a method for obtaining stationary points in the BCM algorithm, in the case of linearly dependent inputs
    • …
    corecore