We construct a pseudorandom generator which uses O(log m + log d + log 3=2 1==) bits and approximates the volume of any combinatorial rectangle in f1; : : : ; mg d to within error. O(log m + log d + log 2 1==) bits. For a subclass of rectangles with at most t log 1== nontriv-ial dimensions and each dimension being an interval, we also give a pseudorandom generator using O(log log d + log 1== lo...

The Weierstrass nowhere diierentiable function, and functions constructed from similar innnite series, have been studied often as examples of functions whose graph is a fractal. Though there is a simple formula for the Hausdorr dimension of the graph which is widely accepted, it has not been rigorously proved to hold. We prove that if arbitrary phases are included in each term of the summation ...

There exist two main solutions for the classification of highdimensional data with small number settings. One is to classify them directly in high-dimensional space with regularization methods, and the other is to reduce data dimension first, then classify them in feature space. However, which is better on earth? In this paper, the comparative studies for regularization and dimension reduction ...