Let X[0..n− 1] and Y [0..m− 1] be two sorted arrays, and define the m × n matrix A by A[j][i] = X[i] + Y [j]. Frederickson and Johnson [7] gave an efficient algorithm for selecting the kth smallest element from A. We show how to make this algorithm IO-efficient. Our cache-oblivious algorithm performs O((m + n)/B) IOs, where B is the block size of memory transfers.

Let P ∈ Q <m...

The novel methods for binary discrete Fourier transform (DFT) computation over the finite field have been proposed. are based on a trace calculation and use cyclotomic DFT. direct DFT computational complexity has reduced due to using function functions of which stored in small tables. inverse representation elements with respect normal basis. proposed can be used encoding/decoding subfield subc...

We establish a number of foundational results on Poincaré spaces which result in several applications. One application settles an old conjecture C.T.C. Wall the affirmative. Another shows that for any natural n <mml:annotation encoding="application/x...

Are there limits to how small one can make a thermodynamic machine? At first sight, this question appears to contradict itself, as thermodynamics usually begins with a kind of macroscopic picture. However, as Nicolas Brunner at the University of Bristol, UK, and colleagues describe in a paper appearing in Physical Review E, this constraint can be circumvented, if one focuses on a special kind o...

Regression with quadratic loss is another basic problem studied in statistical learning theory. We have a random couple Z = (X ,Y ), where, as before, X is anRd -valued feature vector (or input vector) and Y is the real-valued response (or output). We assume that the unknown joint distribution P = PZ = PX Y of (X ,Y ) belongs to some class P of probability distributions over Rd ×R. The learning...