Learn More
Historical datasets have much to offer. We analyse data from winter wheat, spring and winter barley, oil seed rape, sugar beet and forage maize from the UK National List and Recommended List trials over the period 1948–2007. We find that since 1982, for the cereal crops and oil seed rape, at least 88% of the improvement in yield is attributable to genetic(More)
A factoring method is presented which, heuristically, splits composite n in O(n1/4+ ) steps. There are two ideas: an integer approximation to √ (q/p) provides an O(n1/2+ ) algorithm in which n is represented as the difference of two rational squares; observing that if a prime m divides a square, then m2 divides that square, a heuristic speed-up to O(n1/4+ )(More)
Lim and Lee 5] describe protocols for server-aided RSA digital signatures involving moduli N with special structure: N = pq where p and q are both of order N 1=2 , and p ? 1 and q ? 1 have a large common factor. We describe a method to factor such numbers in time O ? N 1=4 == and show that this renders the proposed system insecure.
We completely describe all integer symmetric matrices that have all their eigenvalues in the interval [−2, 2]. Along the way we classify all signed graphs, and then all charged signed graphs, having all their eigenvalues in this same interval. We then classify subsets of the above for which the integer symmetric matrices, signed graphs and charged signed(More)
In recent years, there has been spectacular progress in the practical art of factoring. By contrast, the theoretical problem of nding deterministic algorithms which provably factor composite n has made little, if any, progress since Pollard ((Pol]) and Strassen ((Str]) showed that FFT techniques could be utilised to factor an integer n in O(n 1=4+) steps.(More)
We construct minimal polynomials of totally positive algebraic integers of small absolute trace by consideration of their reductions modulo auxiliary polynomials. Many new examples of such polynomials of minimal absolute trace (for given degree) are found. The computations are pushed to degrees that previously were unattainable, and one consequence is that(More)
Most web services take a \one size ts all" approach: all visitors see the same generic content, formatted in the same generic manner. But of course each visitor has her own information needs and preferences. In contrast to most personalization systems, we are interested in how effective personalization can be with zero additional user input or feedback.(More)
We show that there are Salem numbers of every trace. The nontrivial part of this result is for Salem numbers of negative trace. The proof has two main ingredients. The first is a novel construction, using pairs of polynomials whose zeros interlace on the unit circle, of polynomials of specified negative trace having one factor a Salem polynomial, with any(More)