In this article, we deal with fast arithmetic in the Picard group of hyperelliptic curves of genus 3 over binary fields. We investigate both the optimal performance curves, where h(x) = 1, and the more general curves where the degree of h(x) is 1, 2 or 3. For the optimal performance curves, we provide explicit halving and doubling formulas; not only for the most frequent case but also for all p...

A pitch determination method based on AMDF (Average Magnitude Difference Function) is proposed in this paper. The AMDF is often used to determine the pitch parameter in real-time speech processing applications. Falling trend of AMDF at higher lags, however, makes the method vulnerable to octave errors (pitch doubling or halving). In this paper, we propose an alignment technique that effectively...

In this paper we deal with the location of hyperplanes in n{ dimensional normed spaces. If d is a distance measure, our objective is to nd a hyperplane H which minimizes points and d(x m ; H) = min z2H d(x m ; z) is the distance from x m to the hyperplane H. In robust statistics and operations research such an optimal hyperplane is called a median hyperplane. We show that for all distance measu...

For FDI to help achieve the international development goal of halving absolute poverty, two conditions have to be met. First, poor developing countries need to be attractive to foreign investors. Second, the host-country environment in which foreign investors operate must be conducive to favourable FDI effects with regard to overall investment, economic spillovers and income growth. This paper ...

We used a genetic search algorithm to find sets of points with many halving lines. There are sets of 10 points with 13 halving lines, 12 points with 18 halving lines, 14 points with 22 halving lines, 16 points with 27 halving lines, and 18 points with 32 halving lines. We find a construction generalizing the 12 point configuration and show that, for any n = 3 · 2, there are configurations of n ...

We construct a dense point set of n points in the plane with ne( √ logn) halving lines. This improves the bound O(n log n) of Edelsbrunner, Valtr and Welzl from 1997. We also observe that the upper bound on the maximum number of halving lines of dense point set can be improved to O(n). Our construction can be generalized to higher dimensions, for any d we construct a dense point set of n points...

We study two problems in the double cut and join (DCJ) model: sorting – transforming one multilinear genome into another and halving – transforming a duplicated genome into a perfectly duplicated one. The DCJ model includes rearrangement operations such as reversals, translocations, fusions and fissions. We can also mimic transpositions or block interchanges by two operations: we extract an app...

In this paper we rederive an old upper bound on the number of halving edges present in the halving graph of an arbitrary set of n points in 2-dimensions which are placed in general position. We provide a different analysis of an identity discovered by Andrejak et al, to rederive this upper bound of O(n). In the original paper of Andrejak et al. the proof is based on a naive analysis whereas in ...

Genome median and halving problems aim at reconstructing ancestral genomes and the evolutionary events leading from the ancestor to extant species. The NP-hardness of the breakpoint distance and reversal distance median problems for unichromosomal genomes do not easily imply the same for the multichromosomal case. Here we find the complexity of several genome median and halving problems, includ...

B) is said to have the Size Four property if the blocks in B can be partitioned into two isomorphic sets. In this paper we construct block with four with the property, thus the exception of 6 A. Rosa [4]).