Sieve-theoretical methods are one of the first historical examples of theoretical tools whose implementational character has largely contributed to the development of computational musicology. According to Xenakis’ original intuition, we distinguish between elementary transformations of sieves and compound ones. This makes sense if the sieve construction is considered as part of the musical mea...

A prime number sieve is an algorithm that nds the primes up to a bound n. We present four new prime number sieves. Each of these sieves gives new space complexity bounds for certain ranges of running times. In particular, we give a linear time sieve that uses only O(p n=(log log n) 2) bits of space, an O l (n= log log n) time sieve that uses O(n=((log n) l log log n)) bits of space, where l > 1...

A prime number sieve is an algorithm for finding all prime numbers in the range [2,n]. For large n, however, the actual run time of existing algorithms on a single processor computer is prohibitive. Fortunately, the classic Sieve of Eratosthenes and its extensions are suitable for massively parallel architectures or networks of workstations. Two mappings of the third extension sieve are present...

A sieve is a technique for bounding the size of a set after the elements with “undesirable properties” (usually of a number theoretic nature) have been removed. The undesirable properties could be divisibility by a prime from a given set, other multiplicative constraints (divisibility by a perfect square for example) or inclusion in a set of residue classes. The methods usually involve some kin...

1 Basic inequality For any real numbers ρ d satisfying ρ 1 = 1, and for any natural number m, we have d|m µ(d) d|m ρ d 2 = e|m λ e , λ e = [d 1 ,d 2 ]=e ρ d 1 ρ d 2. Our goal is to optimize the choice of (ρ d) d1. Let m = (n, P (z)), multiply by a n and sum over n using (g): say. Minimizing XG + R is quite difficult. However, if we restrict the support of ρ to d √ D, it is relatively easy to mi...

This paper first establishes the asymptotic normality of plug-in sieve M estimators of possibly irregular functionals of semi-nonparametric time series models. We show that, even when the sieve score process is not a martingale difference, the asymptotic variances of plug-in sieve M estimators of irregular (i.e., slower than root-T estimable) functionals are the same as those for independent da...

Although the enucleate conducting cells of the phloem are incapable of protein synthesis, phloem exudates characteristically contain low concentrations of soluble proteins. The role of these proteins and their movement into and out of the sieve tubes poses important questions for phloem physiology and for cell-to-cell protein movement via plasmodesmata. The occurrence of protein turnover in sie...

The sieve method is a classic one in number theory (see, for example, [FI]). Recently it found some applications in a non-commutative setting. On the one hand, Bourgain-Gamburd-Sarnak [BGS1] applied it in studying almost-prime vectors in orbits of non-commutative groups acting on Z. On the other hand, Rivin [Ri] and Kowalski [Ko] used it to study generic properties of elements in the mapping cl...