For parametrized families of dynamical systems, two major goals are classifying the systems up to topological conjugacy, and understanding the structure of the bifurcation locus. The family Fλ = z n + λ/z gives a 1-parameter, n+ d degree family of rational maps of the Riemann sphere, which arise as singular perturbations of the polynomial z. This work presents several results related to these g...

In this paper we present an algorithm for generating the lexicographi cally smallest representatives of all the n bead necklaces in k colors The time required is O nN k where N n k is the number of necklaces with n beads of k colors To our knowledge this is the rst algorithm for this problem which has been proved to asymptotically improve the obvious O n k approach of examining all k ary n tupl...

We investigate D-term strings in angled inflation and show how they could be distinguished from conventional cosmic strings. In angled inflation, D-term strings are Dp−2 branes that are extended between Dp branes. The Dp−2 brane has a flat direction in compactified space, along which the endpoint of the Dp−2 brane can move freely on the Dp brane. Then naturally the position of the Dp−2 brane co...

A k-ary necklace of order n is an equivalence class of strings of length n of symbols from {0, 1, . . . , k − 1} under cyclic rotation. In this paper we define an ordering on the free semigroup on two generators such that the binary strings of length n are in Gray-code order for each n. We take the binary necklace class representatives to be the least of each class in this ordering. We examine ...

We study the problem of indexing irreducible polynomials over finite fields, and give the first efficient algorithm for this problem. Specifically, we show the existence of poly(n, log q)-size circuits that compute a bijection between {1, . . . , |S|} and the set S of all irreducible, monic, univariate polynomials of degree n over a finite field Fq. This has applications in pseudorandomness, an...

We show how a recently proposed supersymmetric quantum mechanics model leads to non-trivial results/conjectures on the combinatorics of binary necklaces and linear-feedback shift-registers. Fermi statistics plays a crucial role by projecting out certain states/necklaces by virtue of Pauli's famous exclusion principle. Some of our results can be rephrased in terms of generalizations of the well-...

We argue that due to various restrictions cosmic strings and monopolestring networks are not likely to produce the observed flux of ultra-high energy cosmic rays (UHECR). Among the topological defects studied so far, the most promising UHECR sources are necklaces and monopolonia. Other viable sources which are similar to topological defects are relic superheavy particles. All these sources have...

We show how a recently proposed supersymmetric quantum mechanics model leads to non-trivial results/conjectures on the combinatorics of binary necklaces and linear-feedback shift-registers. Pauli's exclusion principle plays a crucial role: by projecting out certain states/necklaces, it allows to represent the supersymmetry algebra in the resulting sub-space. Some of our results can be rephrased...