The universal period-doubling scaling of a unimodal map with an asymmetric critical point is governed by a period-2 point of a renormalisation operator. The period-2 point is parametrised by the degree of the critical point and the asymmetry modulus. In this paper we study the asymptotics of period-2 points and their associated scaling parameters in the singular limit of degree tending to 1.

We used functional magnetic resonance imaging (fMRI) to investigate the psychological refractory period (PRP), the delay in the response to the second of two tasks occurring in immediate succession (Pashler, 1994). Consistent with prior work on the PRP, we found that when two visual-manual tasks were presented within an interval of 100ms of each other, the second response was delayed on the ord...

We focus on obtaining sparse representations of metrics: these are called spanners, and they have been studied extensively both for general and Euclidean metrics. Formally, a t-spanner for a metric M = (V, d) is an undirected graph G = (V,E) such that the distances according to dG (the shortest-path metric of G) are close to the distances in d: i.e., d(u, v) ≤ dG(u, v) ≤ t d(u, v). Clearly, one...

This conjecture is now established for quadratic polynomials (as a consequence of [Su] or [La]) and work is in progress toward generalization for higher degree polynomials [Hu]. The interest in such a conjecture comes from Theorems A and B below (see section 2.1) and the fact that topological entropy (conceived as an invariant of topological conjugacy [AKM]) is also one way to measure the compl...

Despite the impressive complexity and processing power of the human brain, it is severely capacity limited. Behavioral research has highlighted three major bottlenecks of information processing that can cripple our ability to consciously perceive, hold in mind, and act upon the visual world, illustrated by the attentional blink (AB), visual short-term memory (VSTM), and psychological refractory...

To interpret recent experiments on the dynamics of step doubling, we have studied a simple model of this phase transition. With Monte Carlo, we compute the time-dependence of the order parameter in the limit of rapid diffusion across terraces. Analysis of the data shows that the limiting step is the time for adjacent steps to touch each other; subsequent “zipping” together happens rapidly. From...

New nonlattice sphere packings in dimensions 20, 22, and 44–47 that are denser than the best previously known sphere packings were recently discovered. We extend these results, showing that the density of many sphere packings in dimensions just below a power of 2 can be doubled using orthogonal binary codes. This produces new dense sphere packings in Rn for n = 25, 26, . . . , 31 and 55, 56, . ...

The Hénon family has been shown to have period-doubling cascades. We show here that the same occurs for a much larger class: Large perturbations do not destroy cascades. Furthermore, we can classify the period of a cascade in terms of the set of orbits it contains, and count the number of cascades of each period. This class of families extends a general theory explaining why cascades occur [5].

Abstract Three local bifurcations in DC-DC converters are reviewed. They are period-doubling bifurcation, saddle-node bifurcation, and Neimark bifurcation. A general sampled-data model is employed to study types of loss of stability of the nominal (periodic) solution and their connection with local bifurcations. More accurate prediction of instability and bifurcation than using the averaging ap...

Parity doubling in excited hadrons is reviewed. Parity degeneracy in hadrons was first experimentally observed 40 years ago. Recently new experimental data on light mesons caused much excitement and renewed interest to the phenomenon, which still remains to be enigmatic. The present retrospective review is an attempt to trace the history of parity doubling phenomenon, thus providing a kind of i...