A simple and practical all-fiber approach for realizing ultrafast optical differentiators is proposed and numerically tested. In particular, it is demonstrated that first-order and second-order temporal differentiation of an arbitrary optical waveform can be realized by simply propagating the waveform through a suitable uniform longperiod grating photoinscribed in the core of an optical fiber (...

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...