Re-evaluating rhythmic attentional switching: Spurious oscillations from shuffling-in-time

How does attention help to focus perceptual processing on the important parts of a visual scene? Although the neural and perceptual effects of attention were traditionally assumed to be sustained over time, the field is converging on a dramatically different view: that covert attention rhythmically switches between objects at 3-8 Hz. Here I demonstrate that ubiquitous analyses in this literature conflate rhythmic oscillations with aperiodic temporal structure. Using computational simulations, I show that the behavioral oscillations reported in this literature could reflect aperiodic dynamics in attention, rather than periodic rhythms. I then propose two analyses (one novel and one widely used in climate science) that discriminate between periodic and aperiodic structure in behavioral time-series. Finally, I apply these alternative analyses to published data-sets, and find no evidence for rhythms in attentional switching after accounting for aperiodic temporal structure. Attention shows rich temporal structure. The techniques presented here will help to clarify the periodic and aperiodic dynamics of perception and cognition.

Propagation of acoustic waves in 2D periodic and quasiperiodic phononic crystals

In this study, we have investigated theoretically the propagation of longitudinal sonic waves in 2D periodic and aperiodic (quasiperiodic) phononic crystals. Fibonacci sequence has been used to generate the aperiodic structure. The effect of transformation from 2D periodic to aperiodic structure has been elucidated by calculating the transmission coefficient. The consequences of inserting a circular solid cylinder inside a host water matrix have been repeated at the same calculating conditions. Changing filling fraction has been used to tune the stop band width.

Supports of Extremal Doubly Stochastic Measures

A doubly stochastic measure on the unit square is a Borel probability measure whose horizontal and vertical marginals both coincide with the Lebesgue measure. The set of doubly stochasticmeasures is convex and compact so its extremal points are of particular interest. The problem number 111 of Birkhoò is to provide a necessary and suõcient condition on the support of a doubly stochastic measure to guarantee extremality. It was proved by Beneš and Štepán that an extremal doubly stochastic measure is concentrated on a set which admits an aperiodic decomposition. Hestir and Williams later found a necessary condition which is nearly sufficient by further refining the aperiodic structure of the support of extremal doubly stochastic measures. Our objective in this work is to provide a more practical necessary and nearly sufficient condition for a set to support an extremal doubly stochastic measure