Hierarchical structure in sequence processing: How to measure it and determine its neural implementation

In many domains of human cognition, hierarchically structured representations are thought to play a key role. In this paper, we start with some foundational definitions of key phenomena like “sequence” and “hierarchy," and then outline potential signatures of hierarchical structure that can be observed in behavioral and neuroimaging data. Appropriate behavioral methods include classic ones from psycholinguistics along with some from the more recent artificial grammar learning and sentence processing literature. We then turn to neuroimaging evidence for hierarchical structure with a focus on the functional MRI literature. We conclude that, although a broad consensus exists about a role for a neural circuit incorporating the inferior frontal gyrus, the superior temporal sulcus, and the arcuate fasciculus, considerable uncertainty remains about the precise computational function(s) of this circuitry. An explicit theoretical framework, combined with an empirical approach focusing on distinguishing between plausible alternative hypotheses, will be necessary for further progress

Dispersion of plasmons in three-dimensional superconductors

We study the plasma branch of an homogeneous three-dimensional electron gas in an s-wave superconducting state. We focus on the regime where the plasma frequency ωp is comparable to the gap ∆, which is experimentally realized in cuprates. Although a sum rule guarantees that the departure of the plasma branch always coincides with the plasma frequency, the dispersion and lifetime of the plasmons is strongly affected by the presence of the pair condensate, especially at energies close to the pair-breaking threshold 2∆. When ωp is above 1.7∆, the level repulsion is strong enough to give the plasma branch an anomalous, negative dispersion with a minimum at finite wavelength. At non-zero temperature and at ωp > 2∆, we treat in a non-perturbative way the coupling of plasmons to the fermionic excitations, and show that a broadened plasma resonance inside the pair-breaking continuum coexists with an undamped solution in the band gap. This resonance splitting is associated with the presence of multiple poles in the analytic continuation of the propagator of the Cooper pairs