Brain activation during anticipation of sound sequences

Music consists of sound sequences that require integration over time. As we become familiar with music, associations between notes, melodies, and entire symphonic movements become stronger and more complex. These associations can become so tight that, for example, hearing the end of one album track can elicit a robust image of the upcoming track while anticipating it in total silence. Here, we study this predictive “anticipatory imagery” at various stages throughout learning and investigate activity changes in corresponding neural structures using functional magnetic resonance imaging. Anticipatory imagery (in silence) for highly familiar naturalistic music was accompanied by pronounced activity in rostral prefrontal cortex (PFC) and premotor areas. Examining changes in the neural bases of anticipatory imagery during two stages of learning conditional associations between simple melodies, however, demonstrates the importance of fronto-striatal connections, consistent with a role of the basal ganglia in “training” frontal cortex (Pasupathy and Miller, 2005). Another striking change in neural resources during learning was a shift between caudal PFC earlier to rostral PFC later in learning. Our findings regarding musical anticipation and sound sequence learning are highly compatible with studies of motor sequence learning, suggesting common predictive mechanisms in both domains.

Barriers to front propagation in ordered and disordered vortex flows

We present experiments on reactive front propagation in a two-dimensional (2D) vortex chain flow (both time-independent and time-periodic) and a 2D spatially disordered (time-independent) vortex-dominated flow. The flows are generated using magnetohydrodynamic forcing techniques, and the fronts are produced using the excitable, ferroin-catalyzed Belousov-Zhabotinsky chemical reaction. In both of these flows, front propagation is dominated by the presence of burning invariant manifolds (BIMs) that act as barriers, similar to invariant manifolds that dominate the transport of passive impurities. Convergence of the fronts onto these BIMs is shown experimentally for all of the flows studied. The BIMs are also shown to collapse onto the invariant manifolds for passive transport in the limit of large flow velocities. For the disordered flow, the measured BIMs are compared to those predicted using a measured velocity field and a three-dimensional set of ordinary differential equations that describe the dynamics of front propagation in advection-reaction-diffusion systems.

Thin Sequences and the Gram Matrix

We provide a new proof of Volberg's Theorem characterizing thin interpolating sequences as those for which the Gram matrix associated to the normalized reproducing kernels is a compact perturbation of the identity. In the same paper, Volberg characterized sequences for which the Gram matrix is a compact perturbation of a unitary as well as those for which the Gram matrix is a Schatten-2 class perturbation of a unitary operator. We extend this characterization from 2 to p, where 2 <= p <= infinity.