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We consider the simplest network of coupled non-identical phase oscillators capable of displaying a "chimera" state (namely, two subnetworks with strong coupling within the subnetworks and weaker coupling between them) and systematically investigate the effects of gradually removing connections within the network, in a random but systematically specified way. We average over ensembles of networks with the same random connectivity but different intrinsic oscillator frequencies and derive ordinary differential equations (ODEs), whose fixed points describe a typical chimera state in a representative network of phase oscillators. Following these fixed points as parameters are varied we find that chimera states are quite sensitive to such random removals of connections, and that oscillations of chimera states can be either created or suppressed in apparent bifurcation points, depending on exactly how the connections are gradually removed.

The purpose of this investigation was to apply the findings of an anatomic study of the levator veli palatini, palatopharyngeus, and superior constrictor muscles in 18 fresh cadaveric specimens of normal adults to analyze current controversies in velopharyngeal function and cleft palate surgery. The levator veli palatini was observed to form a muscular sling, suspending the velum from the cranial base. Its fibers occupied the middle 50 percent of the velum, lying in transverse orientation and without significant overlap across the midline. It is well placed to function as the prime mover in the velar component of velopharyngeal closure. The velar component of the palatopharyngeus consisted of two heads clasping the levator and inserting into the latter just short of the midline. Its pharyngeal component inserted into the superior constrictor in the lateral and posterior pharyngeal walls. Together, these two muscles formed a sphincter around the velopharyngeal port, suggesting that both muscles are involved in the pharyngeal component of velopharyngeal closure. Based on the premise that the goal of palatoplasty is to restore normal anatomy, the intravelar veloplasty has a sound basis, and theoretically improves both velar and pharyngeal wall function because it corrects the dysmorphology of both the levator and palatopharyngeus. Although the Furlow palatoplasty also reorients these velar muscles correctly in the transverse position, the resulting overlap of the levator and palatopharyngeus across the midline is morphologically abnormal. In addition, the use of large Z-plasty flaps in wide clefts may cause excessive lateral tension, increasing the risk of fistula formation and causing an impairment of velar stretch capacity. The raising of a vertical pharyngeal flap divides the fibers of the superior constrictor and has the potential to impair pharyngeal wall function. The sphincter pharyngoplasty interferes less with pharyngeal wall anatomy. The potential for an obstructive outcome seems to be related to the use of wide, long flaps and a tight, overlapping type of flap inset. In addition, the level of flap inset is important: an inset at the level of the uvula has the greatest risk of causing obstruction, whereas a higher inset at the level of attempted velopharyngeal closure seems to provide the best opportunity for achieving velopharyngeal competence while avoiding hyponasality and obstruction.