A q-analogue of gl_3 hierarchy and q-Painleve VI

A q-analogue of the gl_3 Drinfel'd-Sokolov hierarchy is proposed as a reduction of the q-KP hierarchy. Applying a similarity reduction and a q-Laplace transformation to the hierarchy, one can obtain the q-Painleve VI equation proposed by Jimbo and Sakai.Comment: 14 pages, IOP style, to appear in J. Phys. A Special issue "One hundred years of Painleve VI

The sixth Painleve equation arising from D_4^{(1)} hierarchy

The sixth Painleve equation arises from a Drinfel'd-Sokolov hierarchy associated with the affine Lie algebra of type D_4 by similarity reduction.Comment: 14 page

A reduction of the resonant three-wave interaction to the generic sixth Painleve' equation

Among the reductions of the resonant three-wave interaction system to six-dimensional differential systems, one of them has been specifically mentioned as being linked to the generic sixth Painleve' equation P6. We derive this link explicitly, and we establish the connection to a three-degree of freedom Hamiltonian previously considered for P6.Comment: 13 pages, 0 figure, J. Phys. A Special issue "One hundred years of Painleve' VI

Changes in Cerebral Hemodynamics during Complex Motor Learning by Character Entry into Touch-Screen Terminals

Introduction Studies of cerebral hemodynamics during motor learning have mostly focused on neurorehabilitation interventions and their effectiveness. However, only a few imaging studies of motor learning and the underlying complex cognitive processes have been performed. Methods We measured cerebral hemodynamics using near-infrared spectroscopy (NIRS) in relation to acquisition patterns of motor skills in healthy subjects using character entry into a touchscreen terminal. Twenty healthy, right-handed subjects who had no previous experience with character entry using a touch-screen terminal participated in this study. They were asked to enter the characters of a randomly formed Japanese syllabary into the touchscreen terminal. All subjects performed the task with their right thumb for 15 s alternating with 25 s of rest for 30 repetitions. Performance was calculated by subtracting the number of incorrect answers from the number of correct answers, and gains in motor skills were evaluated according to the changes in performance across cycles. Behavioral and oxygenated hemoglobin concentration changes across task cycles were analyzed using Spearman\u27s rank correlations. Results Performance correlated positively with task cycle, thus confirming motor learning. Hemodynamic activation over the left sensorimotor cortex (SMC) showed a positive correlation with task cycle, whereas activations over the right prefrontal cortex (PFC) and supplementary motor area (SMA) showed negative correlations. Conclusions We suggest that increases in finger momentum with motor learning are reflected in the activity of the left SMC. We further speculate that the right PFC and SMA were activated during the early phases of motor learning, and that this activity was attenuated with learning progress