Kinematic geometry of mass-triangles and reduction of Schrödinger’s equation of three-body systems to partial differential equations solely defined on triangular parameters

Schrödinger’s equation of a three-body system is a linear partial differential equation (PDE) defined on the 9-dimensional configuration space, ℝ9, naturally equipped with Jacobi’s kinematic metric and with translational and rotational symmetries. The natural invariance of Schrödinger’s equation with respect to the translational symmetry enables us to reduce the configuration space to that of a 6-dimensional one, while that of the rotational symmetry provides the quantum mechanical version of angular momentum conservation. However, the problem of maximizing the use of rotational invariance so as to enable us to reduce Schrödinger’s equation to corresponding PDEs solely defined on triangular parameters—i.e., at the level of ℝ6/SO(3)—has never been adequately treated. This article describes the results on the orbital geometry and the harmonic analysis of (SO(3),ℝ6) which enable us to obtain such a reduction of Schrödinger’s equation of three-body systems to PDEs solely defined on triangular parameters.

Shift in speed selectivity of visual cortical neurons: A neural basis of perceived motion contrast

The perceived speed of motion in one part of the visual field is influenced by the speed of motion in its surrounding fields. Little is known about the cellular mechanisms causing this phenomenon. Recordings from mammalian visual cortex revealed that speed preference of the cortical cells could be changed by displaying a contrast speed in the field surrounding the cell’s classical receptive field. The neuron’s selectivity shifted to prefer faster speed if the contextual surround motion was set at a relatively lower speed, and vice versa. These specific center–surround interactions may underlie the perceptual enhancement of speed contrast between adjacent fields.

Neural systems underlying learning and representation of global motion

We demonstrate performance-related changes in cortical and cerebellar activity. The largest learning-dependent changes were observed in the anterior lateral cerebellum, where the extent and intensity of activation correlated inversely with psychophysical performance. After learning had occurred (a few minutes), the cerebellar activation almost disappeared; however, it was restored when the subjects were presented with a novel, untrained direction of motion for which psychophysical performance also reverted to chance level. Similar reductions in the extent and intensity of brain activations in relation to learning occurred in the superior colliculus, anterior cingulate, and parts of the extrastriate cortex. The motion direction-sensitive middle temporal visual complex was a notable exception, where there was an expansion of the cortical territory activated by the trained stimulus. Together, these results indicate that the learning and representation of visual motion discrimination are mediated by different, but probably interacting, neuronal subsystems.

Origin of nanomechanical cantilever motion generated from biomolecular interactions

Generation of nanomechanical cantilever motion from biomolecular interactions can have wide applications, ranging from high-throughput biomolecular detection to bioactuation. Although it has been suggested that such motion is caused by changes in surface stress of a cantilever beam, the origin of the surface-stress change has so far not been elucidated. By using DNA hybridization experiments, we show that the origin of motion lies in the interplay between changes in configurational entropy and intermolecular energetics induced by specific biomolecular interactions. By controlling entropy change during DNA hybridization, the direction of cantilever motion can be manipulated. These thermodynamic principles were also used to explain the origin of motion generated from protein–ligand binding.