New classes of quasi-solvable potentials, their exactly-solvable limit and related orthogonal polynomials

We have generated, using an sl(2,R) formalism, several new classes of quasi-solvable elliptic potentials, which in the appropriate limit go over to the exactly solvable forms. We have obtained exact solutions of the corresponding spectral problems for some real values of the potential parameters. We have also given explicit expressions of the families of associated orthogonal polynomials in the energy variable.Comment: 14 pages, 5 tables, LaTeX2

Emergence of a stable cortical map for neuroprosthetic control.

Cortical control of neuroprosthetic devices is known to require neuronal adaptations. It remains unclear whether a stable cortical representation for prosthetic function can be stored and recalled in a manner that mimics our natural recall of motor skills. Especially in light of the mixed evidence for a stationary neuron-behavior relationship in cortical motor areas, understanding this relationship during long-term neuroprosthetic control can elucidate principles of neural plasticity as well as improve prosthetic function. Here, we paired stable recordings from ensembles of primary motor cortex neurons in macaque monkeys with a constant decoder that transforms neural activity to prosthetic movements. Proficient control was closely linked to the emergence of a surprisingly stable pattern of ensemble activity, indicating that the motor cortex can consolidate a neural representation for prosthetic control in the presence of a constant decoder. The importance of such a cortical map was evident in that small perturbations to either the size of the neural ensemble or to the decoder could reversibly disrupt function. Moreover, once a cortical map became consolidated, a second map could be learned and stored. Thus, long-term use of a neuroprosthetic device is associated with the formation of a cortical map for prosthetic function that is stable across time, readily recalled, resistant to interference, and resembles a putative memory engram

Soliton Lattice and Single Soliton Solutions of the Associated Lam\'e and Lam\'e Potentials

We obtain the exact nontopological soliton lattice solutions of the Associated Lam\'e equation in different parameter regimes and compute the corresponding energy for each of these solutions. We show that in specific limits these solutions give rise to nontopological (pulse-like) single solitons, as well as to different types of topological (kink-like) single soliton solutions of the Associated Lam\'e equation. Following Manton, we also compute, as an illustration, the asymptotic interaction energy between these soliton solutions in one particular case. Finally, in specific limits, we deduce the soliton lattices, as well as the topological single soliton solutions of the Lam\'e equation, and also the sine-Gordon soliton solution.Comment: 23 pages, 5 figures. Submitted to J. Math. Phy

Electrically modulated photoluminescence in ferroelectric liquid crystal

Electrical modulation and switching of photoluminescence (PL) have been demonstrated in pure deformed helix ferroelectric liquid crystal (DHFLC) material. The PL intensity increases and peak position shifts towards lower wavelength above a threshold voltage which continues up to a saturation voltage. This is attributed to the helix unwinding phenomenon in the DHFLC on the application of an electric field. Moreover, the PL intensity could be switched between high intensity (field-on) and low intensity (field-off) positions. These studies would add a new dimension to ferroelectric liquid crystal's application in the area of optical devices.Comment: 4 figure

Emergent modular neural control drives coordinated motor actions.

A remarkable feature of motor control is the ability to coordinate movements across distinct body parts into a consistent, skilled action. To reach and grasp an object, 'gross' arm and 'fine' dexterous movements must be coordinated as a single action. How the nervous system achieves this coordination is currently unknown. One possibility is that, with training, gross and fine movements are co-optimized to produce a coordinated action; alternatively, gross and fine movements may be modularly refined to function together. To address this question, we recorded neural activity in the primary motor cortex and dorsolateral striatum during reach-to-grasp skill learning in rats. During learning, the refinement of fine and gross movements was behaviorally and neurally dissociable. Furthermore, inactivation of the primary motor cortex and dorsolateral striatum had distinct effects on skilled fine and gross movements. Our results indicate that skilled movement coordination is achieved through emergent modular neural control