An effective spin-orbit coupling can be generated in a cold atom system by engineering atom-light interactions. In this Letter we study spin-1/2 and spin-1 Bose-Einstein condensates with Rashba spin-orbit coupling, and find that the condensate wave function will develop nontrivial structures. From numerical simulation we have identified two different phases. In one phase the ground state is a single plane wave, and often we find the system splits into domains and an array of vortices plays the role of a domain wall. In this phase, time-reversal symmetry is broken. In the other phase the condensate wave function is a standing wave, and it forms a spin stripe. The transition between them is driven by interactions between bosons. We also provide an analytical understanding of these results and determine the transition point between the two phases.
BackgroundA large number of robotic or gravity-supporting devices have been developed for rehabilitation of upper extremity post-stroke. Because these devices continuously monitor performance data during training, they could potentially help to develop predictive models of the effects of motor training on recovery. However, during training with such devices, patients must become adept at using the new “tool” of the exoskeleton, including learning the new forces and visuomotor transformations associated with the device. We thus hypothesized that the changes in performance during extensive training with a passive, gravity-supporting, exoskeleton device (the Armeo Spring) will follow an initial fast phase, due to learning to use the device, and a slower phase that corresponds to reduction in overall arm impairment. Of interest was whether these fast and slow processes were related.MethodsTo test the two-process hypothesis, we used mixed-effect exponential models to identify putative fast and slow changes in smoothness of arm movements during 80 arm reaching tests performed during 20 days of exoskeleton training in 53 individuals with post-acute stroke.ResultsIn line with our hypothesis, we found that double exponential models better fit the changes in smoothness of arm movements than single exponential models. In contrast, single exponential models better fit the data for a group of young healthy control subjects. In addition, in the stroke group, we showed that smoothness correlated with a measure of impairment (the upper extremity Fugl Meyer score - UEFM) at the end, but not at the beginning, of training. Furthermore, the improvement in movement smoothness due to the slow component, but not to the fast component, strongly correlated with the improvement in the UEFM between the beginning and end of training. There was no correlation between the change of peaks due to the fast process and the changes due to the slow process. Finally, the improvement in smoothness due to the slow, but not the fast, component correlated with the number of days since stroke at the onset of training – i.e. participants who started exoskeleton training sooner after stroke improved their smoothness more.ConclusionsOur results therefore demonstrate that at least two processes are involved in in performance improvements measured during mechanized training post-stroke. The fast process is consistent with learning to use the exoskeleton, while the slow process independently reflects the reduction in upper extremity impairment.
Whether the CNS minimizes variability or effort in planning arm movements can be tested by measuring the preferred movement duration and end-point variability. Here, we conducted an experiment in which subjects performed arm-reaching movements without visual feedback in fast, medium, slow, and preferred duration conditions. Results show that (i) total endpoint variance was smallest in the medium duration condition, and (ii) subjects preferred to carry out movements that were slower than this medium duration condition. A parsimonious explanation for the overall pattern of end-point errors across fast, medium, preferred, and slow movement durations is that movements are planned to minimize effort as well as endpoint error due to both signal-dependent and constant noise
In motor skill learning, larger doses of practice lead to greater efficacy of practice, lower efficiency of practice, and better long-term retention. Whether such learning principles apply to motor practice after stroke is unclear. Here, we developed novel mixed-effects models of the change in the perceived quality of arm movements during and following task practice. The models were fitted to data from a recent randomized controlled trial of the effect of dose of task practice in chronic stroke. Analysis of the models’ learning and retention rates demonstrated an increase in efficacy of practice with greater doses, a decrease in efficiency of practice with both additional dosages and additional bouts of training, and fast initial decay following practice. Two additional effects modulated retention: a positive “self-practice” effect, and a negative effect of dose. Our results further suggest that for patients with sufficient arm use post-practice, self-practice will further improve use.
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