Observation of lyotropic chromonic liquid crystals droplets with the perpendicular boundary condition

Department of PhysicsControlling anchoring conditions of liquid crystals (LCs) is crucial for the study of liquid crystals and development of liquid crystals-based displays and sensors. Although many studies have been made on thermotropic liquid crystals, the anchoring conditions of lyotropic chromonic liquid crystals (LCLCs) are difficult to control even through properties of LCLCs were actively studied. Conventional alignment methods have no effect on LCLCs, even work, anchoring is very weak. Only a few perpendicular alignment layers (a.k.a. homeotropic anchoring) in solid-LCs interfaces were reported through non-covalent interactions of hydrophobic polymer films and solid substrates such as graphene. However, the vertical alignment layers of LCLCs at the liquid interface has never been reported. We report, for the first time, the study of the homeotropic anchoring of liquid and LCLCs interfaces using hydrophobic oils without surfactants. As reported in thermotropic liquid crystals, a radial structure with a point defect has been found, but an unusual feature is the axial structure with ring disclination, which did not apply the external field. It implies that this anchoring strength is very weak anchoring conditions and another supporting evidence is the anchoring transition, which changes to the horizontal orientation from the perpendicular orientation. Also, because of the weak twist modulus of the LCLCs, the structure of the defects seemed to be twisted. This twist structure is consistent with previous reports. To observe the structures of homeotropic chiral nematic, brucine sulfate was used as a chiral dopants. Basically, we reproduced the director configurations of the droplets of the thermotropic chiral nematic LCs both with planar and homeotropic anchoring. Specifically, with the homeotropic anchoring, we noticed an increase in the effective helical pitch in the droplets according to the droplet size, i.e. the untwisting of the helical structure, which originates from the frustration of chiral nematic liquid crystals with the perpendicular boundary condition.ope

Geometric control condition for the wave equation with a time-dependent observation domain

We characterize the observability property (and, by duality, the controllability and the stabilization) of the wave equation on a Riemannian manifold $\Omega,$ with or without boundary, where the observation (or control) domain is time-varying. We provide a condition ensuring observability, in terms of propagating bicharacteristics. This condition extends the well-known geometric control condition established for fixed observation domains. As one of the consequences, we prove that it is always possible to find a time-dependent observation domain of arbitrarily small measure for which the observability property holds. From a practical point of view, this means that it is possible to reconstruct the solutions of the wave equation with only few sensors (in the Lebesgue measure sense), at the price of moving the sensors in the domain in an adequate way.We provide several illustrating examples, in which the observationdomain is the rigid displacement in $\Omega$ of a fixed domain, withspeed $v,$ showing that the observability property depends both on $v$and on the wave speed. Despite the apparent simplicity of some of ourexamples, the observability property can depend on nontrivial arithmeticconsiderations

Randomized controlled trial of a home-based action observation intervention to improve walking in Parkinson disease

Published in final edited form as: Arch Phys Med Rehabil. 2016 May ; 97(5): 665–673. doi:10.1016/j.apmr.2015.12.029.OBJECTIVE: To examine the feasibility and efficacy of a home-based gait observation intervention for improving walking in Parkinson disease (PD). DESIGN: Participants were randomly assigned to an intervention or control condition. A baseline walking assessment, a training period at home, and a posttraining assessment were conducted. SETTING: The laboratory and participants' home and community environments. PARTICIPANTS: Nondemented individuals with PD (N=23) experiencing walking difficulty. INTERVENTION: In the gait observation (intervention) condition, participants viewed videos of healthy and parkinsonian gait. In the landscape observation (control) condition, participants viewed videos of moving water. These tasks were completed daily for 8 days. MAIN OUTCOME MEASURES: Spatiotemporal walking variables were assessed using accelerometers in the laboratory (baseline and posttraining assessments) and continuously at home during the training period. Variables included daily activity, walking speed, stride length, stride frequency, leg swing time, and gait asymmetry. Questionnaires including the 39-item Parkinson Disease Questionnaire (PDQ-39) were administered to determine self-reported change in walking, as well as feasibility. RESULTS: At posttraining assessment, only the gait observation group reported significantly improved mobility (PDQ-39). No improvements were seen in accelerometer-derived walking data. Participants found the at-home training tasks and accelerometer feasible to use. CONCLUSIONS: Participants found procedures feasible and reported improved mobility, suggesting that observational training holds promise in the rehabilitation of walking in PD. Observational training alone, however, may not be sufficient to enhance walking in PD. A more challenging and adaptive task, and the use of explicit perceptual learning and practice of actions, may be required to effect change

Computational Complexity versus Statistical Performance on Sparse Recovery Problems

We show that several classical quantities controlling compressed sensing performance directly match classical parameters controlling algorithmic complexity. We first describe linearly convergent restart schemes on first-order methods solving a broad range of compressed sensing problems, where sharpness at the optimum controls convergence speed. We show that for sparse recovery problems, this sharpness can be written as a condition number, given by the ratio between true signal sparsity and the largest signal size that can be recovered by the observation matrix. In a similar vein, Renegar's condition number is a data-driven complexity measure for convex programs, generalizing classical condition numbers for linear systems. We show that for a broad class of compressed sensing problems, the worst case value of this algorithmic complexity measure taken over all signals matches the restricted singular value of the observation matrix which controls robust recovery performance. Overall, this means in both cases that, in compressed sensing problems, a single parameter directly controls both computational complexity and recovery performance. Numerical experiments illustrate these points using several classical algorithms.Comment: Final version, to appear in information and Inferenc

Measuring athlete imagery ability: the Sport Imagery Ability Questionnaire

Based on literature identifying movement imagery, observation, and execution to elicit similar areas of neural activity, research has demonstrated movement imagery and observation to successfully prime movement execution. To investigate whether movement and observation could prime ease of imaging from an external visual imagery perspective, an internal visual imagery perspective, and kinaesthetic modality, 36 participants (M$_{age}$ = 20.58; SD = 3.11; 18 female, 18 male) completed the Movement Imagery Questionnaire-3 under four modes of delivery (movement prime, external observation prime, internal observation prime, and image-only). Results revealed ease of imaging was significantly greater during the movement and observation prime conditions compared to the image-only condition (p < .05). Specifically when priming external visual imagery and internal visual imagery, observation only facilitated ease of imaging when the perspective was congruent with the imagery perspective. Results support the utilization of movement and observation to facilitate ease of imaging, but highlight the importance of considering visual perspective when using observation

Stability of nonlinear filters in nonmixing case

The nonlinear filtering equation is said to be stable if it ``forgets'' the initial condition. It is known that the filter might be unstable even if the signal is an ergodic Markov chain. In general, the filtering stability requires stronger signal ergodicity provided by the, so called, mixing condition. The latter is formulated in terms of the transition probability density of the signal. The most restrictive requirement of the mixing condition is the uniform positiveness of this density. We show that it might be relaxed regardless of an observation process structure.Comment: Published at http://dx.doi.org/10.1214/105051604000000873 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org