203 research outputs found

    Distributional Hessian and divdiv complexes on triangulation and cohomology

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    In this paper, we construct discrete versions of some Bernstein-Gelfand-Gelfand (BGG) complexes, i.e., the Hessian and the divdiv complexes, on triangulations in 2D and 3D. The sequences consist of finite elements with local polynomial shape functions and various types of Dirac measure on subsimplices. The construction generalizes Whitney forms (canonical conforming finite elements) for the de Rham complex and Regge calculus/finite elements for the elasticity (Riemannian deformation) complex from discrete topological and Discrete Exterior Calculus perspectives. We show that the cohomology of the resulting complexes is isomorphic to the continuous versions, and thus isomorphic to the de~Rham cohomology with coefficients.Comment: keywords: Bernstein-Gelfand-Gelfand sequences, cohomology, finite element exterior calculus, discrete exterior calculus, Regge calculu

    Nonstandard finite element de Rham complexes on cubical meshes

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    We propose two general operations on finite element differential complexes on cubical meshes that can be used to construct and analyze sequences of "nonstandard" convergent methods. The first operation, called DoF-transfer, moves edge degrees of freedom to vertices in a way that reduces global degrees of freedom while increasing continuity order at vertices. The second operation, called serendipity, eliminates interior bubble functions and degrees of freedom locally on each element without affecting edge degrees of freedom. These operations can be used independently or in tandem to create nonstandard complexes that incorporate Hermite, Adini and "trimmed-Adini" elements. We show that the resulting elements provide convergent, non-conforming methods for problems requiring stronger regularity and satisfy a discrete Korn inequality. We discuss potential benefits of applying these elements to Stokes, biharmonic and elasticity problems.Comment: 31 page

    Adaptive Learning based Upper-Limb Rehabilitation Training System with Collaborative Robot

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    Rehabilitation training for patients with motor disabilities usually requires specialized devices in rehabilitation centers. Home-based multi-purpose training would significantly increase treatment accessibility and reduce medical costs. While it is unlikely to equip a set of rehabilitation robots at home, we investigate the feasibility to use the general-purpose collaborative robot for rehabilitation therapies. In this work, we developed a new system for multi-purpose upper-limb rehabilitation training using a generic robot arm with human motor feedback and preference. We integrated surface electromyography, force/torque sensors, RGB-D cameras, and robot controllers with the Robot Operating System to enable sensing, communication, and control of the system. Imitation learning methods were adopted to imitate expert-provided training trajectories which could adapt to subject capabilities to facilitate in-home training. Our rehabilitation system is able to perform gross motor function and fine motor skill training with a gripper-based end-effector. We simulated system control in Gazebo and training effects (muscle activation level) in OpenSim and evaluated its real performance with human subjects. For all the subjects enrolled, our system achieved better training outcomes compared to specialist-assisted rehabilitation under the same conditions. Our work demonstrates the potential of utilizing collaborative robots for in-home motor rehabilitation training

    Comparisons of serum miRNA expression profiles in patients with diabetic retinopathy and type 2 diabetes mellitus

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    OBJECTIVES: The aim of this study was to compare the expression levels of serum miRNAs in diabetic retinopathy and type 2 diabetes mellitus. METHODS: Serum miRNA expression profiles from diabetic retinopathy cases (type 2 diabetes mellitus patients with diabetic retinopathy) and type 2 diabetes mellitus controls (type 2 diabetes mellitus patients without diabetic retinopathy) were examined by miRNA-specific microarray analysis. Quantitative real-time polymerase chain reaction was used to validate the significantly differentially expressed serum miRNAs from the microarray analysis of 45 diabetic retinopathy cases and 45 age-, sex-, body mass index- and duration-of-diabetes-matched type 2 diabetes mellitus controls. The relative changes in serum miRNA expression levels were analyzed using the 2-ΔΔCt method. RESULTS: A total of 5 diabetic retinopathy cases and 5 type 2 diabetes mellitus controls were included in the miRNA-specific microarray analysis. The serum levels of miR-3939 and miR-1910-3p differed significantly between the two groups in the screening stage; however, quantitative real-time polymerase chain reaction did not reveal significant differences in miRNA expression for 45 diabetic retinopathy cases and their matched type 2 diabetes mellitus controls. CONCLUSION: Our findings indicate that miR-3939 and miR-1910-3p may not play important roles in the development of diabetic retinopathy; however, studies with a larger sample size are needed to confirm our findings
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