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Related Concept Videos

Functional Classification of Joints01:09

Functional Classification of Joints

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Functional Classification of Joints
The functional classification of joints is determined by the amount of mobility between the adjacent bones. Joints are functionally classified as a synarthrosis or immobile joint, an amphiarthrosis or slightly moveable joint, or as a diarthrosis, a freely moveable joint. Fibrous and cartilaginous joints can be functionally classified as either synarthroses  or amphiarthroses, whereas all synovial joints are classified as diarthroses.
Synarthrosis
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Body planes in anatomy are imaginary flat surfaces used as reference points to divide the body into sections for anatomical study. These planes are essential for understanding the orientation, relationships, and spatial organization of anatomical structures.
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When a structural member undergoes plastic deformation due to bending, it is crucial to understand the position of the neutral axis and the stress distribution. This member, characterized by a single plane of symmetry, exhibits a uniform stress distribution, with negative stress above the neutral axis and positive stress below. Notably, the neutral axis does not align with the centroid of the cross-section. This misalignment is typical in cases where the cross-section is not rectangular or...
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When analyzing elongated structures like bars subjected to uniformly distributed loads, it is essential to understand the transformation of plane strain when coordinate axes are rotated. This transformation helps to assess how material deformation characteristics vary with orientation, which is crucial in materials science and structural engineering.
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Hyperbolas01:30

Hyperbolas

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A hyperbola is a conic section produced when a double-napped cone is intersected by a plane at an angle steeper than the slope of the cone, such that it cuts through both nappes. This intersection yields two separate, mirror-image curves known as branches, which open away from each other along the transverse axis. The nearest points on each branch to the hyperbola’s center are termed vertices, and the distance from the center to a vertex is denoted by a. Perpendicular to the transverse axis...
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Planar Rigid-Body Motion01:22

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Understanding the movement of a rigid body in planar motion involves recognizing that every particle within this body is traversing a path that maintains a consistent distance from a specific plane. This concept is fundamental in the study of physics and mechanical engineering, and it allows us to comprehend better how objects move in space.
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    The deep adaptive hinging hyperplane (DAHH) model extends piecewise linear representations for high-dimensional problems. This interpretable neural network efficiently tackles large-scale systems without gradient vanishing, offering convex optimization advantages.

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    Area of Science:

    • Machine Learning
    • System Identification
    • Artificial Intelligence

    Background:

    • The adaptive hinging hyperplane (AHH) model is a successful piecewise linear representation for dynamic system identification.
    • Existing AHH models face limitations with high-dimensional and large-scale problems.

    Purpose of the Study:

    • To introduce the deep adaptive hinging hyperplane (DAHH) model, generalizing AHH for high-dimensional data.
    • To develop an efficient and interpretable neural network architecture for complex system identification.

    Main Methods:

    • DAHH employs a forward growth network construction with an activity ratio for neuron selection.
    • Skip-layer connections allow flexible neuron-to-output linking, optimizing only output weights.
    • The backpropagation algorithm is adapted for DAHH, avoiding gradient vanishing and ensuring convex optimization.

    Main Results:

    • The DAHH model demonstrates efficient training for large-scale problems, overcoming gradient vanishing.
    • DAHH offers enhanced interpretability through sparse connections and ANOVA decomposition for variable interaction analysis.
    • Theoretical analysis confirms DAHH's universal approximation ability and explicit domain partitioning.

    Conclusions:

    • The proposed DAHH model effectively generalizes AHH for high-dimensional system identification.
    • DAHH provides an interpretable, efficient, and robust framework for complex machine learning tasks.
    • Numerical experiments validate the superior performance and advantages of the DAHH model.