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Related Concept Videos

Spherical Coordinates01:23

Spherical Coordinates

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Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...
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Relative Motion Analysis using Rotating Axes-Problem Solving01:29

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Consider a crane whose telescopic boom rotates with an angular velocity of 0.04 rad/s and angular acceleration of 0.02 rad/s2. Along with the rotation, the boom also extends linearly with a uniform speed of 5 m/s. The extension of the boom is measured at point D, which is measured with respect to the fixed point C on the other end of the boom. For the given instant, the distance between points C and D is 60 meters.
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Relative Motion Analysis using Rotating Axes01:25

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Consider a component AB undergoing a linear motion. Along with a linear motion, point B also rotates around point A. To comprehend this complex movement, position vectors for both points A and B are established using a stationary reference frame.
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Linear Approximation in Frequency Domain01:26

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Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
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Linear Approximation in Time Domain01:21

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Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
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Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

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A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half...
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Unsupervised and Semi-Supervised Robust Spherical Space Domain Adaptation.

Xiang Gu, Jian Sun, Zongben Xu

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    This study introduces a novel spherical adversarial domain adaptation method for learning domain-invariant features. The approach enhances performance in both unsupervised and semi-supervised settings using spherical classifiers and discriminators.

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    Area of Science:

    • Machine Learning
    • Computer Vision
    • Artificial Intelligence

    Background:

    • Adversarial domain adaptation effectively learns domain-invariant features through adversarial training.
    • Existing methods often struggle with leveraging target domain data, especially in semi-supervised scenarios.

    Purpose of the Study:

    • To propose a novel adversarial domain adaptation approach in a spherical feature space.
    • To enhance feature learning for both unsupervised and semi-supervised domain adaptation.
    • To improve the robust utilization of pseudo-labels and reduce intra-domain discrepancy.

    Main Methods:

    • Introduced a spherical feature space with spherical classifiers and discriminators.
    • Developed a spherical robust pseudo-label loss using a Gaussian-uniform mixture model.
    • Proposed a reweighted adversarial training strategy for semi-supervised domain adaptation.

    Main Results:

    • The proposed method achieves competitive or superior performance on object, digit, and face recognition benchmarks.
    • Ablation studies validate the effectiveness of individual components: spherical classifier, discriminator, pseudo-label loss, and reweighted training.

    Conclusions:

    • The novel spherical adversarial domain adaptation approach is effective for both unsupervised and semi-supervised settings.
    • The method demonstrates robust feature learning and improved performance across various recognition tasks.