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Related Concept Videos

Cross Product01:25

Cross Product

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The cross product is a fundamental concept in vector algebra that is a vector operation on two different vectors to obtain a third vector. Unlike the scalar product, the cross product results in a vector quantity perpendicular to both the original vectors.
The magnitude of the cross product is obtained by multiplying the magnitude of both the vectors and the sine of the angle between them. This means that a larger angle between the vectors will lead to a greater magnitude of the cross product.
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Collisions in Multiple Dimensions: Introduction01:05

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It is far more common for collisions to occur in two dimensions; that is, the initial velocity vectors are neither parallel nor antiparallel to each other. Let's see what complications arise from this. The first idea is that momentum is a vector. Like all vectors, it can be expressed as a sum of perpendicular components (usually, though not always, an x-component and a y-component, and a z-component if necessary). Thus, when the statement of conservation of momentum is written for a...
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Collisions in Multiple Dimensions: Problem Solving01:06

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In multiple dimensions, the conservation of momentum applies in each direction independently. Hence, to solve collisions in multiple dimensions, we should write down the momentum conservation in each direction separately. To help understand collisions in multiple dimensions, consider an example.
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Law of Independent Assortment02:03

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While Mendel’s Law of Segregation states that the two alleles for one gene are separated into different gametes, a different question of how different genes are inherited remains. For example, is the gene for tall plants inherited with the gene for green peas? Mendel asked this question by experimenting with a dihybrid cross; a cross in which both parents are homozygous for two distinct traits resulting in an F1 generation that are heterozygous for both traits.
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Vector Product (Cross Product)01:17

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Vector multiplication of two vectors yields a vector product, with the magnitude equal to the product of the individual vectors multiplied by the sine of the angle between both the vectors and the direction perpendicular to both the individual vectors. As there are always two directions perpendicular to a given plane, one on each side, the direction of the vector product is governed by the right-hand thumb rule.
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Cross-Modal Multivariate Pattern Analysis
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Flexible Cross-Modal Hashing.

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    Summary
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    This study introduces Flexible Cross-Modal Hashing (FlexCMH) for efficient data retrieval from weakly paired multimodal data. FlexCMH overcomes limitations of existing methods by handling unknown correspondence and unequal sample sizes, improving retrieval accuracy.

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    Area of Science:

    • Computer Science
    • Machine Learning
    • Information Retrieval

    Background:

    • Hashing is crucial for efficient large-scale data retrieval, offering low storage and high speed.
    • Current cross-modal hashing methods rely on readily available sample correspondence, which is often unrealistic.
    • Existing methods lack flexibility due to requirements for equal sample numbers across modalities.

    Purpose of the Study:

    • To propose a flexible cross-modal hashing approach (FlexCMH) for learning effective hashing codes from weakly paired data.
    • To address the challenge of partially or totally unknown correspondence between samples across modalities.
    • To overcome the inflexibility of existing methods regarding sample size disparities.

    Main Methods:

    • Introduced a clustering-based matching strategy to identify potential correspondence between samples across modalities.
    • Jointly optimized potential correspondence, cross-modal hashing functions, and a hashing quantitative loss in a unified objective.
    • Employed an alternative optimization technique to coordinate correspondence and hash functions for mutual reinforcement.

    Main Results:

    • FlexCMH demonstrated significantly improved performance compared to state-of-the-art methods on public multimodal datasets.
    • The proposed method effectively handles weakly paired data with unknown or partial correspondence.
    • Experiments confirmed FlexCMH's high degree of flexibility for practical cross-modal hashing applications.

    Conclusions:

    • FlexCMH provides a robust and flexible solution for cross-modal hashing, particularly with imperfectly paired data.
    • The method's ability to learn from weakly paired data opens new possibilities for real-world multimodal retrieval systems.
    • FlexCMH advances the field by enabling effective hashing despite challenges in data correspondence and sample distribution.