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Position Vectors01:29

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A position vector is a fundamental concept in mathematics that helps determine the position of one point with respect to another point in space. It is a vector that describes the direction and distance between two points. Position vectors are highly useful in the field of math and science, as they help represent spatial relationships and make calculations easier.
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To describe the motion of an object, one should first be able to describe its position (where it is at any particular time). More precisely, the position needs to be specified relative to a convenient frame of reference. A frame of reference is an arbitrary set of axes from which the position and motion of an object are described. Earth is often used as a frame of reference to describe the position of an object in relation to stationary objects on Earth.
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Orthogonal Trajectories01:26

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Orthogonal trajectories describe the geometric relationship between two families of curves that intersect each other at right angles. One illustrative case involves a family of parabolas that open sideways along the x-axis. These curves share a common shape but differ by a scaling parameter, resulting in a set of curves that all pass through the origin and widen at different rates.Determining Orthogonal TrajectoriesTo identify the orthogonal trajectories for these parabolas, the first step...
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It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like addition, subtraction, and multiplication. There are two ways to circumvent this algebraic complexity. One way is to draw the vectors to scale, as in navigation, and read approximate vector lengths and angles (directions) from the graphs. The other way is to use the method of components.
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Related Experiment Video

Updated: Mar 16, 2026

Tracking Rats in Operant Conditioning Chambers Using a Versatile Homemade Video Camera and DeepLabCut
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Tracking Rats in Operant Conditioning Chambers Using a Versatile Homemade Video Camera and DeepLabCut

Published on: June 15, 2020

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Visual Tracking With Convolutional Random Vector Functional Link Network.

Le Zhang, Ponnuthurai Nagaratnam Suganthan

    IEEE Transactions on Cybernetics
    |August 20, 2016
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a simplified visual tracking method using a convolutional random vector functional link (CRVFL) neural network. The CRVFL model achieves high precision without extensive pretraining, demonstrating the potential to reduce reliance on large auxiliary datasets.

    Related Experiment Videos

    Last Updated: Mar 16, 2026

    Tracking Rats in Operant Conditioning Chambers Using a Versatile Homemade Video Camera and DeepLabCut
    08:32

    Tracking Rats in Operant Conditioning Chambers Using a Versatile Homemade Video Camera and DeepLabCut

    Published on: June 15, 2020

    13.6K

    Area of Science:

    • Computer Vision
    • Machine Learning
    • Deep Learning

    Background:

    • Deep neural networks excel in visual tracking but require large datasets like ImageNet for pretraining.
    • Domain discrepancy between auxiliary data and target objects necessitates fine-tuning, increasing sensitivity to hyperparameters.
    • Conventional pretraining and fine-tuning methods for visual tracking are complex and parameter-sensitive.

    Purpose of the Study:

    • To investigate the necessity of pretraining and fine-tuning in visual tracking.
    • To propose a simplified visual tracking system that reduces reliance on auxiliary data.
    • To introduce the convolutional random vector functional link (CRVFL) neural network for visual tracking.

    Main Methods:

    • Proposed a convolutional random vector functional link (CRVFL) neural network, integrating convolutional neural networks and random vector functional link networks.
    • Kept convolutional layer parameters randomly initialized and fixed, learning only fully connected layer parameters.
    • Developed an elegant update approach for the tracker.

    Main Results:

    • A single CRVFL model achieved 79.0% precision (20-pixel threshold) on a standard visual tracking benchmark without auxiliary data.
    • An ensemble of CRVFL models achieved a leading result of 86.3% precision.
    • Demonstrated effective visual tracking performance without extensive pretraining or fine-tuning.

    Conclusions:

    • The proposed CRVFL network simplifies visual tracking systems.
    • Pretraining and fine-tuning via conventional backpropagation may not be essential for effective visual tracking.
    • CRVFL offers a promising alternative for visual tracking, reducing data requirements and hyperparameter sensitivity.