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Energy Diagrams - II01:10

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Energy diagrams are important to understand the dynamics of a system. The topology of an energy diagram helps illustrate the equilibrium points of the system.
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Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...
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The dynamics of a mechanical system can be easily understood by interpreting a potential energy diagram. Since energy is a scalar quantity, the interpretation of the dynamics of the system becomes even simpler.
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A Gran plot is used to predict the equivalence volume or endpoint of a potentiometric or acid-base titration without reaching the endpoint. Typically, titration data is collected as a function of the titrant's volume up to a point less than the equivalence volume and then transformed into a linear format. The straight line is extended to the x-axis, indicating the necessary titrant volume to achieve the equivalence point.
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Related Experiment Video

Updated: Oct 5, 2025

Trajectory Data Analyses for Pedestrian Space-time Activity Study
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SEEM: A Sequence Entropy Energy-Based Model for Pedestrian Trajectory All-Then-One Prediction.

Dafeng Wang, Hongbo Liu, Naiyao Wang

    IEEE Transactions on Pattern Analysis and Machine Intelligence
    |February 1, 2022
    PubMed
    Summary
    This summary is machine-generated.

    We introduce SEEM, a new model for pedestrian trajectory prediction. SEEM enhances diversity, accuracy, and stability by optimizing sequence entropy and using an energy network for representative trajectory selection.

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    Area of Science:

    • Computer Science
    • Robotics
    • Artificial Intelligence

    Background:

    • Pedestrian trajectory prediction is crucial for autonomous systems.
    • Existing models lack diversity, accuracy, and stability.

    Purpose of the Study:

    • To propose a novel Sequence Entropy Energy-based Model (SEEM) for improved pedestrian trajectory prediction.
    • To address limitations of current models in diversity, accuracy, and stability.

    Main Methods:

    • SEEM utilizes a generator and an energy network.
    • Optimizes sequence entropy via local variational inference of f-divergence to maximize mutual information.
    • Employs probability distribution clipping and an energy network for trajectory selection (all-then-one strategy).
    • Incorporates zero-centered potential energy regularization for training stability.

    Main Results:

    • SEEM demonstrates superior performance over state-of-the-art methods.
    • Achieves significant improvements in diversity, accuracy, and stability.
    • Validated on synthetic and public benchmark datasets.

    Conclusions:

    • SEEM offers a robust solution for diverse, accurate, and stable pedestrian trajectory prediction.
    • The proposed methods effectively address key challenges in the field.
    • SEEM advances the capabilities of autonomous driving and social robot applications.