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End Point Prediction: Gran Plot

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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: Sep 11, 2025

Trajectory Data Analyses for Pedestrian Space-time Activity Study
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MSTT: A Multi-Spatio-Temporal Graph Attention Model for Pedestrian Trajectory Prediction.

Qingrui Zhang1, Xuxiu Zhang1, Zilang Ye2

  • 1School of Automation & Electrical Engineering, Dalian Jiaotong University, Dalian 116028, China.

Sensors (Basel, Switzerland)
|August 14, 2025
PubMed
Summary

Predicting pedestrian movement is key for autonomous driving. A new relative spatio-temporal encoding (RSTE) and multi-spatio-temporal graph (MSTG) model improve accuracy by analyzing interactions, outperforming older methods.

Keywords:
attentional mechanismgraph structure learningpedestrian trajectory prediction

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Area of Science:

  • Computer Science
  • Robotics
  • Artificial Intelligence

Background:

  • Accurate pedestrian movement prediction is crucial for autonomous driving and intelligent systems.
  • Existing models often fail to capture complex spatio-temporal interactions between individuals due to reliance on absolute positioning.

Purpose of the Study:

  • To develop a novel approach for predicting pedestrian movements by effectively modeling spatio-temporal interactions.
  • To introduce a relative spatio-temporal encoding (RSTE) strategy and a multi-spatio-temporal graph (MSTG) modeling technique.

Main Methods:

  • Implemented a relative spatio-temporal encoding (RSTE) strategy to capture inter-pedestrian relationships.
  • Designed a multi-spatio-temporal graph (MSTG) to model interactions across multiple individuals over time and space.
  • Developed an attention-based MSTT model for end-to-end learning of the MSTG structure.

Main Results:

  • The study found that an individual's prior trajectory significantly influences the future movements of others.
  • The proposed MSTT model demonstrated superior predictive performance compared to traditional trajectory-based methods.
  • Evaluations on two challenging datasets confirmed the effectiveness of the MSTT model.

Conclusions:

  • The RSTE strategy and MSTT model offer a significant advancement in accurately predicting pedestrian behavior.
  • Modeling relative spatio-temporal interactions is essential for robust pedestrian movement forecasting.
  • This research contributes to safer and more efficient autonomous systems and human-computer interactions.