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Materials

Superconductivity in the pressurized altermagnet candidate MnTe

Z. Y. Liu, J. J. Zhang, J. K. Bao, S. S. Wang, Y. P. Qi

Featured May 21, 2026

Original Paper

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Simply

This paper creates new math tools to better predict hidden signals, like a patient's health, even when important updates or events happen at scheduled, predictable times, which old methods couldn't handle well.

In depth
The paper extends classical nonlinear filtering theory to scenarios where both the hidden signal and noisy observations exhibit predictable jump times, unlike the traditionally assumed totally inaccessible (unpredictable) jumps. The authors derive new Kushner-Stratonovich and Zakai equations that explicitly incorporate these scheduled discontinuities, providing a systematic framework for applications like clinical studies or event-driven machine learning models.

Key Takeaways

  • 1
    The study provides explicit Kushner-Stratonovich equations for filtering problems where signals and observations have predictable jump times, extending classical results.
  • 2
    A novel Zakai formulation is derived using a tailored Girsanov-type change of measure, offering a linear and computationally advantageous approach for predictable jump scenarios.
  • 3
    The framework is illustrated with practical applications, including a Kalman filter with predictable jumps for health monitoring and neural jump ODEs.

Conceptual Flow

HIGH LEVEL
1
Methodology: Extending Filtering for Scheduled Events

The paper takes the old way of predicting things, which only worked for surprise events, and updates it to work for events that are planned or scheduled.

Hidden Signal
Noisy Observations
Predictable Jumps
New Filtering Equations
2
Results: More Accurate Predictions with Predictable Jumps

By using the new math, the paper shows that we can make much better predictions about hidden things when we know when big changes are going to happen.

Old Prediction Method
New Prediction Method
Compare Accuracy
Better Estimates
Clearer Insights