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Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
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A Y-connected synchronous generator, grounded through a neutral impedance, is designed to produce balanced internal phase voltages with only positive-sequence components. The generator's sequence networks include a source voltage that is exclusively in the positive-sequence network. The sequence components of line-to-ground voltages at the generator terminals illustrate this configuration.
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Inferring Higher-Order Couplings with Neural Networks.

Aurélien Decelle1, Alfonso de Jesús Navas Gómez2, Beatriz Seoane3

  • 1Universidad Complutense de Madrid, Universidad Politécnica de Madrid, Escuela Técnica Superior de Ingenieros Industriales, Calle de José Gutiérrez Abascal 2, Madrid 28006, Spain and Departamento de Física Teórica, 28040 Madrid, Spain.

Physical Review Letters
|November 30, 2025
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Summary
This summary is machine-generated.

This study introduces a novel method to extract higher-order interactions from complex systems using Restricted Boltzmann Machines (RBMs). This approach efficiently models many-body couplings, outperforming traditional methods in bioinformatics and neuroscience applications.

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Area of Science:

  • Statistical Physics
  • Machine Learning
  • Bioinformatics
  • Neuroscience

Background:

  • Maximum entropy methods infer pairwise interactions in complex systems but miss higher-order effects.
  • Existing machine learning models capture higher-order interactions but are computationally expensive.
  • Restricted Boltzmann Machines (RBMs) offer an efficient alternative for modeling correlations.

Purpose of the Study:

  • To develop a method for extracting arbitrary-order interactions from complex systems.
  • To leverage RBMs for efficient modeling of many-body couplings.
  • To enable accurate reconstruction of higher-order structures in biological data.

Main Methods:

  • Mapping Restricted Boltzmann Machines (RBMs) to generalized Potts models.
  • Utilizing large-N approximations for efficient extraction of many-body couplings.
  • Developing a framework for recovering higher-order interactions in generative models.

Main Results:

  • Accurate recovery of two- and three-body interactions demonstrated on synthetic data.
  • High-fidelity reconstruction of protein contact maps using real sequence data.
  • Outperformance of state-of-the-art inverse Potts models in contact map prediction.

Conclusions:

  • RBMs provide a computationally efficient and powerful tool for modeling higher-order structures.
  • The developed method enables systematic extraction of complex interactions.
  • This approach has significant implications for fields requiring analysis of high-dimensional categorical data.