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Related Concept Videos

¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

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.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...
Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule01:10

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule

In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1  triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the others.
¹H NMR Signal Multiplicity: Splitting Patterns01:13

¹H NMR Signal Multiplicity: Splitting Patterns

When protons A and X are coupled, their nuclear spin energy levels are slightly modified. This is because the energy required to excite proton A to a spin state parallel to proton X is slightly different from the energy required for it to become anti-parallel to spin X. Consequently, there are two possible excitation frequencies for A (A1 and A2), depending on the spin state of X, and vice versa. The mutual nature of coupling implies that the difference between frequencies A1 and A2, indicated...
Propagation of Action Potentials01:23

Propagation of Action Potentials

The propagation of an action potential refers to the process by which a nerve impulse, or "action potential," travels along a neuron.
Neurons (nerve cells) have a resting membrane potential, with a slightly negative charge inside compared to outside. This is maintained by ion channels, such as sodium (Na+) and potassium (K+) channels, which control the flow of ions. When a stimulus, like a touch or a signal from another neuron, triggers the neuron, sodium channels open, allowing sodium ions to...
¹H NMR: Long-Range Coupling01:27

¹H NMR: Long-Range Coupling

The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene π orbitals.
Sequence Networks of Rotating Machines01:24

Sequence Networks of Rotating Machines

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.
Zero-sequence current induces a voltage drop across the generator's neutral impedance and other...

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Related Experiment Video

Updated: May 21, 2026

Cross-Modal Multivariate Pattern Analysis
13:51

Cross-Modal Multivariate Pattern Analysis

Published on: November 9, 2011

Weighted patterns as a tool for improving the Hopfield model.

Iakov Karandashev1, Boris Kryzhanovsky, Leonid Litinskii

  • 1Center of Optical Neural Technologies of Scientific Research Institute for System Analysis, Russian Academy of Sciences, Vavilova str. 44-2, Moscow 119333, Russia.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 12, 2012
PubMed
Summary

This study introduces a weighted Hopfield network, preventing memory loss from overfilling. It identifies a critical weight threshold for pattern recall, enabling online learning without catastrophic forgetting.

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Area of Science:

  • Computational Neuroscience
  • Statistical Physics
  • Machine Learning

Background:

  • The standard Hopfield model suffers from catastrophic memory destruction when overfilled.
  • Assigning weights to input patterns, representing occurrence frequency, offers a potential solution.

Purpose of the Study:

  • To generalize the Hopfield model by incorporating input pattern weights.
  • To analyze the memory capacity and learning dynamics of this weighted model.
  • To develop methods for determining pattern retrievability based on weights.

Main Methods:

  • Utilizing a statistical physics approach to derive a saddle-point equation for network memory.
  • Developing an algorithm to calculate the critical weight threshold for pattern recall.
  • Analyzing memory performance across various weight distributions.

Main Results:

  • The weighted model avoids catastrophic memory destruction, unlike the standard Hopfield model.
  • Memory recall is limited to patterns exceeding a critical weight, determined by weight distribution.
  • While overall memory capacity may decrease, the network supports online learning without data loss.

Conclusions:

  • The generalized weighted Hopfield network offers a more robust memory system.
  • Pattern weighting and critical threshold mechanisms are key to stable online learning.
  • This model provides a framework for understanding associative memory with varying input importance.