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Energy Manifold Natural Gradient Descent: From Riemannian Optimization to Modern Neuroscience, NeuroAI and Quantum Physics

Dr. Rishabh Pathak
When Geometry, Energy, Artificial Intelligence and Neuroscience Converge Modern Artificial Intelligence is rapidly moving beyond the idea that learning simply means minimizing an error function. Increasingly, researchers are asking a deeper question: what is the structure of the space in which learning takes place? This question becomes particularly important when the system being modelled is constrained, nonlinear, dynamic, or governed by physical principles. A recent work titled “Energy Manifold Natural Gradient Descent: Riemannian Optimization for Neural PDE Solvers” , by Zhangyong Liang and Huanhuan Gao, introduces Energy Manifold Natural Gradient Descent (EMNGD) , a mathematical framework that extends energy-based natural-gradient optimization from unconstrained Euclidean parameter spaces to constrained Riemannian parameter manifolds . At its core, the framework proposes a simple but powerful principle: An optimization algorithm should not only determine how to reduce error; it sh...
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Cardiac Artifacts compared to Benign Epileptiform Transients of Sleep

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Dr. Rishabh Pathak

Cardiac artifacts and benign epileptiform transients of sleep (BETS) are distinct patterns that can be observed in EEG recordings. Some of the key points differentiating cardiac artifacts from BETS:

1.     Cardiac Artifacts:

o  Source: Cardiac artifacts, such as ECG artifacts, pacemaker artifacts, and pulse artifacts, result from the electrical or mechanical effects of cardiac activity on EEG electrodes.

o  Characteristics: These artifacts are time-locked to cardiac contractions and may exhibit waveform distortions resembling poorly formed QRS complexes.

o  Location: Cardiac artifacts are often prominent in channels that include electrodes low on the head, such as ear or mastoid electrodes.

o Regular Intervals: Cardiac artifacts may show periodic occurrences with intervals that are multiples of a similar time interval related to the cardiac cycle.

2.   Benign Epileptiform Transients of Sleep (BETS):

o Description: BETS are transient epileptiform discharges that occur during non-REM sleep and are considered benign physiological phenomena.

o Characteristics: BETS typically comprise individual transients of low amplitude, unchanged waveform, and occur in the mid-temporal regions during sleep.

oTemporal Correspondence: The temporal correspondence to simultaneously recorded ECG can help differentiate BETS from other patterns.

o Regular Intervals: BETS may exhibit a regular interval between the waves, but this feature is less consistent compared to cardiac artifacts.

Key Differences:

  • Waveform: Cardiac artifacts often exhibit poorly formed QRS complexes, while BETS show unchanged waveform characteristics during sleep.
  • Location: Cardiac artifacts are more likely to occur in channels with electrodes low on the head, whereas BETS are typically observed in the mid-temporal regions during sleep.
  • Regularity: Cardiac artifacts may demonstrate more regular intervals related to the cardiac cycle, whereas the regularity of BETS intervals can vary.

Understanding these differences is essential for accurate interpretation of EEG recordings, as distinguishing between cardiac artifacts and BETS can help prevent misinterpretations and ensure the reliability of EEG data analysis in clinical and research settings.

 

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