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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 Focal Ictal Interictal Epileptiform Discharges

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Dr. Rishabh Pathak

Cardiac artifacts and focal ictal and interictal epileptiform discharges are distinct patterns that can be observed in EEG recordings. 

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, especially 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.   Focal Ictal and Interictal Epileptiform Discharges:

o Description: Focal epileptiform discharges represent abnormal electrical activity in a specific brain region, which can occur during seizures (ictal) or between seizures (interictal).

o  Characteristics: These discharges often manifest as sharp or spike-like waveforms with a fast component and may disrupt the EEG background activity.

o Location: Focal epileptiform discharges are typically localized to specific brain regions and may exhibit a consistent spatial distribution.

o Episodic Occurrence: Ictal discharges occur during seizures and may have a distinct episodic pattern, while interictal discharges occur between seizures.

Key Differences:

  • Waveform: Cardiac artifacts often exhibit poorly formed QRS complexes with a fast component, while focal epileptiform discharges show sharp or spike-like waveforms disrupting the EEG background activity.
  • Location: Cardiac artifacts are more likely to occur in channels with electrodes low on the head, especially ear or mastoid electrodes, whereas focal epileptiform discharges are localized to specific brain regions.
  • Occurrence Pattern: Cardiac artifacts are time-locked to cardiac activity, while focal epileptiform discharges have an episodic occurrence pattern related to seizure activity.

Understanding these differences is crucial for accurate interpretation of EEG recordings, as distinguishing between cardiac artifacts and focal epileptiform discharges can help clinicians and researchers differentiate between physiological and pathological patterns in EEG data analysis.

 

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