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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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Criteria's of Low-Voltage EEG and Electrocerebral Inactivity

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Dr. Rishabh Pathak

The criteria for low-voltage EEG and electrocerebral inactivity (ECI) are essential for accurate diagnosis and interpretation in clinical settings. Here are the key criteria for each:

Low-Voltage EEG Criteria

1.      Definition: Low-voltage EEG is characterized by the persistent absence of any cerebrally generated waves greater than 20 µV 33.

2.     Clinical Context: Low-voltage activity can occur in various contexts and may not be specific to any particular condition. It can be a normal variant, especially in older adults, but may also indicate pathological conditions 34.

3.     Common Causes: Low-voltage EEG may be associated with degenerative diseases (e.g., Alzheimer's, Huntington's disease), metabolic disturbances, or extrinsic factors like scalp edema 34, 34.

Electrocerebral Inactivity (ECI) Criteria

4.    Definition: ECI is defined as the absence of any detectable electrical activity in the brain, with no potentials greater than 2 µV when reviewed at a sensitivity of 2 µV/mm 33.

5.     Recording Standards: To confirm ECI, the following criteria must be met:

§  Electrode Coverage: At least eight scalp electrodes must be used, covering midline and at least one ear.

§  Impedance: Electrode impedances should be between 0.1 and 10 kΩ.

§  Interelectrode Distance: Distances between electrodes should be at least 10 cm.

§  Sensitivity: The sensitivity of the EEG recording should be set to 2 µV/mm.

§  Filters: Low-frequency filter should be set to 1 Hz or less, and high-frequency filter should be set to 30 Hz or greater.

§  Technologist Testing: Each electrode must be tested by physical manipulation to ensure proper function.

§  Stimulation: The patient should undergo somatosensory, auditory, and visual stimulation during the recording.

§  Duration: The EEG must be recorded and reviewed for at least 30 minutes.

§  Additional Electrodes: Electrodes on extracerebral sites, including the chest for ECG, should be included.

§  Qualified Personnel: The recording must be conducted by a qualified EEG technologist 33.

Summary

Both low-voltage EEG and ECI have specific criteria that must be adhered to for accurate diagnosis. Low-voltage EEG indicates reduced brain activity, while ECI signifies a complete absence of detectable brain activity. Understanding these criteria is crucial for clinicians in assessing neurological function and determining prognosis.

 

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