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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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Electrode Placement according to standardized head measurements

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Dr. Rishabh Pathak

Electrode placement in EEG recordings follows standardized head measurements to ensure consistency and accuracy in electrode positioning. The process involves specific landmarks on the head and precise measurements along the sagittal and coronal midlines. Here is an overview of electrode placement according to standardized head measurements:


1.      Landmarks:

oNasion: The nasion is the depression between the forehead and the bridge of the nose.

oInion: The inion is the bump at the back of the head where the skull meets the neck.

oPreauricular Points: These points are located above the ears where the ear meets the head.

2.     Sagittal and Coronal Midlines:

o    The sagittal midline is defined by the nasion and inion.

o    The coronal midline is defined by the preauricular points.

3.     Incremental Measurements:

o    Measurements are taken along the sagittal and coronal midlines in increments of 10% and 20%.

o Additional lines are defined based on these increments to guide electrode placement.

4.    Electrode Positions:

o Electrodes are placed at specific locations corresponding to the measured percentages along the midlines.

o    Common electrode positions include Fp1, Fp2, F7, F8, F3, F4, C3, C4, P3, P4, O1, O2, T3, T4, T5, and T6.

5.     Circumferential Electrodes:

o Additional electrodes are positioned around the head based on measurements and divisions along the midlines.

o  These circumferential electrodes provide additional recording sites for comprehensive EEG data collection.

6.    Consistency and Standardization:

o  Standardized head measurements and electrode placements ensure consistency in EEG recordings across different individuals and settings.

o   By following these standardized measurements, EEG technicians can accurately position electrodes for optimal signal acquisition.

By adhering to these standardized head measurements and electrode placement guidelines, EEG technicians and clinicians can maintain consistency and accuracy in EEG recordings, facilitating proper interpretation and analysis of brainwave activity.

 

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