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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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International 10-20 System Rules

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Dr. Rishabh Pathak

The International 10-20 System is a standardized method for electrode placement in EEG recordings. The system is based on specific rules for positioning electrodes on the scalp relative to anatomical landmarks. Here are some key rules of the International 10-20 System:


1.Measurement Method: Electrode placement is determined by measuring distances between specific landmarks on the head. The nasion (bridge of the nose) and inion (bump at the back of the head) define the sagittal midline, while the preauricular points (above the ears) define the coronal midline.


2.Incremental Measurements: Electrodes are positioned at specific percentages along the sagittal and coronal midlines. The 10-20 System uses 10% and 20% increments along these lines to determine electrode locations.


3.Letter Prefix and Number Suffix: Electrode locations are named using a letter prefix indicating the region of the head (e.g., F for frontal, C for central) and a number suffix indicating the exact location within the region. Odd numbers typically represent the left side, even numbers the right side, and "z" indicates the midline.


4.Consistency in Naming: The naming convention ensures consistency in electrode location identification across different EEG recordings and interpretations. For example, Fp1 represents the left frontal pole, F4 is over the right frontal lobe, and Cz is at the vertex.


5.10-10 System: A revised version of the 10-20 System, known as the 10-10 System, addresses inconsistencies in electrode naming, especially for midtemporal electrodes. It provides a more precise naming scheme for electrode locations.


6.Standardization and Accuracy: The 10-20 System promotes standardization in EEG electrode placement, minimizing variations in electrode positioning across different individuals and ensuring accurate correspondence between electrodes and brain structures.


By following these rules and guidelines of the International 10-20 System, EEG technicians and clinicians can accurately and consistently place electrodes on the scalp for EEG recordings, facilitating proper interpretation and analysis of EEG data.

 

Electrode Location Names according to the International 10-20 System

The International 10-20 System is a standardized method for electrode placement in EEG recordings. Here are the electrode location names according to the International 10-20 System:

1.      Fp1, Fp2: Frontopolar (Prefrontal)

2.     F7, F8: Frontal

3.     F3, F4: Frontal

4.    C3, C4: Central

5.     P3, P4: Parietal

6.    O1, O2: Occipital

7.     T3, T4: Temporal

8.    T5, T6: Temporal

These electrode locations are crucial for standardizing EEG electrode placement across individuals and institutions, ensuring consistency in recording and interpretation of EEG data.

 

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