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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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Mu Rhythms compared to Rolandic Rhythms

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Dr. Rishabh Pathak

The Mu rhythm and Rolandic rhythm are two distinct EEG patterns with unique characteristics that can be compared based on various features. 

1.     Location:

o    Mu Rhythm:

§The Mu rhythm is maximal at the C3 or C4 electrode, with occasional involvement of the Cz electrode.

§It is predominantly observed in the central and precentral regions of the brain.

o    Rolandic Rhythm:

§  The Rolandic rhythm is typically located in the Rolandic region, which includes the central sulcus and surrounding areas.

§It is associated with the sensorimotor cortex and the Rolandic area of the brain.

2.   Frequency:

o    Mu Rhythm:

§The Mu rhythm typically exhibits a frequency similar to the alpha rhythm, around 10 Hz.

§Frequencies within the range of 7 to 11 Hz are considered normal for the Mu rhythm.

o    Rolandic Rhythm:

§The frequency characteristics of the Rolandic rhythm may vary but are often associated with sensorimotor processing and motor tasks.

3.   Response to Movement:

oThe Mu rhythm is known to be reactive to motor activity, thoughts planning motor activity, or somatosensory attention.

oThe Rolandic rhythm is also related to sensorimotor processing and may exhibit reactivity to motor tasks and movements.

4.   Waveform:

oThe Mu rhythm is characterized by alternating sharply contoured and rounded phases, resembling the Greek letter μ.

oThe waveform of the Rolandic rhythm may have distinct characteristics related to sensorimotor processing and motor functions.

5.    Distinguishing Features:

o The Mu rhythm and Rolandic rhythm can be differentiated based on their specific locations, frequency ranges, and responses to motor tasks.

oWhile both rhythms may have some similarities in terms of reactivity to motor activity, their distinct features help in their identification and interpretation in EEG recordings.

Understanding the differences between Mu rhythms and Rolandic rhythms is essential for accurate EEG interpretation and the assessment of brain activity patterns related to sensorimotor processing and motor functions. By recognizing their unique characteristics, healthcare professionals can effectively differentiate between these two EEG patterns and gain insights into neural processing in clinical contexts.

 

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