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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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Fourteen and Six Per Second Positive Bursts (Ctenoids) compared to Rhythmic Mid-temporal Theta

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Dr. Rishabh Pathak

Fourteen and Six Per Second Positive Bursts (Ctenoids) can be differentiated from Rhythmic Midtemporal Theta (RMT) based on the following characteristics:


1.     Distribution:

o Ctenoids have a broader distribution compared to RMT. Ctenoids commonly involve not only the temporal and frontal lobes but also extend to the occipital and parietal regions.

o RMT is typically localized to the temporal lobe and adjacent frontal regions, with less extension to other areas of the brain.

2.   Frequency:

o Ctenoids exhibit rhythmic activity at frequencies ranging from 6 to 14 Hz, with a characteristic burst pattern.

o RMT is characterized by rhythmic theta activity in the midtemporal regions, usually at frequencies lower than those seen in Ctenoids.

3.   Duration:

o Ctenoids bursts typically last for about 1 second, with durations rarely exceeding 2 seconds.

o RMT may have longer durations, often lasting more than 2 seconds but can also be as brief as 1 to 2 seconds.

4.   Presence of Beta Activity:

o The presence of beta frequency range activity can help distinguish Ctenoids from RMT. The occurrence of beta activity provides a clear distinction between the two patterns.

5.    Spatial Characteristics:

o Ctenoids have a broad and uniformly distributed field, often best recorded with long interelectrode distances to capture the pattern accurately.

o  RMT is more localized to the midtemporal regions and may not extend as widely across the scalp as Ctenoids.

6.   Clinical Implications:

o  Ctenoids are considered benign epileptiform variants and are typically not associated with pathological conditions or epileptic seizures.

o RMT may have different clinical implications depending on the context in which it is observed, such as in epilepsy or other neurological conditions.

Understanding these differences between Fourteen and Six Per Second Positive Bursts (Ctenoids) and Rhythmic Midtemporal Theta (RMT) patterns is essential for accurate EEG interpretation and clinical decision-making in patients with suspected neurological conditions or epileptiform activities.

 

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