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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 phantom spikes and waves

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Dr. Rishabh Pathak


Fourteen and Six Per Second Positive Bursts (Ctenoids) can be differentiated from Phantom Spikes and Waves based on the following characteristics:


1.     Frequency and Morphology:

o Ctenoids exhibit rhythmic activity at frequencies ranging from 6 to 14 Hz, with bursts lasting for about 1 second and typically showing an arciform appearance.

o Phantom Spikes and Waves, on the other hand, are characterized by a diphasic morphology with low-amplitude spikes occurring bisynchronously at 6 Hz, particularly in children during drowsiness.

2.   Distribution:

o Ctenoids have a broad and uniformly distributed field across the scalp, often involving regions like the occipital and parietal areas.

o Phantom Spikes and Waves typically have a maximal distribution along the midline, while Ctenoids are more lateralized in their distribution.

3.   Duration:

o Ctenoids bursts usually last for about 1 second, rarely exceeding 2 seconds in duration.

o  Phantom Spikes and Waves also have durations typically less than 2 seconds, similar to Ctenoids, but may vary in their temporal characteristics.

4.   Clinical Implications:

o  Ctenoids are considered benign epileptiform variants and are often observed in children during drowsiness, with a prevalence that varies depending on age and EEG montage.

o Phantom Spikes and Waves are also associated with childhood EEG patterns during drowsiness but are characterized by their diphasic morphology and midline distribution, distinguishing them from the lateralized Ctenoids.

5.    Electrode Configuration:

o  Ctenoids are best recorded with long interelectrode distances to capture their broad field distribution accurately, while short interelectrode distances may result in lower amplitude recordings.

oPhantom Spikes and Waves may exhibit different characteristics based on electrode montages and configurations, with a focus on the midline distribution and diphasic morphology.

Understanding these distinctions between Fourteen and Six Per Second Positive Bursts (Ctenoids) and Phantom Spikes and Waves is crucial for accurate EEG interpretation and differentiation between benign epileptiform variants and other EEG patterns observed in clinical practice.

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