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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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Normal EEG

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Dr. Rishabh Pathak

A normal EEG (Electroencephalogram) is characterized by specific patterns of electrical activity in the brain that are considered typical and healthy. Understanding what constitutes a normal EEG is essential for accurately interpreting abnormal findings. Here are some key points about a normal EEG:


1.Alpha Rhythm: The alpha rhythm is a prominent feature of a normal EEG. It is a regular, rhythmic oscillation in the frequency range of 8 to 13 Hz, typically seen over the posterior head regions when the individual is awake and relaxed. The alpha rhythm may attenuate with eye opening and increase in frequency upon eye closure.


2.Wakefulness and Age: The state of wakefulness and age are critical factors in interpreting the normal EEG. The alpha rhythm is expected to be present and stable between 8 and 12 Hz in adults, with variations based on age and individual characteristics.


3.Bilateral Posterior Dominant Rhythm: In a normal EEG, a bilateral posterior dominant rhythm is observed over the posterior head regions. This rhythm is a key component of the normal brain activity pattern and serves as a reference point for analyzing EEG recordings.


4.Variants of Normal: While there are typical patterns associated with a normal EEG, there can be variations and benign abnormalities that do not necessarily indicate pathology. Understanding these variants of normal is important to differentiate them from abnormal findings.


5.Fluctuations Throughout the Lifecycle: Normal EEG patterns can vary throughout an individual's life, from youth to old age. Recognizing how EEG activity changes with age and in different physiological states is crucial for accurate interpretation.


6.Foundation for Abnormality Identification: Knowledge of normal EEG patterns forms the foundation for identifying abnormalities in EEG recordings. Clinicians use their understanding of normal brain activity to recognize deviations that may indicate underlying neurological conditions.


In summary, a normal EEG is characterized by specific rhythmic patterns of electrical activity in the brain, such as the alpha rhythm and bilateral posterior dominant rhythm. Understanding what is considered normal in EEG recordings is essential for distinguishing between healthy brain function and abnormal findings indicative of neurological disorders.

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