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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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Distinguishing Features of Alpha Activity

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Dr. Rishabh Pathak

Alpha activity in EEG recordings has distinguishing features that differentiate it from other brain wave patterns. 

1.     Frequency Range:

o Alpha activity typically occurs in the frequency range of 8 to 13 Hz.

o The alpha rhythm is most prominent in the posterior head regions during relaxed wakefulness with eyes closed.

2.   Location:

o Alpha activity is often observed over the occipital regions of the brain, known as the occipital alpha rhythm or posterior dominant rhythm.

o In drowsiness, the alpha rhythm may extend anteriorly to include the frontal region bilaterally.

3.   Modulation:

o The alpha rhythm can attenuate or disappear with drowsiness, concentration, stimulation, or visual fixation.

o Abrupt loss of the alpha rhythm due to visual or cognitive activity is termed blocking.

4.   Behavioral State:

o The presence of alpha activity is associated with a state of relaxed wakefulness with eyes closed.

o The alpha rhythm may be present with eyes open in the absence of visual fixation or in drowsy individuals who awaken without immediate visual fixation.

5.    Amplitude:

o The amplitude of the alpha rhythm typically ranges between 40 and 50 μV in adults, with higher amplitudes observed in children.

o The amplitude of alpha activity can vary among individuals and tends to decrease with aging.

6.   Co-occurring Patterns:

o Alpha activity is typically accompanied by other EEG signs of wakefulness, such as eye blink artifact and muscle artifact.

o  Co-occurring patterns with alpha activity may include the mu rhythm, wicket rhythm, generalized and frontal-central beta activity, and rhythmic mid-temporal theta activity.

7.    Clinical Significance:

oThe alpha rhythm is considered a normal EEG pattern associated with relaxed wakefulness and visual attention.

o Changes in the alpha rhythm, such as slowing or alterations in blocking, may indicate underlying neurological conditions or encephalopathies.

Understanding these distinguishing features of alpha activity in EEG recordings is essential for interpreting brain wave patterns, assessing cognitive states, and identifying abnormalities in neurological function.

 

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