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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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Occipital Alpha Rhythm

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Dr. Rishabh Pathak

The Occipital Alpha Rhythm, also known as the Posterior Dominant Rhythm (PDR) or Posterior Basic Rhythm, is a prominent rhythmic brainwave activity observed in the occipital and posterior regions of the brain in electroencephalography (EEG) recordings. 


1.     Definition:

o  The Occipital Alpha Rhythm refers to the dominant rhythmic activity in the alpha frequency range (8 to 13 Hz) observed over the occipital and posterior head regions in EEG recordings.

o It is characterized by rhythmic oscillations that are typically most prominent when an individual is in a state of relaxed wakefulness with the eyes closed.

2.   Location:

o The Occipital Alpha Rhythm is primarily localized over the occipital lobes at the back of the brain, which includes the visual cortex.

o It is often most prominent in EEG electrodes placed over the posterior regions of the head.

3.   Behavior:

o The Occipital Alpha Rhythm tends to attenuate or disappear with drowsiness, concentration, visual fixation, or cognitive tasks.

o It reflects changes in attention, arousal levels, and cognitive processing, with variations in response to external stimuli.

4.   Clinical Significance:

o Monitoring the Occipital Alpha Rhythm in EEG recordings provides insights into the individual's wakeful state, attention levels, and visual processing.

oChanges in the Occipital Alpha Rhythm may indicate alterations in mental states, alertness, or responses to sensory stimuli.

5.    Variants:

o Variations in the frequency, amplitude, and reactivity of the Occipital Alpha Rhythm may be observed among individuals.

o Slow alpha and fast alpha variants of the rhythm can exhibit distinct characteristics related to the alpha frequency band.

6.   Abnormalities:

o Deviations in the Occipital Alpha Rhythm, such as abnormal frequency patterns, lack of reactivity, or asymmetries, can be indicative of underlying neurological conditions.

oComplete absence of the Occipital Alpha Rhythm or abnormal changes in its characteristics may suggest cerebral dysfunction or pathological processes.

Understanding the Occipital Alpha Rhythm in EEG recordings is crucial for interpreting brainwave activity, assessing cognitive states, and monitoring changes in neural oscillations related to visual processing and attention. Studying the characteristics and behavior of the Occipital Alpha Rhythm contributes to the broader understanding of brain function, neural dynamics, and the relationship between EEG patterns and cognitive processes.

 

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