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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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Positive Occipital Sharp Transients of Sleep Compared to Lambda Waves

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Dr. Rishabh Pathak

Positive Occipital Sharp Transients of Sleep (POSTS) and lambda waves are both EEG patterns that occur in the occipital region, but they have distinct characteristics, contexts, and clinical implications. 

Positive Occipital Sharp Transients of Sleep (POSTS)

1.      Definition:

§  POSTS are sharp waveforms that occur predominantly during sleep, particularly in non-rapid eye movement (NREM) sleep.

2.     Waveform Characteristics:

§  They typically exhibit a triangular shape and can be monophasic or diphasic. The first phase usually has a higher amplitude than the second phase.

3.     Location:

§  Recorded primarily from the occipital leads (O1 and O2) of the EEG, with a positive field at the occiput. Phase reversals are often observed at these electrodes.

4.    Duration and Frequency:

§  Each transient lasts approximately 80 to 200 milliseconds and can occur in trains, typically lasting about 1 to 2 seconds.

5.     Clinical Significance:

§  Generally considered a normal variant in healthy individuals, especially in children and adolescents. They are not associated with any pathological conditions and are common in the EEGs of healthy adults.

6.    Age-Related Variability:

§  More prevalent in younger populations and tend to decrease with age. Rarely observed in individuals over 70 years old.

Lambda Waves

7.     Definition:

§  Lambda waves are EEG patterns that occur during wakefulness, particularly when an individual is actively engaged in visual exploration or scanning the environment.

8.    Waveform Characteristics:

§  Lambda waves typically have a similar triangular shape but are often more pronounced and can be associated with higher amplitude. They are usually seen as sharp waves with a clear positive peak.

9.    Location:

§  Primarily recorded from the occipital region (O1 and O2) but can also be seen in adjacent areas. They are associated with visual processing and exploration.

10.                        Duration and Frequency:

§  Lambda waves can occur as isolated events or in bursts, but they are generally shorter in duration compared to POSTS and are not typically seen in trains.

11.  Clinical Significance:

§  Lambda waves are produced during active visual processing and are considered a normal finding during wakefulness. They are not associated with sleep and indicate cognitive engagement with visual stimuli.

12. Age-Related Variability:

§  Lambda waves are more common in younger individuals and are typically absent in infants and very young children, as they develop with visual exploration skills.

Summary

In summary, while both Positive Occipital Sharp Transients of Sleep and lambda waves are observed in the occipital region, they differ significantly in their characteristics, contexts, and clinical implications. POSTS are associated with sleep and are generally benign, while lambda waves occur during wakefulness and are linked to visual processing. The presence of POSTS indicates normal sleep activity, whereas lambda waves reflect active cognitive engagement with visual stimuli.

 

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