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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 Cone waves

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Dr. Rishabh Pathak

Positive Occipital Sharp Transients of Sleep (POSTS) and cone waves are both EEG patterns observed during sleep, but they have distinct characteristics, clinical significance, and implications. 

Positive Occipital Sharp Transients of Sleep (POSTS)

1.      Definition:

§  POSTS are sharp waveforms that occur predominantly in the occipital region 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 positive peak is prominent, followed by a negative potential of lower amplitude.

3.     Location:

§  Recorded primarily from the occipital leads (O1 and O2) of the EEG. They may also show phase reversals at these electrodes.

4.    Duration and Frequency:

§  Each transient lasts about 80 to 200 milliseconds and can occur as individual events or in trains of up to six per second. The trains usually last 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 become less common with age. Rarely observed in individuals over 70 years old.

Cone Waves

7.     Definition:

§  Cone waves are a type of EEG pattern that can be observed during sleep, characterized by a specific morphology that resembles a cone or a pointed shape.

8.    Waveform Characteristics:

§  Cone waves typically have a more pronounced peak and a rapid return to the baseline, creating a sharp, pointed appearance. They may not have the same triangular shape as POSTS.

9.    Location:

§  Cone waves can be recorded from various regions of the scalp, not limited to the occipital area. Their distribution may vary depending on the underlying condition or the specific context in which they are observed.

10.                        Duration and Frequency:

§  The duration and frequency of cone waves can vary, and they may not follow the same patterns of occurrence as POSTS. They can appear in bursts or as isolated events.

11.  Clinical Significance:

§  Cone waves may be associated with specific neurological conditions or sleep disorders, and their presence can indicate underlying pathology. Unlike POSTS, they may not be considered a normal variant and could warrant further investigation.

12. Age-Related Variability:

§  The occurrence of cone waves may not have the same age-related patterns as POSTS, and their clinical significance can vary widely based on the context in which they are observed.

Summary

In summary, while both Positive Occipital Sharp Transients of Sleep and cone waves are EEG patterns observed during sleep, they differ significantly in their characteristics, clinical implications, and associations with neurological conditions. POSTS are generally benign and common in healthy individuals, while cone waves may indicate underlying pathology and require careful interpretation in the context of the patient's clinical picture.

 

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