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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 Interictal Epileptiform Discharges

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Dr. Rishabh Pathak

Positive Occipital Sharp Transients of Sleep (POSTS) and interictal epileptiform discharges (IEDs) are both EEG patterns, but they have distinct characteristics, clinical implications, and contexts. 

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.

Interictal Epileptiform Discharges (IEDs)

7.     Definition:

§  IEDs are abnormal EEG patterns that occur between seizures in individuals with epilepsy. They represent a transient abnormality in the brain's electrical activity.

8.    Waveform Characteristics:

§  IEDs can vary in morphology but are often characterized by sharp waves or spikes. They typically have a more asymmetric shape compared to POSTS and may show a sharper contour.

9.    Location:

§  IEDs can occur in various regions of the brain, depending on the type of epilepsy. They are not limited to the occipital region and can be localized to specific areas associated with seizure activity.

10.                        Duration and Frequency:

§  IEDs are usually brief, lasting less than 100 milliseconds, and can occur sporadically or in bursts. They do not typically occur in trains like POSTS.

11.  Clinical Significance:

§  The presence of IEDs is indicative of an underlying epileptic condition and may correlate with seizure activity. They are considered abnormal findings and can help in diagnosing epilepsy.

12. Age-Related Variability:

§  IEDs can occur in individuals of any age with epilepsy, but their presence and frequency may vary based on the type of epilepsy and the individual's age.

Summary

In summary, while both Positive Occipital Sharp Transients of Sleep and interictal epileptiform discharges are observed in EEG recordings, they differ significantly in their characteristics, clinical implications, and contexts. POSTS are generally benign and associated with normal sleep activity, while IEDs are abnormal findings indicative of epilepsy and potential seizure activity. The identification of POSTS suggests normal sleep function, whereas the presence of IEDs raises concerns about underlying neurological conditions.

 

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