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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

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Dr. Rishabh Pathak

Positive Occipital Sharp Transients of Sleep (POSTS) are a specific type of EEG pattern observed during sleep, particularly in the occipital region of the brain. 

Key Features of POSTS

1.      Waveform Characteristics:

§  POSTS are characterized by sharp waves that typically have a triangular, monophasic, or diphasic shape. The second phase of the waveform usually has a lower amplitude than the first phase, which is a typical feature of these transients.

2.     Location:

§  These transients are predominantly recorded from the occipital leads (O1 and O2) of the EEG. They may also be seen in adjacent temporal leads, but their primary location is at the occiput.

3.     Duration and Frequency:

§  Each train of POSTS lasts approximately 1 to 2 seconds and can occur in bursts. They are often seen during light sleep and may be more prominent in certain sleep stages.

4.    Clinical Context:

§  POSTS are generally considered a normal variant in the EEG of healthy individuals, particularly in children and adolescents. They are not typically associated with any pathological conditions and are often seen in the context of normal sleep architecture.

Clinical Significance

5.     Normal Variant:

§  In most cases, POSTS are regarded as a benign and normal finding in the EEG, especially in children. They do not indicate any underlying neurological disorder and are often seen in healthy individuals.

6.    Differentiation from Pathological Patterns:

§  It is important to differentiate POSTS from other abnormal EEG patterns, such as epileptiform discharges. The presence of POSTS does not imply a risk for seizures or epilepsy, making them distinct from other sharp wave patterns that may indicate pathology.

7.     Potential Association with Sleep Disorders:

§  While generally benign, the presence of POSTS may warrant further investigation if they are accompanied by other abnormal findings or clinical symptoms. In some cases, they may be observed in patients with sleep disorders, but this is not common.

8.    Age-Related Variability:

§  The prevalence of POSTS is higher in children and tends to decrease with age. Their presence in the EEG of older adults is less common and may reflect age-related changes in brain activity.

Summary

Positive Occipital Sharp Transients of Sleep are typically benign EEG findings that reflect normal brain activity during sleep, particularly in the occipital region. They are characterized by specific waveform patterns and are most commonly observed in children. While they are generally not associated with any pathological conditions, their presence should be interpreted in the context of the overall clinical picture and other EEG findings.

 

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