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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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Clinical Significance of Positive Occipital Sharp Transients of Sleep

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Dr. Rishabh Pathak

Positive Occipital Sharp Transients of Sleep (POSTS) have several important clinical implications, particularly in the context of EEG interpretation and the assessment of sleep patterns. 

1.      Normal Variant:

§  POSTS are generally considered a normal variant in the EEG of healthy individuals, especially in children and adolescents. Their presence is not indicative of any pathological condition and is often seen in the EEGs of healthy adults when adequate sleep is recorded.

2.     Age-Related Findings:

§  They are most commonly observed in younger populations, particularly from late childhood through middle adulthood. Their occurrence tends to decrease with age, and they are rarely seen in individuals over 70 years old. This age-related variability is important for clinicians to consider when interpreting EEG results.

3.     Association with Sleep Stages:

§  POSTS typically occur during late stage 1 non-rapid eye movement (NREM) sleep and may persist into slow wave sleep. They are most frequent during the first 30 minutes after sleep onset, which can help differentiate them from other EEG patterns that may occur during wakefulness or REM sleep.

4.    Differentiation from Pathological Patterns:

§  The identification of POSTS is crucial for differentiating them from pathological EEG patterns, such as interictal epileptiform discharges (IEDs). POSTS have a consistent triangular morphology and do not exhibit the asymmetry or sharper contours characteristic of IEDs. This distinction is vital in avoiding misdiagnosis of epilepsy or other neurological conditions.

5.     Clinical Context:

§  While POSTS are benign, their presence should be interpreted in the context of the patient's clinical history and symptoms. In patients with suspected epilepsy or other neurological disorders, the presence of POSTS alongside other abnormal findings may require further investigation to rule out underlying conditions.

6.    Common Finding:

§  Studies indicate that the EEGs of about 50% to 94% of healthy adults demonstrate POSTS if adequate sleep is recorded, highlighting their prevalence and normalcy in the general population.

Summary

In summary, Positive Occipital Sharp Transients of Sleep are a common and generally benign finding in EEG recordings, particularly in younger individuals. Their clinical significance lies in their role as a normal variant, their association with specific sleep stages, and their ability to help differentiate between normal and pathological EEG patterns. Understanding the characteristics and implications of POSTS is essential for accurate EEG interpretation and patient management.

 

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