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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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How does hepatic encephalopathy relate to the triphasic pattern?

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Dr. Rishabh Pathak

Hepatic encephalopathy is closely related to the triphasic pattern observed in electroencephalography (EEG) due to several key factors:

1.      Pathophysiology: Hepatic encephalopathy occurs when the liver is unable to adequately remove toxins from the blood, leading to the accumulation of substances such as ammonia. This accumulation can disrupt normal brain function and result in altered mental status, which is reflected in the EEG.

2.     EEG Characteristics: The triphasic pattern is characterized by complexes with three distinct phases that recur at approximately 2 Hz. This pattern is typically seen in patients with significant cognitive impairment, such as those experiencing hepatic encephalopathy. The presence of this pattern indicates a severe level of encephalopathy and is often associated with a poor prognosis.

3.     Clinical Correlation: The triphasic pattern is considered a hallmark of hepatic encephalopathy, although it can also appear in other metabolic conditions. Its presence suggests a significant impairment in mentation, which is a common feature of hepatic encephalopathy. The pattern may vary in appearance but generally indicates a severe underlying metabolic disturbance.

4.    Prognostic Implications: The presence of the triphasic pattern in patients with hepatic encephalopathy is associated with a more severe form of the condition. Studies have shown that patients exhibiting this pattern have a poorer long-term prognosis, as it often correlates with more severe metabolic derangements.

In summary, hepatic encephalopathy is a primary condition associated with the triphasic pattern in EEG, reflecting the underlying metabolic disturbances and cognitive impairments characteristic of this disorder.

 

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