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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 Beta Activity

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Dr. Rishabh Pathak

Beta activity in EEG recordings has various clinical significances depending on its characteristics and context.

Normal Wakefulness:

o  In normal wakefulness, beta activity is typically low in amplitude and not the predominant frequency band in healthy individuals.

o Beta activity less than 20 μV is observed in 98% of healthy awake subjects, with less than 10 μV in 70% of cases.

2.     Generalized Beta Activity:

o Generalized beta activity refers to abundant, high-amplitude beta activity that may occur symmetrically or with a frontal predominance.

o It is characterized by rhythms with frequencies within the beta range and individual waves with durations specific to the beta frequency range.

3.     Age-Related Changes:

o While generalized beta activity can occur at any age, the amount of beta activity may change late in life, with varying reports on whether there is an increase or decrease in beta activity.

o Frontal-central beta activity, which is state-dependent, may occur with drowsiness and continue through stage 2 of non-rapid eye movement (NREM) sleep.

4.    Pathological Conditions:

o Hypothyroidism, anxiety, and hyperthyroidism may be associated with generalized beta activity, with beta activity becoming more visible in the context of decreased alpha activity.

o Asymmetric, generalized beta activity can indicate abnormalities such as cortical injuries, fluid collections in the subdural or epidural space, or cerebral gliomas.

5.     Sensitivity to Changes:

o The loss of beta activity may be a sensitive EEG sign of cortical injuries or fluid collections, particularly when there is a focal or regional finding.

o Cerebrovascular ischemia or ischemic injury may lead to a decrease in ipsilateral beta activity, while cerebral gliomas may be associated with an increase in ipsilateral beta activity.

Understanding the clinical significance of beta activity in EEG recordings is essential for interpreting brain wave patterns, identifying abnormalities, and assessing neurological conditions in both routine and specialized EEG studies. The presence, distribution, and characteristics of beta activity can provide valuable insights into brain function and pathology across various clinical contexts.

 

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