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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 the Mu Rhythms

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Dr. Rishabh Pathak

The clinical significance of Mu rhythms, a normal EEG pattern associated with the cerebral motor system, is important in understanding their role in brain function and their implications in clinical practice.


1.     Normal Pattern:

o The Mu rhythm is considered a normal EEG pattern that is the cerebral motor system's analogue to the visual system's alpha rhythm.

o Its presence is not considered abnormal, but its absence may draw attention due to its genetic nature with possibly autosomal dominant inheritance.

2.   Genetic Inheritance:

oThe presence of Mu rhythms is suggested to have a genetic basis with possible autosomal dominant inheritance.

oThis genetic component may influence the occurrence and characteristics of Mu rhythms in individuals.

3.   Source Analysis:

oMagnetoencephalographic source analysis has revealed that the Mu rhythm consists of two independent and adjacent signals: a 10-Hz signal from the somatosensory cortex and a 20-Hz signal slightly more anterior from the premotor cortex.

oSimultaneous EEG and functional MRI studies have identified similar sources for the two frequency components of the Mu rhythm.

4.   Function:

o The function of the Mu rhythm has been proposed to relate to the processing of perception into a single action.

oIt may play a role in sensorimotor integration and coordination, potentially influencing motor planning and execution processes.

5.    Clinical Applications:

oUnderstanding the presence and characteristics of Mu rhythms in EEG recordings can aid in differentiating normal brain activity from abnormal patterns associated with neurological disorders.

oMonitoring Mu rhythms in clinical settings may provide insights into motor system function and cortical excitability, particularly in the context of movement-related tasks and cognitive processes.

Overall, the clinical significance of Mu rhythms lies in their role as a normal EEG pattern reflecting motor system activity, their genetic basis, and their potential implications for motor function and cognitive processing. Recognizing and interpreting Mu rhythms in EEG recordings can contribute to a comprehensive assessment of brain activity and may have implications for understanding motor-related disorders and cognitive functions.

 

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