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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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Motor Evoked Potential (MEP)

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Dr. Rishabh Pathak

Motor Evoked Potentials (MEPs) are electrical signals recorded from muscles in response to transcranial magnetic stimulation (TMS) of the motor cortex. Here is an overview of MEPs and their significance in neuroscience research and clinical applications:


1.      Generation:

o MEPs are generated when the motor cortex is stimulated using TMS, leading to the activation of corticospinal neurons that project to the muscles.

o The electrical signals generated by these neurons travel along the corticospinal tract and result in muscle contractions, which can be detected and recorded as MEPs.

2.     Measurement:

o MEPs are typically recorded using surface electromyography (EMG) electrodes placed on the target muscles.

o The amplitude, latency, and shape of the MEPs provide information about the excitability and integrity of the corticospinal pathway and motor cortex.

3.     Clinical Applications:

oDiagnostic Tool: MEPs are used in clinical neurophysiology to assess the function of the corticospinal tract and diagnose conditions such as spinal cord injury, multiple sclerosis, stroke, and motor neuron diseases.

oIntraoperative Monitoring: MEPs are valuable for monitoring motor function during neurosurgical procedures to prevent damage to the motor pathways.

oAssessment of Motor Function: MEPs can help evaluate motor deficits, monitor recovery after neurological injuries, and assess the effects of therapeutic interventions.

4.    Research Applications:

o  Brain Mapping: MEPs are used in brain mapping studies to identify the cortical representation of specific muscles and motor areas.

o Plasticity and Learning: MEPs can be used to study neuroplastic changes in the motor cortex associated with motor learning, rehabilitation, and adaptation.

oInvestigation of Motor Control: Researchers use MEPs to investigate motor control mechanisms, motor imagery, and motor planning processes in the brain.

5.     Factors Affecting MEPs:

o    The amplitude and latency of MEPs can be influenced by factors such as the intensity of TMS, coil orientation, muscle properties, and individual variability.

o Changes in MEP characteristics over time or in response to interventions can provide insights into neural plasticity and motor system function.

6.    Interpretation:

o Abnormalities in MEPs, such as reduced amplitudes or prolonged latencies, can indicate dysfunction in the corticospinal pathway and motor cortex.

o Comparison of MEPs between different conditions or populations can reveal differences in motor system excitability and connectivity.

In summary, Motor Evoked Potentials (MEPs) are valuable neurophysiological signals that provide insights into motor system function, cortical excitability, and motor pathway integrity. Their clinical and research applications make MEPs a crucial tool for studying motor control, diagnosing neurological disorders, and monitoring motor function in various settings.

 

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