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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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Central Motor Conduction Time (CMCT)

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Dr. Rishabh Pathak

Central Motor Conduction Time (CMCT) is a neurophysiological parameter that measures the time taken for a motor impulse to travel along the central motor pathways from the motor cortex to the spinal motor neurons. Here is a detailed explanation of Central Motor Conduction Time:


1.  Definition: CMCT is a measure of the conduction time through the central nervous system, specifically along the corticospinal tract, which is responsible for voluntary motor control. It reflects the integrity and efficiency of the neural pathways connecting the motor cortex to the spinal cord and peripheral muscles.


2.     Methodology:

o  Stimulation: CMCT is typically assessed using transcranial magnetic stimulation (TMS) to stimulate the primary motor cortex and evoke motor responses in the target muscles. The timing of the motor evoked potentials (MEPs) elicited by TMS is measured to determine the conduction time from the cortex to the muscles.

o  Recording: Electromyography (EMG) recordings are used to capture the MEPs in the muscles of interest. By analyzing the onset latency of the MEPs relative to the TMS pulse, researchers can calculate the CMCT, which includes the time for synaptic transmission, conduction along the corticospinal tract, and neuromuscular junction transmission.

3.     Significance:

o  Motor Pathway Integrity: CMCT provides information about the functional integrity of the central motor pathways, including the corticospinal tract. Prolonged CMCT may indicate disruptions or abnormalities in the neural conduction along these pathways, which can be associated with neurological conditions affecting motor function.

o  Diagnostic Value: Changes in CMCT can be observed in various neurological disorders, such as multiple sclerosis, motor neuron diseases, and stroke. Monitoring CMCT alterations can aid in diagnosing and monitoring disease progression, as well as assessing the effects of therapeutic interventions.

4.    Clinical Applications:

o   Neurological Disorders: CMCT measurements are used in clinical neurophysiology to evaluate motor pathway function in patients with neurological conditions affecting the central nervous system. Abnormal CMCT values can indicate underlying pathology and help guide treatment decisions.

o   Research: CMCT assessments are also valuable in research settings to investigate motor system physiology, plasticity, and adaptations in response to interventions such as rehabilitation, pharmacological treatments, or neurostimulation techniques. Studying CMCT can provide insights into motor control mechanisms and neural plasticity.

In summary, Central Motor Conduction Time is a neurophysiological parameter that assesses the conduction time along the central motor pathways from the motor cortex to the muscles. By measuring CMCT, clinicians and researchers can evaluate the integrity of the corticospinal tract, diagnose neurological disorders affecting motor function, and monitor changes in motor pathway function over time.

 

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