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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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Cortical Silent Period (CSP)

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Dr. Rishabh Pathak

The Cortical Silent Period (CSP) is a neurophysiological phenomenon that occurs in response to transcranial magnetic stimulation (TMS) of the primary motor cortex. Here is a detailed explanation of the Cortical Silent Period:


1.      Definition:

o CSP: The CSP is a transient suppression of muscle activity that follows the initial muscle response evoked by TMS of the motor cortex. It represents a period during which voluntary muscle contractions are inhibited, reflecting the temporary suppression of corticospinal excitability.

2.     Mechanism:

o TMS: During TMS, a brief and intense magnetic pulse is delivered to the motor cortex, leading to the activation of corticospinal neurons and the generation of motor evoked potentials (MEPs) in the target muscles.

o  CSP Onset: Following the MEP, there is a period of inhibition during which the electromyographic (EMG) activity in the target muscle decreases or ceases. This inhibition is thought to result from the activation of inhibitory circuits in the motor cortex and spinal cord.

3.     Measurement and Interpretation:

o EMG Recording: The CSP duration is typically measured using EMG recordings of the target muscle. The onset and offset of the CSP are determined based on changes in muscle activity following the TMS pulse.

o Interpretation: The duration of the CSP can provide insights into the balance between excitatory and inhibitory mechanisms in the motor cortex. Changes in CSP duration or amplitude may indicate alterations in cortical excitability and inhibitory control.

4.    Significance:

o Motor Control: The CSP reflects the inhibitory processes that regulate motor output and prevent excessive muscle activity. It plays a role in fine-tuning motor responses and coordinating muscle contractions during voluntary movements.

o    Clinical Applications:

§ Neurological Disorders: Alterations in CSP duration or amplitude have been observed in various neurological conditions, such as movement disorders, stroke, and epilepsy. Studying CSP can help assess cortical function and monitor changes in motor system excitability in patients with neurological disorders.

§Treatment Monitoring: In clinical settings, CSP measurements can be used to evaluate the effects of therapeutic interventions, such as medications, brain stimulation techniques, or rehabilitation programs, on cortical excitability and motor function.

5.     Research and Applications:

o Neurophysiology: CSP assessments are valuable in research settings to investigate cortical excitability, plasticity, and motor system function. Researchers use CSP measurements to study the mechanisms underlying motor control, learning, and adaptation in healthy individuals and patients with neurological conditions.

oTherapeutic Target: Understanding the mechanisms of CSP modulation can guide the development of novel therapeutic approaches for conditions characterized by abnormal cortical excitability, such as dystonia, Parkinson's disease, or chronic pain disorders.

In summary, the Cortical Silent Period is a neurophysiological phenomenon that reflects the temporary suppression of muscle activity following TMS-induced cortical stimulation. Studying CSP provides insights into cortical inhibitory mechanisms, motor control processes, and alterations in cortical excitability associated with neurological disorders and therapeutic interventions.

 

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