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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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How force is generated in the muscles

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Dr. Rishabh Pathak

The generation of force in muscles is a complex physiological process involving intricate interactions at the molecular, cellular, and tissue levels. Muscle contraction, which leads to force production, is primarily driven by the sliding filament theory and the cross-bridge cycle within muscle fibers. Here is a discussion on how force is generated in muscles:

Mechanisms of Force Generation in Muscles:

1.    Sliding Filament Theory:

o    Actin and Myosin Interaction:

§  Muscle contraction is based on the sliding filament theory, where actin and myosin filaments within muscle fibers slide past each other to generate force.

§  Myosin heads on the thick filaments interact with actin filaments on the thin filaments, forming cross-bridges that undergo cyclic interactions to produce force.

2.    Cross-Bridge Cycle:

o    Cross-Bridge Formation:

§  The cross-bridge cycle involves the binding of myosin heads to actin filaments, forming cross-bridges that generate force during muscle contraction.

§  ATP hydrolysis provides the energy for myosin heads to pivot and generate force, leading to the sliding of actin filaments along myosin filaments.

3.    Excitation-Contraction Coupling:

o    Neuromuscular Transmission:

§  The process of force generation in muscles begins with neuromuscular transmission, where motor neurons stimulate muscle fibers at the neuromuscular junction.

§  Action potentials propagate along the sarcolemma and into the transverse tubules, triggering the release of calcium ions from the sarcoplasmic reticulum.

4.    Calcium Regulation:

o    Calcium Binding:

§  Calcium ions released into the muscle cell bind to troponin, causing a conformational change in the troponin-tropomyosin complex.

§  This change exposes the myosin-binding sites on actin, allowing myosin heads to interact with actin and initiate the cross-bridge cycle.

5.    Force-Length Relationship:

o    Optimal Length:

§  The force-generating capacity of a muscle is influenced by its length, with an optimal length for maximal force production.

§  The overlap between actin and myosin filaments affects the number of cross-bridges formed and the force generated during contraction.

6.    Motor Unit Recruitment:

o    Motor Unit Activation:

§  Force generation in muscles is also regulated by the recruitment of motor units, where motor neurons activate muscle fibers based on the required force output.

§  As the demand for force increases, additional motor units are recruited to generate more force through synchronous muscle contractions.

7.    Energy Metabolism:

o    ATP Utilization:

§  Muscle force generation relies on ATP hydrolysis to power the cross-bridge cycle and maintain muscle contraction.

§  ATP is continuously regenerated through various metabolic pathways to sustain muscle activity and force production.

Understanding the mechanisms of force generation in muscles is essential for athletes, clinicians, and researchers to optimize training programs, diagnose muscle disorders, and enhance performance outcomes. The coordinated interactions between actin, myosin, calcium ions, and neural control systems play a critical role in the generation of force during muscle contractions.

 

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