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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 the Force is transmitted to the Bones

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Dr. Rishabh Pathak

The transmission of force from muscles to bones is a crucial aspect of human movement and biomechanics. This process involves the conversion of muscle contraction forces into joint movements and ultimately the generation of mechanical loads on the skeletal system. The following points explain how force is transmitted from muscles to bones:

Transmission of Force from Muscles to Bones:

1.    Tendon Attachment:

o    Tendon Structure:

§  Tendons are dense connective tissues that connect muscles to bones, serving as the primary means of transmitting force.

§  Muscle contraction generates tension in the tendons, which is then transmitted to the bones through the tendon-bone interface.

2.    Tendon-Bone Junction:

o    Enthesis Structure:

§  The enthesis is the specialized region where tendons or ligaments attach to bone, optimizing force transmission and load distribution.

§  The enthesis structure includes fibrocartilage and mineralized fibrocartilage zones that help to anchor the tendon to the bone and withstand tensile forces.

3.    Mechanical Coupling:

o    Force Transfer:

§  The mechanical coupling between muscles, tendons, and bones allows for efficient force transmission during muscle contractions.

§  Tendons act as compliant structures that store and release elastic energy, enhancing the efficiency of force transmission to the skeletal system.

4.    Muscle-Tendon Unit:

o    Functional Unit:

§  The muscle-tendon unit functions as a coordinated system where muscle contraction generates tension in the tendon, leading to joint movement and force application on the bones.

§  The length-tension relationship of the muscle-tendon unit influences the force transmission capacity and joint stability during movement.

5.    Biomechanical Pathways:

o    Force Distribution:

§  Forces generated by muscles are transmitted through tendons to the bones along specific biomechanical pathways based on muscle architecture and joint mechanics.

§  The orientation of muscle fibers, tendon insertion angles, and joint geometry influence the direction and magnitude of force transmission.

6.    Lever Systems:

o    Mechanical Advantage:

§  Muscles and tendons act as components of lever systems within the musculoskeletal system, providing mechanical advantage for force transmission.

§  The arrangement of bones, joints, and muscle-tendon units determines the leverage and efficiency of force transmission for producing joint movements.

7.    Joint Loading:

o    Load Distribution:

§  Force transmission from muscles to bones results in joint loading, where mechanical loads are distributed across the articular surfaces of the bones.

§  Proper force transmission is essential for maintaining joint stability, preventing injury, and optimizing movement efficiency.

Understanding the mechanisms of force transmission from muscles to bones is essential for biomechanical analyses, sports performance optimization, rehabilitation strategies, and injury prevention. The coordinated interactions between muscles, tendons, and bones ensure effective force transfer, joint motion control, and overall musculoskeletal function during various activities and movements.
 

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