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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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Shear Force

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Dr. Rishabh Pathak

Shear force is a type of mechanical load that acts parallel to a surface or plane, causing one part of a material to slide or shift in relation to another part. Here are key points regarding shear force and its effects on bones and biomechanics:

1. Description:

  • Direction: Shear force acts parallel to the surface of a bone or structure, inducing deformation by sliding or twisting the material along the plane of application.

  • Magnitude: The magnitude of shear force is determined by the external load applied tangentially to the surface, leading to shear stresses within the material.

2. Effects on Bones:

  • Fracture Risk: Excessive shear forces can increase the risk of bone fractures, especially in situations of sudden impact, rotational movements, or uneven loading.

  • Bone Integrity: Shear force influences bone microarchitecture, cortical bone thickness, and trabecular orientation, affecting the material properties and structural stability.

  • Stress Distribution: Shear forces alter the stress distribution within bones, leading to localized strains, microdamage accumulation, and potential failure points.

3. Biomechanical Significance:

  • Joint Loading: Shear forces are present during activities involving twisting, pivoting, or lateral movements that subject the joints to rotational or sliding stresses.

  • Sports Injuries: Shear forces play a role in sports-related injuries, such as ankle sprains, ligament tears, and stress fractures, where sudden or excessive shear loading occurs.

  • Biomechanical Modeling: Understanding shear forces is crucial for biomechanical modeling, injury prevention strategies, and optimizing load transfer mechanisms in the musculoskeletal system.

4. Clinical Applications:

  • Orthopedic Assessments: Shear force analysis is used in orthopedic assessments to evaluate joint stability, ligament integrity, and the risk of injury during functional movements.

  • Rehabilitation Protocols: Managing shear forces is essential in designing rehabilitation protocols for patients recovering from musculoskeletal injuries, surgical procedures, or joint instability.

  • Footwear and Orthotics: Proper footwear design and orthotic interventions aim to minimize shear forces, provide support, and enhance biomechanical alignment during gait and weight-bearing activities.

5. Biomechanical Analysis:

  • Joint Mechanics: Shear forces influence joint mechanics, articular surface loading, and the transmission of forces across joint structures during movements like rotation, translation, or gliding.

  • Material Properties: Shear force testing is used to assess the shear strength, shear modulus, and shear resistance of bone tissues, implants, or biomaterials in biomechanical studies.

Conclusion:

Shear force plays a significant role in bone biomechanics, joint stability, and injury mechanisms, highlighting the importance of understanding and managing shear stresses in various contexts. Recognizing the effects of shear forces on bones is essential for optimizing movement patterns, injury prevention strategies, and clinical interventions aimed at enhancing musculoskeletal health, function, and performance.

 

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