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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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Mobility

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Dr. Rishabh Pathak

Mobility in the context of biomechanics refers to the ability of a joint or the body as a whole to move through a full range of motion efficiently and effectively. Mobility is essential for performing daily activities, sports, and exercises with proper technique and reduced risk of injury. Here are key concepts related to mobility in biomechanics:

1. Joint Mobility:

  • Joint mobility refers to the range of motion available at a specific joint. Factors influencing joint mobility include the structure of the joint, surrounding ligaments, tendons, muscles, and joint capsule. Optimal joint mobility is essential for functional movement patterns.

2. Flexibility:

  • Flexibility is the ability of muscles and connective tissues to lengthen and allow joints to move through their full range of motion. Adequate flexibility is crucial for joint mobility, posture, and movement efficiency.

3. Muscle Length and Extensibility:

  • Muscle length and extensibility play a significant role in mobility. Muscles that are too tight or shortened can restrict joint movement, while well-conditioned and flexible muscles support optimal joint mobility.

4. Dynamic Mobility:

  • Dynamic mobility refers to the ability to move joints through a full range of motion actively and with control. Dynamic mobility exercises, such as dynamic stretching and mobility drills, help improve joint function and movement quality.

5. Passive Mobility:

  • Passive mobility involves the range of motion achieved with external assistance, such as a partner, gravity, or a prop. Passive stretching techniques can help improve joint mobility and flexibility by gently elongating muscles and connective tissues.

6. Functional Mobility:

  • Functional mobility refers to the ability to perform daily tasks, sports-specific movements, and exercises with proper joint mechanics and range of motion. Functional mobility training focuses on enhancing movement patterns relevant to individual needs and activities.

7. Mobility Training:

  • Mobility training includes exercises and techniques designed to improve joint mobility, flexibility, and movement quality. It may involve static stretching, dynamic stretching, foam rolling, mobility drills, and corrective exercises to address movement restrictions.

8. Mobility vs. Stability:

  • Mobility and stability are interconnected concepts in biomechanics. While mobility refers to the ability to move freely, stability provides support and control during movement. Optimal movement patterns require a balance between mobility and stability at each joint.

9. Mobility Assessment:

  • Assessing joint mobility and movement patterns is essential for identifying limitations, asymmetries, and areas of improvement. Functional movement assessments, range of motion tests, and mobility screens help tailor mobility training programs to individual needs.

Conclusion:

Enhancing mobility is crucial for optimizing movement quality, preventing injuries, and improving performance in various activities. By addressing joint mobility, flexibility, muscle extensibility, and functional movement patterns through targeted training and assessments, individuals can improve their overall mobility and movement efficiency.

 

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