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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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Closed Packed Positions

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Dr. Rishabh Pathak

Closed packed positions, also known as close-packed positions or close-packed joints, refer to specific joint positions where the articular surfaces are maximally congruent and the ligaments and joint capsule are taut. These positions are considered to be the most stable and least mobile configurations of a joint. Here are key points regarding closed packed positions:

1. Definition:

  • Closed packed position is the joint position where the articular surfaces have the maximum contact with each other, providing the greatest stability and resistance to external forces.

2. Characteristics:

  • Maximal Congruency: The joint surfaces fit together tightly, maximizing contact and minimizing joint play.
  • Taut Ligaments and Capsule: The ligaments and joint capsule are under tension, contributing to joint stability.
  • Least Mobility: Closed packed positions are associated with the least amount of joint mobility.

3. Functions:

  • Joint Stability: Closed packed positions provide inherent stability to the joint, making it less susceptible to dislocation or excessive movement.
  • Weight-Bearing Support: These positions are often utilized during weight-bearing activities to enhance joint integrity and load distribution.

4. Examples:

  • Knee: Full extension is the closed packed position of the knee joint.
  • Shoulder: Maximum abduction and external rotation is the closed packed position of the shoulder joint.
  • Hip: Full extension and internal rotation is the closed packed position of the hip joint.

5. Clinical Significance:

  • Assessment: Closed packed positions are used in clinical assessments to evaluate joint stability, range of motion, and integrity.
  • Treatment: Therapeutic interventions may target closed packed positions to enhance joint stability and function, especially in cases of joint instability or injury.

6. Comparison with Open Packed Positions:

  • Open Packed Positions: In contrast to closed packed positions, open packed positions refer to joint positions where the articular surfaces are not maximally congruent, allowing for more joint play and mobility. Open packed positions are often used during joint mobilization techniques and functional activities.

Conclusion:

Understanding closed packed positions is essential in biomechanics, physical therapy, and sports medicine to assess joint stability, function, and movement patterns. By recognizing the characteristics and significance of closed packed positions, healthcare professionals can effectively evaluate and manage joint conditions, optimize rehabilitation protocols, and promote overall joint health and performance.

 

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