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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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Pivot Joints

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Dr. Rishabh Pathak

Pivot joints are a type of synovial joint that allows rotational movement around a single axis. These joints are crucial for specific movements that involve rotation without significant displacement. Here is an overview of pivot joints:

Pivot Joints:

1.    Structure:

o    Pivot joints consist of a rounded or pointed surface of one bone fitting into a ring or sleeve of another bone or ligament.

o    The structure allows for rotation around a central axis without significant translation.

2.    Function:

o    Pivot joints primarily facilitate rotational movement around a single axis.

o    They provide stability and support for movements that involve twisting or turning.

3.    Examples:

o    Atlantoaxial Joint:

§  The joint between the first (atlas) and second (axis) cervical vertebrae is a classic example of a pivot joint.

§  The dens (odontoid process) of the axis rotates within the ring of the atlas, allowing for rotation of the head.

o    Proximal Radioulnar Joint:

§  The joint between the head of the radius and the radial notch of the ulna is another example of a pivot joint.

§  This joint allows for rotation of the radius around the ulna, contributing to movements like pronation and supination of the forearm.

4.    Movements:

o    Rotation: The primary movement at pivot joints is rotation around a central axis.

o    Pronation: Rotational movement that turns the palm downward or backward.

o    Supination: Rotational movement that turns the palm upward or forward.

5.    Stability:

o    Pivot joints provide stability during rotational movements.

o    Ligaments and surrounding structures help maintain the alignment of the bones during rotation.

6.    Clinical Significance:

o    Injuries or conditions affecting pivot joints can impact specific activities that require rotational movements.

o    Rehabilitation programs focus on restoring range of motion, strength, and stability in pivot joints after injuries or surgeries.

Understanding the structure and function of pivot joints is essential for healthcare professionals, athletes, and individuals seeking to maintain joint health and optimize movement capabilities. Proper care, exercise, and biomechanical awareness can help preserve the function and longevity of pivot joints in the body.

 

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