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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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What is anthropometric system in biomechanics?

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Dr. Rishabh Pathak


 

In biomechanics, the anthropometric system refers to the measurement and analysis of the physical dimensions, proportions, and characteristics of the human body. Anthropometry plays a crucial role in understanding human movement, ergonomics, sports performance, and injury prevention by providing valuable data on body segment lengths, joint centers, muscle attachment points, and other anatomical parameters. The anthropometric system involves the following key components:


1.     Body Segment Lengths: Anthropometric measurements are used to determine the lengths of various body segments such as the arms, legs, trunk, and head. These segment lengths are essential for calculating joint angles, lever arms, and moment arms during movement analysis.


2.   Joint Centers: By identifying the locations of joint centers (e.g., hip, knee, ankle), researchers and practitioners can accurately assess joint kinematics and kinetics during activities like walking, running, and sports movements.


3. Muscle Attachment Points: Anthropometric data help in locating muscle attachment points on bones, which is crucial for understanding muscle moment arms, force generation, and joint stability.


4.   Body Mass Distribution: Knowledge of body mass distribution across different body segments is important for analyzing balance, stability, and energy expenditure during various tasks and activities.


5.  Limb Circumferences and Diameters: Measurements of limb circumferences and diameters provide information on muscle girth, bone size, and body composition, which can influence movement patterns, strength capabilities, and injury risk.


6.     Center of Mass Location: Determining the center of mass location in the body or specific body segments is essential for studying balance, coordination, and dynamic stability in human movement.


7. Segmental Inertial Properties: Anthropometric data are used to calculate segmental inertial properties such as mass, moment of inertia, and radius of gyration, which are critical for biomechanical modeling and analysis.


8. Ergonomic Design: Anthropometric measurements are applied in ergonomic design to create products, workspaces, and equipment that fit the diverse range of human body sizes and shapes, promoting comfort, safety, and efficiency.


By utilizing the anthropometric system in biomechanics, researchers, clinicians, and practitioners can tailor interventions, training programs, and equipment to individual characteristics, optimize performance, prevent injuries, and enhance overall well-being in various populations and settings.

 

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