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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Cancellous bone,
also known as trabecular or spongy bone, is the other main type of bone tissue
found in the human skeleton alongside cortical bone. Cancellous bone has a
porous and lattice-like structure, providing flexibility, shock absorption, and
a site for hematopoiesis (blood cell formation). Here are key features and
characteristics of cancellous bone:
1.
Structure:
o Trabeculae: Cancellous bone is composed of a
network of thin, bony trabeculae that form an interconnected lattice structure.
o Bone Marrow: The spaces between trabeculae
contain red bone marrow, which is involved in the production of blood cells
(hematopoiesis).
o Less Compact: Cancellous bone is less dense
and compact than cortical bone, with a higher surface area-to-volume ratio.
2.
Composition:
o Trabecular Bone: The trabeculae are made up of
lamellae, osteocytes, and canaliculi similar to cortical bone but with a more
open and porous arrangement.
o Collagen and Mineralization: Cancellous bone contains
collagen fibers and mineral components like hydroxyapatite, providing a balance
of strength and flexibility.
3.
Function:
o Shock Absorption: The porous structure of
cancellous bone allows it to absorb impact forces and distribute loads,
reducing the risk of fractures.
o Hematopoiesis: Red bone marrow within
cancellous bone is a primary site for the production of red blood cells, white
blood cells, and platelets.
o Metabolic Activity: Cancellous bone is metabolically
active and responds to mechanical stimuli, hormonal signals, and changes in
bone density.
4.
Location:
o Ends of Long Bones: Cancellous bone is typically
found at the ends (epiphyses) of long bones, where it provides cushioning and
support at joints.
o Vertebrae and Pelvis: It also forms the internal
structure of vertebrae, pelvis, and other flat bones, contributing to their
strength and flexibility.
5.
Vascularization:
o Cancellous bone has a higher
vascular supply compared to cortical bone, with blood vessels penetrating the
trabecular network to deliver nutrients and remove waste products.
o The vascular network supports the
metabolic needs of bone cells and facilitates the exchange of gases and
nutrients.
6.
Mechanical Properties:
o Cancellous bone is more flexible
and compliant than cortical bone, making it well-suited for adapting to dynamic
loads and maintaining bone health.
o Its porous structure allows for
rapid bone turnover, remodeling, and adaptation in response to mechanical
stress and hormonal influences.
Understanding the
unique characteristics and functions of cancellous bone is essential for
comprehending the biomechanics of bone tissue, the role of bone marrow in
hematopoiesis, and the structural adaptations of the skeleton to mechanical
demands and metabolic requirements.
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