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...
Cortical folding is a complex
phenomenon in brain development that is driven by differential growth
processes. This mechanical instability arises from the differential growth
rates between the cortical layers, leading to the formation of the characteristic
gyri and sulci on the surface of the cerebral cortex. Here is an overview of
how cortical folding is a mechanical instability driven by differential growth:
1.
Differential Growth: The process of cortical folding is fundamentally
linked to the concept of differential growth, where different regions of the
developing brain expand at varying rates. This uneven growth results in
mechanical stresses within the cortical tissue, as certain areas experience
more growth than others. The differential growth between the outer cortical
layers and the underlying structures, such as the white matter, plays a key
role in initiating cortical folding.
2. Physics-Based Approach: A physics-based approach has
been increasingly utilized to understand cortical folding as a mechanical
instability phenomenon. This perspective considers the mechanical forces
generated by differential growth and how they influence the morphological
changes in the brain. By modeling the cortical tissue as a multi-layered system
undergoing constrained growth, researchers can simulate the patterns of
cortical folding observed in the developing brain.
3.
Constrained Differential Growth: The theory of cortical folding
as a constrained differential growth process suggests that the early radial
expansion of the cortical plate is relatively uniform across its thickness and
does not lead to folding. However, the later tangential expansion, particularly
in the superficial cortical layers, is constrained by the inner layers and the
underlying structures, promoting the formation of gyri and sulci. This
differential growth pattern creates mechanical instabilities that drive the
folding of the cortex.
4.
Role of Neuronal Connectivity: While the differential growth
is a primary driver of cortical folding, other factors such as neuronal
connectivity also play a significant role in shaping the folding patterns. The
establishment of neural circuits and synaptic connections influences the
distribution of mechanical forces within the cortex, further contributing to
the folding process. Changes in synaptic pruning, myelination, and neuronal
migration also impact the mechanical properties of the developing brain and
influence cortical folding during different stages of development.
5. Implications for Developmental Disorders: Disruptions in the mechanisms
underlying cortical folding and differential growth can lead to cortical
malformations and neurodevelopmental disorders. Conditions such as
lissencephaly, characterized by a smooth brain surface due to disrupted neuronal
migration, highlight the importance of proper mechanical interactions in
cortical development. Understanding the interplay between differential growth,
mechanical forces, and neuronal processes is crucial for elucidating the
origins of cortical malformations and associated neurological conditions.
In summary, cortical folding
represents a dynamic interplay between differential growth processes and
mechanical instabilities in the developing brain. By considering the physical
principles that govern cortical morphogenesis, researchers can gain insights
into the mechanisms driving the formation of gyri and sulci, as well as the
implications of disrupted cortical folding for brain structure and function.
Comments
Post a Comment