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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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Microglial Cells control Neuronal Proliferation and Differentiation

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Dr. Rishabh Pathak

Microglial cells, the resident immune cells of the central nervous system, play a crucial role in controlling neuronal proliferation and differentiation during brain development. Here is an explanation of how microglial cells contribute to these processes:


1. Neuronal Proliferation: Microglial cells are involved in regulating the proliferation of neural progenitor cells and the generation of new neurons in the developing brain. By interacting with neural stem cells and progenitor cells, microglia can influence the rate of neuronal proliferation and the production of new neurons in specific brain regions.


2.  Neuronal Differentiation: Microglial cells also play a role in promoting the differentiation of neural progenitor cells into mature neurons with specific functional properties. Through the release of signaling molecules and growth factors, microglia can influence the fate determination and differentiation of neural precursor cells, guiding them towards specific neuronal lineages.


3.  Clearance of Debris: In addition to their role in neuronal proliferation and differentiation, microglial cells are responsible for clearing cellular debris, apoptotic cells, and excess synapses during brain development. By phagocytosing unwanted cellular material, microglia help sculpt the developing neural circuitry and ensure the proper refinement of neuronal connections.


4.  Synaptic Remodeling: Microglial cells contribute to synaptic remodeling and plasticity by eliminating weak or redundant synapses and promoting the formation of new synaptic connections. Through their interactions with neurons and synapses, microglia participate in the dynamic process of synaptic pruning and refinement, shaping the functional connectivity of the developing brain.


5.   Inflammatory Responses: While microglial cells primarily have a supportive role in neuronal development, they can also mount inflammatory responses in the presence of pathogens, injury, or neurodegenerative conditions. The balance between the neuroprotective and neurotoxic functions of microglia is crucial for maintaining brain homeostasis and supporting healthy neuronal development.


In summary, microglial cells play a multifaceted role in controlling neuronal proliferation and differentiation during brain development. Through their functions in regulating neural progenitor cell behavior, promoting neuronal differentiation, clearing cellular debris, and modulating synaptic remodeling, microglia contribute to the intricate process of neural circuit formation and maturation in the developing brain. Understanding the interactions between microglial cells and developing neurons is essential for unraveling the complexities of brain development and ensuring the proper establishment of functional neural networks that underlie cognitive and behavioral functions.

 

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