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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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The expression of Notch-related genes in the differentiation of BMSCs into dopaminergic neuron-like cells.

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Dr. Rishabh Pathak


 

The expression of Notch-related genes plays a crucial role in the differentiation of human bone marrow mesenchymal stem cells (h-BMSCs) into dopaminergic neuron-like cells. The Notch signaling pathway is involved in regulating cell fate decisions, including the differentiation of BMSCs. In the study discussed in the PDF file, changes in the expression of Notch-related genes were observed during the differentiation process.

Specifically, the study utilized a human Notch signaling pathway PCR array to detect the expression levels of 84 genes related to the Notch signaling pathway, including ligands, receptors, target genes, cell proliferation and differentiation-related genes, and neurogenesis-related genes. The array also included genes from other signaling pathways that intersect with the Notch pathway, such as Sonic hedgehog and Wnt receptor signaling pathway members.

During the differentiation of h-BMSCs into dopaminergic neuron-like cells, the expression levels of Notch-related genes were found to be altered compared to the control group. For example, the expression of Notch ligands like Jagged1 and Jagged2, as well as key proteins like Presenilin2 (PSEN2) and ADAM metallopeptidase domain 10 (ADAM10) involved in Notch receptor cleavage, showed significant changes during the induction process.

Furthermore, the study observed downregulation of HES1, a target gene of Notch signaling, indicating suppression of the Notch pathway during differentiation. These findings suggest that the Notch signaling pathway is dynamically regulated during the differentiation of BMSCs into dopaminergic neuron-like cells, highlighting the importance of Notch-related genes in this process.

In conclusion, the expression of Notch-related genes is a key aspect of the molecular mechanisms involved in the differentiation of BMSCs into dopaminergic neuron-like cells, providing insights into the role of the Notch signaling pathway in this cellular differentiation process.

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