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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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How do NTN and Lmx1α influence the Notch signaling pathway during this differentiation process?

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Dr. Rishabh Pathak


 In the differentiation of human bone marrow mesenchymal stem cells (h-BMSCs) into dopaminergic neuron-like cells, NTN (Neurturin) and Lmx1α (LIM homeobox transcription factor 1 alpha) play a significant role in influencing the Notch signaling pathway. The study discussed in the PDF file investigated the impact of NTN and Lmx1α on the differentiation process and the associated changes in Notch-related gene expression.

1. Neurturin (NTN):

   - Neurturin is a neurotrophic factor that belongs to the glial cell line-derived neurotrophic factor (GDNF) family. It has been shown to promote the survival and differentiation of dopaminergic neurons.

   - In the study, h-BMSCs overexpressing NTN were induced to differentiate into dopaminergic neuron-like cells. The presence of NTN likely influenced the expression of Notch-related genes, leading to changes in the Notch signaling pathway during differentiation.

 2. LIM homeobox transcription factor 1 alpha (Lmx1α):

   - Lmx1α is a transcription factor that plays a crucial role in the development of dopaminergic neurons. It is involved in specifying the dopaminergic phenotype and regulating the expression of genes essential for dopaminergic neuron differentiation.

   - Overexpression of Lmx1α in h-BMSCs also contributed to the differentiation process, potentially affecting the Notch signaling pathway through its regulatory functions.

The combined effects of NTN and Lmx1α on h-BMSCs likely modulated the expression of Notch-related genes, leading to alterations in the Notch signaling pathway during the differentiation into dopaminergic neuron-like cells. These factors may have influenced the downstream signaling cascades and gene expression patterns associated with Notch signaling, ultimately contributing to the successful differentiation of h-BMSCs into dopaminergic neuron-like cells.


Overall, NTN and Lmx1α act as key regulators in the differentiation process, potentially interacting with the Notch signaling pathway to orchestrate the cellular changes necessary for the generation of dopaminergic neuron-like cells from h-BMSCs.

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