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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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Presentation Of the Structure Of NCAM

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Dr. Rishabh Pathak

The Neural Cell Adhesion Molecule (NCAM) is a glycoprotein that plays a crucial role in cell-cell adhesion, neurite outgrowth, and synaptic plasticity in the nervous system. Here is a brief overview of the structure of NCAM:

1.      General Structure:

o NCAM is a transmembrane protein that belongs to the immunoglobulin superfamily.

o    It consists of five immunoglobulin-like domains (Ig domains) in the extracellular region, followed by two fibronectin type III repeats and a transmembrane domain.

o The cytoplasmic domain of NCAM interacts with intracellular signaling molecules to mediate cellular responses.

2.     Ig-Like Domains:

o    The extracellular region of NCAM contains five Ig-like domains (Ig1 to Ig5) that are involved in cell adhesion and recognition.

o These Ig domains mediate homophilic interactions between NCAM molecules on adjacent cells, promoting cell adhesion and signaling.

3.     Fibronectin Type III Repeats:

o    Following the Ig-like domains, NCAM contains two fibronectin type III repeats that contribute to the structural integrity and flexibility of the protein.

o    These repeats may also play a role in ligand binding and cell adhesion processes.

4.    Glycosylation:

o   NCAM is extensively glycosylated, with carbohydrate chains attached to the extracellular domains of the protein.

o Glycosylation of NCAM is important for its adhesive properties, stability, and interactions with other molecules in the extracellular matrix.

5.     Transmembrane Domain:

o   The transmembrane domain anchors NCAM to the cell membrane, allowing it to span the lipid bilayer and interact with intracellular signaling pathways.

o    This domain is critical for the localization and function of NCAM at the cell surface.

6.    Functional Regions:

o  The extracellular domains of NCAM, including the Ig-like domains and fibronectin repeats, are involved in cell adhesion, neurite outgrowth, and synaptic plasticity.

o    The cytoplasmic domain of NCAM interacts with cytoskeletal proteins and signaling molecules to regulate cellular processes and intracellular signaling cascades.

In summary, the structure of NCAM is characterized by its extracellular Ig-like domains and fibronectin repeats responsible for cell adhesion and recognition, extensive glycosylation for stability and interactions, and a transmembrane domain for membrane anchoring and intracellular signaling. This structural organization enables NCAM to mediate various functions in neural development, synaptic connectivity, and neuronal plasticity in the nervous system.

 

 

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