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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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Role of NCAM in Health and Disease

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Dr. Rishabh Pathak

The Neural Cell Adhesion Molecule (NCAM) plays a crucial role in various physiological and pathological processes in the nervous system. Here are some key points regarding the role of NCAM in health and disease:

1.      Cell Adhesion and Neural Development:

oCell-Cell Interactions: NCAM is involved in mediating cell-cell adhesion and interactions between neurons, glial cells, and other cell types in the nervous system, contributing to neural development, synaptogenesis, and neural circuit formation.

oNeurite Outgrowth: NCAM promotes neurite outgrowth, axon guidance, and neuronal migration during brain development, facilitating the establishment of neural connections and the wiring of the nervous system.

2.     Plasticity and Learning:

oSynaptic Plasticity: NCAM is implicated in synaptic plasticity, including long-term potentiation (LTP) and long-term depression (LTD), which are cellular mechanisms underlying learning and memory processes in the brain.

oLearning and Memory: Alterations in NCAM expression or function can impact cognitive functions, learning abilities, and memory formation, highlighting the importance of NCAM in neural plasticity and cognitive processes.

3.     Neuroprotection and Regeneration:

oNeuroprotection: NCAM plays a role in promoting neuronal survival, protecting against neurotoxic insults, and modulating inflammatory responses in the brain, contributing to neuroprotection and maintenance of neuronal health.

oNeuronal Regeneration: NCAM is involved in neuronal regeneration, axon sprouting, and axon pathfinding after neural injury, suggesting its potential therapeutic implications for promoting neural repair and functional recovery in neurodegenerative conditions.

4.    Neurodevelopmental Disorders:

o Autism Spectrum Disorders (ASD): Altered NCAM expression has been associated with neurodevelopmental disorders such as ASD, implicating NCAM in the pathophysiology of these conditions characterized by social communication deficits and repetitive behaviors.

o Schizophrenia and Depression: Dysregulation of NCAM levels has been linked to schizophrenia, depression, and other psychiatric disorders, highlighting the involvement of NCAM in neural circuits, neurotransmitter systems, and emotional regulation.

5.     Neurological Diseases:

o Alzheimer's Disease: Changes in NCAM expression and function have been observed in Alzheimer's disease, suggesting a potential role of NCAM in the pathogenesis of this neurodegenerative disorder characterized by cognitive decline and neuronal loss.

oEpilepsy and Stroke: NCAM has been implicated in epilepsy, stroke, and other neurological conditions associated with neuronal hyperexcitability, neuroinflammation, and neuronal damage, indicating its involvement in the pathophysiology of these disorders.

In summary, NCAM plays a multifaceted role in health and disease, influencing various aspects of neural development, synaptic plasticity, neuroprotection, and neuroregeneration in the nervous system. Understanding the functions of NCAM in physiological processes and its dysregulation in neurological and neurodevelopmental disorders provides insights into potential therapeutic targets for modulating NCAM-mediated pathways and improving brain health and function in diverse pathological conditions.

 

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