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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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Molecular, Cellular and Behavioral Aspects of Mental Retardation and Autism

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Dr. Rishabh Pathak

Mental retardation and autism are complex neurodevelopmental disorders characterized by a wide range of molecular, cellular, and behavioral abnormalities. Understanding the underlying mechanisms at the molecular and cellular levels is crucial for developing effective interventions and treatments for individuals with these conditions. Here is an overview of the molecular, cellular, and behavioral aspects of mental retardation and autism:


1.      Molecular Aspects:

oGenetic Factors: Both mental retardation and autism have strong genetic components, with mutations in various genes implicated in their pathogenesis. These genetic alterations can affect neuronal development, synaptic function, and signaling pathways crucial for brain development and function.

oEpigenetic Modifications: Dysregulation of epigenetic mechanisms, such as DNA methylation, histone modifications, and non-coding RNAs, has been associated with mental retardation and autism. Epigenetic changes can influence gene expression patterns critical for neuronal connectivity and plasticity.

oNeurotransmitter Imbalance: Alterations in neurotransmitter systems, including dopamine, serotonin, and glutamate, have been linked to cognitive impairments and behavioral abnormalities in individuals with mental retardation and autism. Imbalances in neurotransmission can impact synaptic communication and neural circuitry.

2.     Cellular Aspects:

oNeuronal Connectivity: Disruptions in neuronal connectivity, including aberrant synapse formation, pruning, and plasticity, are common features of mental retardation and autism. Defects in synaptic transmission and connectivity can lead to cognitive deficits and social communication impairments.

oNeuronal Morphology: Abnormalities in neuronal morphology, such as dendritic arborization, spine density, and axonal growth, have been observed in individuals with mental retardation and autism. These structural changes can impact neuronal function and information processing in the brain.

o Glial Dysfunction: Dysregulation of glial cells, including astrocytes and microglia, has been implicated in the pathogenesis of mental retardation and autism. Glial dysfunction can contribute to neuroinflammation, synaptic pruning abnormalities, and altered neuronal support mechanisms.

3.     Behavioral Aspects:

o Cognitive Impairments: Individuals with mental retardation and autism often exhibit intellectual disabilities, including deficits in learning, memory, and problem-solving skills. Cognitive impairments can vary in severity and impact daily functioning and adaptive behaviors [T7].

oSocial Communication Deficits: Impairments in social interaction, communication skills, and emotional regulation are hallmark features of autism spectrum disorders. Difficulties in understanding social cues, forming relationships, and expressing emotions can significantly impact social functioning [T8].

o Stereotyped Behaviors: Repetitive behaviors, restricted interests, and sensory sensitivities are common behavioral traits observed in individuals with autism. These stereotyped behaviors can serve as coping mechanisms or manifestations of sensory processing differences [T9].

In conclusion, the molecular, cellular, and behavioral aspects of mental retardation and autism are interconnected and contribute to the complex nature of these neurodevelopmental disorders. By unraveling the underlying mechanisms at multiple levels, researchers and clinicians can gain insights into the pathophysiology of these conditions and develop targeted interventions to improve outcomes and quality of life for individuals affected by mental retardation and autism.

 

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