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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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Progressive Supranuclear Palsy (PSP)

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Dr. Rishabh Pathak

Progressive Supranuclear Palsy (PSP) is a rare neurodegenerative disorder that affects movement, balance, vision, speech, and cognition. Here is an overview of Progressive Supranuclear Palsy:


1.      Clinical Features:

oPSP is characterized by the progressive deterioration of brain cells in certain areas of the brain, leading to motor and cognitive impairments.

oCommon symptoms include difficulties with balance and walking (resulting in frequent falls), stiffness and slowness of movement, changes in eye movements (such as difficulty looking up and down), speech difficulties, and cognitive impairment.

oPSP is often misdiagnosed initially as Parkinson's disease due to overlapping symptoms, but it has distinct features such as early postural instability and vertical gaze palsy.

2.     Pathology:

oThe hallmark pathological feature of PSP is the accumulation of abnormal tau protein in nerve cells in specific brain regions, leading to cell dysfunction and death.

oThe affected brain areas in PSP include the basal ganglia, brainstem, and regions of the cerebral cortex involved in motor control and cognition.

3.     Diagnosis:

oDiagnosis of PSP is challenging and often requires a comprehensive evaluation by a neurologist specializing in movement disorders.

oClinical criteria, neuroimaging studies (such as MRI), and sometimes cerebrospinal fluid analysis may be used to support the diagnosis.

4.    Treatment:

oThere is no cure for PSP, and treatment focuses on managing symptoms and improving quality of life.

oMedications may be prescribed to address specific symptoms such as movement difficulties, depression, and sleep disturbances.

oPhysical therapy, occupational therapy, speech therapy, and assistive devices can help maintain function and independence.

5.     Research and Future Directions:

oOngoing research aims to better understand the underlying mechanisms of PSP, develop biomarkers for early diagnosis, and explore potential disease-modifying treatments.

oClinical trials investigating novel therapies, including tau-targeting drugs and symptomatic treatments, are underway to address the unmet medical needs of PSP patients.

In summary, Progressive Supranuclear Palsy (PSP) is a complex neurodegenerative disorder characterized by motor impairments, cognitive changes, and visual disturbances. While there is currently no cure for PSP, ongoing research offers hope for improved diagnostic tools and therapeutic interventions to enhance the quality of life for individuals affected by this condition.

 

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