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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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Paroxysmal Fast Activity Different Neurological Conditions

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Dr. Rishabh Pathak

Paroxysmal Fast Activity (PFA) is associated with various neurological conditions, particularly those involving seizure disorders. 

1. Generalized Epilepsy

    • PFA is frequently seen in patients with generalized-onset seizures, including:
      • Tonic Seizures: Characterized by muscle stiffness and rigidity.
      • Clonic Seizures: Involving rhythmic jerking movements.
      • Tonic-Clonic Seizures: A combination of tonic and clonic phases.
      • Absence Seizures: Brief lapses in consciousness.

2. Lennox-Gastaut Syndrome

    • PFA is a common finding in this severe form of epilepsy, which is characterized by multiple seizure types, cognitive impairment, and often associated with developmental delays. The presence of PFA can indicate the severity and complexity of the condition.

3. Focal Epilepsies

    • While PFA is more commonly associated with generalized seizures, it can also occur in focal-onset seizures. In these cases, PFA may indicate a focal area of seizure activity that can secondarily generalize.

4. Post-Traumatic Epilepsy

    • PFA has been reported in patients with focal seizures due to post-traumatic epilepsy, although this occurrence is less common. The presence of PFA in this context may indicate underlying brain injury and the potential for seizure activity.

5. Cognitive Disabilities

    • PFA is often observed in patients with cognitive disabilities and structural brain abnormalities. Its presence can reflect the underlying neurological dysfunction and may correlate with the severity of cognitive impairment.

6. Older Adults with Tonic Seizures

    • PFA can manifest in older adults who develop tonic seizures, particularly in the context of multiple medical problems and polypharmacy. This highlights the relevance of PFA in a geriatric population, where it may indicate new-onset seizures.

7. Other Neurological Conditions

    • PFA may also be seen in various other neurological conditions, particularly those that involve significant brain dysfunction or structural abnormalities. Its presence can provide insights into the underlying pathology and help guide clinical management.

Summary

In summary, Paroxysmal Fast Activity (PFA) is associated with a range of neurological conditions, primarily seizure disorders such as generalized epilepsy and Lennox-Gastaut syndrome. It can also occur in focal epilepsies, post-traumatic epilepsy, and in patients with cognitive disabilities. Understanding the context in which PFA appears can aid in diagnosing and managing these neurological conditions effectively.

 

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