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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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Interictal Epileptiform Patterns in Different Neurological Conditions

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Dr. Rishabh Pathak


Interictal epileptiform patterns (IEDs) can be observed in various neurological conditions beyond epilepsy. Their presence and characteristics can provide insights into the underlying pathology and help differentiate between different neurological disorders.

. Epilepsy

  • Primary Role: IEDs are most commonly associated with epilepsy, serving as a key diagnostic criterion. They indicate the presence of abnormal electrical activity in the brain that can lead to seizures.
  • Types of IEDs: Different types of IEDs (e.g., spikes, sharp waves) can correlate with specific epilepsy syndromes, such as temporal lobe epilepsy or focal cortical dysplasia.

2. Cerebral Dysgenesis and Malformations

  • Cortical Dysplasia: IEDs, particularly focal polyspikes, are often linked to cortical dysplasia, a condition where the brain's structure is abnormal due to developmental issues. This can lead to a higher likelihood of seizures.
  • Other Malformations: Conditions like polymicrogyria or lissencephaly may also present with IEDs, reflecting the underlying structural abnormalities in the brain.

3. Intellectual Disability

  • Association with IEDs: IEDs are frequently observed in individuals with intellectual disabilities, particularly when these disabilities are related to metabolic or chromosomal abnormalities. The presence of IEDs in this population often correlates with more severe cognitive impairment.

4. Traumatic Brain Injury (TBI)

  • Post-TBI Changes: Patients with a history of TBI may exhibit IEDs on EEG, which can indicate ongoing cortical irritability or damage. The presence of IEDs in this context may suggest a higher risk of developing post-traumatic epilepsy.

5. Neurodegenerative Disorders

  • Alzheimer’s Disease and Other Dementias: IEDs can occasionally be seen in patients with neurodegenerative conditions, such as Alzheimer’s disease. Their presence may reflect underlying cortical dysfunction and could be associated with cognitive decline.
  • Frontotemporal Dementia: Similar to Alzheimer’s, IEDs may appear in frontotemporal dementia, indicating abnormal electrical activity in the affected brain regions.

6. Psychiatric Disorders

  • Schizophrenia and Other Psychoses: Some studies have reported the presence of IEDs in patients with schizophrenia or other psychotic disorders. The clinical significance of these findings is still under investigation, but they may reflect underlying neurobiological changes.

7. Metabolic Disorders

  • Metabolic Encephalopathies: Conditions such as hepatic encephalopathy or uremic encephalopathy can lead to the appearance of IEDs on EEG. These patterns may indicate the brain's response to metabolic derangements.

Conclusion

Interictal epileptiform patterns are not exclusive to epilepsy and can be observed in a variety of neurological conditions. Their presence can provide valuable diagnostic information and insights into the underlying pathology. Understanding the context in which IEDs occur is essential for accurate diagnosis and management of patients with neurological disorders.

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