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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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Delta Activities in Different Neurological Conditions

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Dr. Rishabh Pathak

Delta activities in EEG recordings can manifest in various neurological conditions, reflecting underlying pathologies and providing valuable diagnostic information. Here are some examples of delta activities in different neurological conditions:


1.     Epilepsy:

oDelta activity can be a common finding in patients with epilepsy, especially during interictal periods.

o Abnormal delta activity patterns, such as focal delta slowing or intermittent rhythmic delta activity (IRDA), may indicate the presence of epileptogenic zones in the brain.

o Monitoring delta activities in patients with epilepsy can help localize seizure foci and guide treatment strategies.

2.   Traumatic Brain Injury (TBI):

o Following a traumatic brain injury, delta activity may be observed in EEG recordings, particularly in cases of diffuse axonal injury or cerebral contusions.

o Increased delta power or the presence of polymorphic delta activity can indicate brain dysfunction and the extent of injury in TBI patients.

o Delta activities in TBI patients can serve as prognostic markers for neurological outcomes and recovery trajectories.

3.   Stroke:

o Delta activity can be seen in patients with acute stroke, reflecting the impact of ischemic or hemorrhagic events on brain function.

o Changes in delta activity patterns in stroke patients may correlate with the location and extent of cerebral infarction or hemorrhage.

o Monitoring delta activities in stroke survivors can provide insights into post-stroke recovery, cognitive impairments, and risk of secondary complications.

4.   Neurodegenerative Diseases:

o Conditions like Alzheimer's disease, Parkinson's disease, and other neurodegenerative disorders may exhibit altered delta activity patterns in EEG recordings.

o Increased delta power or abnormal delta slowing in specific brain regions can be associated with cognitive decline and disease progression in neurodegenerative diseases.

o Delta activities in neurodegenerative diseases can aid in differential diagnosis, disease monitoring, and assessment of treatment responses.

5.    Encephalopathies:

o Various metabolic, infectious, or toxic encephalopathies can present with delta activity abnormalities in EEG recordings.

o Delta slowing or periodic delta activity may be observed in patients with hepatic encephalopathy, uremic encephalopathy, or toxic-metabolic disturbances.

o Monitoring delta activities in encephalopathic patients is crucial for assessing brain function, guiding treatment decisions, and predicting outcomes.

By recognizing the presence and characteristics of delta activities in EEG recordings across different neurological conditions, healthcare providers can enhance diagnostic accuracy, treatment planning, and prognostic assessments for patients with diverse neurological disorders. Understanding the role of delta activities in specific disease contexts is essential for comprehensive neurological evaluations and personalized patient care.

 

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