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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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Types of Wicket Rhythms

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Dr. Rishabh Pathak

Wicket rhythms can manifest in various forms, each with specific characteristics and patterns. 


1.     Wicket Fragment:

o Wicket fragments consist of rhythmic trains of waves that bear similarity to the wicket rhythm pattern.

o These fragments typically exhibit a repetitive nature and may resemble segments of the complete wicket rhythm waveform.

o Distinguishing wicket fragments from interictal epileptiform discharges (IEDs) is essential, as they share morphological similarities but are considered normal variants.

2.   Wicket Spike:

oWicket spikes are components of the wicket rhythm characterized by a negative sharp component followed by a rounded component.

o Morphologically, wicket spikes resemble diphasic spike and slow wave complexes commonly associated with epileptiform activity.

o These spikes often occur over temporal regions, which are frequent sites for interictal epileptiform discharges.

3.   Wicket Wave:

o Wicket waves exhibit an arciform appearance with alternating sharply contoured and rounded phases, similar to the overall wicket rhythm pattern.

o The polarity of wicket waves consists of negative sharp components followed by positive rounded components, contributing to their distinct waveform.

o These waves are typically observed in the alpha frequency range and have medium-range amplitudes compared to other alpha activities.

Recognizing and understanding the different types of wicket rhythms, including fragments, spikes, and waves, is crucial for accurate interpretation of EEG recordings. By identifying these specific patterns and their characteristics, healthcare professionals can differentiate normal wicket rhythms from abnormal epileptiform discharges and avoid misdiagnosis or misinterpretation of EEG findings.

 

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