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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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Ictal Epileptiform Patterns Compared to Fourteen and Six Per Second Positive Spikes

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Dr. Rishabh Pathak


When comparing ictal epileptiform patterns to fourteen and six per second positive spikes (14&6), several distinguishing features can be identified.

1.      Duration:

o  Ictal Patterns: Ictal patterns for focal-onset seizures typically last several seconds or longer. They are characterized by sustained activity that evolves over time.

o  14&6 Spikes: The 14&6 positive spikes usually last less than 1 second and rarely extend beyond 2 seconds. This brief duration is a significant distinguishing feature.

2.     Distribution:

o    Ictal Patterns: Ictal patterns often begin in a focal area and may evolve to involve broader regions of the cortex. They are less likely to present bilaterally at onset.

o 14&6 Spikes: The 14&6 pattern can occur bilaterally, either synchronously or asynchronously. This bilateral occurrence is a key differentiator, as focal-onset seizures typically do not have bilateral fields at their onset.

3.     Evolution:

o  Ictal Patterns: Ictal patterns are characterized by clear evolution, which may include changes in frequency, amplitude, and waveform. This evolution is crucial for identifying the onset of a seizure.

o 14 & 6 Spikes: The 14&6 pattern may show some evolving characteristics but is generally more stable and does not demonstrate the same level of progressive change as ictal patterns.

4.    Clinical Significance:

o  Ictal Patterns: The presence of ictal patterns is clinically significant as they indicate the occurrence of a seizure. They are associated with behavioral changes and can lead to cognitive impairment.

o  14&6 Spikes: While the 14&6 pattern may appear suggestive of an ictal pattern, it is not necessarily indicative of a seizure. It can occur in various contexts and does not have the same clinical implications as ictal patterns.

5.     Association with Behavioral Changes:

o Ictal Patterns: Ictal patterns are typically associated with stereotyped behavioral changes, which are critical for seizure identification.

o  14&6 Spikes: The 14&6 pattern does not have a consistent association with behavioral changes indicative of seizure activity.

6.    Electrographic Features:

o    Ictal Patterns: Ictal patterns may include a variety of electrographic features, such as rhythmic slowing, spikes, and sharp waves, which evolve over the course of the seizure.

o 14&6 Spikes: The 14&6 pattern is characterized by its specific frequency and morphology, which can be mistaken for ictal activity but lacks the complexity and evolution of true ictal patterns.

In summary, while both ictal epileptiform patterns and fourteen and six per second positive spikes may present as rhythmic activity on EEG, they differ significantly in terms of duration, distribution, evolution, clinical significance, and association with behavioral changes. Understanding these distinctions is essential for accurate EEG interpretation and seizure diagnosis.

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