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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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Phantom Spike and Wave

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Dr. Rishabh Pathak

Phantom Spike and Wave (PhSW) is a specific EEG pattern characterized by distinct spike and wave complexes. 

Definition

Phantom Spike and Wave refers to a pattern of EEG activity that consists of bursts of spike and wave complexes. These complexes are typically time-locked, meaning that the spikes occur in a specific temporal relationship with the slow waves that follow them. This pattern can be observed in various clinical contexts, particularly in patients with certain neurological conditions.

EEG Characteristics

1.      Waveform:

§  The spike and wave complexes in PhSW are characterized by a greater amplitude similarity between the spike and the slow wave within each complex. This contrasts with other patterns where there may be a more pronounced difference in amplitude.

2.     Duration and Frequency:

§  The bursts of PhSW typically occur over a short duration, often lasting less than a second, and can appear in clusters. The frequency of these bursts can vary depending on the underlying condition of the patient.

3.     Location:

§  PhSW is often recorded from specific regions of the scalp, with the occipital region being a common site for observation. The location can provide clues about the underlying pathology.

Clinical Significance

4.    Associated Conditions:

§  Phantom Spike and Wave patterns are often associated with conditions such as:

§  Migraine: Particularly in patients with a history of migraine, PhSW can be observed during headache episodes or in the interictal period.

§  Seizure Disorders: While not a classic epileptiform pattern, PhSW may be seen in patients with certain types of epilepsy or seizure disorders.

§  Other Neurological Disorders: It can also be present in patients with various neurological conditions, including encephalopathies.

5.     Prognostic Implications:

§  The presence of PhSW can indicate underlying neurological dysfunction, but its specific prognostic implications can vary widely depending on the associated clinical context. In some cases, it may suggest a transient phenomenon, while in others, it may indicate more chronic issues.

Summary

Phantom Spike and Wave is an EEG pattern characterized by bursts of spike and wave complexes that are time-locked and show amplitude similarity. It is associated with various neurological conditions, particularly migraines and seizure disorders. Understanding this pattern is important for clinicians in diagnosing and managing patients with neurological symptoms.

 

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