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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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Distinguishing Features of Mittens

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Dr. Rishabh Pathak

The distinguishing features of "mittens" in EEG recordings are critical for differentiating them from other waveforms, particularly K complexes and interictal epileptiform discharges (IEDs).

1. Waveform Composition

    • Polarity: Both components of a mitten (the sharp wave and the slow wave) have the same polarity, whereas K complexes consist of two sharp waves of opposite polarity.
    • Shape and Duration: The sharp wave in a mitten has a longer duration and a less sharp contour compared to the initiating sharp wave of an IED. This longer duration contributes to the characteristic appearance of the mitten.

2. Temporal Relationship

    • Inconsistency: The temporal relationship between the sharp wave and the slow wave in mittens is inconsistent, which distinguishes them from IEDs. In IEDs, the sharp wave and the slow wave have a relatively fixed temporal relationship, with the sharp wave occurring at a consistent distance from the slow wave's peak.

3. Location

    • Midline Positioning: Mittens are typically centered in the frontal-central midline regions, while K complexes are located at the vertex. This localization can aid in distinguishing between the two patterns.

4. Associated Features

    • Accompanying EEG Patterns: Mittens are often seen in conjunction with other features of NREM sleep, such as sleep spindles, K complexes, and positive occipital sharp transients of sleep (POSTS). The presence of these accompanying features can help confirm the identification of mittens.

5. Clinical Context

    • Normal Variants: Mittens are generally considered normal variants in adults and are rarely seen in individuals under 15 years of age. Their presence in the appropriate context (e.g., during deep sleep) supports their classification as benign.

Summary

Mittens are characterized by their unique waveform composition, temporal relationships, and localization. Recognizing these features is essential for accurate EEG interpretation and for distinguishing mittens from other similar patterns, such as K complexes and IEDs. Proper identification can prevent misdiagnosis and ensure appropriate clinical management.

 

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