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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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Secondary bilateral synchrony

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Dr. Rishabh Pathak


Secondary bilateral synchrony is a specific pattern observed in electroencephalography (EEG) that involves the spread of epileptiform discharges from a focal source to both hemispheres, resulting in synchronized activity.

1.      Definition:

o    Secondary bilateral synchrony refers to the phenomenon where focal interictal epileptiform discharges (IEDs) initially arise from a specific region of the brain and then spread to involve both hemispheres, leading to synchronized spike and wave activity across the EEG.

2.     Characteristics:

o    This pattern is characterized by the presence of spike and slow wave discharges that begin at a focal point (e.g., a specific electrode) and then propagate to other areas, resulting in a generalized pattern that is not typical of primary generalized epileptiform discharges. The spread of activity is often seen as a transition from focal discharges to more generalized activity.

3.     Clinical Significance:

o    Secondary bilateral synchrony is often associated with more complex forms of epilepsy and can indicate a higher likelihood of seizures. It may suggest that the underlying pathology is more diffuse or that there is significant cortical involvement beyond the initial focal area.

o    This pattern can be seen in various epilepsy syndromes and may be indicative of a more severe clinical course, especially if it is associated with frequent seizures.

4.    Occurrence:

o    Secondary bilateral synchrony typically occurs in patients with focal epilepsy where the initial discharges are localized but then spread to involve both hemispheres. This can happen in conditions such as temporal lobe epilepsy or frontal lobe epilepsy, where the focal discharges can lead to secondary generalization.

5.     Diagnosis:

o    The identification of secondary bilateral synchrony on an EEG is crucial for understanding the nature of the epileptic activity. It helps differentiate between purely generalized epileptiform discharges and those that have a focal origin but have spread to involve both hemispheres.

6.    Prognosis:

o    The presence of secondary bilateral synchrony can indicate a more complex seizure disorder and may be associated with a higher frequency of seizures that are less responsive to treatment. This pattern may require careful monitoring and management to optimize therapeutic strategies.

7.     Impact of Treatment:

o    Patients exhibiting secondary bilateral synchrony may need more aggressive treatment approaches, including polytherapy with multiple antiepileptic drugs, to manage their seizures effectively. The presence of this pattern often necessitates ongoing evaluation and adjustment of treatment plans based on seizure control and patient response.

In summary, secondary bilateral synchrony is an important EEG finding that indicates the spread of epileptiform activity from a focal source to both hemispheres, resulting in synchronized discharges. Its identification is crucial for diagnosing and managing complex epilepsy syndromes, as it suggests a more severe underlying pathology and may require more intensive treatment strategies. Understanding the characteristics and implications of secondary bilateral synchrony is essential for clinicians managing patients with epilepsy.

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