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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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Freezing of Gait (FOG)

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Dr. Rishabh Pathak

Freezing of Gait (FOG) is a common and debilitating symptom in patients with Parkinson's disease and other movement disorders. Here is an overview of Freezing of Gait, its characteristics, contributing factors, and potential mechanisms:


1.      Definition:

o  Freezing of Gait (FOG) is a sudden, brief, and involuntary cessation of forward movement, often described as feeling "stuck to the ground."

o  It typically occurs during gait initiation, turning, or when navigating through narrow spaces, leading to significant mobility issues and an increased risk of falls.

2.     Characteristics:

o FOG episodes are unpredictable and can occur intermittently, causing frustration and anxiety in affected individuals.

o Patients may exhibit trembling, shuffling steps, or a feeling of being unable to lift their feet off the ground during freezing episodes.

o FOG is more common in advanced stages of Parkinson's disease but can also occur in other conditions such as atypical parkinsonism.

3.     Contributing Factors:

o Neural Circuit Dysfunction: FOG is believed to result from dysfunction within neural circuits involving the basal ganglia, supplementary motor area (SMA), mesencephalic locomotor region (MLR), and cerebellum.

o Interplay Between Brain Regions: The interaction between the basal ganglia and the cerebellum, along with other motor control regions, plays a crucial role in gait initiation and execution.

o Dopaminergic Deficiency: Reduced dopamine levels in the brain, a hallmark of Parkinson's disease, contribute to motor impairments including FOG.

oEnvironmental Triggers: Stress, anxiety, dual-tasking, and complex environments can trigger or exacerbate episodes of freezing.

4.    Mechanisms:

o Cerebellar Involvement: The cerebellum, traditionally associated with motor coordination, has been implicated in the pathophysiology of FOG.

o Basal Ganglia Dysfunction: Disruptions in the basal ganglia circuits, which regulate movement initiation and execution, can lead to gait disturbances including freezing.

o    Neural Network Dysfunction: Alterations in the connectivity and communication between brain regions involved in motor control may underlie the manifestation of FOG.

5.     Treatment:

o    Medication: Adjusting dopaminergic medications to optimize motor function and reduce FOG episodes.

o Deep Brain Stimulation (DBS): Surgical intervention involving the implantation of electrodes in the brain to modulate neural activity and alleviate symptoms.

o Physical Therapy: Gait training, balance exercises, and cueing strategies can help improve gait performance and reduce freezing episodes.

o Cognitive Behavioral Therapy: Addressing anxiety and stress management techniques to minimize triggers for FOG.

In conclusion, Freezing of Gait is a complex and multifaceted symptom observed in movement disorders like Parkinson's disease, characterized by sudden and transient episodes of gait impairment. Understanding the neural mechanisms and contributing factors to FOG is essential for developing effective interventions and improving the quality of life for individuals affected by this challenging symptom.

 

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