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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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Position Emission Tomography (PET)

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Dr. Rishabh Pathak

Position Emission Tomography (PET) is a nuclear imaging technique that uses radioactive tracers to produce detailed three-dimensional images of functional processes in the body. Here is an overview of PET imaging:


1.      Principle:

oPET imaging relies on the detection of gamma rays emitted by a radioactive tracer that is introduced into the body. The tracer is typically a biologically active molecule that targets specific processes or tissues.

oWhen the tracer undergoes radioactive decay, it emits positrons (positively charged electrons) that travel a short distance before annihilating with electrons in the body. This annihilation produces pairs of gamma rays that are detected by a PET scanner.

2.     Radiotracers:

oRadiotracers used in PET imaging are labeled with short-lived positron-emitting isotopes such as fluorine-18, carbon-11, or oxygen-15. These isotopes are incorporated into molecules that target specific biological processes, such as glucose metabolism, protein synthesis, or neurotransmitter activity.

oCommon radiotracers used in PET imaging include FDG (Fluorodeoxyglucose) for assessing glucose metabolism, amyloid tracers for detecting amyloid plaques in Alzheimer's disease, and dopamine tracers for studying neurotransmitter function.

3.     Clinical Applications:

oPET imaging is widely used in oncology for cancer diagnosis, staging, treatment planning, and monitoring of treatment response. It can visualize metabolic activity in tumors and detect metastases.

oIn neurology, PET imaging is used to assess brain function, study neurotransmitter systems, diagnose neurodegenerative disorders like Alzheimer's disease, and evaluate epilepsy and movement disorders.

oCardiac PET imaging can assess myocardial perfusion, viability, and function, providing valuable information for the diagnosis and management of heart conditions.

4.    Image Reconstruction:

oPET images are reconstructed using sophisticated algorithms that analyze the detected gamma rays to create detailed three-dimensional images of tracer distribution in the body.

oQuantitative analysis of PET images involves measuring standardized uptake values (SUVs) to assess tracer uptake in tissues and compare metabolic activity between regions of interest.

5.     Advantages:

oPET imaging provides functional information about physiological processes in the body, complementing the anatomical information obtained from other imaging modalities like CT or MRI.

oIt is a sensitive technique for early detection of disease, monitoring treatment response, and guiding personalized treatment strategies.

6.    Limitations:

oPET imaging involves exposure to ionizing radiation due to the use of radioactive tracers, limiting repeat scans and requiring careful dose optimization.

oThe cost of PET imaging and availability of radiotracers can be limiting factors in some healthcare settings.

In summary, PET imaging is a valuable tool in clinical practice for visualizing and quantifying physiological processes in the body. It plays a crucial role in oncology, neurology, cardiology, and research applications, providing insights into disease mechanisms and guiding patient care.

 

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