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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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Advanced Strategies for Fate Mapping in Vivo

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Dr. Rishabh Pathak

Fate mapping in vivo is a powerful technique used to track the developmental origins and lineage relationships of cells within complex tissues and organs. Advanced strategies for fate mapping in vivo involve sophisticated genetic tools and imaging technologies that enable precise and dynamic visualization of cell fate decisions and lineage trajectories. Here are some key advanced strategies for fate mapping in vivo:


1.      Genetic Lineage Tracing:

o    Cre-Lox Recombination: Utilizing Cre-Lox recombination systems allows for cell type-specific labeling and tracking of cell lineages based on the expression of Cre recombinase in specific cell populations. This technique enables spatial and temporal control over lineage tracing events.

o    Inducible Systems: Incorporating inducible Cre systems, such as tamoxifen-inducible CreERT2, enables temporal control over lineage tracing experiments, allowing researchers to activate genetic labeling at specific developmental stages or in response to external stimuli.

o    Intersectional Approaches: Intersectional strategies involving the intersection of multiple genetic drivers (e.g., dual recombinase systems) provide increased specificity and combinatorial labeling of distinct cell populations, facilitating more precise fate mapping analyses.

2.     Single-Cell Fate Mapping:

o  Single-Cell Resolution: Advanced fate mapping techniques now enable single-cell resolution tracking of cell lineages, allowing researchers to follow the fate of individual cells over time and assess clonal dynamics within tissues and organs.

oBarcoding Strategies: Barcoding approaches, such as DNA barcoding or RNA sequencing-based barcoding, can be employed to uniquely label individual cells or clones, providing a molecular signature for tracking cell lineages and fate decisions.

3.     Live Imaging and Microscopy:

o    Intravital Imaging: In vivo imaging techniques, such as intravital microscopy and two-photon microscopy, allow for real-time visualization of cell behaviors, lineage relationships, and tissue dynamics within live organisms, providing insights into developmental processes and cellular interactions.

o    Longitudinal Tracking: Longitudinal imaging approaches enable continuous monitoring of cell fate decisions and lineage progression over extended periods, offering dynamic insights into cell behavior, migration patterns, and fate transitions in vivo.

4.    Computational Modeling and Analysis:

o    Quantitative Analysis: Computational modeling and quantitative analysis of fate mapping data can provide insights into lineage relationships, cell fate determinants, and regulatory networks governing cell differentiation and tissue development.

oSingle-Cell Transcriptomics: Integration of single-cell transcriptomic data with fate mapping information allows for the identification of molecular signatures associated with specific cell fates, lineage trajectories, and developmental transitions, enhancing our understanding of cellular heterogeneity and fate decisions in vivo.

In summary, advanced strategies for fate mapping in vivo leverage cutting-edge genetic tools, imaging technologies, single-cell analyses, and computational modeling to unravel the complexities of cell fate determination, lineage dynamics, and tissue development in living organisms. These sophisticated approaches provide unprecedented insights into the spatiotemporal regulation of cell fate decisions, lineage relationships, and developmental processes, advancing our knowledge of tissue morphogenesis, regeneration, and disease pathogenesis.

 

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