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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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Mapping Lineage in The Developing Nervous System with Brainbow Multicolour Transgenes

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Dr. Rishabh Pathak

Mapping lineage in the developing nervous system with Brainbow multicolour transgenes involves a powerful genetic tool that enables the visualization and tracking of individual cells and their progeny with distinct fluorescent colors. Here are some key points related to mapping lineage in the developing nervous system using Brainbow multicolour transgenes:

1.      Principle of Brainbow Technology:

o  Genetic Mosaicism: Brainbow transgenes utilize combinatorial expression of fluorescent proteins to create a diverse color palette within individual cells, resulting in a unique color identity for each cell and its descendants.

o    Random Recombination: By incorporating multiple fluorescent protein variants and employing stochastic Cre-lox recombination events, Brainbow transgenes generate a spectrum of colors that can be used to label and trace cell lineages in a spatially and temporally controlled manner.

2.     Lineage Tracing in the Developing Nervous System:

o    Cell Fate Mapping: Brainbow multicolour transgenes allow for the precise labeling and visualization of individual cells and their progeny during neural development, facilitating the mapping of cell lineages, clonal relationships, and migration patterns in the developing nervous system.

o  Axon Tracing: In addition to lineage analysis, Brainbow technology can be used to trace axonal projections, synaptic connections, and neural circuits, providing insights into the wiring of the developing brain and the establishment of functional neuronal networks.

3.     Cellular Diversity and Connectivity:

o Neuronal Diversity: By labeling individual cells with distinct colors, Brainbow transgenes reveal the cellular diversity and heterogeneity within developing neural populations, highlighting the generation of different neuronal subtypes, glial cells, and neural progenitors during embryogenesis.

o    Synaptic Connectivity: Mapping lineage with Brainbow technology enables the visualization of synaptic connections between neurons, the formation of neural circuits, and the refinement of connectivity patterns essential for sensory processing, motor control, and cognitive functions in the developing nervous system.

4.    Functional Insights and Developmental Dynamics:

o Functional Analysis: Brainbow-mediated lineage mapping provides functional insights into cell fate decisions, proliferation dynamics, migration behaviors, and differentiation trajectories of neural progenitors and precursor cells during neurogenesis and gliogenesis in the developing brain.

o  Developmental Plasticity: By tracking individual cells over time and across brain regions, Brainbow transgenes offer a dynamic view of developmental plasticity, cellular interactions, and morphogenetic processes shaping the architecture and function of the nervous system during embryonic and postnatal stages.

In summary, mapping lineage in the developing nervous system with Brainbow multicolour transgenes offers a sophisticated approach to visualize, analyze, and understand the cellular diversity, connectivity, and developmental dynamics of neural populations during embryogenesis and early brain maturation. By leveraging the unique color-coding capabilities of Brainbow technology, researchers can unravel the complexities of neural development, circuit formation, and functional organization in the developing nervous system, advancing our knowledge of brain development and neurodevelopmental disorders.

 

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