Skip to main content

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...
Post a Comment

Mechanisms of Brain Development

Image
Dr. Rishabh Pathak

Brain development is a complex and highly orchestrated process involving a series of intricate mechanisms that shape the structure and function of the brain. Here are some key mechanisms of brain development:


1.     Neurogenesis: Neurogenesis is the process by which neurons are generated from neural stem cells. It occurs predominantly during embryonic development but continues in certain brain regions throughout life. Neurogenesis is essential for the formation of the brain's neuronal circuitry.


2. Cell Migration: Once neurons are generated, they must migrate to their appropriate locations within the brain to form functional circuits. Cell migration is crucial for establishing the correct connectivity and organization of the brain.


3.  Axon Guidance: Axon guidance is the process by which developing axons navigate to their target regions and establish connections with other neurons. Guidance cues, such as growth factors and cell adhesion molecules, play a critical role in directing axon growth and pathfinding.


4.  Synaptogenesis: Synaptogenesis is the formation of synapses, the connections between neurons that allow for communication in the brain. Synaptic connections are essential for neural signaling and the establishment of functional circuits.


5. Apoptosis: Apoptosis, or programmed cell death, is a natural process that eliminates excess neurons and synapses during brain development. Apoptosis helps sculpt the developing brain by removing unnecessary or improperly connected cells.


6.  Myelination: Myelination is the process by which axons are insulated with myelin, a fatty substance that enhances the speed and efficiency of neural signaling. Myelination occurs throughout development and is essential for proper brain function.


7.     Experience-Dependent Plasticity: Experience-dependent plasticity refers to the brain's ability to reorganize and adapt in response to sensory experiences and environmental stimuli. This mechanism plays a crucial role in shaping neural circuits and optimizing brain function.


8. Critical Periods: Critical periods are specific windows of time during development when the brain is particularly sensitive to certain types of stimuli. During these periods, neural circuits are more malleable and can be shaped by sensory experiences.


9.  Hormonal Influence: Hormones play a significant role in brain development, influencing processes such as cell proliferation, differentiation, and synaptic connectivity. Hormonal signals help coordinate various aspects of brain development.


10. Genetic Regulation: Genetic factors play a fundamental role in brain development, influencing the formation of neural structures, cell types, and connectivity patterns. Genetic regulation guides the intricate processes of brain development from the molecular level up to the macroscopic organization of the brain.


Understanding these mechanisms of brain development is essential for unraveling the complexities of how the brain forms and functions. Researchers continue to investigate these processes to gain insights into neurodevelopmental disorders, brain plasticity, and the fundamental principles underlying brain structure and function.

 

Categories:

Comments

Post a Comment

Popular posts from this blog

Review Settings of EEG

Dr. Rishabh Pathak
The review settings of an EEG recording refer to the parameters that can be adjusted to optimize the visualization and interpretation of electrical brain activity. Here is an overview of the key review settings in EEG analysis: 1.       Amplification (Gain/Sensitivity) : o Definition : Amplification, also known as gain or sensitivity, determines how much the electrical signals from the brain are amplified before being displayed on the EEG recording. o Measurement : Typically measured in microvolts per millimeter (μV/mm). o Impact : Adjusting the amplification setting can affect the visibility of high-amplitude and low-amplitude activity. High-amplitude activity may require vertical compression to fit within the display range, while low-amplitude activity may require lower sensitivity settings for better visualization. 2.      Frequency Filtering : o Bandpass : The frequency range within which EEG signals are analyzed. Common settings include ...
Post a Comment
Read more

Cancellous Bone

Dr. Rishabh Pathak
Cancellous bone, also known as trabecular or spongy bone, is the other main type of bone tissue found in the human skeleton alongside cortical bone. Cancellous bone has a porous and lattice-like structure, providing flexibility, shock absorption, and a site for hematopoiesis (blood cell formation). Here are key features and characteristics of cancellous bone: 1.     Structure : o     Trabeculae : Cancellous bone is composed of a network of thin, bony trabeculae that form an interconnected lattice structure. o     Bone Marrow : The spaces between trabeculae contain red bone marrow, which is involved in the production of blood cells (hematopoiesis). o     Less Compact : Cancellous bone is less dense and compact than cortical bone, with a higher surface area-to-volume ratio. 2.     Composition : o     Trabecular Bone : The trabeculae are made up of lamellae, osteocytes, and canaliculi similar to corti...
Post a Comment
Read more

Anatomical Classification of Bones

Dr. Rishabh Pathak
Bones in the human body can be classified into five main anatomical categories based on their shape and structure. These classifications provide insights into the functions and characteristics of different bone types. Here are the five anatomical classifications of bones: 1.     Long Bones : o     Description : Long bones are characterized by their elongated shape, with a shaft (diaphysis) and two expanded ends (epiphyses). o     Examples : Femur, humerus, radius, ulna, tibia, fibula. o     Function : Long bones provide support, leverage, and mobility. They are essential for body movement and weight-bearing activities. 2.     Short Bones : o     Description : Short bones are roughly cube-shaped or have a similar length and width, providing stability and support. o     Examples : Carpals (wrist bones), tarsals (ankle bones). o     Function : Short bones contribute to we...
Post a Comment
Read more

Amphiarthrodial or Cartilaginous Joints

Dr. Rishabh Pathak
Amphiarthrodial joints, also known as cartilaginous joints, are joints where the adjacent bones are connected by cartilage. These joints allow for limited movement and provide both stability and flexibility to the skeletal system. Here is an overview of amphiarthrodial or cartilaginous joints: Amphiarthrodial or Cartilaginous Joints: 1.     Structure : o     Cartilage : §   Amphiarthrodial joints are characterized by the presence of cartilage between the articulating surfaces of the bones. §   The cartilage can be hyaline cartilage or fibrocartilage, depending on the specific joint and its function. o     Lack of Joint Cavity : §   Similar to fibrous joints, cartilaginous joints do not have a synovial cavity, and the bones are held together by the cartilaginous tissue. 2.     Types : o     Synchondroses : §   Synchondroses are cartilaginous joints where the connecting material is hyaline carti...
Post a Comment
Read more

What analytical model is used to estimate critical conditions at the onset of folding in the brain?

Dr. Rishabh Pathak
The analytical model used to estimate critical conditions at the onset of folding in the brain is based on the Föppl–von Kármán theory. This theory is applied to approximate cortical folding as the instability problem of a confined, layered medium subjected to growth-induced compression. The model focuses on predicting the critical time, pressure, and wavelength at the onset of folding in the brain's surface morphology. The analytical model adopts the classical fourth-order plate equation to model the cortical deflection. This equation considers parameters such as cortical thickness, stiffness, growth, and external loading to analyze the behavior of the brain tissue during the folding process. By utilizing the Föppl–von Kármán theory and the plate equation, researchers can derive analytical estimates for the critical conditions that lead to the initiation of folding in the brain. Analytical modeling provides a quick initial insight into the critical conditions at the onset of foldi...
Post a Comment
Read more