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

Increasing the Cortical Thickness Increases the Gyral Wavelength

Image
Dr. Rishabh Pathak

Increasing the cortical thickness has been shown to influence the gyral wavelength during brain development. Here is an explanation of how changes in cortical thickness can impact the gyral wavelength:


1.     Physics-Based Models: Physics-based models predict that the gyral wavelength, which refers to the distance between adjacent gyri on the brain's surface, increases with increasing cortical thickness. These models take into account the mechanical properties of the cortical tissue and how variations in thickness can affect the folding patterns observed in the cerebral cortex.


2.     Radial Organization: The cortical thickness is largely determined by the radial organization of the cortical plate during early stages of development. As the cortex expands and thickens due to differential growth processes, the spacing between gyri is influenced by the overall thickness of the cortical tissue. Changes in cortical thickness can modulate the surface morphogenesis of the brain, leading to alterations in the gyral wavelength.


3.     Surface Morphology: Studies have shown that decreasing the cortical thickness can result in an increased number of folds and a decrease in the gyral wavelength. Conversely, increasing the cortical thickness leads to changes in the folding patterns, affecting the complexity of the brain's surface. These variations in cortical thickness and folding dynamics contribute to the overall structural organization of the cerebral cortex.


4.     Geological Analogies: The concept of cortical folding and its relationship to cortical thickness draws parallels to geological folding processes. Just as geological structures exhibit folding patterns based on the thickness and composition of rock layers, the brain's folding patterns are influenced by the mechanical interactions within the cortical tissue. Understanding how changes in cortical thickness impact the gyral wavelength provides insights into the mechanisms underlying brain morphogenesis.


5.     Developmental Implications: The relationship between cortical thickness and gyral wavelength has implications for brain development and function. Variations in cortical thickness can affect the surface area of the cortex, neuronal connectivity, and the distribution of functional areas across the brain. By studying how changes in cortical thickness influence the folding patterns of the cerebral cortex, researchers can gain a better understanding of the structural adaptations that occur during neurodevelopment.


In conclusion, increasing the cortical thickness is associated with an increase in the gyral wavelength, reflecting the intricate relationship between cortical morphology and brain development. By exploring the effects of cortical thickness on folding patterns, researchers can uncover the underlying mechanisms that shape the convoluted structure of the human brain and its functional implications.

 

Categories:

Comments

Post a Comment

Popular posts from this blog

Cell Maturation (Dendrite and Axon Growth)

Dr. Rishabh Pathak
Cell maturation, encompassing dendrite and axon growth, is a crucial stage of brain development where neurons undergo structural changes to establish connections and form functional neural circuits. Here is an overview of cell maturation in the context of dendrite and axon growth: 1.      Dendrite Growth : o     Definition : Dendrites are branched extensions of a neuron that receive signals from other neurons and transmit these signals to the cell body. o     Dendritic Arborization : During maturation, neurons extend and elaborate their dendritic arbors, increasing the surface area available for synaptic connections. o     Synaptic Integration : Dendritic growth is essential for forming synapses with other neurons, allowing for the integration of incoming signals and information processing. o     Activity-Dependent Plasticity : Dendritic growth can be influenced by neural activity and sensory experiences, sh...
Post a Comment
Read more

Ocular Artifacts

Dr. Rishabh Pathak
Ocular artifacts in EEG recordings are commonly caused by movements of the eyes, such as blinking, eye flutter, and eye movements associated with eye opening and closure. These artifacts can mimic epileptiform discharges and other EEG patterns, making them important to recognize and differentiate.  Nature of Ocular Artifacts : o    Ocular artifacts are primarily due to the movement of the electrical dipoles created by the eyes, particularly during activities like eye opening, closure, and directed gaze. o    The movement of these dipoles generates changing electrical fields that appear as EEG activity, with characteristics such as slow waves and spikes. o    Ocular artifacts are typically limited to the frontal region and do not extend into the central region of the brain. 2.      Differentiation from Epileptiform Discharges : o   Ocular artifacts can sometimes appear as bifrontal spike and slow wave complexes, resembling inter...
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

Cell Migration

Dr. Rishabh Pathak
Cell migration is a crucial stage of brain development where newly generated neurons move to their appropriate locations within the developing brain. Here is an overview of cell migration in the context of brain development: 1.      Definition : §   Cell migration refers to the process by which neurons and glial cells move from their site of origin to their final destination in the developing brain. §   Proper cell migration is essential for establishing the correct architecture and connectivity of the brain. 2.      Types of Cell Migration : §   Radial Migration : Radial migration involves neurons moving along radial glial fibers that span the developing brain. This type of migration is common in the cerebral cortex and helps neurons reach their appropriate cortical layers. §   Tangential Migration : Tangential migration occurs when neurons migrate horizontally across the developing brain. Interneurons, for example...
Post a Comment
Read more

Unrestricted Sampling

Dr. Rishabh Pathak
Unrestricted sampling, also known as simple random sampling, is a fundamental sampling technique where each element in the population has an equal and independent chance of being selected for the sample. In unrestricted sampling: 1.     Equal Probability of Selection : §   In simple random sampling, every element in the population has an equal probability of being chosen for the sample. This ensures that each unit is selected independently of other units, without any bias towards specific elements. 2.     Random Selection : §   The selection of sample elements is done randomly, without any systematic pattern or predetermined order. This randomness is essential to ensure that the sample is representative of the population and to minimize selection bias. 3.     Independence of Selection : §   Each selection is made independently of previous selections, meaning that the inclusion or exclusion of one element does not influence the ...
Post a Comment
Read more