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

Cortical Folding is a Mechanical Instability Driven by Differential Growth

Image
Dr. Rishabh Pathak

Cortical folding is a complex phenomenon in brain development that is driven by differential growth processes. This mechanical instability arises from the differential growth rates between the cortical layers, leading to the formation of the characteristic gyri and sulci on the surface of the cerebral cortex. Here is an overview of how cortical folding is a mechanical instability driven by differential growth:


1.     Differential Growth: The process of cortical folding is fundamentally linked to the concept of differential growth, where different regions of the developing brain expand at varying rates. This uneven growth results in mechanical stresses within the cortical tissue, as certain areas experience more growth than others. The differential growth between the outer cortical layers and the underlying structures, such as the white matter, plays a key role in initiating cortical folding.


2. Physics-Based Approach: A physics-based approach has been increasingly utilized to understand cortical folding as a mechanical instability phenomenon. This perspective considers the mechanical forces generated by differential growth and how they influence the morphological changes in the brain. By modeling the cortical tissue as a multi-layered system undergoing constrained growth, researchers can simulate the patterns of cortical folding observed in the developing brain.


3.     Constrained Differential Growth: The theory of cortical folding as a constrained differential growth process suggests that the early radial expansion of the cortical plate is relatively uniform across its thickness and does not lead to folding. However, the later tangential expansion, particularly in the superficial cortical layers, is constrained by the inner layers and the underlying structures, promoting the formation of gyri and sulci. This differential growth pattern creates mechanical instabilities that drive the folding of the cortex.


4.     Role of Neuronal Connectivity: While the differential growth is a primary driver of cortical folding, other factors such as neuronal connectivity also play a significant role in shaping the folding patterns. The establishment of neural circuits and synaptic connections influences the distribution of mechanical forces within the cortex, further contributing to the folding process. Changes in synaptic pruning, myelination, and neuronal migration also impact the mechanical properties of the developing brain and influence cortical folding during different stages of development.


5. Implications for Developmental Disorders: Disruptions in the mechanisms underlying cortical folding and differential growth can lead to cortical malformations and neurodevelopmental disorders. Conditions such as lissencephaly, characterized by a smooth brain surface due to disrupted neuronal migration, highlight the importance of proper mechanical interactions in cortical development. Understanding the interplay between differential growth, mechanical forces, and neuronal processes is crucial for elucidating the origins of cortical malformations and associated neurological conditions.


In summary, cortical folding represents a dynamic interplay between differential growth processes and mechanical instabilities in the developing brain. By considering the physical principles that govern cortical morphogenesis, researchers can gain insights into the mechanisms driving the formation of gyri and sulci, as well as the implications of disrupted cortical folding for brain structure and function.

 

Categories:

Comments

Post a Comment

Popular posts from this blog

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 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

Distinguishing Features of Electrode Artifacts

Dr. Rishabh Pathak
Electrode artifacts in EEG recordings can present with distinct features that differentiate them from genuine brain activity.  1.      Types of Electrode Artifacts : o Variety : Electrode artifacts encompass several types, including electrode pop, electrode contact, electrode/lead movement, perspiration artifacts, salt bridge artifacts, and movement artifacts. o Characteristics : Each type of electrode artifact exhibits specific waveform patterns and spatial distributions that aid in their identification and differentiation from true EEG signals. 2.    Electrode Pop : o Description : Electrode pop artifacts are characterized by paroxysmal, sharply contoured transients that interrupt the background EEG activity. o Localization : These artifacts typically involve only one electrode and lack a field indicating a gradual decrease in potential amplitude across the scalp. o Waveform : Electrode pop waveforms have a rapid rise and a slower fall compared to in...
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

Beta Activity compared to Muscles Artifacts

Dr. Rishabh Pathak
Beta activity in EEG recordings can sometimes be confused with muscle artifacts due to their overlapping frequency components. Frequency Components : o   Muscle artifacts often have frequency components of 25 Hz and greater, which can overlap with the frequency range of beta activity. o   Beta activity in EEG recordings typically falls within the beta frequency range of 13-30 Hz, with variations based on specific brain states and cognitive processes. 2.      Waveform Characteristics : o   Electromyographic (EMG) artifacts, which represent muscle activity, have distinct waveform characteristics that can help differentiate them from beta activity. o   EMG artifacts may exhibit a sharper contour with less rhythmicity, especially when the high-frequency filter is set at 70 Hz or higher, compared to the smoother contour and rhythmicity of beta activity. 3.      High-Frequency Filter Settings : o   Adjusting the high-frequency f...
Post a Comment
Read more