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

Mittens compared to K Complexes

Image
Dr. Rishabh Pathak

When comparing mittens to K complexes in EEG recordings, several distinguishing features can be highlighted as:

1. Waveform Composition

    • Polarity:
      • Mittens: Both components (the sharp wave and the slow wave) have the same polarity.
      • K Complexes: Composed of two sharp waves of opposite polarity.

2. Shape and Duration

    • Duration:
      • Mittens: The sharp wave in a mitten typically has a longer duration (about 400 to 500 milliseconds) and a less sharp contour compared to the sharp wave in K complexes.
      • K Complexes: The sharp waves in K complexes are usually shorter and have a more defined, sharper contour.

3. Temporal Relationship

    • Inconsistency:
      • Mittens: The temporal relationship between the sharp wave and the slow wave is inconsistent, meaning that the timing can vary from one occurrence to another.
      • K Complexes: The two components of K complexes have a relatively fixed temporal relationship, with the sharp waves occurring at a consistent distance from the peak of the slow wave.

4. Location

    • Positioning:
      • Mittens: Typically centered in the frontal-central midline regions, with possible extension into the parasagittal regions.
      • K Complexes: Generally found at the vertex of the scalp.

5. Associated Features

    • Accompanying EEG Patterns:
      • Mittens: Often occur alongside other features of NREM sleep, such as sleep spindles and positive occipital sharp transients of sleep (POSTS).
      • K Complexes: Also associated with NREM sleep but are distinct in their morphology and the nature of their accompanying features.

Summary

Mittens and K complexes can be differentiated based on their waveform composition, duration, temporal relationships, localization, and associated EEG features. Understanding these differences is crucial for accurate EEG interpretation and for distinguishing between normal variants and potential pathological findings.

 

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

Control Variables

Dr. Rishabh Pathak
Control variables play a crucial role in research methodology by helping researchers isolate the effects of independent variables on the dependent variable. Here are key points to understand about control variables: 1.     Definition : o   Control variables  are factors that are held constant or systematically varied by the researcher to prevent them from confounding the relationship between the independent and dependent variables. By controlling for these variables, researchers can more accurately assess the impact of the independent variable on the outcome of interest. 2.     Role : o     Control variables are used to reduce the influence of extraneous variables and other sources of variability that could potentially affect the dependent variable. By controlling for specific factors that are not the focus of the study but could impact the results, researchers can enhance the internal validity of their research. 3.   ...
Post a Comment
Read more

Translocation, Retention and Potential Neurological Lesion in The Brain and Following Nanoparticle Exposure

Dr. Rishabh Pathak
Translocation, retention, and potential neurological lesions in the brain following nanoparticle exposure are important considerations in nanotoxicology and neurotoxicology research. Here are some key points regarding the impact of nanoparticle exposure on the brain: 1.       Translocation to the Brain : o Nanoparticles can enter the brain through various routes, including systemic circulation, olfactory nerve pathways, and disrupted blood-brain barrier (BBB) integrity. o Factors such as nanoparticle size, surface properties, shape, and surface modifications influence their ability to cross biological barriers and reach the brain parenchyma. 2.      Retention in the Brain : o Once nanoparticles translocate to the brain, they may exhibit different retention times depending on their physicochemical properties and interactions with brain cells. o Nanoparticles can accumulate in specific brain regions, such as the olfactory bulb, hippocampus, and...
Post a Comment
Read more

Regressive Events in the Postnatal Period

Dr. Rishabh Pathak
Regressive events in the postnatal period refer to processes in brain development that involve the elimination or reduction of certain neural elements, such as neurons and glial cells, to refine and optimize neural circuits. These regressive events are essential for sculpting the developing brain and ensuring its proper functioning. Here are key points regarding regressive events in the postnatal period: 1.      Cell Death in Glial Populations : o     While neural apoptosis peaks during prenatal development, apoptosis in glial cell populations occurs postnatally and is essential for the refinement of neural circuits. o     Glial cells, particularly oligodendrocytes, undergo apoptosis after differentiating, with signals from nearby axons influencing the survival of oligodendrocytes to match the local axonal surface area, a process crucial for myelination and neural connectivity. 2.      Synaptic Pruning : o  ...
Post a Comment
Read more