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

Cone Waves Compared to Positive Occipital Sharp Transients of Sleep

Image
Dr. Rishabh Pathak

Cone waves and Positive Occipital Sharp Transients of Sleep (POSTS) are distinct EEG patterns that share some similarities but also have key differences. Here is a comparison between cone waves and POSTS:


1.     Morphology:

o  Both cone waves and POSTS exhibit a triangular morphology, with a sharp, distinctive shape resembling a cone.

o Cone waves and POSTS may appear similar in their waveform characteristics, including the presence of a sharp onset and offset.

2.   Occipital Distribution:

oBoth cone waves and POSTS are typically localized over the occipital regions of the brain.

o The occipital distribution of these waveforms distinguishes them from patterns that are more widespread or localized to other brain regions.

3.   Duration:

o Cone waves have a duration typically more than 250 milliseconds, while POSTS have a shorter duration, typically less than 200 milliseconds.

o The difference in duration can aid in distinguishing between cone waves and POSTS on EEG recordings.

4.   Age Dependency:

o Cone waves are more likely to occur in younger children, typically between the ages of 6 months and 3 years.

o POSTS are rare before 3 years of age and most common after childhood, indicating an age-dependent occurrence.

5.    Phase Reversal:

o POSTS are characterized by a phase reversal, with positivity at the center of the field, which is evident in the waveform.

o Cone waves do not exhibit a phase reversal in the same manner as POSTS, providing a distinguishing feature between the two patterns.

6.   Clinical Significance:

o Cone waves are considered a normal variant with no clinical significance in their presence or absence.

o POSTS, while also a normal variant, may have implications for EEG interpretation and clinical assessment due to their association with specific age groups and sleep states.

7.    Co-occurring Waves:

o Cone waves occur during non-rapid eye movement (NREM) sleep and are accompanied by other EEG features of this state, such as diffuse theta or delta background activity.

o POSTS are also observed during NREM sleep and may co-occur with other sleep-related EEG patterns, such as sleep spindles and K complexes.

Understanding the similarities and differences between cone waves and POSTS is essential for accurate EEG interpretation and recognition of normal variants versus abnormal patterns. By considering the unique characteristics of each waveform, clinicians can effectively differentiate between cone waves and POSTS in EEG recordings and assess their clinical significance in the context of patient evaluation.

 

Categories:

Comments

Post a Comment

Popular posts from this blog

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

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

Composition of Bone Tissue

Dr. Rishabh Pathak
Bone tissue is a complex and dynamic connective tissue composed of various components that contribute to its structure, strength, and functionality. The composition of bone tissue includes: 1.     Cells : o     Osteoblasts : Bone-forming cells responsible for synthesizing and depositing the organic matrix of bone. o     Osteocytes : Mature bone cells embedded in the bone matrix, involved in maintaining bone tissue and responding to mechanical stimuli. o     Osteoclasts : Bone-resorbing cells responsible for breaking down and remodeling bone tissue. 2.     Organic Matrix : o     Collagen Fibers : Type I collagen is the predominant protein in the organic matrix of bone, providing flexibility, tensile strength, and resilience to bone tissue. o     Non-Collagenous Proteins : Include osteocalcin, osteopontin, and osteonectin, which play roles in mineralization, cell adhesion, and matrix o...
Post a Comment
Read more

Frontal–central - Beta Activity

Dr. Rishabh Pathak
Frontal-central beta activity in EEG recordings refers to a specific pattern of beta waves that are predominantly observed in the frontal and central regions of the brain. Description : o   Frontal-central beta activity is characterized by increased beta waves present diffusely, with a buildup of greater beta activity specifically in the frontal-central regions. o   This pattern may be accompanied by generalized theta activity, which can be more visible when the beta activity declines. 2.      Frequency Range : o   Frontal-central beta activity typically falls within the beta frequency range, which is defined as 13 Hz or greater in EEG recordings. o   The frequency of frontal-central beta activity tends to be within the narrower range of 20 to 30 Hz, with variations in frequency observed based on age and state of consciousness. 3.      State Dependency : o    Frontal-central beta activity is considered state-dependent...
Post a Comment
Read more