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

Haphazard Sampling or Convenience Sampling

Image
Dr. Rishabh Pathak

Haphazard sampling, also known as convenience sampling, is a non-probability sampling technique where sample units are selected based on their convenient availability to the researcher. This method is characterized by its reliance on easily accessible subjects rather than random selection. Here are some key points about haphazard sampling or convenience sampling:


1.    Definition:

o    Haphazard sampling, or convenience sampling, involves selecting sample units based on their easy accessibility and convenience to the researcher.

o    Researchers choose participants who are readily available or easily reached, without following a systematic or random selection process.

2.    Characteristics:

o    Convenience sampling is a non-probability sampling method that does not involve randomization or known probabilities of selection.

o Sample units are typically chosen based on the researcher's proximity, availability, or ease of access.

3.    Process:

o    In convenience sampling, researchers may select participants who are nearby, willing to participate, or easily reachable through existing networks.

o  This method is often used when time, resources, or logistical constraints make random sampling impractical.

4.    Advantages:

o    Convenience sampling is quick, easy, and cost-effective, making it suitable for exploratory research, pilot studies, or preliminary investigations.

o  This method can be useful for generating initial insights, identifying trends, or exploring research questions in a flexible manner.

5.    Limitations:

o Results obtained from convenience samples may not be representative of the larger population due to selection bias.

o    The lack of randomization in convenience sampling can lead to sampling errors and limit the generalizability of findings.

o    Researchers should be cautious in drawing broad conclusions or making population inferences based on convenience samples.

6.    Applications:

o    Convenience sampling is commonly used in educational research, small-scale studies, qualitative research, and situations where random sampling is impractical.

o    This method is often employed in situations where the focus is on exploring phenomena, generating hypotheses, or gaining initial insights rather than making population estimates.

7.    Considerations:

o Researchers should clearly acknowledge the limitations of convenience sampling in terms of generalizability and potential bias in sample selection.

o  While convenience sampling can be a useful starting point in research, efforts should be made to supplement or validate findings with more rigorous sampling methods when possible.

Convenience sampling, or haphazard sampling, offers a practical and accessible approach to sampling in certain research contexts. While this method provides convenience and flexibility, researchers should be mindful of its limitations in terms of representativeness and potential bias. Careful consideration of the research objectives and constraints is essential when choosing convenience sampling as a sampling strategy.

 

Categories:

Comments

  1. SRIJune 29, 2024 at 2:59 AM

    Insightful to learn about Research Methods. Thanks for your effort sir (@Dr. Rishabh Pathak)

    ReplyDelete

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