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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...
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Random Sampling Software’s

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Dr. Rishabh Pathak

Random sampling software tools are computer programs designed to facilitate the process of selecting random samples from populations for research, surveys, experiments, and other data collection activities. These software tools use algorithms to generate random numbers or selections, ensuring unbiased and systematic sampling. Here are some popular random sampling software tools commonly used by researchers:


1.    R: R is a widely used open-source statistical computing software that offers various packages and functions for random sampling. Researchers can use functions like sample() in R to generate random samples from populations based on specified criteria. R provides flexibility and customization options for conducting different types of random sampling techniques.


2.    Python: Python is a versatile programming language with libraries such as NumPy and SciPy that support random sampling functionalities. Researchers can leverage functions like numpy.random.choice() in Python to perform random sampling with or without replacement. Python's ease of use and extensive libraries make it a popular choice for implementing random sampling algorithms.


3. SPSS: IBM SPSS Statistics is a statistical software package that includes features for random sampling and data analysis. Researchers can use the sampling options in SPSS to select random samples from datasets based on various sampling methods. SPSS provides a user-friendly interface for conducting random sampling and analyzing the sampled data.


4.    SAS: SAS (Statistical Analysis System) is a software suite commonly used for data management and statistical analysis. SAS offers procedures like SURVEYSELECT for random sampling in complex survey designs. Researchers can specify sampling parameters and criteria to generate random samples using SAS programming capabilities.


5.  Excel: Microsoft Excel, a popular spreadsheet software, can also be used for random sampling purposes. Researchers can utilize Excel functions like RAND() or RANDBETWEEN() to generate random numbers and select samples based on those numbers. While Excel may not offer advanced sampling features compared to dedicated statistical software, it can still be effective for simple random sampling tasks.


6.    Qualtrics: Qualtrics is an online survey platform that includes random sampling features for creating surveys and collecting data. Researchers can use Qualtrics to set up random sampling rules for survey distribution, ensuring that respondents are selected randomly from target populations. Qualtrics simplifies the process of conducting random sampling in survey research.


7.    SurveyMonkey: SurveyMonkey is another popular online survey tool that offers random sampling capabilities for creating surveys and collecting responses. Researchers can use SurveyMonkey's random sampling options to distribute surveys to random subsets of participants from larger populations. SurveyMonkey provides user-friendly features for implementing random sampling in survey studies.


These random sampling software tools offer researchers efficient and reliable ways to select random samples from populations, ensuring the validity and representativeness of research findings. Researchers can choose the software tool that best fits their study requirements and data analysis needs to conduct random sampling effectively.

 

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