Simple Random Sampling: 6 Basic Steps With Examples

A simple random sample is a subset of a statistical population where each member of the population is equally likely to be ...
IEEE

Sparse Sampling in Fractional Fourier Domain: Recovery Guarantees and Cramér–Rao Bounds

Abstract: Sampling theory in fractional Fourier Transform (FrFT) domain has been studied extensively in the last decades. This interest stems from the ability of the FrFT to generalize the traditional ...
IEEE

Dual-Conditional Diffusion Model for Seismic Data Reconstruction: Integrating Observed Data and Sampling Matrix Constraints

Abstract: Seismic exploration relies heavily on high-quality data acquisition, but practical limitations often result in incomplete seismic data, violating the Nyquist sampling theorem and introducing ...
IEEE

Parameter Identification for Inverse Scattering Problem of Electrically Large Curved Surfaces

Abstract: Inverse scattering problems (ISPs) often suffer from severe ill-posedness and nonlinearity. In this article, a parameter identification method that determines the necessary conditions of ...
Scientific American

This mathematician proved a brilliant theorem to justify his social awkwardness

More than 100 years ago Hungarian-born mathematician George Pólya found himself trapped in a loop of social awkwardness. A professor at the Swiss Federal Institute of Technology Zurich, he enjoyed ...
IEEE

On Optimal Sampling for Learning SDF Using MLPs Equipped With Positional Encoding

Abstract: Neural implicit fields, such as the neural signed distance field (SDF) of a shape, have emerged as a powerful representation for many applications, e.g., encoding a 3D shape and performing ...
IEEE

Sampling and Layout of OPM Arrays for MCG Based on the Sampling Theorem

Abstract: Given that the sampling and arrangement of the array need a reasonable standard to guide in high-precision magnetocardiography (MCG) imaging, the sampling range required for robust ...
VentureBeat

Lean4: How the theorem prover works and why it's the new competitive edge in AI

Large language models (LLMs) have astounded the world with their capabilities, yet they remain plagued by unpredictability and hallucinations – confidently outputting incorrect information. In ...