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Related Concept Videos

Transfer Function in Control Systems01:21

Transfer Function in Control Systems

The transfer function is a fundamental concept in the analysis and design of linear time-invariant (LTI) systems. It offers a concise way to understand how a system responds to different inputs in the frequency domain. It serves as a bridge between the time-domain differential equations that describe system dynamics and the frequency-domain representation that facilitates easier manipulation and analysis.
To derive the transfer function, consider a general nth-order linear time-invariant...
Network Function of a Circuit01:25

Network Function of a Circuit

Frequency response analysis in electrical circuits provides vital insights into a circuit's behavior as the frequency of the input signal changes. The transfer function, a mathematical tool, is instrumental in understanding this behavior. It defines the relationship between phasor output and input and comes in four types: voltage gain, current gain, transfer impedance, and transfer admittance. The critical components of the transfer function are the poles and zeros.
Introduction to Normal Distributions01:29

Introduction to Normal Distributions

Standardized test scores often follow a symmetric distribution that can be modeled with the normal distribution, a fundamental concept in statistics. This distribution is particularly useful for interpreting test performance fairly across populations, as it provides a mathematical framework for understanding variability and central tendency in large datasets.From Histogram to Frequency DistributionRaw test data are often displayed using histograms, where the height of each bar represents the...
Transfer Function to State Space01:23

Transfer Function to State Space

State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an RLC...
State Space to Transfer Function01:21

State Space to Transfer Function

The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
Region of Convergence of Laplace Tarnsform01:20

Region of Convergence of Laplace Tarnsform

The Region of Convergence (ROC) is a fundamental concept in signal processing and system analysis, particularly associated with the Laplace transform. The ROC represents an area in the complex plane where the Laplace transform of a given signal converges, determining the transform's applicability and utility.
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This substitution...

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Related Experiment Videos

Contrast Transfer Functions Help Quantify Neural Network Out-Of-Distribution Generalization in HRTEM.

Luis Rangel DaCosta1,2, Mary C Scott1,2

  • 1Department of Materials Science and Engineering, University of California, Hearst Memorial Mining Building, Berkeley, CA 94720, USA.

Microscopy and Microanalysis : the Official Journal of Microscopy Society of America, Microbeam Analysis Society, Microscopical Society of Canada
|July 15, 2026
PubMed
Summary

Neural networks show stable performance in high-resolution transmission electron microscopy (HRTEM) segmentation tasks. However, their accuracy predictably declines as imaging conditions deviate from the training data distribution.

Keywords:
HRTEMgeneralizationneural networkssegmentation

Related Experiment Videos

Area of Science:

  • Materials Science
  • Computational Science
  • Machine Learning

Background:

  • Neural networks excel at scientific tasks but struggle with out-of-distribution (OOD) generalization.
  • Understanding OOD generalization is crucial for deploying AI in experimental settings with variable conditions.

Purpose of the Study:

  • To investigate the OOD generalization of neural network segmentation models in high-resolution transmission electron microscopy (HRTEM).
  • To analyze the impact of varying imaging conditions on model performance using synthetic data.

Main Methods:

  • Trained and evaluated over 12,000 neural networks on synthetic HRTEM data.
  • Utilized random structure sampling and multislice simulation for data generation.
  • Developed a framework using the HRTEM contrast transfer function to quantify OOD domain shifts.

Main Results:

  • Neural network segmentation models demonstrated significant performance stability.
  • Model performance degraded smoothly and predictably as imaging conditions shifted away from the training distribution.
  • Quantified OOD domain shifts based on imaging condition variations.

Conclusions:

  • Neural network segmentation models exhibit predictable OOD generalization behavior concerning imaging conditions in HRTEM.
  • The study provides a framework for assessing OOD shifts in imaging data.
  • Acknowledges limitations in explaining OOD shifts related to atomic structures and suggests complementary approaches.