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Related Concept Videos

Echo01:06

Echo

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The human ear cannot distinguish between two sources of sound if they happen to reach within a specific time interval, typically 0.1 seconds apart. More than this, and they are perceived as separate sources.
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Integrals involving non-rational functions are often difficult to evaluate using standard techniques, especially when radicals appear in the integrand. Rationalizing substitution provides a systematic method for simplifying such integrals by converting them into rational forms that are easier to handle.Consider a rod whose linear mass density depends on a constant linear density, a characteristic length, and the distance from the left end of the rod. Determining the total mass requires...
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Rational expressions are algebraic fractions in which both the numerator and the denominator are polynomials. These expressions follow the arithmetic rules of numerical fractions but require extra care due to the presence of variables. A fundamental part of working with rational expressions is identifying values that make the expression undefined, typically those that result in division by zero or undefined radicals.Determining the DomainThe domain of a rational expression includes all real...
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Asymptotes in Rational Functions01:30

Asymptotes in Rational Functions

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A rational function is defined as the quotient of two polynomials:  where Q(x)≠0, These functions often exhibit asymptotes, which are the lines that the graph approaches but never touches. These asymptotes are classified based on how the function behaves near specific values of the input.Vertical asymptotes occur where the denominator is zero, and the numerator is not, causing the function to be undefined. These are found by solving Q(x)=0. For example:  has a vertical...
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Related Experiment Video

Updated: Feb 6, 2026

Fabrication of Soft Pneumatic Network Actuators with Oblique Chambers
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Large networks of rational agents form persistent echo chambers.

Jens Koed Madsen1, Richard M Bailey2, Toby D Pilditch3

  • 1School of Geography and the Environment, University of Oxford, OX1 3QY, South Parks Road, Oxford, United Kingdom. jens.madsen@ouce.ox.ac.uk.

Scientific Reports
|August 19, 2018
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Summary

Echo chambers (ECs) can form even without cognitive errors, driven by network structures. Larger networks amplify EC growth, suggesting system architects must mitigate their formation and persistence.

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Area of Science:

  • Computational Social Science
  • Network Science
  • Information Theory

Background:

  • Echo chambers (ECs) are social networks where individuals reinforce pre-existing beliefs.
  • The necessity of cognitive errors for EC emergence and persistence remains debated.
  • Understanding EC dynamics is crucial in the age of widespread information dissemination.

Purpose of the Study:

  • To investigate whether cognitive errors are essential for echo chamber formation.
  • To determine the role of network structure in the emergence and persistence of echo chambers.
  • To evaluate the effectiveness of interventions in mitigating echo chambers.

Main Methods:

  • Theoretical modeling of Bayesian agents within network structures.
  • Simulation of echo chamber formation and growth under varying network sizes.
  • Testing stylized interventions, such as educational broadcasts, on agent behavior.

Main Results:

  • Echo chambers can emerge theoretically among error-free Bayesian agents.
  • Larger network sizes correlate with increased echo chamber formation.
  • System-wide educational broadcasts reduce but do not eliminate echo chambers, with greater impact on new agents.

Conclusions:

  • Network structure, not solely cognitive errors, drives echo chamber formation.
  • System architects bear responsibility for designing networks that mitigate echo chambers.
  • Targeted interventions can reduce echo chamber effects, particularly for newer network participants.