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Related Concept Videos

Static Equilibrium - II01:07

Static Equilibrium - II

Static equilibrium is a special case in mechanics that is very important in everyday life. It occurs when the net force and the net torque on an object or system are both zero. This means that both the linear and angular accelerations are zero. Thus, the object is at rest, or its center of mass is moving at a constant velocity. However, this does not mean that no forces are acting on the object within the system. In fact, there are very few scenarios on Earth in which no forces are acting upon...
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A Vibrotactile Feedback Device for Seated Balance Assessment and Training
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A Vibrotactile Feedback Device for Seated Balance Assessment and Training

Published on: January 20, 2019

Continuous-time model of structural balance.

Seth A Marvel1, Jon Kleinberg, Robert D Kleinberg

  • 1Center for Applied Mathematics, and Department of Computer Science, Cornell University, Ithaca, NY 14853, USA.

Proceedings of the National Academy of Sciences of the United States of America
|January 5, 2011
PubMed
Summary
This summary is machine-generated.

Social networks under stress typically split into two factions or achieve harmony. This study proves these are the only outcomes, with initial friendliness determining the final state of large networks.

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Area of Science:

  • Social network dynamics
  • Mathematical modeling of social behavior
  • Game theory applications

Background:

  • Social networks often exhibit polarization under stress, seen in politics, business, and international relations.
  • Previous simulations of a specific dynamical system suggested dichotomous outcomes: complete friendliness or factional division.

Purpose of the Study:

  • To mathematically prove the possible long-term behaviors of a dynamical system modeling social network interactions.
  • To establish a closed-form expression for predicting faction membership based on initial network conditions.

Main Methods:

  • Analysis of the dynamical system dX/dt = X(2), where X represents pairwise relationships in a network.
  • Derivation of a closed-form solution for faction membership as a function of initial conditions.

Main Results:

  • The study mathematically confirms that for generic initial conditions, the system converges to one of two states: universal friendliness or the emergence of two hostile factions.
  • A precise formula is derived to predict the final network state based on the initial distribution of friendliness.

Conclusions:

  • The initial degree of friendliness in a social network is the critical determinant of its future state, leading to either global harmony or intractable conflict.
  • This finding has implications for understanding and potentially mitigating polarization in various types of social systems.