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Related Concept Videos

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Projectile motion is commonly observed in our day-to-day life. For example, a basketball thrown by a player, an arrow shot from a bow, and kids jumping into the pool, all undergo projectile motion.
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Kinematic Equations - II01:17

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The second kinematic equation expresses the final position of an object in terms of its initial position, the distance traveled with the initial constant velocity, and the distance traveled due to a change in velocity. Similar to the first kinematic equation, this equation is also only valid when the acceleration is constant throughout the motion of an object.
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When analyzing one-dimensional motion with constant acceleration, the problem-solving strategy involves identifying the known quantities and choosing the appropriate kinematic equations to solve for the unknowns. Either one or two kinematic equations are needed to solve for the unknowns, depending on the known and unknown quantities. Generally, the number of equations required is the same as the number of unknown quantities in the given example. Two-body pursuit problems always require two...
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Consider a lawn roller with a mass of 100 kg, a radius of 0.2 meters, and a radius of gyration of 0.15 meters. A force of 200 N is applied to this roller, angled at 60 degrees from the horizontal plane. What will be the angular acceleration of the lawn roller?
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In the context of a rigid body's movement within a general plane, it is important to understand that this motion is typically triggered by external forces or couple moments exerted onto it. This principle can be explained through Newton's second law, which stipulates the translational motion of the body's center of mass along each axis.
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When an object moves with constant acceleration, the velocity of the object changes at a constant rate throughout the motion. The kinematic equations of motions are derived for such cases where the acceleration of the object is constant. The first kinematic equation gives an insight into the relationship between velocity, acceleration, and time. We can see, for example:
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Trajectory Data Analyses for Pedestrian Space-time Activity Study
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Single-trajectory map equation.

Tatsuro Kawamoto1

  • 1Artificial Intelligence Research Center, National Institute of Advanced Industrial Science and Technology, Tokyo, 135-0064, Japan. kawamoto.tatsuro@aist.go.jp.

Scientific Reports
|April 22, 2023
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Summary
This summary is machine-generated.

We introduce the single-trajectory map equation, a novel formulation that enhances community detection. This method offers a more balanced network structure and reduces overfitting in complex systems analysis.

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Area of Science:

  • Complex systems analysis
  • Network science
  • Information theory

Background:

  • Community detection is crucial for understanding complex systems.
  • The map equation is a popular, information-theoretic method for community detection.
  • The internal mechanisms of the map equation require further investigation.

Purpose of the Study:

  • To explore the original formulation of the map equation.
  • To introduce and analyze the single-trajectory map equation.
  • To improve the balance and reduce overfitting in community detection.

Main Methods:

  • Revisiting the original formulation of the map equation.
  • Analyzing the single-trajectory map equation derived from random walks.
  • Comparing community structures generated by different map equation forms.

Main Results:

  • The single-trajectory map equation reveals hidden details of the map equation's principles.
  • This raw form provides a more balanced community structure.
  • Overfitting tendencies within the map equation are naturally reduced.

Conclusions:

  • The single-trajectory map equation offers a deeper understanding of network community detection.
  • This formulation enhances the robustness and balance of community structures.
  • It presents a valuable advancement for analyzing complex systems on networks.