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Related Concept Videos

Root Loci for Positive-Feedback Systems01:23

Root Loci for Positive-Feedback Systems

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The Hartley oscillator is a positive feedback system that sustains oscillations by feeding the output back to the input in phase, thereby reinforcing the signal. Positive feedback systems can be viewed as negative feedback systems with inverted feedback signals. In these systems, the root locus encompasses all points on the s-plane where the angle of the system transfer function equals 360 degrees.
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Linear time-invariant Systems01:23

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A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
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An outlier is an observation of data that does not fit the rest of the data. It is sometimes called an extreme value. When you graph an outlier, it will appear not to fit the pattern of the graph. Some outliers are due to mistakes (for example, writing down 50 instead of 500), while others may indicate that something unusual is happening. Outliers are present far from the least squares line in the vertical direction. They have large "errors," where the "error" or residual is the...
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Multi-input and Multi-variable systems01:22

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Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
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Classification of Systems-I01:26

Classification of Systems-I

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Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
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Linear Approximation in Frequency Domain01:26

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Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
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Influencer identification in dynamical complex systems.

Sen Pei1, Jiannan Wang2, Flaviano Morone3

  • 1Department of Environmental Health Sciences, Mailman School of Public Health, Columbia University, 722 West 168th Street, New York, NY, USA.

Journal of Complex Networks
|August 11, 2020
PubMed
Summary
This summary is machine-generated.

Identifying key influencers is crucial for complex systems. This review covers methods for finding structurally vital nodes and dynamically essential units impacting network behavior and dynamics.

Keywords:
influencer identificationk-core percolationoptimal percolationspreading dynamicsthreshold models

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Area of Science:

  • Complex Systems Science
  • Network Science
  • Statistical Physics

Background:

  • Real-world systems rely on pivotal nodes (influencers) for integrity and function.
  • Influencers are defined by structural importance (connectivity) or dynamic impact (process influence).
  • Identifying optimal influencers is critical across diverse scientific and engineering disciplines.

Purpose of the Study:

  • To review recent advances in influencer identification from multiple perspectives.
  • To present state-of-the-art solutions for various influencer identification objectives.
  • To consolidate knowledge on finding nodes critical for network structure and dynamics.

Main Methods:

  • Surveying methods for the network dismantle problem (minimal node removal for breakdown).
  • Reviewing techniques for identifying nodes influencing global dynamics via continuous (e.g., independent cascading) and discontinuous (e.g., threshold) models.
  • Analyzing approaches from network science, statistical physics, and dynamical systems theory.

Main Results:

  • The review categorizes influencer identification strategies based on structural and dynamical criteria.
  • It highlights methods for pinpointing nodes essential for network connectivity and stability.
  • It details approaches for finding nodes that drive macroscopic changes in system dynamics.

Conclusions:

  • Influencer identification is a multifaceted problem with diverse solutions.
  • Understanding influencer roles is key to controlling and predicting complex system behavior.
  • Future research should integrate structural and dynamical perspectives for comprehensive influencer analysis.