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Related Concept Videos

Probability Distributions01:32

Probability Distributions

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 The probability of a random variable x  is the likelihood of its occurrence. A probability distribution represents the probabilities of a random variable using a formula, graph, or table. There are two types of probability distribution– discrete probability distribution and continuous probability distribution.
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Thermodynamics: Activity Coefficient01:24

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Activity is the measure of the effective concentration of the species in solution. It can be expressed as the product of the molar concentration of the species and its activity coefficient. The activity coefficient is a dimensionless quantity and depends on the total ionic strength of the solution.
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Continuous-time systems have continuous input and output signals, with time measured continuously. These systems are generally defined by differential or algebraic equations. For instance, in an RC circuit, the relationship between input and output voltage is expressed through a differential equation derived from Ohm's law and the capacitor relation,
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Thermodynamics: Chemical Potential and Activity01:10

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The effective concentration of a species in a solution can be expressed precisely in terms of its activity. Activity considers the effect of electrolytes present in the vicinity of the species of interest and depends on the ionic strength of the solution. The activity of a species is expressed as the product of molar concentration and the activity coefficient of the species.
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System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
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Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
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Continuous-Time Discrete-Distribution Theory for Activity-Driven Networks.

Lorenzo Zino1, Alessandro Rizzo2, Maurizio Porfiri3

  • 1Dipartimento di Scienze Matematiche "G. L. Lagrange," Politecnico di Torino, 10129 Torino, Italy.

Physical Review Letters
|December 8, 2016
PubMed
Summary
This summary is machine-generated.

This study introduces a new continuous-time model for analyzing epidemic spreading in dynamic networks. The framework offers analytical predictions for disease onset and endemic equilibrium, improving upon discrete simulations.

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Area of Science:

  • Epidemiology
  • Network Science
  • Mathematical Modeling

Background:

  • Activity-driven networks are crucial for understanding epidemic dynamics.
  • Current models often rely on discrete-time simulations with continuous distributions, limiting analytical insights.
  • Analyzing epidemic spreading in time-varying networks presents significant challenges.

Purpose of the Study:

  • To develop a continuous-time, discrete-distribution framework for analytical treatment of epidemic spreading.
  • To enable accurate modeling from disease onset to endemic equilibrium.
  • To provide a foundation for short- and long-term epidemic predictions.

Main Methods:

  • Derivation of a nonlinear dynamical system in the thermodynamic limit.
  • Application of differential inclusions and adaptive estimation techniques.
  • Analysis of real-world case studies with varying phenomena and time scales.

Main Results:

  • A novel analytical framework for epidemic spreading in activity-driven networks.
  • Accurate modeling of epidemic dynamics from initiation to stable states.
  • Demonstrated utility through diverse real-world case studies.

Conclusions:

  • The proposed continuous-time framework offers a powerful analytical approach to epidemic spreading in dynamic networks.
  • This method enhances prediction capabilities for disease dynamics.
  • The framework is versatile, applicable to various epidemic scenarios and network structures.