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Related Concept Videos

Time-Series Graph00:54

Time-Series Graph

A time-series graph is a line graph with repeated measurements taken at successive intervals of time. It is also called a time series chart. To construct a time-series graph, one must look at both pieces of a paired data set. The horizontal axis is used to plot the time increments, and the vertical axis is used to plot the values of the variable that one is measuring. By using the axes in this way, each point on the graph will correspond to time and a measured quantity. The points on the graph...
Graphs of Two-Variable Functions01:27

Graphs of Two-Variable Functions

A weather map provides a practical example of a function of two variables. Across a wide region such as the United States, temperatures vary from one location to another. Each location can be identified by two geographic coordinates: longitude and latitude. Since a single temperature value is assigned to each coordinate pair, the situation can be represented mathematically as a function with two inputs and one output.In mathematical notation, longitude and latitude can be labeled as x and y,...
Graphs of Equations in Two Variables01:30

Graphs of Equations in Two Variables

An equation with two variables, typically written in the form y = f(x) or Ax + By = C, describes a relationship between quantities represented by x and y. Each solution to such an equation is an ordered pair (x, y) that satisfies the equation when substituted. These pairs can be represented graphically to understand the variables' relationship visually.A common technique for constructing the graph of a two-variable equation is to create a value table. Begin by choosing several values for the...
Graphs of Functions01:30

Graphs of Functions

Graphs of functions provide a visual representation of how output values change in response to varying inputs. Each point on the graph corresponds to an ordered pair, where the x-coordinate (independent variable) determines the horizontal position and the y-coordinate (dependent variable) determines the vertical position. Linear functions like y = x give a straight line, indicating a constant rate of change.Nonlinear functions display more complex behaviors. Even power functions generate...
Entropy Changes Accompanying Specific Processes01:21

Entropy Changes Accompanying Specific Processes

Entropy, a measure of disorder in a system, changes during phase transitions like freezing or boiling. At the transition temperature Ttrs, where two phases are in equilibrium, the phase transition is a reversible process. The entropy change can be calculated from a substance's enthalpy of transition using the equation ΔStrs = ΔtrsH /Ttrs.When a perfect gas expands isothermally from one volume to another, entropy increases logarithmically with volume. Conversely, isothermal compression results...
Woodward–Hoffmann Selection Rules and Microscopic Reversibility01:34

Woodward–Hoffmann Selection Rules and Microscopic Reversibility

Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are concerted pericyclic reactions that proceed via a cyclic transition state. These reactions are stereospecific and regioselective. The stereochemistry of the products depends on the symmetry characteristics of the interacting orbitals and the reaction conditions. Accordingly, pericyclic reactions are classified as either symmetry-allowed or symmetry-forbidden. Woodward and Hoffmann presented the selection criteria for...

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Related Experiment Video

Updated: Jun 8, 2026

A System for Tracking the Dynamics of Social Preference Behavior in Small Rodents
08:38

A System for Tracking the Dynamics of Social Preference Behavior in Small Rodents

Published on: November 21, 2019

Small-world behavior in time-varying graphs.

J Tang1, S Scellato, M Musolesi

  • 1Computer Laboratory, University of Cambridge, 15 J. J. Thomson Avenue, Cambridge CB3 0FD, United Kingdom.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2010
PubMed
Summary
This summary is machine-generated.

Complex networks change over time. This study introduces temporal paths and distances to define temporal small worlds, revealing small-world behavior in dynamic systems.

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Area of Science:

  • Network Science
  • Complex Systems Analysis
  • Temporal Dynamics

Background:

  • Standard static graph measures fail to capture the full dimensionality of fluctuating connections in complex networks.
  • Time-varying networks, such as those formed by mobile agents or social interactions, present unique analytical challenges.
  • Understanding the dynamic nature of network connections is crucial for various scientific domains.

Purpose of the Study:

  • To introduce novel concepts of temporal paths and temporal distance for analyzing time-varying graphs.
  • To define and identify 'temporal small world' characteristics in dynamic networks.
  • To explore the prevalence of small-world behavior in both synthetic and real-world time-varying systems.

Main Methods:

  • Development of definitions for temporal paths and temporal distance within time-varying graph frameworks.
  • Formulation of the 'temporal small world' concept based on temporal clustering and average temporal distance.
  • Application and analysis of these concepts to synthetic time-varying networks of mobile agents.
  • Investigation of temporal small-world properties in real-world social and biological time-varying systems.

Main Results:

  • The study successfully defines and applies temporal paths and distances to quantify network dynamics.
  • The proposed 'temporal small world' metric effectively characterizes networks with high temporal link clustering and short average temporal node distances.
  • Observed small-world behavior in both simulated mobile agent networks and empirical social/biological networks, confirming the model's applicability.

Conclusions:

  • Temporal paths and distances offer a more comprehensive approach to analyzing complex, dynamic networks than static measures.
  • The temporal small-world concept provides a valuable framework for understanding information diffusion and network resilience in time-varying systems.
  • This research highlights the importance of considering temporal dynamics in network science and its applications.