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Related Concept Videos

State Space Representation01:27

State Space Representation

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
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...
Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
Sequence Networks of Rotating Machines01:24

Sequence Networks of Rotating Machines

A Y-connected synchronous generator, grounded through a neutral impedance, is designed to produce balanced internal phase voltages with only positive-sequence components. The generator's sequence networks include a source voltage that is exclusively in the positive-sequence network. The sequence components of line-to-ground voltages at the generator terminals illustrate this configuration.
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Related Experiment Video

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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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Published on: December 7, 2021

Characterizing global evolutions of complex systems via intermediate network representations.

Koji Iwayama1, Yoshito Hirata, Kohske Takahashi

  • 1FIRST, Aihara Innovative Mathematical Modelling Project, JST, 4-6-1 Komaba, Meguro-ku, Tokyo, Japan. koji@sat.t.u-tokyo.ac.jp

Scientific Reports
|May 29, 2012
PubMed
Summary

We developed a new method to visualize how interactions change over time in complex systems. This approach reveals patterns like the daily cycles in financial markets and brain activity.

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Area of Science:

  • Complex Systems Science
  • Data Visualization
  • Network Analysis

Background:

  • Modern measurement techniques allow simultaneous observation of multiple time series.
  • Understanding interactions within complex systems is crucial but challenging.
  • Few methods exist to describe global changes in interactions over time.

Purpose of the Study:

  • To propose a novel approach for visualizing the temporal evolution of global interaction changes in complex systems.
  • To develop a method applicable to diverse fields, including finance and neuroscience.

Main Methods:

  • A two-step approach involving the construction of a meta-time series of networks.
  • Analysis and visualization of the meta-time series using distance and recurrence plots.
  • Intermediate network representations to capture dynamic interactions.

Main Results:

  • Successfully visualized time-evolution of global interaction changes.
  • Identified half-a-day periodicity in foreign exchange markets.
  • Revealed a singular functional network in the brain associated with perceptual alternations.

Conclusions:

  • The proposed two-step method effectively visualizes dynamic interaction changes in complex systems.
  • Demonstrated the utility of the approach in analyzing financial markets and neural activity.
  • Offers a new tool for understanding complex system dynamics.