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Circuit Terminology

Circuit Terminology

An electrical network is a system composed of interconnected elements, such as resistors, capacitors, inductors, and voltage or current sources. Unlike a circuit, an electrical network does not necessarily form a closed path. In other words, while all circuits can be considered networks due to their interconnected nature, not every network qualifies as a circuit.
A circuit, on the other hand, is also an interconnected system of electrical elements but must contain one or more closed paths.

Network Function of a Circuit

Network Function of a Circuit

Frequency response analysis in electrical circuits provides vital insights into a circuit's behavior as the frequency of the input signal changes. The transfer function, a mathematical tool, is instrumental in understanding this behavior. It defines the relationship between phasor output and input and comes in four types: voltage gain, current gain, transfer impedance, and transfer admittance. The critical components of the transfer function are the poles and zeros.

Block Diagram Reduction

Block Diagram Reduction

The process of deriving the transfer function of a control system often involves reducing its block diagram to a single block. This simplification can be achieved through a series of strategic operations, including relocating branch points and comparators. These operations preserve the overall function of the system while allowing for easier manipulation and combination of blocks.
The first step in this process is the identification and relocation of a branch point. A branch point, where a...

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Related Experiment Video

Updated: May 30, 2026

Modeling the Functional Network for Spatial Navigation in the Human Brain

Modeling the Functional Network for Spatial Navigation in the Human Brain

Published on: October 13, 2023

Brain network analysis: separating cost from topology using cost-integration.

Cedric E Ginestet¹, Thomas E Nichols, Ed T Bullmore

¹Department of Neuroimaging, Institute of Psychiatry, King's College London, London, United Kingdom. cedric.ginestet@kcl.ac.uk

|August 11, 2011

Summary

This summary is machine-generated.

Brain network analysis is improved by cost-integrated topological metrics, which disentangle wiring cost from network topology. This method is more statistically principled than using weighted metrics alone for comparing brain networks.

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Published on: May 7, 2014

Area of Science:

Neuroscience
Network Science
Graph Theory

Background:

Comparing brain networks across populations is challenging due to topology's dependence on wiring cost.
Existing methods lack a statistically principled approach for brain network analysis.
Wiring cost, defined as the number of edges, influences graph topology.

Purpose of the Study:

To evaluate the benefits and limitations of cost-integrated topological metrics for brain network analysis.
To develop a statistically sound method for comparing weighted undirected graphs, focusing on global efficiency.
To disentangle differences in topology from differences in wiring cost.

Main Methods:

Evaluation of cost-integrated topological metrics for comparing populations of weighted undirected graphs.
Analysis focused on global efficiency and its behavior under cost integration.
Development of a Monte Carlo method for approximating cost-integrated topological measures.

Main Results:

Integrating topological measures over cost is equivalent to controlling for monotonic transformations of graph weights.
Cost-integration effectively isolates topological differences from variations in wiring cost.
Weighted versions of topological metrics, like global efficiency, are often invalid for this purpose, potentially equating to comparing weighted costs.

Conclusions:

Cost-integration offers a statistically principled approach to brain network comparison, disentangling topology from wiring cost.
Recommend reporting both weighted costs and cost-integrated topological measures across different cost distributions.
Limitations include potential issues with zero weights, rank multiplicities, and masking subtle cost-dependent differences.