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Related Concept Videos

Hückel's Rule Diagram of π MOs: Frost Circle01:08

Hückel's Rule Diagram of π MOs: Frost Circle

The Frost circle or the inscribed polygon method is a graphical method for determining the relative energies of π molecular orbitals (MOs) for planar, fully conjugated, and monocyclic compounds. This method was first described by A. A. Frost and Boris Musulin in 1953.
A Frost circle is constructed by drawing a polygon whose number of edges is equal to the number of carbons of the given cyclic system, with one of the vertices pointing down. Then, a circle is drawn enclosing the polygon so that...
Vector Algebra: Graphical Method01:10

Vector Algebra: Graphical Method

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Equivalent Resistance01:16

Equivalent Resistance

In circuit analysis, situations often arise where resistors are neither in series nor parallel configurations. To tackle such scenarios, three-terminal equivalent networks like the wye (Y) (Figure 1 (a)) or tee (T) and delta (Δ) (Figure 1 (b)) or pi (π) networks come into play. These networks offer versatile solutions and are frequently encountered in various applications, including three-phase electrical systems, electrical filters, and matching networks.
Norton Equivalent Circuits01:16

Norton Equivalent Circuits

Norton's theorem is a fundamental concept in the field of electrical engineering that allows for the simplification of complex AC circuits. The theorem states that any two-terminal linear network can be replaced with an equivalent circuit that consists of an impedance, which is parallel with a constant current source. Figure 1 shows the AC circuit portioned into two parts: Circuit A and Circuit B, while Figure 2 depicts the circuit obtained by replacing Circuit A by its Norton equivalent...
Network Function of a Circuit01:25

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.
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Updated: Jul 15, 2026

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Comparison of Orchard Networks Using Their Extended μ-Representation.

Gabriel Cardona, Joan Carles Pons, Gerard Ribas

    IEEE/ACM Transactions on Computational Biology and Bioinformatics
    |February 1, 2024
    PubMed
    Summary

    This study introduces an extended representation for phylogenetic networks, enhancing their analysis. This new method efficiently distinguishes orchard networks and defines a computable metric for their comparison.

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    Area of Science:

    • Computational Biology
    • Evolutionary Biology
    • Network Theory

    Background:

    • Phylogenetic trees are well-studied for evolutionary history, but modeling reticulation events requires more complex phylogenetic networks.
    • Comparing phylogenetic networks is computationally challenging compared to phylogenetic trees.
    • Existing methods like the μ-representation efficiently classify tree-child networks by counting paths to leaves.

    Purpose of the Study:

    • To introduce an extended μ-representation for phylogenetic networks that includes paths to reticulation nodes.
    • To enable the distinction and metric-based comparison of orchard networks.
    • To explore the computational feasibility of this representation for biologically significant network classes.

    Main Methods:

    • Developed an extended μ-representation by incorporating path counts to reticulation nodes.
    • Applied this representation to analyze orchard networks.
    • Defined and computed a metric on the space of orchard networks.

    Main Results:

    • The extended μ-representation successfully distinguishes between different orchard networks.
    • A novel, efficiently computable metric for orchard networks was established.
    • The study highlights the potential of this representation for generic network classes.

    Conclusions:

    • The extended μ-representation offers a powerful tool for analyzing and comparing phylogenetic networks, particularly orchard networks.
    • This approach provides a foundation for metric-based evolutionary network analysis.
    • The findings suggest broader applicability for complex phylogenetic network structures.