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In concrete, the pore size distribution significantly influences the material's properties. Capillary pores, markedly larger than gel pores, form a vast network within partially hydrated cement paste, reducing the concrete's strength and increasing its permeability. This heightened permeability leads to a greater risk of damage from environmental factors like freeze-thaw cycles and chemical attacks, with the extent of vulnerability also being tied to the water-to-cement ratio.
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    This summary is machine-generated.

    This study introduces a new gene tree diameter to better understand the minimizing deep coalescence (MDC) approach. The new diameter provides a practical measure for reconciling gene and species trees, offering insights into phylogenetic inference.

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    Area of Science:

    • Phylogenetics
    • Computational Biology
    • Evolutionary Biology

    Background:

    • The minimizing deep coalescence (MDC) approach infers species trees from gene trees using deep coalescence cost.
    • Deep coalescence cost quantifies reconciliation between gene and species trees via leaf labeling.
    • Gene tree diameter is a key property influencing deep coalescence cost.

    Purpose of the Study:

    • Investigate the gene tree diameter's role in the MDC approach.
    • Address limitations of the infinite species tree assumption for gene tree diameter.
    • Introduce a practical, size-constrained gene tree diameter for phylogenetic analysis.

    Main Methods:

    • Defined a novel, size-constrained gene tree diameter.
    • Derived an exact formula for this new diameter.
    • Classified gene tree topologies yielding the maximum diameter.

    Main Results:

    • Proved the standard gene tree diameter is often infinite under unrealistic assumptions.
    • Developed an exact formula for the constrained gene tree diameter.
    • Derived formulas for the mean and variance of the constrained diameter.

    Conclusions:

    • The new gene tree diameter offers a practical metric for phylogenetic studies.
    • The derived formulas and classifications aid in understanding deep coalescence costs.
    • Comparative studies demonstrate the utility of the new diameter in phylogenetic inference.