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When analyzing beams under unsymmetrical loads, such as a train moving on a bridge, it is crucial to accurately determine the points of maximum stress and deflection. The process involves identifying the maximum deflection of the beam, which may not always occur at its midpoint due to the uneven distribution of the load.
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Numerous practical applications within engineering disciplines, such as telecommunications, necessitate optimizing power delivery to a connected load. This pursuit, however, entails inherent internal losses, which can either equal or exceed the power supplied to the load. The Thevenin equivalent circuit is helpful in finding the maximum power a linear circuit can deliver to a load. It is assumed in this context that the load resistance can be adjusted.
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The maximum power flow for lossy transmission lines is derived using ABCD parameters in phasor form. These parameters create a matrix relationship between the sending-end and receiving-end voltages and currents, allowing the determination of the receiving-end current. This relationship facilitates calculating the complex power delivered to the receiving end, from which real and reactive power components are derived.
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Related Experiment Video

Updated: Feb 15, 2026

Determining the Likelihood of Variant Pathogenicity Using Amino Acid-level Signal-to-Noise Analysis of Genetic Variation
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TreeTime: Maximum-likelihood phylodynamic analysis.

Pavel Sagulenko1, Vadim Puller1,2,3, Richard A Neher1,2,3

  • 1Max Planck Institute for Developmental Biology, Spemannstrasse 35, Tübingen 72076, Germany.

Virus Evolution
|January 18, 2018
PubMed
Summary
This summary is machine-generated.

Genomic mutations reveal pathogen evolution and spread. TreeTime, a new Python framework, efficiently analyzes large viral genome datasets for phylodynamics, overcoming limitations of traditional methods.

Keywords:
molecular clock phylogeniesphylodynamicspython

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Area of Science:

  • Genomics
  • Evolutionary Biology
  • Computational Biology

Background:

  • Genomic mutations track organismal evolution and spatiotemporal spread.
  • Phylodynamic analysis of viral pathogens is crucial for epidemiology.
  • Increasing genomic data strains traditional analysis methods.

Purpose of the Study:

  • To introduce TreeTime, a scalable Python framework for phylodynamic analysis.
  • To address the computational challenges posed by large genomic datasets.
  • To provide tools for inferring evolutionary history and epidemiological patterns.

Main Methods:

  • Developed TreeTime, a Python framework utilizing an approximate Maximum Likelihood approach.
  • Implemented linear scaling runtime for large datasets.
  • Integrated functionalities for ancestral state estimation, evolution model inference, tree rerooting, molecular clock phylogeny, and population size history estimation.

Main Results:

  • TreeTime demonstrates linear scalability with increasing dataset size.
  • The framework enables efficient estimation of key phylodynamic parameters.
  • Successfully addresses the limitations of traditional methods for large-scale genomic analysis.

Conclusions:

  • TreeTime offers an efficient and scalable solution for phylodynamic analysis of large genomic datasets.
  • The framework enhances our ability to understand the evolution and spread of rapidly evolving pathogens.
  • Facilitates more robust epidemiological insights from genomic data.