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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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Maximum Size of Aggregate01:12

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The maximum size of aggregate is defined as the aperture of the sieve retaining 15 percent or more of the particles present in the aggregate sample. The aggregate's maximum size impacts the concrete's water requirement, workability, and strength. Larger aggregates reduce the surface area needing cement paste coverage, which can lower water needs, thereby allowing a decrease in the water-to-cement ratio when the desired workability and richness of the mix are to be maintained, which can...
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Polynomial division is an essential algebraic process to simplify expressions and solve equations. Just as numerical division separates a number into quotient and remainder, polynomial long division partitions a polynomial into simpler components; in this context, the dividend is the polynomial being divided, the divisor is the expression dividing it, and the result is expressed in terms of a quotient and a remainder.The division begins by arranging the dividend and divisor in standard...
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Consider a linear AC Thevenin equivalent circuit connected to a load impedance.
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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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Hierarchical and Programmable One-Pot Oligosaccharide Synthesis
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Divisive hierarchical maximum likelihood clustering.

Alok Sharma1,2,3, Yosvany López1,4, Tatsuhiko Tsunoda5,6,7

  • 1Laboratory for Medical Science Mathematics, RIKEN Center for Integrative Medical Sciences, Yokohama, Kanagawa, 230-0045, Japan.

BMC Bioinformatics
|January 4, 2018
PubMed
Summary
This summary is machine-generated.

A new divisive hierarchical clustering algorithm, DRAGON, offers computational efficiency comparable to agglomerative methods. It accurately clusters complex biological data, including cancer subtypes, outperforming existing approaches.

Keywords:
Divisive approachHierarchical clusteringMaximum likelihood

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Area of Science:

  • Bioinformatics
  • Computational Biology
  • Statistical Genetics

Background:

  • Biological data analysis is complex due to diverse data topologies.
  • Increasing data volumes necessitate efficient statistical methods for accurate analysis.
  • Hierarchical clustering is vital for analyzing complex biological data, such as in genome-wide association studies and multi-omics.

Purpose of the Study:

  • To develop a computationally efficient divisive hierarchical clustering method.
  • To create a method that rivals the performance of agglomerative clustering approaches.
  • To accurately cluster biological data with distinct topologies.

Main Methods:

  • Development of a novel divisive hierarchical clustering algorithm named DRAGON.
  • Validation of DRAGON using synthetic and real-world biological datasets.
  • Comparison of DRAGON's performance against standard clustering methods.

Main Results:

  • DRAGON demonstrated high clustering accuracy on mixed-lineage leukemia data across multiple dimensions.
  • The algorithm outperformed existing methods for 3-, 4-, and 5-dimensional acute leukemia data.
  • DRAGON achieved optimal performance on 2-dimensional mutation data.

Conclusions:

  • The proposed DRAGON algorithm provides a computationally efficient divisive hierarchical clustering solution.
  • DRAGON effectively clusters data exhibiting diverse topological structures.
  • A MATLAB implementation of DRAGON is available for research use.