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Multimachine Stability

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Multimachine stability analysis is crucial for understanding the dynamics and stability of power systems with multiple synchronous machines. The objective is to solve the swing equations for a network of M machines connected to an N-bus power system.
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At the transition from prophase to metaphase, there is a reduction in cohesion along the chromosomal arms, resulting in the resolution of sister chromatids. However, residual cohesin connections remain to hold the sister chromatids together until the transition from metaphase to anaphase. The residual connection prevents any premature separation of sister chromatids, blocking the risks of aneuploidy within the daughter cells.
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Cohesin protein complexes are a molecular glue that holds two sister chromatids together. They play an important role both in mitosis and meiosis. In mitosis, all cohesin complexes present on the chromosomes are removed before the start of the anaphase stage.
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During meiosis, chromosomes occasionally separate improperly. This occurs due to failure of homologous chromosome separation during meiosis I or failed sister chromatid separation during meiosis II. In some species, notably plants, nondisjunction can result in an organism with an entire additional set of chromosomes, which is called polyploidy. In humans, nondisjunction can occur during male or female gametogenesis and the resulting gametes possess one too many or one too few chromosomes.
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Trans-inner Cell Mass Injection of Embryonic Stem Cells Leads to Higher Chimerism Rates
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Stable Chimeras and Independently Synchronizable Clusters.

Young Sul Cho1,2, Takashi Nishikawa1,3, Adilson E Motter1,3

  • 1Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208, USA.

Physical Review Letters
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Summary
This summary is machine-generated.

Network synchronization can form stable patterns based on network symmetries. This study introduces a theoretical framework to independently analyze cluster synchronization stability, enabling new methods for finding stable chimera states.

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Area of Science:

  • Complex systems
  • Network theory
  • Nonlinear dynamics

Background:

  • Cluster synchronization involves networks organizing into synchronized sets.
  • Network symmetries dictate stable synchronization patterns.
  • Chimera states represent complex network dynamics.

Purpose of the Study:

  • To establish a theoretical basis for dividing symmetry clusters into independently synchronizable sets.
  • To develop a new approach for identifying permanently stable chimera states.

Main Methods:

  • Developing a theoretical framework to decouple synchronization stability across different cluster sets.
  • Analyzing the relationship between symmetry, cluster stability, and chimera state formation.

Main Results:

  • Demonstrated that arbitrary symmetry cluster patterns can be divided into independently synchronizable sets.
  • Showcased a method to find stable chimera states by combining stable and unstable symmetry clusters.

Conclusions:

  • The proposed framework provides a theoretical foundation for understanding and controlling cluster synchronization.
  • This approach offers novel strategies for discovering and stabilizing complex network states like chimera states.