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Controller configurations are crucial in a car's cruise control system because they manage speed over time to maintain a consistent pace regardless of road conditions, thereby meeting design goals. In traditional control systems, fixed-configuration design involves predetermined controller placement. System performance modifications are known as compensation.
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Electron configurations and orbital diagrams can be determined by applying the Aufbau principle (each added electron occupies the subshell of lowest energy available), Pauli exclusion principle (no two electrons can have the same set of four quantum numbers), and Hund’s rule of maximum multiplicity (whenever possible, electrons retain unpaired spins in degenerate orbitals).
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The alkali metal sodium (atomic number 11) has one more electron than the neon atom. This electron must go into the lowest-energy subshell available, the 3s orbital, giving a 1s22s22p63s1 configuration. The electrons occupying the outermost shell orbital(s) (highest value of n) are called valence electrons, and those occupying the inner shell orbitals are called core electrons. Since the core electron shells correspond to noble gas electron configurations, we can abbreviate electron...
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Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
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The stability of equilibrium configurations is an important concept in physics, engineering, and other related fields. In simple terms, it refers to the tendency of an object or system to return to its equilibrium position after being disturbed. The stability of an equilibrium configuration can be analyzed by considering the potential energy function of the system and examining its behavior near the equilibrium point.
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Construction of and efficient sampling from the simplicial configuration model.

Jean-Gabriel Young1, Giovanni Petri2, Francesco Vaccarino2,3

  • 1Département de Physique, de Génie Physique, et d'Optique, Université Laval, G1V 0A6 Québec (Québec), Canada.

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Summary

We introduce a simplicial configuration model to analyze complex systems. This model helps reveal organization beyond local interactions in real-world data.

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Area of Science:

  • Complex systems science
  • Network science
  • Computational topology

Background:

  • Simplicial complexes offer a richer description of complex systems by explicitly encoding multi-node interactions, surpassing traditional network models.
  • The analysis of complex systems necessitates robust null models for comparing empirical data and identifying underlying organizational principles.

Purpose of the Study:

  • To propose and implement an efficient null model for simplicial complexes, termed the simplicial configuration model.
  • To provide a method for assessing the significance of topological features in real-world systems.

Main Methods:

  • Development of a uniform Markov chain Monte Carlo sampler for the simplicial configuration model.
  • Application of the model to analyze the topology of three real-world systems using Betti numbers.

Main Results:

  • The proposed sampler is efficient and generates uniform samples from the simplicial configuration model.
  • Topological analysis using Betti numbers revealed significant organization beyond local interactions in two out of three empirical systems.

Conclusions:

  • The simplicial configuration model serves as a valuable tool for null hypothesis testing in the study of complex systems.
  • The findings suggest that multi-node interactions encoded in simplicial complexes can reveal non-local organizational structures in empirical data.