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This is achieved by finding an empirical and theoretical connection between positive semidefinite matrices and certain metric space properties.
We use the heat equation to establish the Lipschitz continuity of Cheeger-harmonic functions in certain metric spaces.
The Camassa Holm equation is rich in geometric structures, it is completely integrable, bi-Hamiltonian, and it represents geodesics for a certain metric in the group of diffeomorphism.
The boundary and interface conditions lead to conservative schemes and strict and strong stability provided that certain metric conditions are met.
However, most of existing methods are designed as generic tools without considering particular features of the data under processing, such as the distance distribution when the data is embedded into a certain metric space.
Methods of analysis are presented which demonstrate the effects of applying various patterns on certain metric scores, the initial conclusion being that the two approaches are indeed mainly congruent.
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Spatial networks, also known as random geometric graphs, are random graphs with certain distance metric, in which each node is connected to some others within its neighborhood disc.
Finally, we discuss a general construction of certain complete metric spaces.
From the figure above, it is possible to have an insight about the probabilities of getting a certain global metric depending on the scheduler in use.
Traditional cache replacement algorithms use the historical information about content requests to decide which item to keep in the cache to maximize a certain performance metric (e.g., hit rate, the amount of saved bandwidth) [101].
Relying on similar threshold triggering algorithms which ask for a certain monitor metric for a specific interval/duration/breach time period, these policy/rule-based scaling solutions provide a simple and convenient means of customized resource scaling control depending on the applications' real-time monitor data.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com