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User-based algorithms produce smaller matrices when the number of users is lower than the number of items and larger matrices when the number of users exceeds the number of items.
We estimate the asymptotics of spherical integrals of real symmetric or Hermitian matrices when the rank of one matrix is much smaller than its dimension.
We show that they can be used very effectively to obtain the dominant eigenvectors of large sparse matrices when the corresponding eigenvalues are known, and provide the relevant theory as well.
Let A(p) be a given (n×n) interval parametric matrix (the set of all (n×n) parametric matrices when the m-dimensional parameter vector p varies within a given interval vector p) whose entries depend affine linearly on p. Also, let L denote the set of all real eigenvalues of the bundle (A(p),B(p)).
Mantel tests are used to test for correlation between distance matrices when the underlying probability distribution of the test statistic is unknown and when dependence is present.
In biological words and in the stochastic context, this is the set of vectors of expected pattern frequencies for mixtures of trees evolving under the model (not necessarily the same tree topology in the mixture, and not necessarily the same transition matrices when the tree topologies coincide).
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"It's like taking the red pill," the artist Kacey Wong said, alluding to the moment in "The Matrix" when the protagonist uncovers the reality underlying his day-to-day life.
To accomplish this, drug is mixed with a polymer powder that forms a solid matrix when the tablet is compressed by a tablet machine.
The problem of particular interest is designing the secondary channel matrix, when the primary channel matrix is fixed.
The B4C powders fully interact with Ti matrix when the energy input increases.
However, ZnO NPs react strongly with the silica matrix when the nanocomposites are annealed at temperatures above 700 °C.
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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