2,585 research outputs found
Dirichlet-to-Robin matrix on networks
In this work, we de ne the Dirichlet{to{Robin matrix associated with a Schr odinger
type matrix on general networks, and we prove that it satis es the alternating
property which is essential to characterize those matrices that can be the response
matrices of a network. We end with some examples of the sign pattern behavior of
the alternating paths.Postprint (author's final draft
Variational Bayes model averaging for graphon functions and motif frequencies inference in W-graph models
W-graph refers to a general class of random graph models that can be seen as
a random graph limit. It is characterized by both its graphon function and its
motif frequencies. In this paper, relying on an existing variational Bayes
algorithm for the stochastic block models along with the corresponding weights
for model averaging, we derive an estimate of the graphon function as an
average of stochastic block models with increasing number of blocks. In the
same framework, we derive the variational posterior frequency of any motif. A
simulation study and an illustration on a social network complete our work
Some remarks on the Krein--von Neumann extension of different Laplacians
We discuss the Krein--von Neumann extensions of three Laplacian-type
operators -- on discrete graphs, quantum graphs, and domains. In passing we
present a class of one-dimensional elliptic operators such that for any infinitely many elements of the class have -dimensional null
space.Comment: 13 page
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