114 citations · 220 across the 9 of their papers we have counts for
15 papers
Analytic relationship of relative synchronizability to network structure and motifs
Joseph T. Lizier, Frank Bauer, Fatihcan M. Atay +1
Synchronization phenomena on networks have attracted much attention in studies of neural, social, economic, and biological systems, yet we still lack a systematic understanding of…
Sharp Davies-Gaffney-Grigor'yan Lemma on Graphs
Frank Bauer, Bobo Hua, Shing-Tung Yau
In this note, we prove the sharp Davies-Gaffney-Grigor'yan lemma for minimal heat kernels on graphs.
Davies-Gaffney-Grigor'yan Lemma on Graphs
Frank Bauer, Bobo Hua, Shing-Tung Yau
We prove a variant of the Davies-Gaffney-Grigor'yan Lemma for the continuous time heat kernel on graphs. We use it together with the Li-Yau inequality to obtain strong heat kernel…
Li-Yau inequality on graphs
Frank Bauer, Paul Horn, Yong Lin +3
We prove the Li-Yau gradient estimate for the heat kernel on graphs. The only assumption is a variant of the curvature-dimension inequality, which is purely local, and can be consi…
On the spectrum of Laplacians on graphs
Frank Bauer, Bobo Hua, Matthias Keller
We study the -independence of spectra of Laplace operators on graphs arising from regular Dirichlet forms on discrete spaces. Here, a sufficient criterion is given solely by a u…
Cheeger inequalities for unbounded graph Laplacians
Frank Bauer, Matthias Keller, Radosław K. Wojciechowski
We use the concept of intrinsic metrics to give a new definition for an isoperimetric constant of a graph. We use this novel isoperimetric constant to prove a Cheeger-type estimate…
The dual Cheeger constant and spectra of infinite graphs
Frank Bauer, Bobo Hua, Juergen Jost
In this article we study the top of the spectrum of the normalized Laplace operator on infinite graphs. We introduce the dual Cheeger constant and show that it controls the top of…
Identifying influential spreaders and efficiently estimating infection numbers in epidemic models: a walk counting approach
Frank Bauer, Joseph T. Lizier
We introduce a new method to efficiently approximate the number of infections resulting from a given initially-infected node in a network of susceptible individuals. Our approach i…
Normalized graph Laplacians for directed graphs
Frank Bauer
We consider the normalized Laplace operator for directed graphs with positive and negative edge weights. This generalization of the normalized Laplace operator for undirected graph…
Ollivier-Ricci curvature and the spectrum of the normalized graph Laplace operator
Frank Bauer, Jürgen Jost, Shiping Liu
We prove the following estimate for the spectrum of the normalized Laplace operator on a finite graph , \begin{equation*}1- (1- k[t])^{\frac{1}{t}}\leq λ_1 \leq \cdots \leq…
Applying Lepskij-Balancing in Practice
Frank Bauer
In a stochastic noise setting the Lepskij balancing principle for choosing the regularization parameter in the regularization of inverse problems is depending on a parameter wh…
Parameter Choice by Fast Balancing
Frank Bauer
Choosing the regularization parameter for inverse problems is of major importance for the performance of the regularization method. We will introduce a fast version of the Lepskij…
Synchronized chaos in networks of simple units
Frank Bauer, Fatihcan M. Atay, Juergen Jost
We study synchronization of non-diffusively coupled map networks with arbitrary network topologies, where the connections between different units are, in general, not symmetric and…
Bipartite and neighborhood graphs and the spectrum of the normalized graph Laplacian
Frank Bauer, Jürgen Jost
We study the spectrum of the normalized Laplace operator of a connected graph . As is well known, the smallest nontrivial eigenvalue measures how difficult it is to decompose $Γ…
Regularization independent of the noise level: an analysis of quasi-optimality
Frank Bauer, Markus Reiss
The quasi-optimality criterion chooses the regularization parameter in inverse problems without taking into account the noise level. This rule works remarkably well in practice, al…