291 citations
- University of CambridgeGB72 papers
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10 papers · 1 filter
Sparse graphs: metrics and random models
Bela Bollobas, Oliver Riordan
Recently, Bollobás, Janson and Riordan introduced a family of random graph models producing inhomogeneous graphs with vertices and edges whose distribution is characteri…
Stability of graph communities across time scales
J. -C. Delvenne, S. N. Yaliraki, M. Barahona
The complexity of biological, social and engineering networks makes it desirable to find natural partitions into communities that can act as simplified descriptions and provide ins…
Popular difference sets
Tom Sanders
We provide further explanation of the significance of a construction in a recent paper of Wolf [Israel J. Math. 179 (2010), 253-278] in the context of the problem of finding large…
On an Auxiliary Function for Log-Density Estimation
Madeleine L. Cule, Lutz Duembgen
In this note we provide explicit expressions and expansions for a special function which appears in nonparametric estimation of log-densities. This function returns the integral of…
Error analysis of variational integrators of unconstrained Lagrangian systems
George W. Patrick, Charles Cuell
A complete error analysis of variational integrators is obtained, by blowing up the discrete variational principles, all of which have a singularity at zero time-step. Divisions by…
Augmented GARCH sequences: Dependence structure and asymptotics
Siegfried Hörmann
The augmented GARCH model is a unification of numerous extensions of the popular and widely used ARCH process. It was introduced by Duan and besides ordinary (linear) GARCH process…