191 citations · 607 across the 22 of their papers we have counts for
22 papers
Incidence and Laplacian matrices of wheel graphs and their inverses
Jerad Ipsen, Sudipta Mallik
It has been an open problem to find the Moore-Penrose inverses of the incidence, Laplacian, and signless Laplacian matrices of families of graphs except trees and unicyclic graphs.…
Nonlinearity-generated Resilience in Large Complex Systems
Sirio Belga Fedeli, Yan V Fyodorov, J. R. Ipsen
We consider a generic nonlinear extension of May's 1972 model by including all higher-order terms in the expansion around the chosen fixed point (placed at the origin) with random…
Consequences of Dale's law on the stability-complexity relationship of random neural networks
J. R. Ipsen, A. D. H. Peterson
In the study of randomly connected neural network dynamics there is a phase transition from a `simple' state with few equilibria to a `complex' state characterised by the number of…
The Laguerre Unitary Process
J. R. Ipsen
We define a new matrix-valued stochastic process with independent stationary increments from the Laguerre Unitary Ensemble, which in a certain sense may be considered a matrix gene…
A generalisation of the relation between zeros of the complex Kac polynomial and eigenvalues of truncated unitary matrices
Peter J. Forrester, Jesper R. Ipsen
The zeros of the random Laurent series , where each is an independent standard complex Gaussian, is known to correspond to the scaled eigenval…
Kac-Rice fixed point analysis for single- and multi-layered complex systems
J. R. Ipsen, P. J. Forrester
We present a null model for single- and multi-layered complex systems constructed using homogeneous and isotropic random Gaussian maps. By means of a Kac-Rice formalism, we show th…