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20082026
most citedAvoiding catastrophic failure in correlated networks of networks

292 citations

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Showing 2014Show all

6 papers · 1 filter

math.AP2014★ 49 cited

Global bifurcation for fractional -Laplacian and application

Leandro M. Del Pezzo, Alexander Quaas

We prove the existence of an unbounded branch of solutions to the non-linear non-local equation $$ (-Δ)^s_p u=λ|u|^{p-2}u + f(x,u,λ) \quad\text{in}\quad Ω,\quad u=0 \quad\text{in}\…

physics.soc-ph2014★ 292 cited

Avoiding catastrophic failure in correlated networks of networks

Saulo D. S. Reis, Yanqing Hu, Andrés Babino +4

Networks in nature do not act in isolation but instead exchange information, and depend on each other to function properly. An incipient theory of Networks of Networks have shown t…

math.MG2014★ 17 cited

Squares and their centers

Tamás Keleti, Dániel T. Nagy, Pablo Shmerkin

We study the relationship between the sizes of two sets when contains either the whole boundary, or the four vertices, of a square with axes-parallel…

math.DS2014★ 58 cited

Absolute continuity of self-similar measures, their projections and convolutions

Pablo Shmerkin, Boris Solomyak

We show that in many parametrized families of self-similar measures, their projections, and their convolutions, the set of parameters for which the measure fails to be absolutely c…

math.DS2014★ 15 cited

On the dimensions of a family of overlapping self-affine carpets

Jonathan Fraser, Pablo Shmerkin

We consider the dimensions of a family of self-affine sets related to the Bedford-McMullen carpets. In particular, we fix a Bedford-McMullen system and then randomise the translati…

math.CA2014★ 12 cited

Dynamics of the scenery flow and geometry of measures

Antti Käenmäki, Tuomas Sahlsten, Pablo Shmerkin

We employ the ergodic theoretic machinery of scenery flows to address classical geometric measure theoretic problems on Euclidean spaces. Our main results include a sharp version o…