Search results for "Nœud"
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Impact of the community structure on the dynamics of complex networks
2023
Networks are everywhere. We encounter them daily in our lives, through our social interactions, how we come up with decisions in our brain, to having phone calls, conducting financial transactions, and traveling from one place to another. Individual actions are influenced by their environment, which is, in turn, influenced by the network's topology. Notably, individuals may change their actions, ideas, or opinions to conform to the aspirations of a particular social group. In the same vein, the spread of a virus can take a certain course if the network's structure induces specific pathways for expansion. In such scenarios, communities substantially impact the evolution of the dynamics. They…
The Links-Gould invariants as generalizations of the Alexander polynomial
2016
In this thesis we focus on the connections that exist between two link invariants: first the Alexander-Conway invariant ∆ that was the first polynomial link invariant to be discovered, and one of the most thoroughly studied since alongside with the Jones polynomial, and on the other hand the family of Links-Gould invariants LGn,m that are quantum link invariants derived from super Hopf algebras Uqgl(n|m). We prove a case of the De Wit-Ishii-Links conjecture: in some cases we can recover powers of the Alexander polynomial as evaluations of the Links-Gould invariants. So the LG polynomials are generalizations of the Alexander invariant. Moreover we give evidence that these invariants should s…