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Maximizing the quality index modularity has become one of the primary methods for identifying the clustering structure within a graph. As contemporary networks are not static but evolve over time, traditional static approaches can be inappropriate for specific tasks. In this work we pioneer the NP-hard problem of online dynamic modularity maximization. We… (More)

Maximizing the quality index <i>modularity</i> has become one of the primary methods for identifying the clustering structure within a graph. Since many contemporary networks are not static but evolve over time, traditional static approaches can be inappropriate for specific tasks. In this work, we pioneer the NP-hard problem of online dynamic modularity… (More)

We consider the distribution of the maximum M T of branching Brownian motion with time-inhomogeneous variance of the form σ 2 (t/T), where σ(·) is a strictly decreasing function. This corresponds to the study of the time-inhomogeneous Fisher–Kolmogorov-Petrovskii-Piskunov (FKPP) equation F t (x, t) = σ 2 (1 − t/T)F xx (x, t)/2 + g(F (x, t)), for appropriate… (More)

- Pascal Maillard
- 2013

We call a point process Z on R exp-1-stable if for every α, β ∈ R with e α + e β = 1, Z is equal in law to T α Z + T β Z ′ , where Z ′ is an independent copy of Z and T x is the translation by x. Such processes appear in the study of the extremal particles of branching Brownian motion and branching random walk and several authors have proven in that setting… (More)

J o u r n a l o f P r o b a b i l i t y Electron. Abstract We consider a system of N particles on the real line that evolves through iteration of the following steps: 1) every particle splits into two, 2) each particle jumps according to a prescribed displacement distribution supported on the positive reals and 3) only the N right-most particles are… (More)

Consider a d-ary rooted tree (d ≥ 3) where each edge e is assigned an i.i.d. (bounded) random variable X(e) of negative mean. Assign to each vertex v the sum S(v) of X(e) over all edges connecting v to the root, and assume that the maximum S * n of S(v) over all vertices v at distance n from the root tends to infinity (necessarily, linearly) as n tends to… (More)

- Pascal Maillard, Yueyun Hu
- 2012

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