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- Aurelien Decelle, Florent Krzakala, Cristopher Moore, Lenka Zdeborová
- Physical review. E, Statistical, nonlinear, and…
- 2011

In this paper we extend our previous work on the stochastic block model, a commonly used generative model for social and biological networks, and the problem of inferring functional groups or communities from the topology of the network. We use the cavity method of statistical physics to obtain an asymptotically exact analysis of the phase diagram. We… (More)

- Aurelien Decelle, Florent Krzakala, Cristopher Moore, Lenka Zdeborová
- Physical review letters
- 2011

We present an asymptotically exact analysis of the problem of detecting communities in sparse random networks generated by stochastic block models. Using the cavity method of statistical physics and its relationship to belief propagation, we unveil a phase transition from a regime where we can infer the correct group assignments of the nodes to one where… (More)

We present an asymptotically exact analysis of the problem of detecting communities in sparse random networks. Our results are also applicable to detection of functional modules, partitions, and colorings in noisy planted models. Using a cavity method analysis, we unveil a phase transition from a region where the original group assignment is undetectable to… (More)

- Michele Castellana, Aurélien Decelle, Silvio Franz, Marc Mézard, Giorgio Parisi
- Physical review letters
- 2010

We introduce a random energy model on a hierarchical lattice where the interaction strength between variables is a decreasing function of their mutual hierarchical distance, making it a non-mean-field model. Through small coupling series expansion and a direct numerical solution of the model, we provide evidence for a spin-glass condensation transition… (More)

- Aurélien Decelle, Federico Ricci-Tersenghi
- Physical review letters
- 2014

In this Letter we propose a new method to infer the topology of the interaction network in pairwise models with Ising variables. By using the pseudolikelihood method (PLM) at high temperature, it is generally possible to distinguish between zero and nonzero couplings because a clear gap separate the two groups. However at lower temperatures the PLM is much… (More)

- Lenka Zdeborová, Aurélien Decelle, Michael Chertkov
- Physical review. E, Statistical, nonlinear, and…
- 2009

We use a power grid model with M generators and N consumption units to optimize the grid and its control. Each consumer demand is drawn from a predefined finite-size-support distribution, thus simulating the instantaneous load fluctuations. Each generator has a maximum power capability. A generator is not overloaded if the sum of the loads of consumers… (More)

- Aurélien Decelle, Federico Ricci-Tersenghi
- Physical review. E
- 2016

In this work we explain how to properly use mean-field methods to solve the inverse Ising problem when the phase space is clustered, that is, many states are present. The clustering of the phase space can occur for many reasons, e.g., when a system undergoes a phase transition, but also when data are collected in different regimes (e.g., quiescent and… (More)

- Aurélien Decelle
- 2011

- Aurélien Decelle, Pan Zhang
- Physical review. E, Statistical, nonlinear, and…
- 2015

In this paper we study the inference of the kinetic Ising model on sparse graphs by the decimation method. The decimation method, which was first proposed in Decelle and Ricci-Tersenghi [Phys. Rev. Lett. 112, 070603 (2014)] for the static inverse Ising problem, tries to recover the topology of the inferred system by setting the weakest couplings to zero… (More)

- Aurelien Decelle, Janina Hüttel, Alaa Saade, Cristopher Moore
- ArXiv
- 2014

These are notes from the lecture of Cristopher Moore given at the autumn school