Submodularity of Infuence in Social Networks: From Local to Global

Social networks are often represented as directed graphs where the nodes are individuals and the edges indicate a form of social relationship. A simple way to model the diffusion of ideas, innovative behavior, or “word-of-mouth” effects on such a graph is to consider an increasing process of “infected” (or active) nodes: each node becomes infected once an activation function of the set of its infected neighbors crosses a certain threshold value. Such a model was introduced by Kempe, Kleinberg, and Tardos (KKT) in [KKT03, KKT05] where the authors also impose several natural assumptions: the threshold values are random and the activation functions are monotone and submodular. The monotonicity condition indicates that a node is more likely to become active if more of its neighbors are active, while the submodularity condition indicates that the marginal effect of each neighbor is decreasing when the set of active neighbors increases. For an initial set of active nodes S, let σ(S) denote the expected number of active nodes at termination. Here we prove a conjecture of KKT: we show that the function σ(S) is submodular under the assumptions above. We prove the same result for the expected value of any monotone, submodular function of the set of active nodes at termination. Roughly, our results demonstrate that “local” submodularity is preserved “globally” under this diffusion process. This is of natural computational interest, as many optimization problems have good approximation algorithms for submodular functions

Slow Emergence of Cooperation for Win-Stay Lose-Shift on Trees

We consider a group of agents on a graph who repeatedly play the prisoner’s dilemma game against their neighbors. The players adapt their actions to the past behavior of their opponents by applying the win-stay lose-shift strategy. On a finite connected graph, it is easy to see that the system learns to cooperate by converging to the all-cooperate state in a finite time. We analyze the rate of convergence in terms of the size and structure of the graph. Dyer et al. (2002) showed that the system converges rapidly on the cycle, but that it takes a time exponential in the size of the graph to converge to cooperation on the complete graph. We show that the emergence of cooperation is exponentially slow in some expander graphs. More surprisingly, we show that it is also exponentially slow in bounded-degree trees, where many other dynamics are known to converge rapidly

Incomplete Lineage Sorting: Consistent Phylogeny Estimation From Multiple Loci

We introduce a simple computationally efficient algorithm for reconstructing phylogenies from multiple gene trees in the presence of incomplete lineage sorting, that is, when the topology of the gene trees may differ from that of the species tree. We show that our technique is statistically consistent under standard stochastic assumptions, that is, it returns the correct tree given sufficiently many unlinked loci. We also show that it can tolerate moderate estimation errors

Learning Nonsingular Phylogenies and Hidden Markov Models

In this paper we study the problem of learning phylogenies and hidden Markov models. We call a Markov model nonsingular if all transition matrices have determinants bounded away from 0 (and 1). We highlight the role of the nonsingularity condition for the learning problem. Learning hidden Markov models without the nonsingularity condition is at least as hard as learning parity with noise, a well-known learning problem conjectured to be computationally hard. On the other hand, we give a polynomial-time algorithm for learning nonsingular phylogenies and hidden Markov models

Evolutionary Trees and the Ising Model on the Bethe Lattice: A Proof of Steel’s Conjecture

A major task of evolutionary biology is the reconstruction of phylogenetic trees from molecular data. The evolutionary model is given by a Markov chain on a tree. Given samples from the leaves of the Markov chain, the goal is to reconstruct the leaf-labelled tree. It is well known that in order to reconstruct a tree on n leaves, sample sequences of length Ω(log n) are needed. It was conjectured by Steel that for the CFN/Ising evolutionary model, if the mutation probability on all edges of the tree is less than p∗=(√2−1)/23/2 , then the tree can be recovered from sequences of length O(log n). The value p* is given by the transition point for the extremality of the free Gibbs measure for the Ising model on the binary tree. Steel’s conjecture was proven by the second author in the special case where the tree is “balanced.” The second author also proved that if all edges have mutation probability larger than p* then the length needed is n Ω(1). Here we show that Steel’s conjecture holds true for general trees by giving a reconstruction algorithm that recovers the tree from O(log n)-length sequences when the mutation probabilities are discretized and less than p*. Our proof and results demonstrate that extremality of the free Gibbs measure on the infinite binary tree, which has been studied before in probability, statistical physics and computer science, determines how distinguishable are Gibbs measures on finite binary trees

Robust Estimation of Latent Tree Graphical Models: Inferring Hidden States With Inexact Parameters

Latent tree graphical models are widely used in computational biology, signal and image processing, and network tomography. Here, we design a new efficient, estimation procedure for latent tree models, including Gaussian and discrete, reversible models, that significantly improves on previous sample requirement bounds. Our techniques are based on a new hidden state estimator that is robust to inaccuracies in estimated parameters. More precisely, we prove that latent tree models can be estimated with high probability in the so-called Kesten-Stigum regime with O(log2n) samples, where n is the number of nodes

Phase transormations involving residual stresses during gaseous nitriding of steel

Nitriding of steels is an important treatment in duplex hardening methods. This treatment is known in the art but some advances still need to be done in terms of residual stress understanding. Although residual stresses originate from volume micro-loading accompanying the precipitation of nitrides, questions about their in-depth distribution of a nitrided layer during the treatment are still a challenge. A chemico-thermo-micromechanical model has been developed on the volume change computation of secondary phase transformation. Supported by some experimental observations (TEM, X-ray analysis, Electron Probe Micro Analysis (EPMA), ...), this model gives some better understanding about nitriding. Residual stresses are mainly due to the precipitation of semi-coherent MN nitrides (M=Cr,V,Mo,. . . ). Moreover carbon, often not enough considered in the literature, is shown to be of importance in the process as it involves a second type of precipitation that is the transformation of carbides M23C6 and M7C3 into incoherent nitrides. The definition of the volume change of this transformation is a critical entry data of the mechanical modelling.We would like to thank Aubert & Duval and SAFRAN Group for supporting this study

Proton Radiation Belt Anisotropy as Seen by ICARE-NG Head-A

International audienceThe ICARE-NG instrument onboard the Argentinian satellite SAC-D detected much more protons during descending orbits (when latitude decreases) than for ascending orbits (increasing latitudes). In this paper we will investigate on the anisotropy seen by the ICARE-NG Head-A for protons in coincidence mode from Monte-Carlo simulations performed with GEANT4. Our simulations show that the difference in the fluxes observed during ascending and descending orbits comes from the fact that the instrument observed trapped protons or not on each point of the orbits as a result of the instrument and satellite orientations. In addition, we show in this paper that the measurements performed by ICARE-NG can be used in conjunction with our GEANT4 simulations to study the anisotropy of trapped protons, i.e. their distribution relative to their equatorial pitch-angle

Network delay inference from additive metrics

We use computational phylogenetic techniques to solve a central problem in inferential network monitoring. More precisely, we design a novel algorithm for multicast-based delay inference, that is, the problem of reconstructing delay characteristics of a network from end-to-end delay measurements on network paths. Our inference algorithm is based on additive metric techniques used in phylogenetics. It runs in polynomial time and requires a sample of size only poly(log n). We also show how to recover the topology of the routing tree

A Privacy-Preserving Contactless Transport Service for NFC Smartphones

International audienceThe development of NFC-enabled smartphones has paved the way to new applications such as mobile payment (m-payment) and mobile ticketing (m-ticketing). However, often the privacy of users of such services is either not taken into account or based on simple pseudonyms, which does not offer strong privacy properties such as the unlinkability of transactions and minimal information leakage. In this paper, we introduce a lightweight privacy-preserving contactless transport service that uses the SIM card as a secure element. Our implementation of this service uses a group signature protocol in which costly cryptographic operations are delegated to the mobile phone