Abstract:In , Robert Axelrod wondered in a highly influential paper "If people tend to become more alike in their beliefs, attitudes, and behavior when they interact, why do not all such di erences eventually disappear?" Axelrod's question highlighted an ongoing quest for formal theoretical answers joined by researchers from a wide range of disciplines. Numerous models have been developed to understand why and under what conditions diversity in beliefs, attitudes and behavior can co-exist with the fact that very o en in interactions, social influence reduces di erences between people. Reviewing three prominent approaches, we discuss the theoretical ingredients that researchers added to classic models of social influence as well as their implications. Then, we propose two main frontiers for future research. First, there is urgent need for more theoretical work comparing, relating and integrating alternative models. Second, the field su ers from a strong imbalance between a proliferation of theoretical studies and a dearth of empirical work. More empirical work is needed testing and underpinning micro-level assumptions about social influence as well as macro-level predictions. In conclusion, we discuss major roadblocks that need to be overcome to achieve progress on each frontier. We also propose that a new generation of empirically-based computational social influence models can make unique contributions for understanding key societal challenges, like the possible e ects of social media on societal polarization.

Let $Y$ be a Gaussian vector whose components are independent with a common unknown variance. We consider the problem of estimating the mean $\mu$ of $Y$ by model selection. More precisely, we start with a collection $\mathcal{S}=\{S_m,m\in\mathcal{M}\}$ of linear subspaces of $\mathbb{R}^n$ and associate to each of these the least-squares estimator of $\mu$ on $S_m$. Then, we use a data driven penalized criterion in order to select one estimator among these. Our first objective is to analyze the performance of estimators associated to classical criteria such as FPE, AIC, BIC and AMDL. Our second objective is to propose better penalties that are versatile enough to take into account both the complexity of the collection $\mathcal{S}$ and the sample size. Then we apply those to solve various statistical problems such as variable selection, change point detections and signal estimation among others. Our results are based on a nonasymptotic risk bound with respect to the Euclidean loss for the selected estimator. Some analogous results are also established for the Kullback loss.Comment: Published in at http://dx.doi.org/10.1214/07-AOS573 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

The authors propose an individual-based model of innovation diffusion and explore its main dynamical properties. In the model, individuals assign an a priori social value to an innovation which evolves during their interactions with the "relative agreement" influence model. This model offers the possibility of including a minority of "extremists" with extreme and very definite opinions. Individuals who give a high social value to the innovation tend to look for information that allows them to evaluate more precisely the individual benefit of adoption. If the social value they assign is low, they neither consider the information nor transmit it. The main finding is that innovations with high social value and low individual benefit have a greater chance of succeeding than innovations with low social value and high individual benefit. Moreover, in some cases, a minority of extremists can have a very important impact on the propagation by polarizing the social value.

Summary 1.Many cultivated species can escape from fields and colonize seminatural habitats as feral populations. Of these, feral oilseed rape is a widespread feature of field margins and roadside verges. Although considered in several studies, the general processes leading to the escape and persistence of feral oilseed rape are still poorly known. Notably, it remains unclear whether these annuals form transient populations resulting mainly from seed immigration (either from neighbouring fields or during seed transport), or whether they show real ability to persist (either through self-recruitment or seed banks). 2. We conducted a 4-year large-scale study of factors involved in the presence of feral oilseed rape populations in a typical open-field area of France. The results were subjected to statistical methods suitable for analysing large data sets, based on a regression approach. We subsequently addressed the relative contribution of the ecological processes identified as being involved in the presence of feral populations. 3. Many feral oilseed rape populations resulted from seed immigration from neighbouring fields (about 35-40% of the observed feral populations). Immigration occurred at harvest time rather than at sowing. Around 15% of such populations were attributed to immigration through seed transport. 4. The other half resulted from processes of persistence, mainly through persistent seed banks (35-40% of the observed feral populations). This was all the more unexpected because seed banks have not yet been documented on road verges (despite being frequent within fields). Local recruitment was rare, accounting for no more than 10% of the feral populations. 5. Synthesis and applications . Understanding the dynamics of feral oilseed rape populations is crucial for evaluating gene flow over an agro-ecosystem. Our results show that, while many feral populations do come from annual seed dispersal, a significant number also result from seeds stored in the soil for several years. In the current context of coexistence and management of transgenic with non-transgenic crops, feral persistence and, especially, the seed bank contribution to the dynamics of feral populations need to be considered seriously. The latter, combined with selfrecruitment, indicates a high potential for the persistence of transgenes and the possible emergence of gene-stacking.

Abstract:We add a rejection mechanism into a 2D bounded confidence (BC) model. The principle is that one shifts away from a close attitude of one's interlocutor, when there is a strong disagreement on the other attitude. The model shows metastable clusters, which maintain themselves through opposite influences of competitor clusters. Our analysis and first experiments support the hypothesis that the number of clusters grows linearly with the inverse of the uncertainty, whereas this growth is quadratic in the BC model.