Dynamics of directed graphs: the world-wide Web

We introduce and simulate a growth model of the world-wide Web based on the dynamics of outgoing links that is motivated by the conduct of the agents in the real Web to update outgoing links (re)directing them towards constantly changing selected nodes. Emergent statistical correlation between the distributions of outgoing and incoming links is a key feature of the dynamics of the Web. The growth phase is characterized by temporal fractal structures which are manifested in the hierarchical organization of links. We obtain quantitative agreement with the recent empirical data in the real Web for the distributions of in- and out-links and for the size of connected component. In a fully grown network of $N$ nodes we study the structure of connected clusters of nodes that are accessible along outgoing links from a randomly selected node. The distributions of size and depth of the connected clusters with a giant component exhibit supercritical behavior. By decreasing the control parameter---average fraction $\beta$ of updated and added links per time step---towards $\beta_c(N) < 10$ the Web can resume a critical structure with no giant component in it. We find a different universality class when the updates of links are not allowed, i.e., for $\beta \equiv 0$, corresponding to the network of science citations.Comment: Revtex, 4 PostScript figures, small changes in the tex

Shame and Guilt in Lancashire: Enforcing Piece Rate Contracts

The ratchet effect undermines firms' ability to pay workers a steady piece rate. Using examples from the nineteenth-century British textile industry, this paper studies the different strategies firms and workers used to enforce piece rates. The strategies depended upon the emotional responses of workers, especially their relationship with their co-workers and with their employers. Following Lazear (1995), I argue that external or shame-based sanctions were prevalent in communities where workers showed indifference between the welfare of their co-workers and that of their bosses. In these cases, blacklists enforced the piece rate. Where workers felt more guilt about the welfare of their coworkers, internal sanctions were common. In guilt cultures, profit-sharing schemes enforced the established piece rate. En général, les employeurs et les employés ont de la difficulté à0501ntenir un niveau de paiement stable quand le paiement est à la pièce. En citant des exemples de l'industrie du textile britannique du 19e siècle, cet article vise à examiner les différentes approches que les acteurs ont utilisées afin de garder le niveau de paiement. Les stratégies adoptées ont dépendu des réponses émotionnelles des travailleurs et surtout de leurs relations avec leurs homologues et leurs patrons. Suivant le modèle de Lazear (1995), je suggère que les sanctions externes étaient privilégiées dans une culture de honte où les travailleurs étaient indifférents à l'égard du bien-être de leurs homologues et de celui de leurs patrons. Dans ces cultures, les acteurs ont utilisé les listes pour protéger la méthode de paiement. Là où les travailleurs ont valorisé davantage leurs relations avec leurs homologues,c'est-à-dire une culture de culpabilité, les sanctions internes étaient utilisées. Dans cette culture, un système de partage des profits était établi afin de garder la méthode de paiement.Methods of pay, piece rates, profit-sharing, British economic history, Méthodes de paiement, paiement à la pièce, partage des profits, hisoire économique britannique

When Piece Rates Work: More Lessons from the Cotton Mills

Workers paid by the piece should in principle cooperate with new techniques that increase their output. In practice, however, firms seem unable to keep piece rates fixed, and when they cut rates workers often respond by restricting output. This paper investigates a case where in fact firms abstained from cutting rates and workers refrained from reducing effort. In Lancashire cotton spinning workers and firms negotiated piece rate lists which fixed standard rates of pay. Both parties had incentives to keep at bay the forces of competition. The lists gave workers a share in the gains of technical change, and they allowed firms to reap the benefits of regional specialisation. The lists were enforced by community standards. Les travailleurs payés à la pièce devraient en principe coopérer avec l'avènement de nouvelles technologies qui augmentent leur production. En pratique toutefois, les firmes semblent incapables de conserver un taux à la pièce fixe et quand elles coupent les taux, les travailleurs répondent souvent en restreignant leur production. Ce texte examine un cas où dans les faits les firmes se sont abstenues de couper les taux et les travailleurs eux, se sont abstenus de réduire leurs efforts. Dans le Lancashire, les ouvriers des filatures de coton et les firmes ont négociés des listes de taux à la pièce qui fixait les taux standards à payer. Les deux parties trouvaient leur avantage à tenir en échec les forces de la compétition. Les listes donnaient aux travailleurs un profit sur les changements technologiques et elles permettaient aux firmes de récolter les bénéfices de la spécialisation régionale. Les listes étaient0501ntenues selon les standards des communautés du Lancashire.Piece rate; Regional specialisation; Technical change, Taux ;a la pièce ; Spécialisation régionale ; Changements technologiques

Long Trend Dynamics in Social Media

A main characteristic of social media is that its diverse content, copiously generated by both standard outlets and general users, constantly competes for the scarce attention of large audiences. Out of this flood of information some topics manage to get enough attention to become the most popular ones and thus to be prominently displayed as trends. Equally important, some of these trends persist long enough so as to shape part of the social agenda. How this happens is the focus of this paper. By introducing a stochastic dynamical model that takes into account the user's repeated involvement with given topics, we can predict the distribution of trend durations as well as the thresholds in popularity that lead to their emergence within social media. Detailed measurements of datasets from Twitter confirm the validity of the model and its predictions