Suchergebnisse

Abstract

[en]Convergence of a stochastic process is an intrinsic property quite relevant for its successful practical for example for the function optimization problem. Lyapunov functions are widely used as tools to prove convergence of optimization procedures. However, identifying a Lyapunov function for a specific stochastic process is a difficult and creative task. This work aims to provide a geometric explanation to convergence results and to state and identify conditions for the convergence of not exclusively optimization methods but any stochastic process. Basically, we relate the expected directions set of a stochastic process with the half-space of a conservative vector field, concepts defined along the text. After some reasonable conditions, it is possible to assure convergence when the expected direction resembles enough to some vector field. We translate two existent and useful convergence results into convergence of processes that resemble to particular conservative vector fields. This geometric point of view could make it easier to identify Lyapunov functions for new stochastic processes which we would like to prove its convergence ; This work is partially supported by the projects Crowd4SDG and Humane-AI-net, which have received funding from the European Union's Horizon 2020 research and innovation programme under grant agreements No. 872944 and No. 952026, respectively. This work is also partially supported by the project CI-SUSTAIN funded by the Spanish Ministry of Science and Innovation (PID2019-104156GB-I00). ; Peer reviewed

International audience ; We use US county-level data to estimate convergence rates for 22 individual states. We find significant heterogeneity. E.g., the California estimate is 19.9% and the New York estimate is 3.3%. Convergence rates are essentially uncorrelated with income levels.

This edited volume provides a heuristic analysis of the challenges facing regulators and media institutions. It explores the nature of the laws and regulations straining under the new technological realities, considers the changes already made to accommodate the new media landscape, and examines new directions and approaches to the regulation of convergent media technologies and media institutions.--[book cover]

Post-9/11 developments in the UK and Germany contrast. On the one hand, in the UK, as a consequence of the 'War on Terror', a group which had been promised participation in a multicultural society has been increasingly stigmatized and branded with 'otherness'. On the other hand, in Germany, groups that had previously been 'outside' as 'foreigners' are being selectively accepted into German society, but the groups which are excluded from this process (and even more branded with 'otherness') are notably the Muslims. These different trajectories led to different reactions: embitterment, disappointment and anger in the UK, and cynicism and resignation in Germany. An overall convergence of policies toward Islam is observable not only in Germany and the UK but throughout Europe. It seems to be more related to the construction of a collective European identity than to Islam itself.