This book deals with averaging dynamics, a paradigmatic example of network based dynamics in multi-agent systems. The book presents all the fundamental results on linear averaging dynamics, proposing a unified and updated viewpoint of many models and convergence results scattered in the literature. Starting from the classical evolution of the powers of a fixed stochastic matrix, the text then considers more general evolutions of products of a sequence of stochastic matrices, either deterministic or randomized. The theory needed for a full understanding of the models is constructed without assuming any knowledge of Markov chains or Perron–Frobenius theory. Jointly with their analysis of the convergence of averaging dynamics, the authors derive the properties of stochastic matrices. These properties are related to the topological structure of the associated graph, which, in the book’s perspective, represents the communication between agents. Special attention is paid to how these properties scale as the network grows in size. Finally, the understanding of stochastic matrices is applied to the study of other problems in multi-agent coordination: averaging with stubborn agents and estimation from relative measurements. The dynamics described in the book find application in the study of opinion dynamics in social networks, of information fusion in sensor networks, and of the collective motion of animal groups and teams of unmanned vehicles. Introduction to Averaging Dynamics over Networks will be of material interest to researchers in systems and control studying coordinated or distributed control, networked systems or multiagent systems and to graduate students pursuing courses in these areas.
The almost invisible images of a hitherto unknown painter called Eusebius, who worked in San Vitale Ravenna and in Vivarium, are a gallery of portraits of his famous contemporaries such as Theodoric, Vitiges, Amalasunta and a visual commentary of Justinian's tyrannical behaviour. Living between two ages, without belonging to either, this solitary man represents the fullest embodiment of a type of cultural "hybridisation" that is well attested throughout history. Eusebius is a spiritual brother of those "hybrid" artists, who have left extraordinary examples of "grotesques" populated by fantastic beings. After having embodied for so long the unbiased tolerance which had been the core of his own life and those of his companions in Ravenna: that mixture of confidentiality, intelligence, pointed irony, fantasy, and – why not? – touch of madness which had helped him to navigate through the troubled waters of his age, always leaving at the margins the demons who haunted him.
In 1816 a violent literary quarrel engulfed Bourbon Restoration Italy. On one side the Romantics wanted an opening up of Italian culture towards Europe, and on the other the Classicists favoured an inward-looking Italy. Giacomo Leopardi wrote a Discourse of an Italian on Romantic Poetry aiming to contribute to the debate from a new perspective.
Even though the policy impact of Catholicism has increasingly been acknowledged, existing scholarship lacks a coherent view on its changing influence over time and in different political contexts. In this book, Fabio Bolzonar investigates the influence of Catholicism on developments in French social protection from World War II to the mid-2010s. He discusses the factors that have favoured or inhibited it and explores the hybridization between Catholic values and secular principles in the social engagement of Catholic actors in secular France. By doing so, this multidisciplinary study integrates current scholarship, which has given limited attention to the changing patterns of Catholic involvement in the social policy domain over a long period of time, and the renewed influence of Catholic values in secularized societies. Catholic mobilization has relocated from the political to the civil society sphere, making voluntary organizations and social movements, rather than political parties, the main channels for defending Catholic values in secular France. Rather than marginalizing Catholicism, this process has opened up new opportunities for Catholic actors and values to play a significant role in society and politics. Bolzonar identifies two divergent scenarios that define Catholic social engagement in contemporary France: either the strengthening of new forms of institutional collaboration between Catholic-inspired philanthropic organizations and public administrations in the interest of socially vulnerable citizens, or the emergence of new ideological conflicts on gender- and sexuality-related issues.
This book deals with averaging dynamics, a paradigmatic example of network based dynamics in multi-agent systems. The book presents all the fundamental results on linear averaging dynamics, proposing a unified and updated viewpoint of many models and convergence results scattered in the literature. Starting from the classical evolution of the powers of a fixed stochastic matrix, the text then considers more general evolutions of products of a sequence of stochastic matrices, either deterministic or randomized. The theory needed for a full understanding of the models is constructed without assuming any knowledge of Markov chains or Perron–Frobenius theory. Jointly with their analysis of the convergence of averaging dynamics, the authors derive the properties of stochastic matrices. These properties are related to the topological structure of the associated graph, which, in the book’s perspective, represents the communication between agents. Special attention is paid to how these properties scale as the network grows in size. Finally, the understanding of stochastic matrices is applied to the study of other problems in multi-agent coordination: averaging with stubborn agents and estimation from relative measurements. The dynamics described in the book find application in the study of opinion dynamics in social networks, of information fusion in sensor networks, and of the collective motion of animal groups and teams of unmanned vehicles. Introduction to Averaging Dynamics over Networks will be of material interest to researchers in systems and control studying coordinated or distributed control, networked systems or multiagent systems and to graduate students pursuing courses in these areas.
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