Multicolored Dynamos on Toroidal Meshes

Detecting on a graph the presence of the minimum number of nodes (target set) that will be able to "activate" a prescribed number of vertices in the graph is called the target set selection problem (TSS) proposed by Kempe, Kleinberg, and Tardos. In TSS's settings, nodes have two possible states (active or non-active) and the threshold triggering the activation of a node is given by the number of its active neighbors. Dealing with fault tolerance in a majority based system the two possible states are used to denote faulty or non-faulty nodes, and the threshold is given by the state of the majority of neighbors. Here, the major effort was in determining the distribution of initial faults leading the entire system to a faulty behavior. Such an activation pattern, also known as dynamic monopoly (or shortly dynamo), was introduced by Peleg in 1996. In this paper we extend the TSS problem's settings by representing nodes' states with a "multicolored" set. The extended version of the problem can be described as follows: let G be a simple connected graph where every node is assigned a color from a finite ordered set C = {1, . . ., k} of colors. At each local time step, each node can recolor itself, depending on the local configurations, with the color held by the majority of its neighbors. Given G, we study the initial distributions of colors leading the system to a k monochromatic configuration in toroidal meshes, focusing on the minimum number of initial k-colored nodes. We find upper and lower bounds to the size of a dynamo, and then special classes of dynamos, outlined by means of a new approach based on recoloring patterns, are characterized

Dynamic Monopolies in Colored Tori

The {\em information diffusion} has been modeled as the spread of an information within a group through a process of social influence, where the diffusion is driven by the so called {\em influential network}. Such a process, which has been intensively studied under the name of {\em viral marketing}, has the goal to select an initial good set of individuals that will promote a new idea (or message) by spreading the "rumor" within the entire social network through the word-of-mouth. Several studies used the {\em linear threshold model} where the group is represented by a graph, nodes have two possible states (active, non-active), and the threshold triggering the adoption (activation) of a new idea to a node is given by the number of the active neighbors. The problem of detecting in a graph the presence of the minimal number of nodes that will be able to activate the entire network is called {\em target set selection} (TSS). In this paper we extend TSS by allowing nodes to have more than two colors. The multicolored version of the TSS can be described as follows: let $G$ be a torus where every node is assigned a color from a finite set of colors. At each local time step, each node can recolor itself, depending on the local configurations, with the color held by the majority of its neighbors. We study the initial distributions of colors leading the system to a monochromatic configuration of color $k$, focusing on the minimum number of initial $k$-colored nodes. We conclude the paper by providing the time complexity to achieve the monochromatic configuration

Rooting opinions in the minds: a cognitive model and a formal account of opinions and their dynamics

The study of opinions, their formation and change, is one of the defining topics addressed by social psychology, but in recent years other disciplines, like computer science and complexity, have tried to deal with this issue. Despite the flourishing of different models and theories in both fields, several key questions still remain unanswered. The understanding of how opinions change and the way they are affected by social influence are challenging issues requiring a thorough analysis of opinion per se but also of the way in which they travel between agents' minds and are modulated by these exchanges. To account for the two-faceted nature of opinions, which are mental entities undergoing complex social processes, we outline a preliminary model in which a cognitive theory of opinions is put forward and it is paired with a formal description of them and of their spreading among minds. Furthermore, investigating social influence also implies the necessity to account for the way in which people change their minds, as a consequence of interacting with other people, and the need to explain the higher or lower persistence of such changes

Understanding opinions. A cognitive and formal account

The study of opinions, their formation and change, is one of the defining topics addressed by social psychology, but in recent years other disciplines, as computer science and complexity, have addressed this challenge. Despite the flourishing of different models and theories in both fields, several key questions still remain unanswered. The aim of this paper is to challenge the current theories on opinion by putting forward a cognitively grounded model where opinions are described as specific mental representations whose main properties are put forward. A comparison with reputation will be also presented

Opinions within Media, Power and Gossip

Despite the increasing diffusion of the Internet technology, TV remains the principal medium of communication. People's perceptions, knowledge, beliefs and opinions about matter of facts get (in)formed through the information reported on by the mass-media. However, a single source of information (and consensus) could be a potential cause of anomalies in the structure and evolution of a society. Hence, as the information available (and the way it is reported) is fundamental for our perceptions and opinions, the definition of conditions allowing for a good information to be disseminated is a pressing challenge. In this paper starting from a report on the last Italian political campaign in 2008, we derive a socio-cognitive computational model of opinion dynamics where agents get informed by different sources of information. Then, a what-if analysis, performed trough simulations on the model's parameters space, is shown. In particular, the scenario implemented includes three main streams of information acquisition, differing in both the contents and the perceived reliability of the messages spread. Agents' internal opinion is updated either by accessing one of the information sources, namely media and experts, or by exchanging information with one another. They are also endowed with cognitive mechanisms to accept, reject or partially consider the acquired information