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

Emergence through Selection: The Evolution of a Scientific Challenge

One of the most interesting scientific challenges nowadays deals with the analysis and the understanding of complex networks' dynamics and how their processes lead to emergence according to the interactions among their components. In this paper we approach the definition of new methodologies for the visualization and the exploration of the dynamics at play in real dynamic social networks. We present a recently introduced formalism called TVG (for time-varying graphs), which was initially developed to model and analyze highly-dynamic and infrastructure-less communication networks such as mobile ad-hoc networks, wireless sensor networks, or vehicular networks. We discuss its applicability to complex networks in general, and social networks in particular, by showing how it enables the specification and analysis of complex dynamic phenomena in terms of temporal interactions, and allows to easily switch the perspective between local and global dynamics. As an example, we chose the case of scientific communities by analyzing portion of the ArXiv repository (ten years of publications in physics) focusing on the social determinants (e.g. goals and potential interactions among individuals) behind the emergence and the resilience of scientific communities. We consider that scientific communities are at the same time communities of practice (through co-authorship) and that they exist also as representations in the scientists' mind, since references to other scientists' works is not merely an objective link to a relevant work, but it reveals social objects that one manipulates, select and refers to. In the paper we show the emergence/selection of a community as a goal-driven preferential attachment toward a set of authors among which there are some key scientists (Nobel prizes)

Exploiting Reputation in Distributed Virtual Environments

The cognitive research on reputation has shown several interesting properties that can improve both the quality of services and the security in distributed electronic environments. In this paper, the impact of reputation on decision-making under scarcity of information will be shown. First, a cognitive theory of reputation will be presented, then a selection of simulation experimental results from different studies will be discussed. Such results concern the benefits of reputation when agents need to find out good sellers in a virtual market-place under uncertainty and informational cheating

ДІАЛЕКТИКА СПРИЙМАННЯ І МИСЛЕННЯ ЯК ЕСТЕТИЧНИЙ ФЕНОМЕН. (The dialectics ofperception and thinking as an aesthetic phenomenon.)

У статті здійснено філософський аналіз характеру взаємодії чуттєвого й раціонального, сприймання і мислення в процесі предметно-практичної діяльності відповідно до естетичного виміру реальності. Естетичне розуміється як закономірний історичний процес переходу об'єктивності чуттєвого сприймання в суб'єктивність мислення і навпаки. (The author of the article explicates the interactive character of the sensual and rational, perception and thinking in the process of objective and practical activities in accordance with the aesthetic dimension of reality. The concept aesthetic designates a natural historic process of transition from objective sensual perception to subjective thinking and vice versa. The investigation has been carried out on the basis of generalization of the aesthetic by German classical philosophers (I. Kant, G.W.F. Hegel) as well as the theses of philosophical dialectics of the 20th century in E.V. Ilyenkov's, A.S. Kanarsky's, F.T. Mikhailov's and G.V. Lobastov's works. It has been identified that both the ability to perceive the world in various modes of human sensuality and think conceptually to conform to the rules and categories of logic and dialectics are specifically human modes of reality reflection; without perception of the culture of human sensuality, it is impossible to understand the content and sense of various modes of human conscience, such as science, morality, politics etc.; both the dialectic identity and contradiction of the aesthetic and sensual concepts do not only reflect a person's attitude to a certain thing, its qualities and characteristic features, but also to himself/herself, the aim and sense of human existence. Reflecting objective reality, the aesthetic is embodied in certain historic ways and modes of subjective activity and mirrors practical forms of the human exploration of the world. The theory of development and the logic of the aesthetic can be perceived only as the dialectics of the aesthetic process and theory ofsensual perception as such. The concept of the aesthetic embodies the objective and the subjective that present the dialectic modes of its existence.

PopRank: Ranking pages' impact and users' engagement on Facebook

Users online tend to acquire information adhering to their system of beliefs and to ignore dissenting information. Such dynamics might affect page popularity. In this paper we introduce an algorithm, that we call PopRank, to assess both the Impact of Facebook pages as well as users' Engagement on the basis of their mutual interactions. The ideas behind the PopRank are that i) high impact pages attract many users with a low engagement, which means that they receive comments from users that rarely comment, and ii) high engagement users interact with high impact pages, that is they mostly comment pages with a high popularity. The resulting ranking of pages can predict the number of comments a page will receive and the number of its posts. Pages impact turns out to be slightly dependent on pages' informative content (e.g., science vs conspiracy) but independent of users' polarization.Comment: 10 pages, 5 figure