Advances in Complex Systems

Levels of a complex system are characterized by the fact that they admit a closed functional description in terms of concepts and quantities intrinsic to that level. Several ideas have come up so far in order to make the notion of a closed description precise. In this paper, we present four of these approaches and investigate their mutual relationships. Our study is restricted to the case of discrete dynamical systems, where the different levels are linked by a coarse-graining of variables and states of the system.

A mathematical model was developed for opinion propagation on online social networks using a scale-free network with an adjustable clustering coefficient. Connected nodes influence each other when the difference between their opinion values is less than a threshold value. The model is used to examine effectiveness of three different approaches for influencing public opinion. The approaches examined include (1) a "Class", defined as an approach (such as a class or book) that greatly influences a small, randomly selected portion of the population, (2) an "Advertisement", defined as an approach (such as a TV or online advertisement) that has a small influence at each viewing on a large randomly selected portion of the population, and (3) an "App", defined as an approach (such as a Facebook game or smartphone "App") that spreads via the online social network (rather than randomly) and has a small influence at each viewing on the affected population. The Class and Advertisement approaches result in similar overall influence on the population, despite the fact that these approaches are highly different. In contrast, the App approach has a much more significant effect on opinion values of users occupying clusters within the social network compared to the overall population.

Studies have revealed that some topological properties of complex networks are robust to random node failures, but highly sensitive to failures in nodes of high centrality (i.e., attacks). This work proposes mechanisms based on local information for detecting vulnerable network configurations and for promoting changes in the topology to mitigate the impact on network connectivity of successive node losses due to attacks and failures. Two scenarios were evaluated: with maintenance of the number of links in the network, and with the creation of new links. For the first case, we show that the removal of the most central nodes affects networks in such a way that is also difficult to preserve their main topological properties, although improvement in the values of global efficiency at the expense of a reduction of the local efficiency was observed. For the second scenario, there was a significant decrease in the impact from attacks and failures. Notably, for failures the connectivity properties not only remained almost unchanged, but in some cases considerably increased, thus improving the overall network performance. The results were also verified in some benchmark real-network topologies, and a comparative performance evaluation with a random self-regenerating process was also analyzed. The study demonstrates the importance and feasibility of local adaptation mechanisms for link rewiring based on the concept of vulnerability.

For the simulation of pedestrians, a method is introduced to find routing alternatives from any origin position to a given destination area in a given geometry composed of walking areas and obstacles. The method includes a parameter which sets a threshold for the approximate minimum size of obstacles to generate routing alternatives. The resulting data structure for navigation is constructed such that it does not introduce artifacts to the movement of simulated pedestrians and locally pedestrians prefer to walk on the shortest path. The generated set of routes can be used with iterating static or dynamic assignment methods.

The evolution of unconditional cooperation is one of the fundamental problems in science. A new solution is proposed to solve this puzzle. We treat this issue with an evolutionary model in which agents play the Prisoner's Dilemma on signed networks. The topology is allowed to co-evolve with relational signs as well as with agent strategies. We introduce a strategy that is conditional on the emotional content embedded in network signs. We show that this strategy acts as a catalyst and creates favorable conditions for the spread of unconditional cooperation. In line with the literature, we found evidence that the evolution of cooperation most likely occurs in networks with relatively high chances of rewiring and with low likelihood of strategy adoption. While a low likelihood of rewiring enhances cooperation, a very high likelihood seems to limit its diffusion. Furthermore, unlike in nonsigned networks, cooperation becomes more prevalent in denser topologies.