Outward-inward information flux in an opinion formation model on different topologies

A simple model of opinion formation dynamics in which binary-state agents make up their opinions due to the influence of agents in a local neighborhood is studied using different network topologies. Each agent uses two different strategies, the Sznajd rule with a probability $q$ and the Galam majority rule (without inertia) otherwise; being $q$ a parameter of the system. Initially, the binary-state agents may have opinions (at random) against or in favor about a certain topic. The time evolution of the system is studied using different network topologies, starting from different initial opinion densities. A transition from consensus in one opinion to the other is found at the same percentage of initial distribution no matter which type of network is used or which opinion formation rule is used.Comment: 11 pages including figures. To appear in Physica

On the formation of structure in growing networks

Based on the formation of triad junctions, the proposed mechanism generates networks that exhibit extended rather than single power law behavior. Triad formation guarantees strong neighborhood clustering and community-level characteristics as the network size grows to infinity. The asymptotic behavior is of interest in the study of directed networks in which (i) the formation of links cannot be described according to the principle of preferential attachment; (ii) the in-degree distribution fits a power law for nodes with a high degree and an exponential form otherwise; (iii) clustering properties emerge at multiple scales and depend on both the number of links that newly added nodes establish and the probability of forming triads; and (iv) groups of nodes form modules that feature less links to the rest of the nodes.Comment: 17 pages, 9 figures, we apply the proposed mechanism to generate network realizations that resemble the degree distribution and clustering properties of an empirical network with no directed cycles (i.e., when the model parameter n=0), updated reference

The Heider balance - a continuous approach

The Heider balance (HB) is investigated in a fully connected graph of $N$ nodes. The links are described by a real symmetric array r(i,j), i,j=1,...,N. In a social group, nodes represent group members and links represent relations between them, positive (friendly) or negative (hostile). At the balanced state, r(i,j)r(j,k)r(k,i)>0 for all the triads (i,j,k). As follows from the structure theorem of Cartwright and Harary, at this state the group is divided into two subgroups, with friendly internal relations and hostile relations between the subgroups. Here the system dynamics is proposed to be determined by a set of differential equations. The form of equations guarantees that once HB is reached, it persists. Also, for N=3 the dynamics reproduces properly the tendency of the system to the balanced state. The equations are solved numerically. Initially, r(i,j) are random numbers distributed around zero with a symmetric uniform distribution of unit width. Calculations up to N=500 show that HB is always reached. Time to get the balanced state varies with the system size N as N^{-1/2}. The spectrum of relations, initially narrow, gets very wide near HB. This means that the relations are strongly polarized. In our calculations, the relations are limited to a given range around zero. With this limitation, our results can be helpful in an interpretation of somestatistical data.Comment: 9 pages, 4 figures. Int. J. Mod. Phys. C (2005), in prin

Bounded Confidence under Preferential Flip: A Coupled Dynamics of Structural Balance and Opinions

In this work we study the coupled dynamics of social balance and opinion formation. We propose a model where agents form opinions under bounded confidence, but only considering the opinions of their friends. The signs of social ties -friendships and enmities- evolve seeking for social balance, taking into account how similar agents' opinions are. We consider both the case where opinions have one and two dimensions. We find that our dynamics produces the segregation of agents into two cliques, with the opinions of agents in one clique differing from those in the other. Depending on the level of bounded confidence, the dynamics can produce either consensus of opinions within each clique or the coexistence of several opinion clusters in a clique. For the uni-dimensional case, the opinions in one clique are all below the opinions in the other clique, hence defining a "left clique" and a "right clique". In the two-dimensional case, our numerical results suggest that the two cliques are separated by a hyperplane in the opinion space. We also show that the phenomenon of unidimensional opinions identified by DeMarzo, Vayanos and Zwiebel (Q J Econ 2003) extends partially to our dynamics. Finally, in the context of politics, we comment about the possible relation of our results to the fragmentation of an ideology and the emergence of new political parties.Comment: 8 figures, PLoS ONE 11(10): e0164323, 201

Stochastic Opinion Formation in Scale-Free Networks

The dynamics of opinion formation in large groups of people is a complex non-linear phenomenon whose investigation is just at the beginning. Both collective behaviour and personal view play an important role in this mechanism. In the present work we mimic the dynamics of opinion formation of a group of agents, represented by two state $\pm 1$, as a stochastic response of each of them to the opinion of his/her neighbours in the social network and to feedback from the average opinion of the whole. In the light of recent studies, a scale-free Barab\'asi-Albert network has been selected to simulate the topology of the interactions. A turbulent-like dynamics, characterized by an intermittent behaviour, is observed for a certain range of the model parameters. The problem of uncertainty in decision taking is also addressed both from a topological point of view, using random and targeted removal of agents from the network, and by implementing a three state model, where the third state, zero, is related to the information available to each agent. Finally, the results of the model are tested against the best known network of social interactions: the stock market. A time series of daily closures of the Dow Jones index has been used as an indicator of the possible applicability of our model in the financial context. Good qualitative agreement is found.Comment: 24 pages and 13 figures, Physical Review E, in pres

A new look at loop quantum gravity

I describe a possible perspective on the current state of loop quantum gravity, at the light of the developments of the last years. I point out that a theory is now available, having a well-defined background-independent kinematics and a dynamics allowing transition amplitudes to be computed explicitly in different regimes. I underline the fact that the dynamics can be given in terms of a simple vertex function, largely determined by locality, diffeomorphism invariance and local Lorentz invariance. I emphasize the importance of approximations. I list open problems.Comment: 15 pages, 5 figure

Charge Transport in Manganites: Hopping Conduction, the Anomalous Hall Effect and Universal Scaling

The low-temperature Hall resistivity \rho_{xy} of La_{2/3}A_{1/3}MnO_3 single crystals (where A stands for Ca, Pb and Ca, or Sr) can be separated into Ordinary and Anomalous contributions, giving rise to Ordinary and Anomalous Hall effects, respectively. However, no such decomposition is possible near the Curie temperature which, in these systems, is close to metal-to-insulator transition. Rather, for all of these compounds and to a good approximation, the \rho_{xy} data at various temperatures and magnetic fields collapse (up to an overall scale), on to a single function of the reduced magnetization m=M/M_{sat}, the extremum of this function lying at m~0.4. A new mechanism for the Anomalous Hall Effect in the inelastic hopping regime, which reproduces these scaling curves, is identified. This mechanism, which is an extension of Holstein's model for the Ordinary Hall effect in the hopping regime, arises from the combined effects of the double-exchange-induced quantal phase in triads of Mn ions and spin-orbit interactions. We identify processes that lead to the Anomalous Hall Effect for localized carriers and, along the way, analyze issues of quantum interference in the presence of phonon-assisted hopping. Our results suggest that, near the ferromagnet-to-paramagnet transition, it is appropriate to describe transport in manganites in terms of carrier hopping between states that are localized due to combined effect of magnetic and non-magnetic disorder. We attribute the qualitative variations in resistivity characteristics across manganite compounds to the differing strengths of their carrier self-trapping, and conclude that both disorder-induced localization and self-trapping effects are important for transport.Comment: 29 pages, 20 figure