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We introduce a growing one-dimensional quenched spin model that bases on asymmetrical one-side Ising interactions in the presence of external field. Numerical simulations and analytical calculations based on Markov chain theory show that when the external field is smaller than the exchange coupling constant J there is a nonmonotonous dependence of the mean magnetization on the temperature in a finite system. The crossover temperature Tc corresponding to the maximal magnetization decays with system size, approximately as the inverse of the Lambert W function. The observed phenomenon can be understood as an interplay between the thermal fluctuations and the presence of the first cluster determined by initial conditions. The effect exists also when spins are not quenched but fully thermalized after the attachment to the chain. By performing tests on real data we conceive the model is in part suitable for a qualitative description of online emotional discussions arranged in a chronological order, where a spin in every node conveys emotional valence of a subsequent post. [ABSTRACT FROM AUTHOR]

We analyze emotionally annotated massive data from Internet relay chat (IRC) as well as from BBC forum website and model the dialogues between chat participants by assuming that the driving force for the discussion is the entropy growth of emotional probability distribution. This process is claimed to be responsible for a power-law distribution of the discussion lengths observed in the dialogues. We perform numerical simulations based on the noticed phenomenon obtaining a good agreement with the real data. Finally, we propose a method to artificially prolong the duration of the discussion that relies on the entropy of emotional probability distribution. [ABSTRACT FROM AUTHOR]

Background: E-communities, social groups interacting online, have recently become an object of interdisciplinary research. As with face-to-face meetings, Internet exchanges may not only include factual information but also emotional information - how participants feel about the subject discussed or other group members. Emotions in turn are known to be important in affecting interaction partners in offline communication in many ways. Could emotions in Internet exchanges affect others and systematically influence quantitative and qualitative aspects of the trajectory of e-communities? The development of automatic sentiment analysis has made large scale emotion detection and analysis possible using text messages collected from the web. However, it is not clear if emotions in e-communities primarily derive from individual group members' personalities or if they result from intra-group interactions, and whether they influence group activities. Methodology/Principal Findings: Here, for the first time, we show the collective character of affective phenomena on a large scale as observed in four million posts downloaded from Blogs, Digg and BBC forums. To test whether the emotions of a community member may influence the emotions of others, posts were grouped into clusters of messages with similar emotional valences. The frequency of long clusters was much higher than it would be if emotions occurred at random. Distributions for cluster lengths can be explained by preferential processes because conditional probabilities for consecutive messages grow as a power law with cluster length. For BBC forum threads, average discussion lengths were higher for larger values of absolute average emotional valence in the first ten comments and the average amount of emotion in messages fell during discussions. Conclusions/Significance: Overall, our results prove that collective emotional states can be created and modulated via Internet communication and that emotional expressiveness is the fuel that sustains some e-communities. [ABSTRACT FROM AUTHOR]

We extend the previously observed scaling equation connecting the internode distances and nodes' degrees onto the case of weighted networks. We show that the scaling takes a similar form in the empirical data obtained from networks characterized by different relations between node's strength and its degree. In the case of explicit equation for s (k) (e.g. linear or scale-free), the new coefficients of scaling equation can be easily obtained. We support our analysis with numerical simulations for Erdös–Rényi random graphs with different weight distributions. [ABSTRACT FROM AUTHOR]

We analyze a nonlinear q-voter model with stochastic noise, interpreted in the social context as independence, on a duplex network. The size of the lobby q (i.e., the pressure group) is a crucial parameter that changes the behavior of the system. The q-voter model has been applied on multiplex networks, and it has been shown that the character of the phase transition depends on the number of levels in the multiplex network as well as on the value of q. The primary aim of this study is to examine phase transition character in the case when on each level of the network the lobby size is different, resulting in two parameters q 1 and q 2 . In a system of a duplex clique (i.e., two fully overlapped complete graphs) we find evidence of successive phase transitions when a continuous phase transition is followed by a discontinuous one or two consecutive discontinuous phase transitions appear, depending on the parameter. When analyzing this system, we even encounter mixed-order (or hybrid) phase transition. The observation of successive phase transitions is a new quantity in binary state opinion formation models and we show that our analytical considerations are fully supported by Monte-Carlo simulations. [ABSTRACT FROM AUTHOR]

We analyze a modified kinetic Ising model, a so-called q-neighbor Ising model, with Metropolis dynamics [Phys. Rev. E 92, 052105 (2015)] on a duplex clique and a partially duplex clique. In the q-neighbor Ising model each spin interacts only with q spins randomly chosen from its whole neighborhood. In the case of a duplex clique the change of a spin is allowed only if both levels simultaneously induce this change. Due to the mean-field-like nature of the model we are able to derive the analytic form of transition probabilities and solve the corresponding master equation. The existence of the second level changes dramatically the character of the phase transition. In the case of the monoplex clique, the q-neighbor Ising model exhibits a continuous phase transition for q=3, discontinuous phase transition for q≥4, and for q=1 and q=2 the phase transition is not observed. On the other hand, in the case of the duplex clique continuous phase transitions are observed for all values of q, even for q=1 and q=2. Subsequently we introduce a partially duplex clique, parametrized by r∈[0,1], which allows us to tune the network from monoplex (r=0) to duplex (r=1). Such a generalized topology, in which a fraction r of all nodes appear on both levels, allows us to obtain the critical value of r=r∗(q) at which a tricriticality (switch from continuous to discontinuous phase transition) appears. [ABSTRACT FROM AUTHOR]

We solve the growing asymmetric Ising model [J. Sienkiewicz, K. Suchecki, and J. A. Hołyst, Phys. Rev. E 89, 012105 (2014)] in the topologies of deterministic and stochastic (random) scale-free trees predicting its nonmonotonous behavior for external fields smaller than the coupling constant J. In both cases, we indicate that the crossover temperature corresponding to maximal magnetization decays approximately as (lnlnN)-1, where N is the number of nodes in the tree. [ABSTRACT FROM AUTHOR]

Echo chambers and polarization dynamics are, as of late, a very prominent topic in scientific communities around the world. As these phenomena directly affect our lives, seemingly more and more as our societies and communication channels evolve, it becomes ever so important for us to understand the intricacies of opinion dynamics in the modern era. Here we extend an existing echo-chamber model with activity-driven agents to a bilayer topology and study the dynamics of the polarized state as a function of interlayer couplings. Different cases of such couplings are presented: unidirectional coupling that can be reduced to a monolayer facing an external bias and symmetric and nonsymmetric couplings. We have assumed that initial conditions impose system polarization and agent opinions are different for both layers. Such a preconditioned polarized state can persist without explicit homophilic interactions provided the coupling strength between agents belonging to different layers is weak enough. For a strong unidirectional or attractive coupling between two layers a discontinuous transition to a radicalized state takes place when mean opinions in both layers are the same. When coupling constants between the layers are of different signs, the system exhibits sustained or decaying oscillations. Transitions between these states are analyzed using a mean field approximation and classified in the framework of bifurcation theory.

Finding hidden layers in complex networks is an important and a nontrivial problem in modern science. We explore the framework of quantum graphs to determine whether concealed parts of a multilayer system exist and if so then what is their extent, i.e., how many unknown layers are there. Assuming that the only information available is the time evolution of a wave propagation on a single layer of a network it is indeed possible to uncover that which is hidden by merely observing the dynamics. We present evidence on both synthetic and real-world networks that the frequency spectrum of the wave dynamics can express distinct features in the form of additional frequency peaks. These peaks exhibit dependence on the number of layers taking part in the propagation and thus allowing for the extraction of said number. We show that, in fact, with sufficient observation time, one can fully reconstruct the row-normalized adjacency matrix spectrum. We compare our propositions to a machine learning approach using a wave packet signature method modified for the purposes of multilayer systems.

We investigate how textual properties of scientific papers relate to the number of citations they receive. Our main finding is that correlations are nonlinear and affect differently the most cited and typical papers. For instance, we find that, in most journals, short titles correlate positively with citations only for the most cited papers, whereas for typical papers, the correlation is usually negative. Our analysis of six different factors, calculated both at the title and abstract level of 4.3 million papers in over 1500 journals, reveals the number of authors, and the length and complexity of the abstract, as having the strongest (positive) influence on the number of citations.

We extend a model of community isolation in the d-dimensional lattice to a case with an imposed imbalance between the birth rates of competing communities. We provide analytical and numerical evidences that in the asymmetric two-species model there exists a well-defined value of the asymmetry parameter when the emergence of the isolated (blocked) subgroups is the fastest, i.e., the characteristic time t(c) is minimal. The critical value of the parameter depends only on the lattice dimensionality and is independent of the system size. A similar phenomenon is observed in the multispecies case with a geometric distribution of the birth rates. We also show that blocked subgroups in the multispecies case are absent or very rare when either there is a strictly dominant species that outnumbers the others or there is a large diversity of species. The number of blocked species of different kinds decreases with the dimension of the multispecies system.

We introduce a simple model of a growing system with m competing communities. The model corresponds to the phenomenon of defeats suffered by social groups living in isolation. A nonequilibrium phase transition is observed when at critical time tc the first isolated cluster occurs. In the one-dimensional system the volume of the new phase, i.e., the number of the isolated individuals, increases with time as Z approximately t3. For a large number of possible communities, the critical density of filled space is equal to rho(c)=(m/N)1/3, where N is the system size. A similar transition is observed for Erdos-Rényi random graphs and Barabási-Albert scale-free networks. Analytical results are in agreement with numerical simulations.

We show how discretization affects two major characteristics in complex networks: internode distances (measured as the shortest number of edges between network sites) and average path length, and as a result there are log-periodic oscillations of the above quantities. The effect occurs both in numerical network models as well as in such real systems as coauthorship, language, food, and public transport networks. Analytical description of these oscillations fits well numerical simulations. We consider a simple case of the network optimization problem, arguing that discrete effects can lead to a nontrivial solution.

Public transport systems in 22 Polish cities have been analyzed. The sizes of these networks range from N = 152 to 2881. Depending on the assumed definition of network topology, the degree distribution can follow a power law or can be described by an exponential function. Distributions of path lengths in all considered networks are given by asymmetric, unimodal functions. Clustering, assortativity, and betweenness are studied. All considered networks exhibit small-world behavior and are hierarchically organized. A transition between dissortative small networks N approximately < or = 500 and assortative large networks N approximately > or = 500 is observed.

Universal scaling of distances between vertices of Erdos-Rényi random graphs, scale-free Barabási-Albert models, science collaboration networks, biological networks, Internet Autonomous Systems and public transport networks are observed. A mean distance between two nodes of degrees k(i) and k(j) equals to (l(ij)) = A - B log(k(i)k(j)). The scaling is valid over several decades. A simple theory for the appearance of this scaling is presented. Parameters A and B depend on the mean value of a node degree (k)nn calculated for the nearest neighbors and on network clustering coefficients.