A Veritable Zoology of Successive Phase Transitions in the Asymmetric q-Voter Model on Multiplex Networks.

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 q1 and q2. 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.

International trade network: fractal properties and globalization puzzle.

Globalization is one of the central concepts of our age. The common perception of the process is that, due to declining communication and transport costs, distance becomes less and less important. However, the distance coefficient in the gravity model of trade, which grows in time, indicates that the role of distance increases rather than decreases. This, in essence, captures the notion of the globalization puzzle. Here, we show that the fractality of the international trade system (ITS) provides a simple solution for the puzzle. We argue that the distance coefficient corresponds to the fractal dimension of ITS. We provide two independent methods, the box counting method and spatial choice model, which confirm this statement. Our results allow us to conclude that the previous approaches to solving the puzzle misinterpreted the meaning of the distance coefficient in the gravity model of trade.

Interplay between tie strength and neighbourhood topology in complex networks.

Granovetter's weak ties theory is a very important sociological theory according to which a correlation between edge weight and the network's topology should exist. More specifically, the neighbourhood overlap of two nodes connected by an edge should be positively correlated with edge weight (tie strength). However, some real social networks exhibit a negative correlation-the most prominent example is the scientific collaboration network, for which overlap decreases with edge weight. It has been demonstrated that the aforementioned inconsistency with Granovetter's theory can be alleviated in the scientific collaboration network through the use of asymmetric measures. In this paper, we explain that while asymmetric measures are often necessary to describe complex networks and to confirm Granovetter's theory, their interpretation is not simple, and there are pitfalls that one must be wary of. The definitions of asymmetric weights and overlaps introduce structural correlations that must be filtered out. We show that correlation profiles can be used to overcome this problem. Using this technique, not only do we confirm Granovetter's theory in various real and artificial social networks, but we also show that Granovetter-like weight-topology correlations are present in other complex networks (e.g. metabolic and neural networks). Our results suggest that Granovetter's theory is a sociological manifestation of more general principles governing various types of complex networks.

Scaling theory of fractal complex networks.

We show that fractality in complex networks arises from the geometric self-similarity of their built-in hierarchical community-like structure, which is mathematically described by the scale-invariant equation for the masses of the boxes with which we cover the network when determining its box dimension. This approach-grounded in both scaling theory of phase transitions and renormalization group theory-leads to the consistent scaling theory of fractal complex networks, which complements the collection of scaling exponents with several new ones and reveals various relationships between them. We propose the introduction of two classes of exponents: microscopic and macroscopic, characterizing the local structure of fractal complex networks and their global properties, respectively. Interestingly, exponents from both classes are related to each other and only a few of them (three out of seven) are independent, thus bridging the local self-similarity and global scale-invariance in fractal networks. We successfully verify our findings in real networks situated in various fields (information-the World Wide Web, biological-the human brain, and social-scientific collaboration networks) and in several fractal network models.

Scientific success from the perspective of the strength of weak ties.

We present the first complete verification of Granovetter's theory of social networks using a massive dataset, i.e. DBLP computer science bibliography database. For this purpose, we study a coauthorship network, which is considered one of the most important examples that contradicts the universality of this theory. We achieve this goal by rejecting the assumption of the symmetry of social ties. Our approach is grounded in well-established heterogeneous (degree-based) mean-field theory commonly used to study dynamical processes on complex networks. Granovetter's theory is based on two hypotheses that assign different roles to interpersonal, information-carrying connections. The first hypothesis states that strong ties carrying the majority of interaction events are located mainly within densely connected groups of people. The second hypothesis maintains that these groups are connected by sparse weak ties that are of vital importance for the diffusion of information-individuals who have access to weak ties have an advantage over those who do not. Given the scientific collaboration network, with strength of directed ties measured by the asymmetric fraction of joint publications, we show that scientific success is strongly correlated with the structure of a scientist's collaboration network. First, among two scientists, with analogous achievements, the one with weaker ties tends to have the higher h-index, and second, teams connected by such ties create more cited publications.

Cellular automata approach to modeling self-organized periodic patterns in nanoparticle-doped liquid crystals.

Elementary cellular automata provide one of the simplest ways to generally describe the phenomena of pattern formation. However, they are considered too simple to be able to describe in detail the more complex phenomena occurring in real experimental systems. In this article, we demonstrate the an application of these methods to optical systems, providing an understanding of the mechanisms behind the formation of periodic patterns in nanoparticle-doped liquid crystals. Our extremely simplified model also explains the observed linear relationship between periodicity and system size.

Sense of taste in patients after cochlear implantation-preliminary study.

Background: Taste is the leading sense in how we determine the quality of consumed food. Proper gustatory sensation largely determines the well-being and health of an organism, and this affects their quality of life. Objectives: The aim of the present study was to estimate the risk of early taste disorders following implantation surgery. Methods: Twenty patients underwent a taste test before, 1 day after, and 1 month after cochlear implantation. The taste sensations of sweet, sour, salty, and bitter were determined. Results: Statistical analysis showed no significant differences (p > 0.05) between individual tests among the entire study group. After dividing the respondents into smoking (n=6) and non-smoking (n=14) groups, only a weak correlation (p = 0.043) was found between the results of the first and second examination in the smoker group. However, a statistically significant decrease in the number of saline-sensitive (p<0.001) and acid-sensitive (p = 0.042) subjects was observed. Conclusion: These findings suggest that people after a cochlear implant may have transient taste disorders. Taste disorder called dysgeusia may be an early complication after the implantation procedure contributing to deterioration of patients quality of life.

Reply to "Comment on 'Partial equivalence of statistical ensembles in a simple spin model with discontinuous phase transitions' ".

In the present Reply we show that a Comment casting doubts on the results of our recent paper [Fronczak, Fronczak, and Siudem, Phys. Rev. E 101, 022111 (2020)2470-004510.1103/PhysRevE.101.022111] results from a misunderstanding of the assumptions of our model and from overinterpretation based on this misunderstanding.

Partial equivalence of statistical ensembles in a simple spin model with discontinuous phase transitions.

In this paper, we draw attention to the problem of phase transitions in systems with locally affine microcanonical entropy, in which partial equivalence of (microcanonical and canonical) ensembles is observed. We focus on a very simple spin model, that was shown to be an equilibrium statistical mechanics representation of the biased random walk. The model exhibits interesting discontinuous phase transitions that are simultaneously observed in the microcanonical, canonical, and grand canonical ensemble, although in each of these ensembles the transition occurs in a slightly different way. The differences are related to fluctuations accompanying the discontinuous change of the number of positive spins. In the microcanonical ensemble, there is no fluctuation at all. In the canonical ensemble, one observes power-law fluctuations, which are, however, size dependent and disappear in the thermodynamic limit. Finally, in the grand canonical ensemble, the discontinuous transition is of mixed order (hybrid) kind with diverging (critical-like) fluctuations. In general, this paper consists of many small results, which together make up an interesting example of phase transitions that are not covered by the known classifications of these phenomena.

Biased random walks in complex networks: the role of local navigation rules.

We study the biased random-walk process in random uncorrelated networks with arbitrary degree distributions. In our model, the bias is defined by the preferential transition probability, which, in recent years, has been commonly used to study the efficiency of different routing protocols in communication networks. We derive exact expressions for the stationary occupation probability and for the mean transit time between two nodes. The effect of the cyclic search on transit times is also explored. Results presented in this paper provide the basis for a theoretical treatment of transport-related problems in complex networks, including quantitative estimation of the critical value of the packet generation rate.

Coagulation with product kernel and arbitrary initial conditions: Exact kinetics within the Marcus-Lushnikov framework.

The time evolution of a system of coagulating particles under the product kernel and arbitrary initial conditions is studied. Using the improved Marcus-Lushnikov approach, the master equation is solved for the probability W(Q,t) to find the system in a given mass spectrum Q={n_{1},n_{2},⋯,n_{g}⋯}, with n_{g} being the number of particles of size g. The exact expression for the average number of particles 〈n_{g}(t)〉 at arbitrary time t is derived and its validity is confirmed in numerical simulations of several selected initial mass spectra.

Kauffman Boolean model in undirected scale-free networks.

We investigate analytically and numerically the critical line in undirected random Boolean networks with arbitrary degree distributions, including the scale-free topology of connections P(k) ~ k(-gamma). We explain that the unattainability of the critical line in numerical simulations of classical random graphs is due to percolation phenomena. We suggest that recent findings of discrepancy between simulations and theory in directed random Boolean networks might have the same reason. We also show that in infinite scale-free networks the transition between frozen and chaotic phases occurs for 3

Critical properties of unlimited gliding: Unexpected flocking behavior driven by the exchange of information.

Inspired by albatrosses that use thermal lifts to fly across oceans we develop a simple model of gliders that serves us to study theoretical limitations of unlimited exploration of the Earth. Our studies, grounded in physical theory of continuous percolation and biased random walks, allow us to identify a variety of percolation transitions, which are understood as providing potentially unlimited movement through a space in a specified direction. We discover an unexpected phenomenon of self-organization of gliders in clusters, which resembles the flock organization of birds. This self-organization is intriguing, as it occurs thanks to exchange of information only and without any particular rules that could favor the clustering of the gliders (in contrast to the causes well known in literature, like, for example, attractive forces used in the Vicsek-type models or fitness functions used in evolutionary computation).

Exact combinatorial approach to finite coagulating systems.

This paper outlines an exact combinatorial approach to finite coagulating systems. In this approach, cluster sizes and time are discrete and the binary aggregation alone governs the time evolution of the systems. By considering the growth histories of all possible clusters, an exact expression is derived for the probability of a coagulating system with an arbitrary kernel being found in a given cluster configuration when monodisperse initial conditions are applied. Then this probability is used to calculate the time-dependent distribution for the number of clusters of a given size, the average number of such clusters, and that average's standard deviation. The correctness of our general expressions is proved based on the (analytical and numerical) results obtained for systems with the constant kernel. In addition, the results obtained are compared with the results arising from the solutions to the mean-field Smoluchowski coagulation equation, indicating its weak points. The paper closes with a brief discussion on the extensibility to other systems of the approach presented herein, emphasizing the issue of arbitrary initial conditions.

Log-periodic oscillations due to discrete effects in complex networks.

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.

Thermodynamic forces, flows, and Onsager coefficients in complex networks.

In this paper the linear theory of nonequilibrium thermodynamics, developed by Onsager and others, is applied to random networks with arbitrary degree distribution. Using the well-known methods of nonequilibrium thermodynamics we identify thermodynamic forces and their conjugated flows induced in networks as a result of single node degree perturbation. The forces and the flows can be understood as a response of the system to events, such as random removal of nodes or intentional attacks on them. Finally, we show that cross effects (such as thermodiffusion, or thermoelectric phenomena), in which one force may not only give rise to its own conjugated flow, but to many other flows, can be observed also in complex networks.

Analysis of scientific productivity using maximum entropy principle and fluctuation-dissipation theorem.

Using data retrieved from the INSPEC database we have quantitatively discussed a few syndromes of the publish-or-perish phenomenon, including the continuous growth of the rate of scientific productivity, and the continuously decreasing percentage of those scientists who stay in science for a long time. Making use of the maximum entropy principle and fluctuation-dissipation theorem, we have shown that the observed fat-tailed distributions of the total number of papers x authored by scientists may result from the density-of-states function g(x;tau) underlying the scientific community. Although different generations of scientists are characterized by different productivity patterns, the function g(x;tau) is inherent to researchers of a given seniority tau , whereas the publish-or-perish phenomenon is caused only by an external field theta influencing researchers.

Exact solution of the isotropic majority-vote model on complete graphs.

The isotropic majority-vote (MV) model, which, apart from the one-dimensional case, is thought to be nonequilibrium and violating the detailed balance condition. We show that this is not true when the model is defined on a complete graph. In the stationary regime, the MV model on a fully connected graph fulfills the detailed balance and is equivalent to the modified Ehrenfest urn model. Using the master equation approach, we derive the exact expression for the probability distribution of finding the system in a given spin configuration. We show that it only depends on the absolute value of magnetization. Our theoretical predictions are validated by numerical simulations.

How transfer flights shape the structure of the airline network.

In this paper, we analyse the gravity model in the global passenger air-transport network. We show that in the standard form, the model is inadequate for correctly describing the relationship between passenger flows and typical geo-economic variables that characterize connected countries. We propose a model for transfer flights that allows exploitation of these discrepancies in order to discover hidden subflows in the network. We illustrate its usefulness by retrieving the distance coefficient in the gravity model, which is one of the determinants of the globalization process. Finally, we discuss the correctness of the presented approach by comparing the distance coefficient to several well-known economic events.

Artificial intelligence in peer review: How can evolutionary computation support journal editors?

With the volume of manuscripts submitted for publication growing every year, the deficiencies of peer review (e.g. long review times) are becoming more apparent. Editorial strategies, sets of guidelines designed to speed up the process and reduce editors' workloads, are treated as trade secrets by publishing houses and are not shared publicly. To improve the effectiveness of their strategies, editors in small publishing groups are faced with undertaking an iterative trial-and-error approach. We show that Cartesian Genetic Programming, a nature-inspired evolutionary algorithm, can dramatically improve editorial strategies. The artificially evolved strategy reduced the duration of the peer review process by 30%, without increasing the pool of reviewers (in comparison to a typical human-developed strategy). Evolutionary computation has typically been used in technological processes or biological ecosystems. Our results demonstrate that genetic programs can improve real-world social systems that are usually much harder to understand and control than physical systems.