There is a number of studies, in which it is established that the observed flows of microposts generated by microblogging social networks (e.g., Twitter) are characterized by avalanche-like behavior. ...Time series of microposts depicting such streams are the time series with a power-law distribution, with 1/f noise and long memory. Despite this, there are no studies devoted to the detection and analysis of self-organized critical state, subcritical phase, and supercritical phase. The presented paper is devoted to the detection and investigation of such critical states and phases. An algorithm is proposed that allowed to detect of critical phases and critical conditions on Twitter, based on the analysis of retweets time series corresponding to the three debates of the 2016 United States Presidential Election, as the most popular debate in the history of America, collecting 84 million live views.
Many real-world systems of various origins are capable of self-organization to the edge of a phase transition, characterized by avalanche-like behavior. Therefore, it is important, by observing the ...behavior of early warning measures for dynamical series generated by systems, to timely see the early warning signals (precursors) of such self-organization and, if necessary, take preventive measures. To date, convincing evidence of self-organization to the edge of a phase transition has been obtained, but no effective precursors for this self-organization have been found. This research explores precursors for the Twitter self-organization based on the analysis of the behavior of measures directly related to the critical slowdown of the network and measures of the phase space reconstructed by the Takens method for the series of the number of network users creating avalanches of retweets in the network, corresponding to the three debates of the 2016 United States Presidential Election. We hydrated the relevant Tweet IDs, which were obtained from the Harvard Dataverse using the Social Feed Manager, to form this series. Preliminarily, we explore the potential of measures for early detection of self-organization of sandpile cellular automata as systems with Twitter-equivalent self-organization mechanisms. The equivalence is justified in the proposed discrete-time model for Twitter self-organization to the edge of a phase transition. It is found that there are more moments of the Twitter self-organization than the moments of time when debates started, and Twitter stays at the edge of a phase transition longer than the debate lasts. The effective measures, as the measures with the lowest number of false early warning signals, among all studied measures and for all studied systems, are dispersion and correlation dimension. Obtained results are practically important in the design and implementation of early warning systems for the systems with similar mechanisms for sandpile cellular automata self-organization to the edge of a phase transition.
Critical phenomena in stock exchange are regularly occurring and difficult to predict events, often leading to disastrous consequences. The presented paper is devoted to the search and research of ...early warning signals of critical transitions in stock exchange based on the results of a multifractal analysis of a series of transactions in shares of public companies. We have proposed and justified the use of certain features of behavior of multifractal spectrum shape parameters such as signals. As model time series, on which methods of multifractal analysis were tested, we used a series of the number of unstable sites of the sandpile automaton on the random Erdős–Rényi graph, self-organizing into critical and bistable states. It was found that the early warning signals for both cellular automata and stock exchanges are an increase in the magnitude of the maximum position, a decrease in the width, and a decrease, followed by a sharp increase, in the value of the spectrum asymmetry parameter.
Many different precursors are known, but not all of which are effective, i.e., giving enough time to take preventive measures and with a minimum number of false early warning signals. The study aims ...to select and study effective early warning measures from a set of measures directly related to critical slowing down as well as to the change in the structure of the reconstructed phase space in the neighborhood of the critical transition point of sand cellular automata. We obtained a dynamical series of the number of unstable nodes in automata with stochastic and deterministic vertex collapse rules, with different topological graph structure and probabilistic distribution law for pumping of automata. For these dynamical series we computed windowed early warning measures. We formulated the notion of an effective measure as the measure that has the smallest number of false signals and the longest early warning time among the set of early warning measures. We found that regardless of the rules, topological structure of graphs, and probabilistic distribution law for pumping of automata, the effective early warning measures are the embedding dimension, correlation dimension, and approximation entropy estimated using the false nearest neighbors algorithm. The variance has the smallest early warning time, and the largest Lyapunov exponent has the greatest number of false early warning signals. Autocorrelation at lag-1 and Welch’s estimate for the scaling exponent of power spectral density cannot be used as early warning measures for critical transitions in the automata. The efficiency definition we introduced can be used to search for and investigate new early warning measures. Embedding dimension, correlation dimension and approximation entropy can be used as effective real-time early warning measures for critical transitions in real-world systems isomorphic to sand cellular automata such as microblogging social network and stock exchange.
The sandpile cellular automata, despite the simplicity of their basic rules, are adequate mathematical models of real-world systems, primarily open nonlinear systems capable to self-organize into the ...critical state. Such systems surround us everywhere. Starting from processes at microscopic distances in the human brain and ending with large-scale water flows in the oceans. The detection of critical transitions precursors in sandpile cellular automata will allow progress significantly in the search for effective early warning signals for critical transitions in complex real systems. The presented paper is devoted to the detection and investigation of such signals based on multifractal analysis of the time series of falls of the cellular automaton cells. We examined cellular automata in square lattice and random graphs using standard and facilitated rules. It has been established that log wavelet leaders cumulant are effective early warning measures of the critical transitions. Common features and differences in the behavior of the log cumulants when cellular automata transit into the self-organized critical state and the self-organized bistability state are also established.
Recently, there has been an increasing number of empirical evidence supporting the hypothesis that spread of avalanches of microposts on social networks, such as Twitter, is associated with some ...sociopolitical events. Typical examples of such events are political elections and protest movements. Inspired by this phenomenon, we built a phenomenological model that describes Twitter’s self-organization in a critical state. An external manifestation of this condition is the spread of avalanches of microposts on the network. The model is based on a fractional three-parameter self-organization scheme with stochastic sources. It is shown that the adiabatic mode of self-organization in a critical state is determined by the intensive coordinated action of a relatively small number of network users. To identify the critical states of the network and to verify the model, we have proposed a spectrum of three scaling indicators of the observed time series of microposts.
Two types of novel graphene-based components, namely, filters and electro-optical switches in guided wave configuration are suggested and analysed. The filters differ from the known ones with ...collinear orientation of the input and output waveguides by geometry and symmetry. The components consist of a circular graphene disk and two nanoribbons oriented at <inline-formula><tex-math notation="LaTeX">90^\circ</tex-math></inline-formula> to each other in the plane of the graphene layer. The graphene elements are placed on a dielectric substrate. We show that change in symmetry leads to a drastic change in the properties of the components. The physical principle of the devices is based on the dipole, quadrupole and hexapole resonances in the graphene disk which define stop-band, pass-band and stop-band frequency characteristics, respectively. A combination of stop-band and pass-band filter properties by shifing the electronic Fermi level allows one to design a switch. Numerical simulations show that the suggested components have very small dimensions, good characteristics and provide a dynamic control of their central frequency via electrostatic gating.
A novel graphene antenna composed of a graphene dipole and four auxiliary graphene sheets oriented at 90∘ to each other is proposed and analyzed. The sheets play the role of reflectors. A detailed ...group-theoretical analysis of symmetry properties of the discussed antennas has been completed. Through electric field control of the chemical potentials of the graphene elements, the antenna can provide a quasi-omnidirectional diagram, a one- or two-directional beam regime, dynamic control of the beam width and, due to the vertical orientation of the dipole with respect to the base substrate, a 360∘ beam steering in the azimuth plane. An additional graphene layer on the base permits control of the radiation pattern in the θ-direction. Radiation patterns in different working states of the antenna are considered using symmetry arguments. We discuss the antenna parameters such as input reflection coefficient, total efficiency, front-to-back ratio, and gain. An equivalent circuit of the antenna is suggested. The proposed antenna operates at frequencies between 1.75 THz and 2.03 THz. Depending on the active regime defined by the chemical potentials set on the antenna graphene elements, the maximum gain varies from 0.86 to 1.63.
Selection of an appropriate gating system for a consumable pattern is a long and time-consuming process that requires considerable effort. Advanced design technologies can be used to design the ...gating system and to simulate the casting process based on the design. Simulation and design of the gating system allow detection of types of defects in the casting at the development stage. Parametrical changing of the gating system 3D model and variation of its characteristics, and repeated simulation of cooling, crystallization and mold filling processes can provide high quality casting.
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