Human mobility is investigated using a continuum approach that allows to calculate the probability to observe a trip to any arbitrary region, and the fluxes between any two regions. The considered ...description offers a general and unified framework, in which previously proposed mobility models like the gravity model, the intervening opportunities model, and the recently introduced radiation model are naturally resulting as special cases. A new form of radiation model is derived and its validity is investigated using observational data offered by commuting trips obtained from the United States census data set, and the mobility fluxes extracted from mobile phone data collected in a western European country. The new modeling paradigm offered by this description suggests that the complex topological features observed in large mobility and transportation networks may be the result of a simple stochastic process taking place on an inhomogeneous landscape.
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Poisson Voronoi diagrams are useful for modeling and describing various natural patterns and for generating random lattices. Although this particular space tessellation is intensively studied by ...mathematicians, in two- and three-dimensional (3D) spaces there is no exact result known for the size distribution of Voronoi cells. Motivated by the simple form of the distribution function in the 1D case, a simple and compact analytical formula is proposed for approximating the Voronoi cell's size-distribution function in the practically important 2D and 3D cases as well. Denoting the dimensionality of the space by
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compact form is suggested for the normalized cell-size distribution function. By using large-scale computer simulations the viability of the proposed distribution function is studied and critically discussed.
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Abstract In his article “The Space-time of Physics: a Kinetic Space” Zoltán Néda reveals why is there a lot of confusion concerning the space-time of modern physics. These concepts are used ...routinely, but if we dig in deeply, finally we have to recognize that usually our knowledge is rather superficial and limited. The logic on which space and time is constructed in physics is an interesting and enlightening story, in which light plays an import role. The space-time of physics is tailored on light, it is built by using the propagation properties of light rays. In such view, it is a kinetic space. The author presents the logic of this construction in a concise and non-technical manner, so that readers without any mathematical background can also enjoy it.
Pattern selection in a ring of Kuramoto oscillators Dénes, Károly; Sándor, Bulcsú; Néda, Zoltán
Communications in nonlinear science & numerical simulation,
November 2019, 2019-11-00, Volume:
78
Journal Article
Peer reviewed
Open access
•Stable and unstable collective states for locally coupled Kuramoto oscillators are identified.•Basins of attraction of the stable states have complicated shapes.•Prediction possibilities for the ...final state of the system are discussed.•Prediction of the final state is limited by the presence of saddle points.•A visual picture is given for the patterns selection process.
Emergence of generalized synchronization patterns in a ring of identical and locally coupled Kuramoto-type rotators are investigated by different methods. These approaches offer a useful visual picture for understanding the complexity of the dynamics in the high dimensional state-space of this system. Beside the known stable stationary points novel unstable states are revealed. We find that the prediction of the final stationary state is limited by the presence of such saddle points. This is illustrated by considering and comparing two different attempts for forecasting the final stationary state.
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The distribution of scientific citations for publications selected with different rules (author, topic, institution, country, journal, etc…) collapse on a single curve if one plots the citations ...relative to their mean value. We find that the distribution of "shares" for the Facebook posts rescale in the same manner to the very same curve with scientific citations. This finding suggests that citations are subjected to the same growth mechanism with Facebook popularity measures, being influenced by a statistically similar social environment and selection mechanism. In a simple master-equation approach the exponential growth of the number of publications and a preferential selection mechanism leads to a Tsallis-Pareto distribution offering an excellent description for the observed statistics. Based on our model and on the data derived from PubMed we predict that according to the present trend the average citations per scientific publications exponentially relaxes to about 4.
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The oscillation and collective behavior of convective flows is studied by a computational fluid dynamics approach. More specifically, the rising dynamics of heated fluid columns is simulated in ...gravitational field using a simplified 2D geometry. The numerical method uses the FEniCS package for solving the coupled Navier–Stokes and heat-diffusion equations. For the flow of a single heated fluid column, the effect of the inflow yield and the nozzle diameter is studied. In agreement with the experiments, for a constant nozzle diameter the oscillation frequency increases approximately linearly as a function of the the flow rate, while for a constant flow rate the frequency decreases as a power law with the increased nozzle diameter. For the collective behavior of two nearby flows, we find a counter-phase synchronization and a decreasing trend of the common oscillation frequency with the distance between the jets. These results are in agreement with the experiments, and our computational study also suggests that the phenomenon is present on largely different length-scales.
At first glance lottery is a form of gambling, a game in which the chances of winning are extremely small. But upon a deeper look, considering that the Jackpot prize of lotteries is a result of the ...active participation of millions of players, we come to the conclusion that the interaction of the simple rules with the high number of players creates an emergent complex system. Such a system is characterized by its time-series that presents some interesting properties. Given the inherent stochastic nature of this game, it can be described within a mean-field type approach, such as the one implemented in the Local Growth and Global Reset (LGGR) model. We argue that the Jackpot time-series behaves ergodic for six lotteries with diverse formats and player pools. Specifying this consideration in the framework of the LGGR model, we model the lotteries with growth rates confirmed by the time-series. The reset rate is deduced mathematically and confirmed by data. Given these parameters, we calculate the probability density of the Jackpot prizes, that fits well the empirically observed ones. We propose to use a single w parameter, as the product of the player pools found under the jurisdiction of the lottery and the chance that a single lottery ticket wins.
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Entropy is being used in physics, mathematics, informatics and in related areas to describe equilibration, dissipation, maximal probability states and optimal compression of information. The Gini ...index, on the other hand, is an established measure for social and economical inequalities in a society. In this paper, we explore the mathematical similarities and connections in these two quantities and introduce a new measure that is capable of connecting these two at an interesting analogy level. This supports the idea that a generalization of the Gibbs-Boltzmann-Shannon entropy, based on a transformation of the Lorenz curve, can properly serve in quantifying different aspects of complexity in socio- and econo-physics.
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The most frequently used indicators for the productivity and impact of scientists are the total number of publication (Npub), total number of citations (Ncit) and the Hirsch (h) index. Since the ...seminal paper of Hirsch, in 2005, it is largely debated whether the h index can be considered as an indicator independent of Npub and Ncit. Exploiting the Paretian form for the distribution of citations for the papers authored by a researcher, here we discuss scaling relations between h, Npub and Ncit. The analysis incorporates the Gini index as an inequality measure of citation distributions and a recently proposed inequality kernel, gintropy (resembling to the entropy kernel). We find a new upper bound for the h value as a function of the total number of citations, confirmed on massive data collected from Google Scholar. Our analyses reveals also that the individualized Gini index calculated for the citations received by the publications of an author peaks around 0.8, a value much higher than the one usually reported for socio-economic inequalities.
•Citations received by the scientific publications of an author follows a Tsallis-Pareto type distribution.•Hirsch index, the number of published papers and total number of citations are statistically connected.•An upper bond for the Hirsch index as a function of the total number of citations is derived.•Data collected from Google Scholar confirms the proposed statistical laws.•The individualized Gini index for the citations received by an author peaks around 0.8.
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A mean-field like stochastic evolution equation with growth and reset terms (LGGR model) is used to model wealth distribution in modern societies. The stationary solution of the model leads to an ...analytical form for the density function that is successful in describing the observed data for all wealth categories. In the limit of high wealth values the proposed density function has the accepted Tsallis–Pareto shape. Our results are in agreement with the predictions of an earlier approach based on a mean-field like wealth exchange process.
•A growth and reset master equation provides a simple description for the observed wealth distributions.•A compact density function is given to describe the wealth inequalities in modern societies.•A collapse of wealth distributions is observed when wealth is normalized to the average wealth.•Experimental data is analyzed for wealth inequalities in USA, Russia and France.•Similarities between wealth and income distributions are discussed.
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