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21.
22.
Scaling properties of strong avalanches in sand-pile
Alexander Shapoval, M. Shnirman, 2005, original scientific article

Keywords: sandpile, distribution, finite-size scaling
Published in RUNG: 19.04.2021; Views: 1669; Downloads: 0
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23.
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How size of target avalanches influences prediction efficiency
Alexander Shapoval, M. Shnirman, 2004, original scientific article

Abstract: Bak, Tang, and Wiesenfeld [Phys. Rev. Lett.59, 381 (1987)] introduced their sand-pile (BTW sand-pile) as the cellular automata coming to their critical state without tuning any inner model parameters. The main model features deal with grains falling slowly onto the two-dimensional lattice and a quick deterministic transport of the superfluous grains to the boundary. The simplest modifications of the BTW sand-pile develop a random transport mechanism instead of a deterministic one. The model transportation of the grains generates avalanches. We find that before the big avalanches the height of the pile increases and the singular grains organize themselves in special clusters. These observations lead to the formal algorithm that predicts the big avalanches in advance with a certain efficiency. However the efficiency for the BTW sand-pile is worse than that for its stochastic modifications.
Keywords: sandpile, prediction, avalanches
Published in RUNG: 19.04.2021; Views: 1584; Downloads: 0
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25.
Strong events in the sand-pile model
Alexander Shapoval, M. Shnirman, 2004, original scientific article

Abstract: Here is a sand-pile introduced by Bak et al. The system accumulates particles one by one. From time to time it topples. Every toppling initiates an event. The distribution of the events' size follows a power law for all the events except the strongest ones. The fraction of the strongest events does not depend on the system length. The number of particles and their clustering increase before the strongest events.
Keywords: sandpile, prediction, power-law
Published in RUNG: 19.04.2021; Views: 1663; Downloads: 0
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26.
Two regimes in the regularity of sunspot number
Alexander Shapoval, Jean-Louis Le Mouël, Vincent Courtillot, M. Shnirman, 2013, original scientific article

Abstract: Sunspot numbers WN display quasi-periodical variations that undergo regime changes. These irregularities could indicate a chaotic system and be measured by Lyapunov exponents. We define a functional λ (an "irregularity index") that is close to the (maximal) Lyapunov exponent for dynamical systems and well defined for series with a random component: this allows one to work with sunspot numbers. We compute λ for the daily WN from 1850 to 2012 within 4 yr sliding windows: λ exhibit sharp maxima at solar minima and secondary maxima at solar maxima. This pattern is reflected in the ratio R of the amplitudes of the main versus secondary peaks. Two regimes have alternated in the past 150 yr, R1 from 1850 to 1915 (large λ and R values) and R2 from 1935 to 2005 (shrinking difference between main and secondary maxima, R values between 1 and 2). We build an autoregressive model consisting of Poisson noise plus an 11 yr cycle and compute its irregularity index. The transition from R1 to R2 can be reproduced by strengthening the autocorrelation a of the model series. The features of the two regimes are stable for model and WN with respect to embedding dimension and delay. Near the time of the last solar minimum (~2008), the irregularity index exhibits a peak similar to the peaks observed before 1915. This might signal a regime change back from R2 to R1 and the onset of a significant decrease of solar activity.
Keywords: Lyapunov exponent, solar activity, solar cycle
Published in RUNG: 19.04.2021; Views: 1761; Downloads: 57
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27.
Predictability and scaling in a BTW sandpile on a self-similar lattice
Alexander Shapoval, Dayana Savostianova, M. Shnirman, 2021, original scientific article

Abstract: This paper explores the predictability of a Bak–Tang–Wiesenfeld isotropic sandpile on a self-similar lattice, introducing an algorithm which predicts the occurrence of target events when the stress in the system crosses a critical level.
Keywords: isotropic sandpiles, predictability, scaling, error diagram
Published in RUNG: 15.04.2021; Views: 1668; Downloads: 0
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Mismatch of supply and demand as a response to demand uncertainty
Alexander Shapoval, Vasily M. Goncharenko, 2016, original scientific article

Keywords: general equilibrium, monopolistic competition
Published in RUNG: 07.04.2021; Views: 2148; Downloads: 0
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30.
Linguistic equilibrium with local and world languages : challenges of globalisation
Denis Davydov, Alexander Shapoval, Shlomo Weber, 2018, original scientific article

Abstract: In this paper we introduce a model of a society with two distinct linguistic groups, each consisting of heterogeneous individuals speaking their native language. There is also a world language so that every individual is faced with four learning choices: to study the other local language only, to study the world language only, to study both, and to refrain from studying either language. We examine the Nash equilibiria of that game determined by communicative benefits (Selten & Pool), and address inefficiency of the equilibrium. We then show that government subsidies for language learning could serve as welfare‐enhancing policies. Finally, we analyze the three‐language policy, certain variants of which have been adopted in multilingual countries or regions.
Keywords: three-language formula, Nash equilibrium, inefficiency
Published in RUNG: 07.04.2021; Views: 1822; Downloads: 95
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