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Global-Scale Synchronization in the Meteorological Data: A Vectorial Analysis That Includes Higher-Order Differences. CLIMATE 2020. [DOI: 10.3390/cli8110128] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
To examine the evidence of global warming, in recent years, there has been a growing interest in the statistical analysis of time-dependent meteorological data. In this paper, for 116 observational stations in the world, sequential variations of the monthly distributions of meteorological data are analyzed vectorially. For specific monthly data, temperatures and precipitations are chosen, both of which are averaged over three decades. Climate change can be revealed through the intersecting angle between two 33-dimensional vectors being composed with monthly mean values. Subsequently, the angle data for the entire stations are analyzed statistically and compared between the former (1931–1980) and the latter (1951–2010) periods. Irrespective of the period and the hemisphere, the variation of the angles is found to show the exponential growth as a function of their latitudes. Furthermore, consistent with other studies, this trend is shown to become stronger in the latter period, indicating that the so-called snow/ice-albedo feedback occurs. In contrast to the temperatures, for the precipitations, no significant correlation is found between the angle and the latitude. To examine the albedo effect in more detail, a regional analysis for 75 stations in Japan is carried out as well. Numerical results show that the effect is significant even for the relatively narrow latitudinal range (19%) of the hemisphere. Finally, a synchronization of the monthly patterns of temperatures is given between the northern district of Japan and both North America and Eastern Europe.
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Aliakbari A, Manshour P, Salehi MJ. Records in fractal stochastic processes. CHAOS (WOODBURY, N.Y.) 2017; 27:033116. [PMID: 28364750 DOI: 10.1063/1.4979348] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The record statistics in stationary and non-stationary fractal time series is studied extensively. By calculating various concepts in record dynamics, we find some interesting results. In stationary fractional Gaussian noises, we observe a universal behavior for the whole range of Hurst exponents. However, for non-stationary fractional Brownian motions, the record dynamics is crucially dependent on the memory, which plays the role of a non-stationarity index, here. Indeed, the deviation from the results of the stationary case increases by increasing the Hurst exponent in fractional Brownian motions. We demonstrate that the memory governs the dynamics of the records as long as it causes non-stationarity in fractal stochastic processes; otherwise, it has no impact on the record statistics.
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Affiliation(s)
- A Aliakbari
- Department of Physics, Faculty of Sciences, Persian Gulf University, 75169 Bushehr, Iran
| | - P Manshour
- Department of Physics, Faculty of Sciences, Persian Gulf University, 75169 Bushehr, Iran
| | - M J Salehi
- Department of Physics, Faculty of Sciences, Persian Gulf University, 75169 Bushehr, Iran
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Ben-Naim E, Krapivsky PL, Lemons NW. Scaling exponents for ordered maxima. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:062139. [PMID: 26764664 DOI: 10.1103/physreve.92.062139] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2015] [Indexed: 06/05/2023]
Abstract
We study extreme value statistics of multiple sequences of random variables. For each sequence with N variables, independently drawn from the same distribution, the running maximum is defined as the largest variable to date. We compare the running maxima of m independent sequences and investigate the probability S(N) that the maxima are perfectly ordered, that is, the running maximum of the first sequence is always larger than that of the second sequence, which is always larger than the running maximum of the third sequence, and so on. The probability S(N) is universal: it does not depend on the distribution from which the random variables are drawn. For two sequences, S(N)∼N(-1/2), and in general, the decay is algebraic, S(N)∼N(-σ(m)), for large N. We analytically obtain the exponent σ(3)≅1.302931 as root of a transcendental equation. Furthermore, the exponents σ(m) grow with m, and we show that σ(m)∼m for large m.
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Affiliation(s)
- E Ben-Naim
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - P L Krapivsky
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA
- Institut de Physique Théorique, Université Paris-Saclay, CEA and CNRS, 91191 Gif-sur-Yvette, France
| | - N W Lemons
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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Sabir B, Santhanam MS. Record statistics of financial time series and geometric random walks. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:032126. [PMID: 25314414 DOI: 10.1103/physreve.90.032126] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2014] [Indexed: 06/04/2023]
Abstract
The study of record statistics of correlated series in physics, such as random walks, is gaining momentum, and several analytical results have been obtained in the past few years. In this work, we study the record statistics of correlated empirical data for which random walk models have relevance. We obtain results for the records statistics of select stock market data and the geometric random walk, primarily through simulations. We show that the distribution of the age of records is a power law with the exponent α lying in the range 1.5≤α≤1.8. Further, the longest record ages follow the Fréchet distribution of extreme value theory. The records statistics of geometric random walk series is in good agreement with that obtained from empirical stock data.
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Affiliation(s)
- Behlool Sabir
- Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pune 411 008, India
| | - M S Santhanam
- Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pune 411 008, India
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Ben-Naim E, Krapivsky PL. Slow kinetics of Brownian maxima. PHYSICAL REVIEW LETTERS 2014; 113:030604. [PMID: 25083626 DOI: 10.1103/physrevlett.113.030604] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/03/2014] [Indexed: 06/03/2023]
Abstract
We study extreme-value statistics of Brownian trajectories in one dimension. We define the maximum as the largest position to date and compare maxima of two particles undergoing independent Brownian motion. We focus on the probability P(t) that the two maxima remain ordered up to time t and find the algebraic decay P ∼ t(-β) with exponent β = 1/4. When the two particles have diffusion constants D(1) and D(2), the exponent depends on the mobilities, β = (1/π) arctan sqrt[D(2)/D(1)]. We also use numerical simulations to investigate maxima of multiple particles in one dimension and the largest extension of particles in higher dimensions.
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Affiliation(s)
- E Ben-Naim
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - P L Krapivsky
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA
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Ben-Naim E, Krapivsky PL. Statistics of superior records. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:022145. [PMID: 24032813 DOI: 10.1103/physreve.88.022145] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2013] [Revised: 07/15/2013] [Indexed: 06/02/2023]
Abstract
We study statistics of records in a sequence of random variables. These identical and independently distributed variables are drawn from the parent distribution ρ. The running record equals the maximum of all elements in the sequence up to a given point. We define a superior sequence as one where all running records are above the average record expected for the parent distribution ρ. We find that the fraction of superior sequences S(N) decays algebraically with sequence length N, S(N)~N(-β) in the limit N→∞. Interestingly, the decay exponent β is nontrivial, being the root of an integral equation. For example, when ρ is a uniform distribution with compact support, we find β=0.450265. In general, the tail of the parent distribution governs the exponent β. We also consider the dual problem of inferior sequences, where all records are below average, and find that the fraction of inferior sequences I(N) decays algebraically, albeit with a different decay exponent, I(N)~N(-α). We use the above statistical measures to analyze earthquake data.
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Affiliation(s)
- E Ben-Naim
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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Shcherbakov R, Davidsen J, Tiampo KF. Record-breaking avalanches in driven threshold systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:052811. [PMID: 23767588 DOI: 10.1103/physreve.87.052811] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2012] [Revised: 02/03/2013] [Indexed: 06/02/2023]
Abstract
Record-breaking avalanches generated by the dynamics of several driven nonlinear threshold models are studied. Such systems are characterized by intermittent behavior, where a slow buildup of energy is punctuated by an abrupt release of energy through avalanche events, which usually follow scale-invariant statistics. From the simulations of these systems it is possible to extract sequences of record-breaking avalanches, where each subsequent record-breaking event is larger in magnitude than all previous events. In the present work, several cellular automata are analyzed, among them the sandpile model, the Manna model, the Olami-Feder-Christensen (OFC) model, and the forest-fire model to investigate the record-breaking statistics of model avalanches that exhibit temporal and spatial correlations. Several statistical measures of record-breaking events are derived analytically and confirmed through numerical simulations. The statistics of record-breaking avalanches for the four models are compared to those of record-breaking events extracted from the sequences of independent and identically distributed (i.i.d.) random variables. It is found that the statistics of record-breaking avalanches for the above cellular automata exhibit behavior different from that observed for i.i.d. random variables, which in turn can be used to characterize complex spatiotemporal dynamics. The most pronounced deviations are observed in the case of the OFC model with a strong dependence on the conservation parameter of the model. This indicates that avalanches in the OFC model are not independent and exhibit spatiotemporal correlations.
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Affiliation(s)
- Robert Shcherbakov
- Department of Earth Sciences, University of Western Ontario, London, Ontario, Canada N6A 5B7.
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Wergen G, Volovik D, Redner S, Krug J. Rounding effects in record statistics. PHYSICAL REVIEW LETTERS 2012; 109:164102. [PMID: 23215081 DOI: 10.1103/physrevlett.109.164102] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/19/2012] [Indexed: 06/01/2023]
Abstract
We analyze record-breaking events in time series of continuous random variables that are subsequently discretized by rounding to integer multiples of a discretization scale Δ>0. Rounding leads to ties of an existing record, thereby reducing the number of new records. For an infinite number of random variables that are drawn from distributions with a finite upper limit, the number of discrete records is finite, while for distributions with a thinner than exponential upper tail, fewer discrete records arise compared to continuous variables. In the latter case, the record sequence becomes highly regular at long times.
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Affiliation(s)
- G Wergen
- Institute for Theoretical Physics, University of Cologne, 50937 Köln, Germany
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