Viscoelasticity and Noise Properties Reveal the Formation of Biomemory in Cells

Living cells are neither perfectly elastic nor liquid and return a viscoelastic response to external stimuli. Nanoindentation provides force distance curves allowing the investigation of cell mechanical properties, and yet, these curves can differ from point to point on cell surface revealing its inhomogeneous character. In the present work, we propose a mathematical method to estimate both viscoelastic and noise properties of cells, as these are depicted on the values of the scaling exponents of relaxation function and power spectral density respectively. The method uses as input the time derivative of the response force in a nanoindentation experiment. Generalized moments method and/or rescaled range analysis are used to study the resulting time series depending on their non-stationary or stationary nature. We conducted experiments in living Ulocladium Chartarum spores. We found that spores, in the approaching phase present a viscoelastic behavior with the corresponding scaling exponent in the range 0.25-0.52, and in the retracting phase present a liquid-like behavior with exponents in the range 0.67-0.85. This substantial difference of the scaling exponents in the two phases suggests the formation of biomemory as response of the spores to the indenting AFM mechanical stimulus. The retracting phase may be described as a process driven by bluish noises, while the approaching one is driven by persistent noise.

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NON-GAUSSIAN STATISTICS OF OIL PRICING TIME-SERIES: A CASE STUDY

Fractals ◽

10.1142/s0218348x10004683 ◽

2010 ◽

Vol 18 (01) ◽

pp. 101-110 ◽

Cited By ~ 2

Author(s):

M. MOMENI ◽

I. KOURAKIS

Keyword(s):

Oil Price ◽

Energy Information Administration ◽

Range Analysis ◽

Scaling Exponents ◽

Price Fluctuations ◽

Rescaled Range ◽

Rescaled Range Analysis ◽

Generalized Hurst Exponent ◽

Oil Pricing ◽

Non Gaussian

The stochastic nature of oil price fluctuations is investigated over a twelve-year period, borrowing feedback from an existing database (USA Energy Information Administration database, available online). We evaluate the scaling exponents of the fluctuations by employing different statistical analysis methods, namely rescaled range analysis (R/S), scale windowed variance analysis (SWV) and the generalized Hurst exponent (GH) method. Relying on the scaling exponents obtained, we apply a rescaling procedure to investigate the complex characteristics of the probability density functions (PDFs) dominating oil price fluctuations. It is found that PDFs exhibit scale invariance, and in fact collapse onto a single curve when increments are measured over microscales (typically less than 30 days). The time evolution of the distributions is well fitted by a Lévy-type stable distribution. The relevance of a Lévy distribution is made plausible by a simple model of nonlinear transfer. Our results also exhibit a degree of multifractality as the PDFs change and converge toward to a Gaussian distribution at the macroscales.

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Characterization of nonlinear dynamics in a circulating fluidized bed by rescaled range analysis and short-term predictability analysis

Chemical Engineering Science ◽

10.1016/s0009-2509(01)00299-8 ◽

2001 ◽

Vol 56 (23) ◽

pp. 6545-6552 ◽

Cited By ~ 17

Author(s):

Ryuji Kikuchi ◽

Atsushi Tsutsumi

Keyword(s):

Nonlinear Dynamics ◽

Fluidized Bed ◽

Circulating Fluidized Bed ◽

Range Analysis ◽

Short Term ◽

Rescaled Range ◽

Rescaled Range Analysis ◽

Predictability Analysis

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A Brief Review of Generalized Entropies

Entropy ◽

10.3390/e20110813 ◽

2018 ◽

Vol 20 (11) ◽

pp. 813 ◽

Cited By ~ 25

Author(s):

José Amigó ◽

Sámuel Balogh ◽

Sergio Hernández

Keyword(s):

Diffusion Processes ◽

Complex Dynamics ◽

Probability Distributions ◽

Point Of View ◽

Scaling Exponent ◽

Scaling Exponents ◽

Physical Systems ◽

New Phenomena ◽

Generalized Entropies

Entropy appears in many contexts (thermodynamics, statistical mechanics, information theory, measure-preserving dynamical systems, topological dynamics, etc.) as a measure of different properties (energy that cannot produce work, disorder, uncertainty, randomness, complexity, etc.). In this review, we focus on the so-called generalized entropies, which from a mathematical point of view are nonnegative functions defined on probability distributions that satisfy the first three Shannon–Khinchin axioms: continuity, maximality and expansibility. While these three axioms are expected to be satisfied by all macroscopic physical systems, the fourth axiom (separability or strong additivity) is in general violated by non-ergodic systems with long range forces, this having been the main reason for exploring weaker axiomatic settings. Currently, non-additive generalized entropies are being used also to study new phenomena in complex dynamics (multifractality), quantum systems (entanglement), soft sciences, and more. Besides going through the axiomatic framework, we review the characterization of generalized entropies via two scaling exponents introduced by Hanel and Thurner. In turn, the first of these exponents is related to the diffusion scaling exponent of diffusion processes, as we also discuss. Applications are addressed as the description of the main generalized entropies advances.

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Comparative analysis of the stock quotes dynamics for IT-sector and the entertainment industry companies based on the characteristics of memory depth

SHS Web of Conferences ◽

10.1051/shsconf/202110701003 ◽

2021 ◽

Vol 107 ◽

pp. 01003

Author(s):

Nataliia Maksyshko ◽

Oksana Vasylieva

Keyword(s):

Time Series ◽

Comparative Analysis ◽

Rapid Development ◽

Entertainment Industry ◽

Long Term Memory ◽

Range Analysis ◽

Goods And Services ◽

Rescaled Range Analysis ◽

Persistence Property ◽

The Impact

The article is devoted to the study and comparative analysis of the stock quotes dynamics for the world’s leading companies in the IT sector and the entertainment industry. Today, these areas are developing the fastest and most powerful, which attracts the attention of investors around the world. This is due to the rapid development of digital communication technologies, the growth of intellectualization and individualization of goods and services, and so on. These spheres have strong development potential, but the question to how their companies’ stock quotes respond to the impact of such a natural but crisis phenomenon as the COVID-19 pandemic remains open. Based on the nonlinear paradigm of the financial markets dynamics, the paper considers and conducts a comprehensive fractal analysis of the quotations dynamics for six leading companies (Apple Inc., Tesla Inc., Alphabet Inc., The Walt Disney Company, Sony Corporation, Netflix) in this area before and during the COVID-19 pandemic. As a result of the application of the rescaled range analysis (R/S analysis), the presence of the persistence property and long-term memory in the stock quotes dynamics for all companies and its absence in their time series of profitability was confirmed. The application of the method of sequential R/S analysis made it possible to construct fuzzy sets of memory depths for the considered time series and to deepen the analysis of the dynamics due to the quantitative characteristics calculated on their basis. Taking into account the characteristics of memory depth in the dynamics of quotations made it possible to conduct a comparative analysis of the dynamics, both under the influence of the natural crisis situation and in terms of investing in different terms. The peculiarities of the delayed profitability dynamics of quotations for each of the companies are also taken into consideration and compared. The developed recommendations can be used in investment activities in the stock market.

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Multivariate rescaled range analysis

Physica A Statistical Mechanics and its Applications ◽

10.1016/j.physa.2021.126631 ◽

2021 ◽

pp. 126631

Author(s):

M. Meraz ◽

J. Alvarez-Ramirez ◽

E. Rodriguez

Keyword(s):

Range Analysis ◽

Rescaled Range ◽

Rescaled Range Analysis

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Solar cycle changes in the geo-effectiveness of small-scale solar wind turbulence measured by Wind and ACE at 1 AU

Annales Geophysicae ◽

10.5194/angeo-25-1183-2007 ◽

2007 ◽

Vol 25 (5) ◽

pp. 1183-1197 ◽

Cited By ~ 3

Author(s):

M. L. Parkinson ◽

R. C. Healey ◽

P. L. Dyson

Keyword(s):

Solar Wind ◽

Solar Cycle ◽

Solar Minimum ◽

Large Scale ◽

Small Scale ◽

Scaling Exponent ◽

Mhd Turbulence ◽

Scaling Exponents ◽

Solar Wind Turbulence ◽

Wind Turbulence

Abstract. Multi-scale structure of the solar wind in the ecliptic at 1 AU undergoes significant evolution with the phase of the solar cycle. Wind spacecraft measurements during 1995 to 1998 and ACE spacecraft measurements during 1997 to 2005 were used to characterise the evolution of small-scale (~1 min to 2 h) fluctuations in the solar wind speed vsw, magnetic energy density B2, and solar wind ε parameter, in the context of large-scale (~1 day to years) variations. The large-scale variation in ε most resembled large-scale variations in B2. The probability density of large fluctuations in ε and B2 both had strong minima during 1995, a familiar signature of solar minimum. Generalized Structure Function (GSF) analysis was used to estimate inertial range scaling exponents aGSF and their evolution throughout 1995 to 2005. For the entire data set, the weighted average scaling exponent for small-scale fluctuations in vsw was aGSF=0.284±0.001, a value characteristic of intermittent MHD turbulence (>1/4), whereas the scaling exponents for corresponding fluctuations in B2 and ε were aGSF=0.395±0.001 and 0.334±0.001, respectively. These values are between the range expected for Gaussian fluctuations (1/2) and Kolmogorov turbulence (1/3). However, the scaling exponent for ε changed from a Gaussian-Kolmogorov value of 0.373±0.005 during 1997 (end of solar minimum) to an MHD turbulence value of 0.247±0.004 during 2003 (recurrent fast streams). Changes in the characteristics of solar wind turbulence may be reproducible from one solar cycle to the next.

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Crosscorrelation Analysis between P2P Lending Market and Stock Market in China

Mathematical Problems in Engineering ◽

10.1155/2020/7134172 ◽

2020 ◽

Vol 2020 ◽

pp. 1-9

Author(s):

Bin Wang ◽

Zhonghui Ding ◽

Xiang Wang ◽

Kai Shi

Keyword(s):

Stock Market ◽

Hurst Index ◽

Range Analysis ◽

Rescaled Range ◽

Rescaled Range Analysis ◽

P2p Lending

We first use the Hurst index and the Vn statistic to study the respective characteristics of the P2P lending market and the stock market by rescaled range analysis. In terms of fluctuations, there is an antipersistence in the P2P lending market and long-term persistence in the stock market. Then, we studied the crosscorrelation between the daily logarithmic return series of P2P lending market and stock market and found that the crosscorrelation was multifractal and antipersistent.

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