Anomalous diffusion behavior in parliamentary presence

Vieira, Denner S.; Riveiros, Jesus M. E.; Jauregui, Max; Mendes, R. S.

doi:10.1103/physreve.99.042141

Cited by 14 publications

(22 citation statements)

References 47 publications

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“…Recently, we have also used the noisy voter model to model parliamentary presence [ 45 ]. A paper by Vieira et al [ 134 ] has inspired us to look into the Lithuanian parliamentary presence data. Unlike Vieira et al, we have observed not a ballistic diffusion regime but superdiffusive behavior; however, both of these regimes can be obtained from the noisy voter model with imperfectly acting agents.…”

Section: Agent-based Model Of the Long-range Memory In The Financial Marketsmentioning

confidence: 99%

Understanding the Nature of the Long-Range Memory Phenomenon in Socioeconomic Systems

Kazakevičius

Kononovičius

Kaulakys

et al. 2021

Entropy

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In the face of the upcoming 30th anniversary of econophysics, we review our contributions and other related works on the modeling of the long-range memory phenomenon in physical, economic, and other social complex systems. Our group has shown that the long-range memory phenomenon can be reproduced using various Markov processes, such as point processes, stochastic differential equations, and agent-based models—reproduced well enough to match other statistical properties of the financial markets, such as return and trading activity distributions and first-passage time distributions. Research has lead us to question whether the observed long-range memory is a result of the actual long-range memory process or just a consequence of the non-linearity of Markov processes. As our most recent result, we discuss the long-range memory of the order flow data in the financial markets and other social systems from the perspective of the fractional Lèvy stable motion. We test widely used long-range memory estimators on discrete fractional Lèvy stable motion represented by the auto-regressive fractionally integrated moving average (ARFIMA) sample series. Our newly obtained results seem to indicate that new estimators of self-similarity and long-range memory for analyzing systems with non-Gaussian distributions have to be developed.

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Section: Agent-based Model Of the Long-range Memory In The Financial Marketsmentioning

confidence: 99%

Understanding the Nature of the Long-Range Memory Phenomenon in Socioeconomic Systems

Kazakevičius

Kononovičius

Kaulakys

et al. 2021

Entropy

View full text Add to dashboard Cite

show abstract

“…which is a beta distribution, where B(•, •) stands for the beta function. This function has been employed to model parliamentary presence and is a solution of the following diffusion equation [19]:…”

Section: A Family Of Generalized Fokker-planck Equationsmentioning

confidence: 99%

“…However, Eq. (19) shows that V (x) can be very different from the harmonic potential if C(x) and D(x) are non-constant functions. On the other hand, if λ = 1, there are infinite possibilities for choosing the functions C(x) and D(x) such that the effective potential V (x) is a harmonic one.…”

Section: Stationary Solutionsmentioning

confidence: 99%

“…In addition, several works have considered generalized diffusion equations which have solutions related to non-Gaussian distributions; for instance, Subbotin and q-Gaussian ones. These generalizations usually involve the use of a variable diffusion coefficient [15,16], the addition of nonlinear terms [16][17][18][19] or the employment of fractional derivatives [20][21][22]. In the context of probability distributions, the linear diffusion equation can be interpreted as a Fokker-Planck equation [17,23].…”

Section: Introductionmentioning

confidence: 99%

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Stationary solution and $H$ theorem for a generalized Fokker-Planck equation

Jauregui,

Lucchi,

Passos

et al. 2021

Preprint

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We investigate a family of generalized Fokker-Planck equations that contains Richardson and porous media equations as members. Considering a confining drift term that is related to an effective potential, we show that each equation of this family has a stationary solution that depends on this potential. This stationary solution encompasses several well-known probability distributions. Moreover, we verify an H theorem for the generalized Fokker-Planck equations using free-energy-like functionals. We show that the energy-like part of each functional is based on the effective potential and the entropy-like part is a generalized Tsallis entropic form, which has an unusual dependence on the position and can be related to a generalization of the Kullback-Leibler divergence. We also verify that the optimization of this entropic-like form subjected to convenient constraints recovers the stationary solution. The analysis presented here includes several studies about H theorems for other generalized Fokker-Planck equations as particular cases.

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“…Then, the porous media problem is a particular case where γ is coupled to ν. The PDF distribution of tracers (23) has numerous applications in complex systems, for example in modeling of protein diffusion within bacteria [29], parliamentary presence data [77] and stock markets [78].…”

Section: B Power-law Diffusionmentioning

confidence: 99%

Random diffusivity scenarios behind anomalous non-Gaussian diffusion

Santos,

Colombo,

Anteneodo

2021

Preprint

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The standard diffusive spreading, characterized by a Gaussian distribution with mean square displacement that grows linearly with time, can break down, for instance, under the presence of correlations and heterogeneity. In this work, we consider the spread of a population of fractional (long-time correlated) Brownian walkers, with time-dependent and heterogeneous diffusivity.We aim to obtain, from a superstatistical approach, the possible scenarios related to these individual-level features from the observation of the temporal evolution of the population spatial distribution. We develop and discuss the possibility and limitations of this connection for the broad class of self-similar diffusion processes. Our results are presented in terms of a general framework, which is then used to address particular cases, including the well-known Laplace and porous media diffusion, and their extensions.

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Anomalous diffusion behavior in parliamentary presence

Cited by 14 publications

References 47 publications

Understanding the Nature of the Long-Range Memory Phenomenon in Socioeconomic Systems

Understanding the Nature of the Long-Range Memory Phenomenon in Socioeconomic Systems

Stationary solution and $H$ theorem for a generalized Fokker-Planck equation

Random diffusivity scenarios behind anomalous non-Gaussian diffusion

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