Fokker-Planck approach to non-Gaussian normal diffusion: Hierarchical dynamics for diffusing diffusivity

Abe, Sumiyoshi

doi:10.1103/physreve.102.042136

Cited by 4 publications

(12 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since cell decision-making is a stochastic process of the continuous internal variable X, we can assume the existence of the Fokker-Planck description. When there exists a timescale separation between two dynamical variables, a Hierarchical Fokker-Planck equation [32] can be derived. In this section, we shall show how this formalism can be applied in cell decision-making and also will show how it helps us to study the origin of biophysical force in terms of the information-theoretic quantities as shown in Fig.…”

Section: Connection Between Hierarchical Fokker-planck Equation and B...mentioning

confidence: 99%

“…In the case of cell decision-making, microscopic dynamics have been studied, specifically in the context of active Brownian motion and cell migration using Langevin equations [22,30,31]. Understanding dynamics induced by a timescale separation at the mesoscopic scale, using Fokker-Planck equations, has been studied only recently by S. Abe [32]. Specifically, we will assume a timescale separation where cell decision time, when internal states evolve, is slower than the characteristic time of the variables that belong to the cellular microenvironment.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Cell decision-making through the lens of Bayesian learning

Barua¹,

Haralampos²

2023

Preprint

View full text Add to dashboard Cite

Cell decision-making refers to the process by which cells gather information from their local microenvironment and regulate their internal states to create appropriate responses. Microenvironmental cell sensing plays a key role in this process. Our hypothesis is that cell decision-making regulation is dictated by Bayesian learning. In this article, we explore the implications of this hypothesis for internal state temporal evolution. By using a timescale separation between internal and external variables on the mesoscopic scale, we derive a hierarchical Fokker-Planck equation for cell-microenvironment dynamics. By combining this with the Bayesian learning hypothesis, we find that changes in microenvironmental entropy dominate cell state probability distribution. Finally, we use these ideas to understand how cell sensing impacts cell decision-making. Notably, our formalism allows us to understand cell state dynamics even without exact biochemical information about cell sensing processes by considering a few key parameters.

show abstract

Section: Connection Between Hierarchical Fokker-planck Equation and B...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Cell decision-making through the lens of Bayesian learning

Barua¹,

Haralampos²

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…Since cell decision making is a stochastic process of the continuous internal variable

, we can assume the existence of the Fokker–Planck description. When there exists a timescale separation between two dynamical variables, a hierarchical Fokker–Planck equation [ 32 ] can be derived. In this section, we shall show how this formalism can be applied in cell decision making and also will show how it helps us to study the origin of biophysical forces in terms of the information-theoretic quantities as shown in Figure 1 .…”

Section: Connection Between Hierarchical Fokker–planck Equation and B...mentioning

confidence: 99%

“…In the case of cell decision making, microscopic dynamics have been studied, specifically in the context of active Brownian motion and cell migration using Langevin equations [ 22 , 30 , 31 ]. Understanding dynamics induced by a timescale separation at the mesoscopic scale, using Fokker–Planck equations, was studied only recently by S. Abe [ 32 ].…”

Section: Introductionmentioning

confidence: 99%

Cell Decision Making through the Lens of Bayesian Learning

Barua

Hatzikirou

2023

Entropy

View full text Add to dashboard Cite

Cell decision making refers to the process by which cells gather information from their local microenvironment and regulate their internal states to create appropriate responses. Microenvironmental cell sensing plays a key role in this process. Our hypothesis is that cell decision-making regulation is dictated by Bayesian learning. In this article, we explore the implications of this hypothesis for internal state temporal evolution. By using a timescale separation between internal and external variables on the mesoscopic scale, we derive a hierarchical Fokker–Planck equation for cell-microenvironment dynamics. By combining this with the Bayesian learning hypothesis, we find that changes in microenvironmental entropy dominate the cell state probability distribution. Finally, we use these ideas to understand how cell sensing impacts cell decision making. Notably, our formalism allows us to understand cell state dynamics even without exact biochemical information about cell sensing processes by considering a few key parameters.

show abstract

“…In particular, a generalization of the Fokker-Planck theory, in which the diffusion coefficient is not a constant but a fluctuating variable that may describe the effects originating from heterogeneity of the crust and a complex landscape of the stress distribution at faults, and see how such an theory can explain the features of the temporal pattern of aftershocks. For this purpose, "a modified version" of the approach recently proposed in Reference [15] is employed for representing the dynamical hierarchy. It is shown that the relaxation function in Equation (2) can be obtained for the subsystem defined through elimination of the fluctuating diffusivity.…”

Section: Introductionmentioning

confidence: 99%

Aftershocks and Fluctuating Diffusivity

Abe

Suzuki

Tayurskiı̆

2023

Entropy

Self Cite

View full text Add to dashboard Cite

The Omori-Utsu law shows the temporal power-law-like decrease of the frequency of earthquake aftershocks and, interestingly, is found in a variety of complex systems/phenomena exhibiting catastrophes. Now, it may be interpreted as a characteristic response of such systems to large events. Here, hierarchical dynamics with the fast and slow degrees of freedom is studied on the basis of the Fokker-Planck theory for the load-state distribution to formulate the law as a relaxation process, in which diffusion coefficient in the space of the load state is treated as a fluctuating slow variable. The evolution equation reduced from the full Fokker-Planck equation and its Green’s function are analyzed for the subdynamics governing the load state as the fast degree of freedom. It is shown that the subsystem has the temporal translational invariance in the logarithmic time, not in the conventional time, and consequently the aging phenomenon appears.

show abstract

Fokker-Planck approach to non-Gaussian normal diffusion: Hierarchical dynamics for diffusing diffusivity

Cited by 4 publications

References 18 publications

Cell decision-making through the lens of Bayesian learning

Cell decision-making through the lens of Bayesian learning

Cell Decision Making through the Lens of Bayesian Learning

Aftershocks and Fluctuating Diffusivity

Contact Info

Product

Resources

About